<?xml version="1.0" encoding="utf-8"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Hestia's Blog</title><link>https://blog.hestia.gay/</link><description>Hestia's blog about Rust, security and messing with code.</description><language>en-us</language><lastBuildDate>Sun, 08 Nov 2026 19:11:59 +0100</lastBuildDate><atom:link href="https://blog.hestia.gay/feed.xml" rel="self" type="application/rss+xml"/><image><url>https://blog.hestia.gay/logo.png</url><title>Hestia's Blog</title><link>https://blog.hestia.gay/</link></image><item><title>SQLX - WHERE-IN queries. The good, the bad and the ugly.</title><link>https://blog.hestia.gay/post/sqlx-where-in-list.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/sqlx-where-in-list.md/</guid><pubDate>Sun, 28 Dec 2025 00:00:00 +0000</pubDate><category>rust</category><description>&lt;p&gt;I love SQLX for many reasons, but one in particular is the possibility to&#10;validate syntax and return types at compile-time with the &lt;code&gt;query!&lt;/code&gt; macros. At&#10;least that&amp;rsquo;s what I thought. For a project recently I wanted to perform a query&#10;to get some role data from from a OAUTH 2.0 custom role claim. The query in and&#10;off itself was quite simple, but it lead me down a rabbit hole of the internals&#10;of sqlx and some limitations of MariaDB. Let&amp;rsquo;s have a look at the query first:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-sql" data-lang="sql"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;roles&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;roles&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;idp_group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;IN&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Looks simple, right? Testing it out with DataGrip even works, because in the prompt you can just&#10;insert the list you want. So now we just pass our slice of strings to the query and:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;error: error returned from database: 1064 (42000): You have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near &amp;#39;?&amp;#39; at line 1&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; --&amp;gt; src/main.rs:3:5&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;3 | sqlx::query!(&amp;#34;SELECT * FROM roles WHERE idp_group IN ?;&amp;#34;, l);&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; | ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; = note: this error originates in the macro `$crate::sqlx_macros::expand_query` which comes from the expansion of the macro `sqlx::query` (in Nightly builds, run with -Z macro-backtrace for more info)&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;error: could not compile `sqlx_list` (bin &amp;#34;sqlx_list&amp;#34;) due to 1 previous error&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Weird. Why is MariaDB suddenly complaining here. The syntax should be right, if it just replaces&#10;the &lt;code&gt;?&lt;/code&gt; with the list I just passed. After some experimentation, to make sure I was not missing&#10;something trivial, I reached out to the developers of SQLX on their discord. They responded me&#10;promptly that MariaDB (and also MySQL) do not support binding arrays like that.&lt;/p&gt;&#10;&lt;p&gt;&lt;img src="https://blog.hestia.gay/post/sqlx-where-in-list.md/discord-response.png" alt="Response from the SQLX developers: Arrays can’t be bound as a parameter in MySQL. Are you trying to use QueryBuilder?" width="1290" height="120" loading="lazy"&gt;&#10;&lt;/p&gt;&#10;&lt;p&gt;So it doesn&amp;rsquo;t work. Now we effectively have two option: Run one query for each group and pray to&#10;god no user has so many groups that this would cause performance issues, or use the &lt;code&gt;QueryBuilder&lt;/code&gt;,&#10;but forego the compile-time type and query checking from SQLX.&lt;/p&gt;&#10;&lt;p&gt;I quickly learned that the second option wasn&amp;rsquo;t feasible. Rust type system was super strict and I&#10;ran into several problems when testing it. And considering that I wanted to use similar queries in&#10;the future (in much less traversed parts than the auth code), this was a no-go.&lt;/p&gt;&#10;&lt;p&gt;So it&amp;rsquo;s the first option then? Well, no. This query will fetch the user auth on every request, any&#10;slowness in this part of the code will haunt the user on every single request. I do not want to&#10;have any surprises coming my way from there.&lt;/p&gt;&#10;&lt;p&gt;So the only solution left: build a solution that does both myself!&lt;/p&gt;&#10;&lt;h2 id="the-implementation"&gt;The implementation&lt;/h2&gt;&#10;&lt;p&gt;The solution that I came up with was essentially another macro, that generates the code for the&#10;&lt;code&gt;QueryBuilder&lt;/code&gt;, while generating a separate &amp;ldquo;example&amp;rdquo; query that gets validated against the&#10;database at compile-time the way SQLX does it. I&amp;rsquo;ll quickly guide you through the steps to&#10;implement such a macro, but first we need to decide what syntax to use.&lt;/p&gt;&#10;&lt;p&gt;The syntax I came up with had the following constraints: You specify a list of either strings or&#10;for-loops in the query. All the strings will be appended to the query, while the for-loops will use&#10;the &lt;a href="https://docs.rs/sqlx/latest/sqlx/query_builder/struct.Separated.html"&gt;QueryBuilder::separated&lt;/a&gt;&#10;function to append the items. The trick here is, that the body of the for-loop functions as a&#10;block, returning the last statement and therefor effectively working like a list-comprehension from&#10;python.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;groups&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;vec!&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;String&lt;/span&gt;::&lt;span class="n"&gt;new&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;/root&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)];&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;roles&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;query_in_list!&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;RoleType&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;SELECT *&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;FROM groups&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;WHERE idp_group IN&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;groups&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Now we just need our macro to actually parse this and generate new valid Rust source code. The&#10;parsing code took huge inspiration from the &lt;code&gt;instrument&lt;/code&gt; macro of the &lt;a href="https://docs.rs/tracing/latest/tracing/index.html"&gt;tracing crate&lt;/a&gt;&#10;as I did not know how to do this prior to actually doing it. The logic is actually quite simple,&#10;like &lt;code&gt;tracing&lt;/code&gt;, I just used the &lt;a href="https://docs.rs/syn/latest/syn/"&gt;syn crate&lt;/a&gt; to parse the actual source-code.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;syn&lt;/span&gt;::&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Block&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Ident&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;LitStr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Stmt&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Token&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Type&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Parse&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;ParseStream&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;QueryInList&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_result_type&lt;/span&gt;: &lt;span class="nc"&gt;Type&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;: &lt;span class="nb"&gt;Vec&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;enum&lt;/span&gt; &lt;span class="nc"&gt;QueryFragment&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LitStr&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;: &lt;span class="nc"&gt;Ident&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;: &lt;span class="nc"&gt;Ident&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expr&lt;/span&gt;: &lt;span class="nb"&gt;Vec&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Stmt&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Parse&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryInList&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;parse&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;: &lt;span class="nc"&gt;ParseStream&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="bp"&gt;Self&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_result_type&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Type&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="fm"&gt;Token!&lt;/span&gt;&lt;span class="p"&gt;[,]&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;fragments&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;vec!&lt;/span&gt;&lt;span class="p"&gt;[];&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;while&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;is_empty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;Ok&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;literal&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;LitStr&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;content&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;literal&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;content&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sc"&gt;&amp;#39; &amp;#39;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;fragments&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;::&lt;span class="n"&gt;Lit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LitStr&lt;/span&gt;::&lt;span class="n"&gt;new&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;content&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lit&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;span&lt;/span&gt;&lt;span class="p"&gt;())));&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;continue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="fm"&gt;Token!&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Ident&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="fm"&gt;Token!&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="k"&gt;in&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Ident&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parse&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Block&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;?&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;fragments&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;::&lt;span class="n"&gt;Loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expr&lt;/span&gt;: &lt;span class="nc"&gt;block&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;stmts&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;Ok&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;QueryInList&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_result_type&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;: &lt;span class="nc"&gt;fragments&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;First we simply parse a type, followed by a comma from the input stream. Then&#10;we move on to the items of the query.&lt;/p&gt;&#10;&lt;p&gt;As you can see, in the parse loop at line 24, I try to parse a string literal&#10;from the input stream. If that does not work, I just assume it contains the&#10;for-loop and parse one after the other: the keyword &lt;code&gt;for&lt;/code&gt;, an identifier that&#10;is used in the loop, the keyword &lt;code&gt;in&lt;/code&gt;, another identifier for the iterable that&#10;is used and lastly a block expression that gives us our value for the query. I&#10;package everything up into a &lt;code&gt;Vec&lt;/code&gt; and with that, we have our data prepared.&lt;/p&gt;&#10;&lt;p&gt;(I also push a space after each string literal, so you don&amp;rsquo;t have to remember&#10;to have the trailing whitespace after each like. You&amp;rsquo;re welcome.)&lt;/p&gt;&#10;&lt;p&gt;The next step now is to turn this data into an example query that we use to&#10;validate against the database. For that we just take our list of elements. If&#10;we encounter a string-literal, we simply concatenate it, if it is a for-loop,&#10;we add the literal &lt;code&gt;(?, ?)&lt;/code&gt; as an example, and keep track of how many&#10;placeholder we inserted:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryInList&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;example_query&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;usize&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;String&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;String&lt;/span&gt;::&lt;span class="n"&gt;new&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;placeholder&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;fragment&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;match&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;fragment&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;::&lt;span class="n"&gt;Lit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lit&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;lit&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;::&lt;span class="n"&gt;Loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;..&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34; ( ?, ? ) &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;placeholder&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sc"&gt;&amp;#39;;&amp;#39;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;placeholder&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;With that done, all that&amp;rsquo;s left to do is assemble all the pieces into valid&#10;Rust code, that we can output from our macro for the compile to process. The&#10;generated code should look something like this:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;roles&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;query_as!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RoleType&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;SELECT * FROM roles WHERE idp_group IN (?, ?)&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;sqlx&lt;/span&gt;::&lt;span class="n"&gt;QueryBuilder&lt;/span&gt;::&lt;span class="n"&gt;new&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;SELECT role_id, BIT_OR(permissions) AS permissions &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;FROM roles &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;WHERE idp_group IN &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34; ( &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;separated&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;separated&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;, &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;groups&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;separated&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_bind&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34; ) &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;So I used the &lt;a href="https://docs.rs/quote/latest/quote/index.html"&gt;quote crate&lt;/a&gt; to&#10;generate the code. The great thing about quote is, that we can do&#10;string-interpolation on our source-code, making it much easier to audit and&#10;understand later.&lt;/p&gt;&#10;&lt;p&gt;As a quick aside: A lot of Rust detractors might say now: &amp;ldquo;See you need to pull&#10;in so many different crates. This is a huge supply-chain risk&amp;rdquo;. Interestingly&#10;enough though, all the crates used (quote, syn and proc-macro2) come from the&#10;same person: David Tolnay (I have sung his praises already, so I&amp;rsquo;ll spare you&#10;from it here). So the supply-chain risk is actually just the same as one crate,&#10;we would just degrade compile time and code re-usability. So please don&amp;rsquo;t just&#10;look at &amp;ldquo;number big&amp;rdquo; and assume that means the supply-chain risk is directly&#10;correlated. There goes much more into that.&lt;/p&gt;&#10;&lt;p&gt;Back to the topic &amp;ndash; let&amp;rsquo;s generate the source code:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;proc_macro&lt;/span&gt;::&lt;span class="n"&gt;TokenStream&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;quote&lt;/span&gt;::&lt;span class="n"&gt;quote&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;syn&lt;/span&gt;::&lt;span class="n"&gt;parse_macro_input&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[proc_macro]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;pub&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;query_in_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;: &lt;span class="nc"&gt;TokenStream&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;TokenStream&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_in_list&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;parse_macro_input!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryInList&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;placeholders&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;qe&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_in_list&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;example_query&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;ph&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;iter&lt;/span&gt;::&lt;span class="n"&gt;repeat_n&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;placeholders&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_result_type&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_in_list&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;query_result_type&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;fragments&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;query_in_list&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;query&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;iter&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;|&lt;/span&gt;&lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="o"&gt;|&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;match&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;::&lt;span class="n"&gt;Lit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lit&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;quote!&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;#&lt;span class="n"&gt;lit&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryFragment&lt;/span&gt;::&lt;span class="n"&gt;Loop&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expr&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;quote!&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34; ( &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;separated&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;separated&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;, &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;#&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;#&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;separated&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_bind&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;#&lt;span class="p"&gt;(&lt;/span&gt;#&lt;span class="n"&gt;expr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34; ) &amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;quote!&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="c1"&gt;// We are generating an example query here, but discarding the result.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="c1"&gt;// This is only used to run at compile-time against the database to&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="c1"&gt;// ensure type-safety.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;sqlx&lt;/span&gt;::&lt;span class="fm"&gt;query_as!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;#&lt;span class="n"&gt;query_result_type&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;#&lt;span class="n"&gt;qe&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;#&lt;span class="p"&gt;(&lt;/span&gt;#&lt;span class="n"&gt;ph&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;sqlx&lt;/span&gt;::&lt;span class="n"&gt;QueryBuilder&lt;/span&gt;::&lt;span class="n"&gt;new&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;#&lt;span class="p"&gt;(&lt;/span&gt;#&lt;span class="n"&gt;fragments&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;into&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;So, what&amp;rsquo;s happening here? First we transform the fragments we collected from&#10;the macro into their respective code-pieces: Just pushing the string in case of&#10;a literal, otherwise creating the &lt;code&gt;Separated&lt;/code&gt; and pushing all the values based&#10;on the for-loop. As you can see, I basically just paste the whole code block&#10;inside the curly-braces into the &lt;code&gt;Separated::push_bind&lt;/code&gt; function, which&#10;actually works great.&lt;/p&gt;&#10;&lt;p&gt;As for our example query, we actually need to push the same number of arguments&#10;into the codes, as we have bindings in the query, for that I just created an&#10;iterator of the value &lt;code&gt;true&lt;/code&gt; that yields exactly the right amount of times.&#10;Surprisingly, this works and MariaDB does not complain about any type&#10;miss-matches either (put a pin in that, we&amp;rsquo;ll need that later again).&lt;/p&gt;&#10;&lt;h2 id="the-good"&gt;The Good&lt;/h2&gt;&#10;&lt;p&gt;We have our cake and can eat it too (mostly, we&amp;rsquo;ll come to that). We can&#10;validate our query at compile-time, while leveraging the &lt;code&gt;QueryBuilder&lt;/code&gt; to&#10;actually avoid the limitations of MariaDB. Nominally I have reached my goal,&#10;but the solution is still far from perfect, as I will explain in the next&#10;sections.&lt;/p&gt;&#10;&lt;h2 id="the-bad"&gt;The Bad&lt;/h2&gt;&#10;&lt;p&gt;While we actually do have the type now, to actually get the data out we still&#10;have to derive &lt;code&gt;FromRow&lt;/code&gt; for the struct and pass through that code.&lt;/p&gt;&#10;&lt;p&gt;Must worse though, this solution is not 100% air-tight. Let me demonstrate&#10;this:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;groups&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;vec!&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;String&lt;/span&gt;::&lt;span class="n"&gt;new&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;/root&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;)];&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;roles&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="fm"&gt;query_in_list!&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;RoleType&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;SELECT *&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;FROM groups&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;WHERE idp_group IN&amp;#34;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;in&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;groups&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;roles&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;query_as&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;OtherType&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;db&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="k"&gt;await&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Since the function &lt;code&gt;query_as&lt;/code&gt; takes a mutable reference, we cannot return just&#10;the query because the builder, to which it holds a reference, would be dropped&#10;at the end of the block. So between the macro and the actual use of the query&#10;it could still come to some type confusion.&lt;/p&gt;&#10;&lt;p&gt;The other alternative is to accept another parameter into the macro: the buffer&#10;itself, hoping that the user (or an especially clever LLM) has not had any&#10;ideas of pre-filling it to avoid a compiler error for the type confusion.&lt;/p&gt;&#10;&lt;p&gt;The second solution could be the prettier one, as we can re-use the specified&#10;type twice, but for now, I opted for solution one. This is definitely a point I&#10;need to come back on. But for now I don&amp;rsquo;t have a solution to actually for this&#10;problem, other than hoping that the borrow checker will become smarter about&#10;this, but I don&amp;rsquo;t think that can work, as reordering drops like that can&#10;break a bunch of Rust code where the block is used to force e.g. a &lt;code&gt;MutexGuard&lt;/code&gt;&#10;to be dropped early.&lt;/p&gt;&#10;&lt;h3 id="edit-2025-12-30-fixing-the-bad"&gt;Edit (2025-12-30): Fixing the bad.&lt;/h3&gt;&#10;&lt;p&gt;This was a real thorn to my side, but I couldn&amp;rsquo;t think of a good solution.&#10;Thankfully I was on the Chaos Communication Congress and my friend Isse&#10;suggested that I should talk to the people at the Rust assembly, maybe they&#10;know something that can be done. And after some discussion we came up with an&#10;idea, that while not the prettiest, resolves this problem for good.&lt;/p&gt;&#10;&lt;p&gt;For the uninitiated in Rust macros: Rust proc-macros work by being compiled&#10;first, and then being called by the compile to generate more code. Right now&#10;they have the limitations that they need to live in a separate crate that can&#10;only export the macros themselves.&lt;/p&gt;&#10;&lt;p&gt;So first we move all the macro code into its separate crate, e.g.&#10;&lt;code&gt;query_macros_impl&lt;/code&gt; and then create a separate crate &lt;code&gt;query_macros&lt;/code&gt; that&#10;re-exports the macros alongside the new code.&lt;/p&gt;&#10;&lt;p&gt;Basically, what we came up with is the following: Create a wrapper type for&#10;the query builder, that takes the row type as a generic parameter and exposes&#10;only one function, which is to get the &lt;code&gt;QueryAs&lt;/code&gt; type, with the correct&#10;lifetime. The actual code is really simple:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;sqlx&lt;/span&gt;::&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Database&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;FromRow&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;QueryBuilder&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;sqlx&lt;/span&gt;::&lt;span class="n"&gt;query&lt;/span&gt;::&lt;span class="n"&gt;QueryAs&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;pub&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;SealedQueryBuilder&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;: &lt;span class="nc"&gt;Database&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;FromRow&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;::&lt;span class="n"&gt;Row&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;: &lt;span class="nc"&gt;QueryBuilder&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;_marker&lt;/span&gt;: &lt;span class="nc"&gt;PhantomData&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;: &lt;span class="nc"&gt;Database&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;FromRow&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;::&lt;span class="n"&gt;Row&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;SealedQueryBuilder&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;pub&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;new&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;: &lt;span class="nc"&gt;QueryBuilder&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;Self&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="bp"&gt;Self&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;_marker&lt;/span&gt;: &lt;span class="nc"&gt;PhantomData&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;pub&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;query_as&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;QueryAs&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;DB&lt;/span&gt;::&lt;span class="n"&gt;Arguments&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;build_query_as&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;We basically just create the struct, the generics can be copied almost 1:1 from&#10;the &lt;code&gt;QueryAs&lt;/code&gt; macro and the &lt;code&gt;QueryAs::fetch_all&lt;/code&gt; method. Then we create a&#10;function that internally calls &lt;code&gt;build_query_as&lt;/code&gt; and&amp;hellip; That&amp;rsquo;s it. Now we can&#10;bring the type all the way through to the point where it is being used.&lt;/p&gt;&#10;&lt;h2 id="the-ugly"&gt;The Ugly&lt;/h2&gt;&#10;&lt;p&gt;I actually lied to you about the implementation earlier to get to not spoiler&#10;the surprise in this section.&lt;/p&gt;&#10;&lt;p&gt;In the code that inserts the binding values we have a edge-case we did not&#10;cover. If the iterable is empty, we generate an invalid query and have a&#10;runtime error and we&amp;rsquo;d have to implement custom logic before every use of the&#10;macro. This is quite counter-intuitive and easy to forget. So we have two&#10;options again: Add a custom error that the user is required to handle, or make&#10;sure the query can run, even if one of the lists is empty.&lt;/p&gt;&#10;&lt;p&gt;I decided to go for the second option and that&amp;rsquo;s where we&amp;rsquo;ll reach back to our&#10;pin from earlier: remember how I said MariaDB will not complain, even if we&#10;have a type-missmatch in our query? That&amp;rsquo;s were it comes back useful: If we&#10;just push a &lt;code&gt;true&lt;/code&gt; for each for-loop, we make sure the actual list is always&#10;(syntactically) valid and you&amp;rsquo;ll get an empty list back, which is what you&amp;rsquo;d&#10;probably expect anyways.&lt;/p&gt;&#10;&lt;p&gt;I want to also take this moment to formally apologize to any potential future&#10;co-workers that look at the queries executed in the database and then have to&#10;go into a rabbit-hole on why every list contains a &lt;code&gt;true&lt;/code&gt; at the beginning.&lt;/p&gt;&#10;&lt;p&gt;While that &amp;ldquo;feature&amp;rdquo; of MariaDB to silently ignore type miss-matches is a&#10;blessing for fixing that edge-case, it&amp;rsquo;s also a curse &amp;ndash; if you accidentally&#10;pass in a list of, say, ids instead of strings, the validation will work&#10;just-fine™ while the query can never return an actual row. But since this&#10;this is not something I can influence in the moment, I have to (begrudgingly)&#10;accept this as part of the deal, not just for my macro, but for all of SQLX.&#10;Nevertheless, I&amp;rsquo;m happy I discovered it, so I can be aware of this behavior&#10;going forward.&lt;/p&gt;&#10;</description></item><item><title>Understanding the Huffman Table Optimization</title><link>https://blog.hestia.gay/post/huffman-table-optimization.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/huffman-table-optimization.md/</guid><pubDate>Tue, 25 Nov 2025 00:00:00 +0000</pubDate><category>beginner</category><category>optimization</category><description>&lt;p&gt;A while ago I was studying the &lt;a href="https://developers.google.com/speed/webp"&gt;webp image format&lt;/a&gt; by&#10;Google out of curiosity. I had written a &lt;del&gt;very incomplete&lt;/del&gt; apng parser in the past and was&#10;interested in seeing how the lossless VP8L encoding in particular was working in that library.&lt;/p&gt;&#10;&lt;p&gt;While I was using a external Rust library to decode the actual image data in the past, I quickly&#10;found myself drawn to trying to implement the decoding myself. Long story short, after several days&#10;of trying to wrap my head around their Huffman decoding optimization I had to give up. I just&#10;couldn’t understand how it worked, given just the C library implementation.&lt;/p&gt;&#10;&lt;p&gt;I moved on, but I couldn’t get the problem out of my head. Only several weeks later, while doing&#10;something completely unrelated to programming, it suddenly all clicked into place. Since I still&#10;haven’t found a good article that explains it, I’m here now to explain how the Huffman-Coding&#10;lookup table works.&lt;/p&gt;&#10;&lt;p&gt;But let’s start at the beginning: what even is a Huffman-Coding and what is this optimization I&#10;was talking about?&lt;/p&gt;&#10;&lt;h2 id="introduction-to-huffman-coding"&gt;Introduction to Huffman Coding&lt;/h2&gt;&#10;&lt;p&gt;If you learned about the basics of this algorithm in college, like I did, feel free to skip this&#10;section. If you’ve never even heard of this, or if it’s been a while and you want a refresher, keep&#10;reading.&lt;/p&gt;&#10;&lt;p&gt;&lt;em&gt;According to Wikipedia:&lt;/em&gt;&lt;/p&gt;&#10;&lt;blockquote&gt;&#10;&lt;p&gt;In computer science and information theory, a Huffman code is a particular type of optimal prefix&#10;code that is commonly used for lossless data compression. The process of finding or using such a&#10;code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at&#10;MIT, and published in the 1952 paper &amp;ldquo;A Method for the Construction of Minimum-Redundancy Codes&amp;rdquo;.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;p&gt;For normal people: Huffman coding is a (very old in CS timelines) method to encode data more&#10;efficiently. It does this by assigning shorter codes to more frequent values, and longer ones to&#10;less frequent values. In aggregate, the resulting encoded string is shorter than the initial one,&#10;approaching the theoretical minimum size defined by the data’s entropy.&lt;/p&gt;&#10;&lt;p&gt;A prefix code in this context just means that there are no control characters in the final string.&#10;No code is a prefix of any other code, so the decoder can always uniquely identify each symbol as&#10;it reads the bits.&lt;/p&gt;&#10;&lt;p&gt;To compress a text with Huffman Coding, we first have to create a Huffman tree, by counting the&#10;frequency of each character and then aggregating it into a tree that’s approximately balanced&#10;according to their frequency. Once you’ve associated a count with each character, we take the&#10;characters with the lowest counts and join them into a tree, inserting the sum of the counts as the&#10;new root node. We then continue this, until all characters are inserted into the tree.&lt;/p&gt;&#10;&lt;p&gt;This works to compress the data because we are using longer codes for less frequent bytes and&#10;shorter codes for more frequent ones. So if a byte appears often, it will get compressed more&#10;efficiently, while bytes that are very rare can actually get longer. But since they appear so&#10;infrequently, we balance that overhead out with the space saved by or more frequent codes.&lt;/p&gt;&#10;&lt;p&gt;As an example, let’s take the string &lt;code&gt;aaaaaaaabbbbbbccccddd&lt;/code&gt;. It contains eight a’s, six b’s, four&#10;c’s and three d’s. So our initial nodes are just those four. For our first step, we see that c and&#10;d have the lowest counts, so we group them into a new node by adding a parent:&lt;/p&gt;&#10;&lt;p&gt;&lt;img src="https://blog.hestia.gay/post/huffman-table-optimization.md/encoding-step1.webp" alt="" width="552" height="328" loading="lazy"&gt;&#10;&lt;/p&gt;&#10;&lt;p&gt;Next up, we see that the new c-d node and the b node are the smallest, so once again, we merge them&#10;into a single node:&lt;/p&gt;&#10;&lt;p&gt;&lt;img src="https://blog.hestia.gay/post/huffman-table-optimization.md/encoding-step2.webp" alt="" width="510" height="511" loading="lazy"&gt;&#10;&lt;/p&gt;&#10;&lt;p&gt;Now only two nodes are left, so in the last merge we create our final Huffman tree:&lt;/p&gt;&#10;&lt;p&gt;&lt;img src="https://blog.hestia.gay/post/huffman-table-optimization.md/encoding-step3.webp" alt="" width="466" height="712" loading="lazy"&gt;&#10;&lt;/p&gt;&#10;&lt;p&gt;As you can see, I’ve also already annotated the prefix of each character. To save an a into our new&#10;string, it now only needs a single bit, a &lt;code&gt;0&lt;/code&gt;. To encode a b it’s &lt;code&gt;10&lt;/code&gt; and c and d are &lt;code&gt;110&lt;/code&gt; and&#10;&lt;code&gt;111&lt;/code&gt;. In total that would be 8 bits for the a’s, 12 bits for the b’s and 21 bits for the c’s and&#10;d’s, leaving us with 41 bits or 6 bytes in total, much shorter than the initial 21 bytes.&lt;/p&gt;&#10;&lt;h2 id="decoding-the-huffman-encoding"&gt;Decoding the Huffman Encoding&lt;/h2&gt;&#10;&lt;p&gt;To decode the compressed string, we can just walk the tree in reverse, treating it as a decision&#10;tree. We start from the root, and for each bit we step one node down. If we hit a leaf node (one&#10;that contains a character), we write that character to our output buffer and jump back up to the&#10;root to start the next code.&lt;/p&gt;&#10;&lt;p&gt;Now while this is efficient to store, it’s not that efficient to decode: walking a tree requires&#10;many random accesses to memory and if statements. Both are not ideal for modern CPUs that try to&#10;predict our next moves to pre-fetch instructions and memory.&lt;/p&gt;&#10;&lt;p&gt;Every if statement is a chance for the CPU to miss-predict, and thus have to flush and re-fetch the&#10;instruction cache, throwing away the speculatively pre-computed result. Every jump to the next node&#10;risks the memory being flushed out of the CPU cache and thus then need to be fetched from a higher&#10;cache or, even worse, from RAM.&lt;/p&gt;&#10;&lt;p&gt;So we want to do as few memory operations as possible. Preferably just pick the result from a&#10;memory location and immediately continue decoding the input string.&lt;/p&gt;&#10;&lt;p&gt;That’s where the Huffman table comes into play. In contrast to the Huffman tree, the table is just&#10;a contiguous slice of memory, easily accessible. But we need to do some pre-computation to produce&#10;the table from the tree.&lt;/p&gt;&#10;&lt;h2 id="the-huffman-table-optimization"&gt;The Huffman Table Optimization&lt;/h2&gt;&#10;&lt;p&gt;Since the Huffman coding guarantees that no code is a prefix of another, we can use that to our&#10;advantage. To start, we need to find the greatest code length (in bits) in the whole tree. In our&#10;case, that would be three, for both c and d.&lt;/p&gt;&#10;&lt;p&gt;Next, we traverse the tree, and for every node that has not yet reached that depth, we push it down&#10;to both of its children. To still know the initial length, we will also store the code length&#10;together with the decoded character.&lt;/p&gt;&#10;&lt;p&gt;Once we’re done with that procedure, we have a tree that’s completely full, all possible nodes are&#10;at the same level:&lt;/p&gt;&#10;&lt;p&gt;&lt;img src="https://blog.hestia.gay/post/huffman-table-optimization.md/decoding-table.webp" alt="" width="990" height="659" loading="lazy"&gt;&#10;&lt;/p&gt;&#10;&lt;p&gt;So how does this help us go forward? We now have more branches in the tree, with more jumps through&#10;memory and more possibilities for the CPU’s speculative execution to go wrong.&lt;/p&gt;&#10;&lt;p&gt;In fact, our tree now has &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;O(2^n)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; leaf nodes, using much more memory in the process as well. Well,&#10;as we can see in this tree, at every node, whichever branch we take, we will always find ourselves&#10;in a valid branch, until we hit the tree’s depth. In other words, every bit-pattern of length &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;n&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&#10;is valid in this search tree.&lt;/p&gt;&#10;&lt;p&gt;If you take a closer look at the leaf nodes, the first leaf node from the left can be accessed with&#10;the bit-pattern &lt;code&gt;000&lt;/code&gt;, the next with &lt;code&gt;001&lt;/code&gt; and the one after that with &lt;code&gt;010&lt;/code&gt; until we reach the&#10;last one with &lt;code&gt;111&lt;/code&gt;. What we did here is simply to create a lookup table for the prefix of the&#10;encoding.&lt;/p&gt;&#10;&lt;p&gt;So what we can do here is to simply discard the rest of the tree. Instead of taking the branches&#10;every time, we simply list the leaf nodes in a chunk of contiguous memory and then take the next&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;n&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; bit from the stream and index directly into it with a single operation, completely eliminating&#10;the need to traverse a tree.&lt;/p&gt;&#10;&lt;p&gt;Once we have our character and prefix code length, we can write the character to the output buffer&#10;and re-use the rest of the index that is longer than the prefix length.&lt;/p&gt;&#10;&lt;p&gt;Now, some of you may wonder if using &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;O(n^2)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; memory is really any kind of optimization at all. And&#10;to that I can clearly say NO. In the worst case, if we are encoding single bytes, we will end up&#10;with &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;256&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;2^{256}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; bytes of memory usage, which is far more memory than humanity has produced so far.&lt;/p&gt;&#10;&lt;p&gt;But Google was aware of that limitation as well when they produced the webp image standard. So they&#10;capped the total tree depth to at most 19, which would use 1MiB of RAM for the lookup table,&#10;maintaining a good trade-off between encoding efficiency and memory usage during decoding.&lt;/p&gt;&#10;&lt;p&gt;In summary, Huffman coding is a cool way to compress data, and the lookup table optimization makes&#10;decoding much faster, at the cost of some extra memory. This helps us improve decoding times,&#10;especially for lower-end devices, as we are repeating the same steps sometimes multiple times per&#10;pixel in image decoding.&lt;/p&gt;&#10;</description></item><item><title>Reconstructing Protected or Hidden Custom Variables in Icinga DB Web</title><link>https://blog.hestia.gay/post/icingadb-web-cve.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/icingadb-web-cve.md/</guid><pubDate>Tue, 04 Nov 2025 00:00:00 +0000</pubDate><category>security</category><category>icinga</category><category>php</category><description>&lt;p&gt;Recently Icinga DB Web had a new security release, fixing a vulnerability where protected or hidden&#10;custom variables could be inferred by any user with object visibility by abusing comparative filters&#10;on those hidden variables. This led to a &lt;a href="https://github.com/Icinga/icingadb-web/security/advisories/GHSA-w57j-28jc-8429"&gt;5.3/10 rated Information Disclosure Vulnerability&lt;/a&gt;,&#10;documented in &lt;a href="https://nvd.nist.gov/vuln/detail/CVE-2025-61789"&gt;CVE-2025-61789&lt;/a&gt;. In this blog post&#10;I’ll go through the discovery and the inner workings of the exploit.&lt;/p&gt;&#10;&lt;h2 id="setting-the-scene"&gt;Setting the Scene&lt;/h2&gt;&#10;&lt;p&gt;Every company has their own specific needs when it comes to monitoring their environments. From&#10;specific metrics they’re interested in, to thresholds, workdays, team composition and shifts, and&#10;company structure, there’s a lot more that goes into effective monitoring than meets the eye.&lt;/p&gt;&#10;&lt;p&gt;Icinga’s approach to this complexity is to provide a framework to specify templates and custom data&#10;fields that lets you adapt the monitoring environment to your needs. It can be used to store&#10;thresholds, parameters for checks or notifications, or flags for searching objects. But most&#10;importantly it can be used to store passwords or API tokens needed for the check itself.&lt;/p&gt;&#10;&lt;p&gt;To make the monitoring results visible to those users who aren’t directly managing the&#10;infrastructure, Icinga Web 2 allows users to access only the monitoring results, or in this case&#10;the Icinga DB view and not Director with the configuration.&lt;/p&gt;&#10;&lt;p&gt;Icinga DB Web further allows you to hide specific custom variables, like the aforementioned&#10;passwords and API tokens. These can be hidden by giving the user a role that sets the restriction&#10;&lt;code&gt;icingadb/protect/variables&lt;/code&gt; to give a list of patterns the user is not allowed to access, e.g.&#10;&lt;code&gt;*pass*,api-token&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;To execute the exploit, an attacker must have at least viewing permissions on the attacked host or&#10;service, and needs to know the name of the variable, which can’t be known in hidden variables, but&#10;can often still be inferred from the check or other properties of the object.&lt;/p&gt;&#10;&lt;h2 id="the-discovery"&gt;The Discovery&lt;/h2&gt;&#10;&lt;p&gt;While I was investigating Icinga DB Web for integration into NetEye, I happened to be working on&#10;understanding these restrictions while at the same time helping a colleague look over a&#10;&lt;a href="https://github.com/Icinga/icingadb-web/pull/1046"&gt;PR to support the customization of the search params.&lt;/a&gt;&lt;/p&gt;&#10;&lt;p&gt;That’s where I made the first connection. So purely out of curiosity for what might happen, I&#10;looked up one of the passwords for an object I had created to test the restriction and ran the&#10;following query against Icinga DB Web: &lt;code&gt;host.name=test-host&amp;amp;host.vars.password=&amp;lt;password&amp;gt;&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;To my surprise the object was actually returned correctly. Weird. So I tried changing the password&#10;and it disappeared. Okay, so apparently the protected variables are only protected AFTER the&#10;filters have already run, giving us access to some information about them.&lt;/p&gt;&#10;&lt;p&gt;If it was just an equality check that in and of itself isn’t the biggest of problems, a normal user&#10;wouldn’t know the password to run this query. And if you already know it, you don’t need the query&#10;any more.&lt;/p&gt;&#10;&lt;p&gt;The worst outcome of this behavior is the possibility of brute-forcing the password in Icinga DB&#10;Web instead of the service directly, in some cases circumventing the service’s brute-force&#10;protection. But we are only marginally improving our options, fundamentally working in the same&#10;time-complexity.&lt;/p&gt;&#10;&lt;h2 id="improving-our-attack"&gt;Improving Our Attack&lt;/h2&gt;&#10;&lt;p&gt;So to actually be able to exploit this vulnerability, we need some way to improve the time&#10;complexity, getting more information for each request. But since we cannot see the actual password,&#10;the only state we can observe is either &lt;code&gt;true&lt;/code&gt; or &lt;code&gt;false&lt;/code&gt;, 1 or 0, depending on whether the object&#10;is still present. So is there no way to actually exploit this small oversight?&lt;/p&gt;&#10;&lt;p&gt;Well, I wouldn’t be writing this blog post if that were the case. A quick look into the UI of&#10;Icinga DB Web show that &lt;code&gt;=&lt;/code&gt; is not the only operator we can apply to the variables. Other than&#10;equality, we can also check for greater or lesser than, i.e. the lexicographical ordering of the&#10;words.&lt;/p&gt;&#10;&lt;p&gt;For this example, let’s assume the password can be found in a dictionary. We all know that the&#10;words there are sorted A-Z. So if we wanted to find it as fast as possible, we could start asking:&#10;&amp;ldquo;does the password start with &lt;code&gt;'&lt;/code&gt;&amp;rdquo;. After we’ve asked that at most 26 times, we’re bound to have&#10;found the initial letter of the password, effectively reducing the amount of words we have to look&#10;for by 96%.&lt;/p&gt;&#10;&lt;p&gt;And it doesn’t stop there. Now we can do the same procedure again for the second letter of the&#10;password. Another 26 questions later, and we’ve removed another 96% of the remaining words, with&#10;only 0.15% of words remaining. Continuing this strategy, we can find the password in the dictionary&#10;in at most 26 times the number of characters in the password, going from exponential to linear.&lt;/p&gt;&#10;&lt;p&gt;We can decrease this even further if we simply ask &amp;ldquo;is the character the password starts with&#10;greater than ?&amp;rdquo;. Then we can start in the middle and with each request exclude half of the&#10;remaining letters. With that we need at most 5 queries to find a character, going from linear to&#10;logarithmic.&lt;/p&gt;&#10;&lt;p&gt;We can use the same strategy for Icinga DB Web. For that we take the known prefix (the part of the&#10;password that we already know) and add the character we want to test afterwards, looking for the&#10;host with the query &lt;code&gt;host.name=test-host&amp;amp;host.vars.password=(known prefix)(character)&lt;/code&gt;, and with&#10;that, perform a binary search for the next character.&lt;/p&gt;&#10;&lt;p&gt;This strategy lets us reduce the overall time complexity from &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;O(A^n)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; to &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;O(n * log_2(A))&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. As an&#10;example, if we had a strong random password with upper and lowercase letters, digits and special&#10;characters, then we have in total &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;A=100&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; options per character, and the difference would look as&#10;follows: Randomly guessing a password with 16 characters would take you at most &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msup&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mn&gt;32&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;100^{16} = 10^{32}&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&#10;tries (yes, this is not a typo).&lt;/p&gt;&#10;&lt;p&gt;Even with 10,000 requests per second it would take over &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mn&gt;32&lt;/mn&gt;&lt;/msup&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;msup&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/msup&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;mn&gt;60&lt;/mn&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;mn&gt;60&lt;/mn&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;mn&gt;24&lt;/mn&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;mn&gt;365&lt;/mn&gt;&lt;mo&gt;≈&lt;/mo&gt;&lt;mn&gt;3.17&lt;/mn&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;10^{32} / 10^4 / 60 / 60 / 24 / 365 \approx 3.17e20&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&#10;years (or 24 billion times the age of the universe) to crack. On the other hand, with our improved&#10;strategy, we could reduce the amount of queries to at most &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;16&lt;/mn&gt;&lt;mo&gt;∗&lt;/mo&gt;&lt;mn&gt;7&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;112&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;16 * ceil(log_2(100)) = 16 * 7 = 112&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&#10;(since &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;g&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mn&gt;100&lt;/mn&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;≈&lt;/mo&gt;&lt;mn&gt;6.64&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;log_2(100) \approx 6.64&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;).&lt;/p&gt;&#10;&lt;p&gt;So with the same 10,000 requests per second it would take just 0.01 seconds before the password is&#10;broken. In a realistic scenario, this will likely take much longer, since we need to perform our&#10;requests strictly sequentially, reducing the number of queries we can perform per second, but it’ll&#10;probably still take less than a minute. Afterwards, to know if you’ve actually found the whole&#10;password, you then simply make the query from the beginning using the equality operator.&lt;/p&gt;&#10;&lt;p&gt;Of course, passwords are just one example, but this attack can be used on any variable protected in&#10;this way, including API tokens, internal IDs or other sensitive information. The credentials could&#10;then also be used to pivot to other services to use the access to trigger exploits there.&lt;/p&gt;&#10;&lt;h2 id="the-aftermath"&gt;The Aftermath&lt;/h2&gt;&#10;&lt;p&gt;Once I had found the vulnerability and verified it actually worked, I immediately reported it to&#10;&lt;code&gt;security@icinga.com&lt;/code&gt;. They investigated it and came to the same conclusion as me that this was a&#10;severe problem.&lt;/p&gt;&#10;&lt;p&gt;Their investigations also uncovered a similar problem in Icinga 2, where the fix was released with&#10;versions &lt;code&gt;2.15.1&lt;/code&gt;, &lt;code&gt;2.14.7&lt;/code&gt; and &lt;code&gt;2.13.13&lt;/code&gt;, while the fix for Icinga DB Web was released in versions&#10;&lt;code&gt;1.1.4&lt;/code&gt; and &lt;code&gt;1.2.3&lt;/code&gt;. All versions were released on October 16th 2025. I encourage all users who run&#10;versions lower than that to update their systems as soon as possible.&lt;/p&gt;&#10;&lt;p&gt;I’ve collaborated with the people from Icinga 2 on the fix for the vulnerability, and hope I can do&#10;that in the future as well to keep all Icinga users safe. This has been a fun experience and a&#10;valuable lesson in how seemingly small bugs can be abused to obtain additional data.&lt;/p&gt;&#10;</description></item><item><title>Plugin Systems and Capabilities</title><link>https://blog.hestia.gay/post/plugin-systems-and-capabilities.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/plugin-systems-and-capabilities.md/</guid><pubDate>Mon, 13 Jan 2025 00:00:00 +0000</pubDate><category>php</category><category>rust</category><category>icinga</category><description>&lt;p&gt;At the 36th Chaos Communication Congresses back before COVID forced a three year break, I attended&#10;a talk from the German tech-blogger &lt;a href="https://blog.fefe.de/"&gt;Fefe&lt;/a&gt;. There he talked about the&#10;&amp;ldquo;nützlich-unbedenklich Spektrum&amp;rdquo; or in English, the useful – harmless spectrum. He argued that all&#10;software lies on that spectrum to some degree.&lt;/p&gt;&#10;&lt;p&gt;Of course one could argue that it’s actually a triangle, where effort can optimize both usefulness&#10;and harmlessness, but for a given complexity budget I think it’s a good enough approximation to the&#10;real world to be useful for our analysis. The more capabilities the user has to impact a program’s&#10;behavior, the more chances there are for security vulnerabilities.&lt;/p&gt;&#10;&lt;p&gt;In this post I’d like to peg on that spectrum three specific plugin-systems, as representatives of&#10;a specific approach, and discuss their advantages and associated risk potential.&lt;/p&gt;&#10;&lt;p&gt;This blog post isn’t meant to be a conclusive enumeration of all possible plugin-systems with all&#10;their advantages and disadvantages, but instead to illustrate the various considerations when&#10;planning a plugin system for your software.&lt;/p&gt;&#10;&lt;p&gt;In particular I’ll be talking about the following the plugin-systems:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;The IcingaWeb 2 plugin system&lt;/li&gt;&#10;&lt;li&gt;The current implementation of the Icinga2 Notifications plugin system&lt;/li&gt;&#10;&lt;li&gt;The plugin system of the open source video game &lt;a href="https://veloren.net/"&gt;veloren&lt;/a&gt;.&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;h2 id="the-icingaweb-2-plugin-system"&gt;The IcingaWeb 2 Plugin System&lt;/h2&gt;&#10;&lt;p&gt;The IcingaWeb 2 plugin system is the one with the most capabilities I’ll discuss in this post. It&#10;works by loading PHP source code files from the plugin directory and executing them. It’s similar&#10;to how GLPI and WordPress work, but since I’m most familiar with IcingaWeb 2, I’ll stick with that.&lt;/p&gt;&#10;&lt;p&gt;This plugin system comes in three flavors. First of all there’s the &lt;code&gt;configuration.php&lt;/code&gt; file. This&#10;file is used to register all the necessary permissions and restrictions the plugin needs, as well&#10;as the side-panel entries and submenus to the module configuration. The configuration part mostly&#10;just provides some extra data to IcingaWeb 2 that it already knows how to handle, with some checks&#10;to only load certain data when multiple plugins are loaded together.&lt;/p&gt;&#10;&lt;p&gt;Secondly there are the hooks. Those get registered when the plugin is loaded in the &lt;code&gt;run.php&lt;/code&gt; file.&#10;They are attached to a hook name and provide a PHP class that implements a specific interface. When&#10;a specific hook is triggered, the application will then look up all classes registered to that hook&#10;name and then loops over the hooks to call them, triggering their behavior.&lt;/p&gt;&#10;&lt;p&gt;Lastly, there’s the &amp;ldquo;Controller&amp;rdquo; that allows custom endpoints and &amp;ldquo;CliCommands&amp;rdquo; to extend the&#10;capabilities of icingacli. These classes are loaded from the directories &lt;code&gt;application/controllers&lt;/code&gt;&#10;and &lt;code&gt;application/clicommands&lt;/code&gt; respectively. Here, the behavior is directly injected into the&#10;routing/cli sub-command resolution of IcingaWeb 2, with no additional code required. They can&#10;contain any PHP code, and handle a lot of logic through reflection and the respective class and&#10;method names.&lt;/p&gt;&#10;&lt;p&gt;While those flavors are very different in what they provide, they actually share one crucial&#10;commonality: They all run in the same process with the same global access to all application&#10;resources. This is great, as it allows the plugin author easy access to all the needed information&#10;in a straightforward way.&lt;/p&gt;&#10;&lt;p&gt;There’s no need to consider every aspect that the plugin might want to access data or state.&#10;Furthermore it allows for an easy way to share dependencies, as they are already loaded in the&#10;application. This means that not every plugin has to include a way to handle database connections&#10;or HTTP routing; it’s all already provided by the application context.&lt;/p&gt;&#10;&lt;p&gt;This pattern is widely used in the PHP world and has certainly helped the huge success of WordPress&#10;and their Plugin ecosystem. It’s extremely useful to easily build vastly extensible software,&#10;allowing plugin developers to customize the experience of the user in a very granular way. But, as&#10;we all know, with great power comes great responsibility.&lt;/p&gt;&#10;&lt;p&gt;Since the plugins share the same process and application context, they need to be reviewed very&#10;carefully. Any security vulnerability in a plugin has the potential to give an attacker full access&#10;to the application, no matter how small the part of the application context that the plugin&#10;actually needs. Furthermore a harmless oversight in one plugin combined with a small bug in another&#10;can cascade into a larger security issue if an attacker manages to chain them together in a&#10;non-trivial way.&lt;/p&gt;&#10;&lt;p&gt;Personally I really dislike this approach for several reasons: First of all, all the permissions&#10;and capabilities of the plugin are implicit. Whatever the code does is the canonical behavior of&#10;the plugin, and there are no further checks in place to prevent misbehaving code from accessing&#10;resources outside its control.&lt;/p&gt;&#10;&lt;p&gt;Furthermore, I believe that as much behavior as possible should be immutable. The permissions&#10;defined should be static in a configuration file instead of being defined in the code. This would&#10;reduce the surface area where behavior can be injected, making it easier to audit the code.&lt;/p&gt;&#10;&lt;p&gt;Lastly, the functional programming side of my brain really dislikes that hooks can directly mutate&#10;data that’s passed in. I know that it’s not that big of an issue in the grand scheme of things, but&#10;I personally like to think of hooks as being behavior outside of the application that should not&#10;have any impact on the state if the code doesn’t explicitly use the returned data.&lt;/p&gt;&#10;&lt;h2 id="the-icinga2-notifications-plugin-system"&gt;The Icinga2 Notifications Plugin System&lt;/h2&gt;&#10;&lt;p&gt;The icinga2-notifications plugin system is much smaller in scope and its developers therefore opted&#10;for a different approach. Instead of running all plugins in the same application, each plugin runs&#10;in its own process, where communication with the main application is conducted via a simple&#10;&lt;a href="https://www.jsonrpc.org/specification"&gt;JSON-RPC&lt;/a&gt; interface over &lt;em&gt;stdin&lt;/em&gt; and &lt;em&gt;stdout&lt;/em&gt;.&lt;/p&gt;&#10;&lt;p&gt;To load the necessary context to run the plugin, the plugin needs to implement two JSON-RPC&#10;methods: The &lt;code&gt;GetInfo&lt;/code&gt; method is called to retrieve the necessary schema for the application&#10;configuration, and then the application makes sure the user can configure the plugin correctly and&#10;provide the requested data. If the configuration can be provided, the &lt;code&gt;SetConfig&lt;/code&gt; RPC call is made&#10;to initialize the plugin with the configuration.&lt;/p&gt;&#10;&lt;p&gt;This approach is really elegant in my opinion. It gives a clear, finite point to inspect the data&#10;the plugin is actually allowed to use while keeping the state of the plugin as isolated as&#10;possible. This also reduces the information exposed to the plugin to the minimum required, reducing&#10;the impact of a possible security vulnerability.&lt;/p&gt;&#10;&lt;p&gt;After the plugin is initialized, the application can call the &lt;code&gt;SendNotification&lt;/code&gt; method for each&#10;notification that needs to be sent, passing in the necessary data of the notification as the method&#10;parameters as defined in the JSON-RPC standard. The plugin can then autonomously handle the request&#10;and must then answer with the result of the action, providing either a &lt;code&gt;result&lt;/code&gt; with an arbitrary&#10;JSON value, or an &lt;code&gt;error&lt;/code&gt; with an error message.&lt;/p&gt;&#10;&lt;p&gt;While this approach limits the plugin authors to implementing only a very specific part of the&#10;user-experience, it also provides a much clearer interface to the user as a very strict separation&#10;of concerns and permissions through the OS process boundary.&lt;/p&gt;&#10;&lt;p&gt;In theory the plugins capabilities could even be further restricted by using a container runtime&#10;like Docker or just plain old &lt;em&gt;selinux&lt;/em&gt;. Depending on the plugin, removing the ability to access&#10;local files, networks or services could all help reduce the blast radius of potential&#10;vulnerabilities.&lt;/p&gt;&#10;&lt;h1 id="the-plugin-system-of-veloren"&gt;The Plugin System of Veloren&lt;/h1&gt;&#10;&lt;p&gt;So until now I’ve focused on two plugin systems from Icinga 2, so why the sudden switch to a video&#10;game? I actually spent quite a bit of time thinking about how to best implement plugin systems&#10;securely and how to balance the usefulness of the interface with the security implications, and the&#10;plugin system of veloren inspired me to finally write my thoughts down.&lt;/p&gt;&#10;&lt;p&gt;I’m writing this blog post at the 38th Chaos Communication Congress in Hamburg, specifically from&#10;the Veloren assembly. I had the great honor to be able to talk to &lt;a href="https://de.linkedin.com/in/christof-petig/en"&gt;Christof Petig&lt;/a&gt;,&#10;one of the core contributors to veloren and an all around brilliant mind. Besides hundreds of&#10;questions about the networking protocols of the game, I also got to extensively talk about the new&#10;plugin system he developed for veloren.&lt;/p&gt;&#10;&lt;p&gt;Christof actually did some work for the Bytecode Alliance himself; he had a little involvement in&#10;the WIT specification and did the majority of the work on the C++ backend of the &lt;a href="https://component-model.bytecodealliance.org/advanced/canonical-abi.html"&gt;canonical ABI&lt;/a&gt;.&#10;He led me through all the code to understand how its plugins are implemented, loaded and executed.&lt;/p&gt;&#10;&lt;p&gt;A veloren plugin consists of a &lt;code&gt;.tar&lt;/code&gt; archive which must contain at least a &lt;code&gt;plugin.toml&lt;/code&gt; file.&#10;That archive can then furthermore contain various assets for models, textures and skeletons. All of&#10;those are static files with no code attached, so assuming security while loading the files (which&#10;is a pretty easy conclusion to come to, as Rust already prevents the majority of memory&#10;vulnerabilities) they pose no real danger to users.&lt;/p&gt;&#10;&lt;p&gt;However should the plugin want to expose custom behavior in code, it allows the plugin author to&#10;include WebAssembly files in the archive. If the plugin file in the archive root specifies any&#10;&lt;em&gt;wasm&lt;/em&gt; components in the &lt;code&gt;modules&lt;/code&gt; section, those will be loaded through the wasmtime runtime. The&#10;runtime then limits the application to only perform &lt;em&gt;stdio&lt;/em&gt; to provide logs to the game.&lt;/p&gt;&#10;&lt;p&gt;To confirm that the plugin is actually compliant with the hooks, the runtime will also check the&#10;wasm module against the WIT (WebAssembly Interface Types) file. Since I’m mostly concerned with&#10;code execution, in this context I’ll focus on those wasm files.&lt;/p&gt;&#10;&lt;p&gt;As already mentioned, the plugins code in veloren is shipped in WebAssembly, a sandboxed execution&#10;environment with a &lt;a href="https://webassembly.github.io/spec/core/appendix/properties.html"&gt;formal proof of its soundness and memory-safety&lt;/a&gt;.&#10;his allows the plugin to run arbitrary code in the same process, while maintaining performance and&#10;security.&lt;/p&gt;&#10;&lt;p&gt;One interesting decision that was made in the veloren plugin-system is that the plugins have&#10;absolutely no access to any operating resources outside stdio. This means that even a malicious&#10;plugin could never access the players’ local files or network, crucial for ensuring the security of&#10;a plugin for a game where servers can ship their own plugins to run on the users’ machines. The&#10;only thing the plugin can do is perform operations and computations on the data passed in by the&#10;game.&lt;/p&gt;&#10;&lt;p&gt;Speaking of which, that’s where WIT and the canonical ABI come back into play. The contract between&#10;the plugin and the game is defined in an WIT file. From that the code for both the server and&#10;plugin side are generated, making sure both sides adhere to the same contract.&lt;/p&gt;&#10;&lt;p&gt;When first loading the plugin, wasmtime will then make sure all the types and method definitions&#10;are actually met, as expected by the game. Then it will compile the WASM down to machine code,&#10;exposing the plugin functions over the canonical ABI. The code generated on the game’s side then&#10;makes sure that the type layout and calling conventions on the Rust side are the same as the ones&#10;in the plugin.&lt;/p&gt;&#10;&lt;p&gt;After the plugin is loaded, it’s basically just more native assembly running in the same process as&#10;the game. The overhead to call such functions is fairly minimal and the performance of the plugin&#10;is also very close to native code, all while maintaining security.&lt;/p&gt;&#10;&lt;p&gt;The obvious downside of this approach is that it’s much more limited in its capabilities. While the&#10;plugins in PHP can usually hijack a lot of the control flow of the application if they’re inclined&#10;to do so, this plugin system only allows you to attach to very specific hooks with very narrowly&#10;defined interfaces.&lt;/p&gt;&#10;&lt;p&gt;While I think this is the perfect choice for a video game, where the game needs to run arbitrary&#10;code from a remote server, this might not be the best choice for code that’s audited and running&#10;locally on a server, since the overhead of defining all the interfaces and developing the plugins&#10;against them might not be worth the security benefits.&lt;/p&gt;&#10;&lt;h2 id="conclusion"&gt;Conclusion&lt;/h2&gt;&#10;&lt;p&gt;Plugin-systems are in a interesting spot, where they both should allow users to extend the software&#10;as much as they like, while balancing it with the inherent security risks of running third-party&#10;code in your application. There are many tradeoffs to consider, such as security, performance,&#10;stability and ease of use for the plugin authors. The decision between those is often not trivial,&#10;and may require a lot of thought be put in in order to balance the different aspects.&lt;/p&gt;&#10;&lt;p&gt;I hope this post gave you some insight into some of the different approaches to implementing&#10;plugins and how they are used in the wild.&lt;/p&gt;&#10;</description></item><item><title>Taking RPITIT ― Rust’s Shiny New Feature ― for a Test Ride with Type-system-level Lambda Calculus.</title><link>https://blog.hestia.gay/post/rust-rpitit-lambda-calc.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/rust-rpitit-lambda-calc.md/</guid><pubDate>Fri, 27 Oct 2023 00:00:00 +0000</pubDate><category>rust</category><description>&lt;p&gt;With the upcoming Rust version &lt;code&gt;1.75.0&lt;/code&gt;, two important new features will be stabilized. These&#10;features go by the names &lt;em&gt;return-position impl Trait in trait&lt;/em&gt; (RPITIT) and &lt;em&gt;async fn in trait&lt;/em&gt;&#10;(AFIT).&lt;/p&gt;&#10;&lt;p&gt;Let me take a moment here to congratulate and thank everyone working on these features for their&#10;incredible work. This really is a big step in the Rust ecosystem. While the latter one is certainly&#10;the one more &lt;code&gt;await&lt;/code&gt;-ed by most people, I will today focus on RPITIT, which is also the foundation&#10;for AFIT.&lt;/p&gt;&#10;&lt;p&gt;I’ll provide some code samples, but for the sake of brevity and to not repeat myself, not all of&#10;the code is explicitly written out. If you want to take a look at the full version, I’ve uploaded&#10;it to &lt;a href="https://github.com/w1ll-i-code/rpitit-lambda/blob/master/src/main.rs"&gt;my GitHub&lt;/a&gt;. Since the&#10;feature is not out right now, it has to be compiled with the nightly: &lt;code&gt;$ cargo +nightly run&lt;/code&gt;.&lt;/p&gt;&#10;&lt;h2 id="impl-trait-in-the-return-type"&gt;impl Trait in the Return Type&lt;/h2&gt;&#10;&lt;p&gt;So what exactly is RPITIT? Rust has had the possibility to specify the trait bound in the return&#10;type instead of the actual type since version &lt;code&gt;1.26.0&lt;/code&gt;. However, one of the limitations was that&#10;this syntax couldn’t be used in traits. With the release of Rust &lt;code&gt;1.75.0&lt;/code&gt; this restriction will be&#10;lifted.&lt;/p&gt;&#10;&lt;p&gt;But what do we even need this for in the first place? Couldn’t this just be accomplished with&#10;generics? To answer that question, let’s first take a look at the function declaration of&#10;&lt;code&gt;serde_json&lt;/code&gt;’s &lt;code&gt;from_str&lt;/code&gt;:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;pub&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;from_str&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Deserialize&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;a&lt;/span&gt; &lt;span class="kt"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;As you can see, this function is generic over &lt;code&gt;T&lt;/code&gt;. But the actual concrete type of &lt;code&gt;T&lt;/code&gt; is in the&#10;hands of the end user. But what if we want to return a value of a distinct type that implements a&#10;trait, but that shouldn’t be left up to the user? Then we need to use the &lt;code&gt;impl&lt;/code&gt; syntax.&lt;/p&gt;&#10;&lt;p&gt;If you think it’s just syntactic sugar to not spell out the whole name of the type, you’re at least&#10;partially right &amp;ndash; if there weren’t Voldemort types. Voldemort types (types which must not be&#10;named) are types that you can’t name in a program. In Rust, both closures and functions are such&#10;Voldemort types. Each function or closure has its own unique type determined during compile-time.&lt;/p&gt;&#10;&lt;p&gt;This means you can’t know the concrete type before the program actually compiles, and therefore&#10;can’t use it to refer to them. But with the return type impl syntax, you can tell the compiler to&#10;figure the type out for you. Let’s look at a quick example:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;get_iter&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;: &lt;span class="kt"&gt;i32&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;: &lt;span class="kt"&gt;i32&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;Iterator&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Item&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;usize&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kt"&gt;i32&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="o"&gt;..&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;into_iter&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;|&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;|&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;filter&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;|&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;|&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;%&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;enumerate&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Besides the obvious error with the Voldemort types of the two closures, this function could have&#10;the return type:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;Enumerate&amp;lt;Filter&amp;lt;Map&amp;lt;Range&amp;lt;i32&amp;gt;, {{closure}}&amp;gt;, {{closure}}&amp;gt;&amp;gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;But that wouldn’t really give the user of our function any additional, useful information. And if&#10;we ever decided to change the function, we would have to change the return type along with it. With&#10;this new feature however, we can pass a lot of the work onto the compiler, so we can be faster when&#10;programming.&lt;/p&gt;&#10;&lt;h2 id="return-position-impl-trait-in-trait"&gt;return-position impl Trait in Trait&lt;/h2&gt;&#10;&lt;p&gt;Now with Rust &lt;code&gt;1.75.0&lt;/code&gt; this feature is finally also available for Traits. Now you can specify a&#10;trait with impl return types. Each implementation of the trait can then return a different concrete&#10;type without violating the Trait bounds. The compiler then figures out (based on the implementation&#10;of the Trait) the concrete type that is returned. Since we need to know the concrete implementation&#10;at compile-time in order to know the type that is returned, this obviously makes the whole Trait no&#10;longer &lt;a href="https://doc.rust-lang.org/reference/items/traits.html#object-safety"&gt;object-safe&lt;/a&gt;, meaning&#10;we cannot create a Trait object &lt;code&gt;Box&amp;lt;dyn Trait&amp;gt;&lt;/code&gt; with it.&lt;/p&gt;&#10;&lt;h2 id="lambda-calculus"&gt;Lambda Calculus&lt;/h2&gt;&#10;&lt;p&gt;Before we can implement Lambda Calculus on the type system, we first need to understand what it&#10;actually is. Lambda Calculus is a model of computation introduced in the 1930s by mathematician&#10;Alonzo Church. It follows a few simple rules:&lt;/p&gt;&#10;&lt;ol&gt;&#10;&lt;li&gt;The only thing that exists in the basic calculus are functions.&lt;/li&gt;&#10;&lt;li&gt;Each function takes exactly one value as an argument and returns exactly one value.&lt;/li&gt;&#10;&lt;li&gt;In the function body, we can apply functions to other functions, or construct new functions.&lt;/li&gt;&#10;&lt;/ol&gt;&#10;&lt;p&gt;The simplest function like this is the identity function: &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;id = \lambda x . x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; which is a function that&#10;just returns its input. This function however isn’t very helpful.&lt;/p&gt;&#10;&lt;p&gt;We can also apply functions, for example the function &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lambda x. x\ x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; applies the function &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; once to&#10;itself. Multiple arguments can be modeled by returning a function that binds the first argument.&#10;With that we can construct new functions. &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lambda x . \lambda y . x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; returns a function that takes one argument&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; and completely ignores it, returning &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; instead.&lt;/p&gt;&#10;&lt;p&gt;In the standard notation, lambda calculus is evaluated from left to right, so the function&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lambda x . x\ x\ x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; is equivalent to &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lambda x . (x\ x)\ x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. Calculation is then performed by applying the&#10;functions until it’s in its minimal form and can no longer be reduced.&lt;/p&gt;&#10;&lt;h2 id="putting-everything-together"&gt;Putting Everything Together&lt;/h2&gt;&#10;&lt;p&gt;So how can we use this to actually calculate things in Rust? We know that we need to store state&#10;to return constructed functions, so each function will be a struct. Then, we need to define the&#10;common interface for our functions. As we just established, the function needs to take one argument&#10;and return one argument, both of which are functions. The function is also allowed a reference to&#10;itself, which does not count as a function argument.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;trait&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;: &lt;span class="nb"&gt;Copy&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;eval&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;: &lt;span class="nc"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;And here we can already see RPITIT in action. We know that each function will return a struct that&#10;has the lambda trait and we know that that function will be a concrete type. So we leave the&#10;concrete type details up to the compiler.&lt;/p&gt;&#10;&lt;h2 id="boolean-logic"&gt;Boolean Logic&lt;/h2&gt;&#10;&lt;p&gt;Let’s warm up to the concept by starting from the very basics of computer science: &lt;code&gt;true&lt;/code&gt; and&#10;&lt;code&gt;false&lt;/code&gt;. We can’t have truth values, as lambda calculus only allows for functions to exist, so we&#10;have to encode these two as functions, e.g. types that implement Lambda. If we think about how we&#10;use true and false, it’s to compare them and change the control flow accordingly. So our two values&#10;will simply be functions that take two inputs and call the respective function: &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;True = \lambda x. \lambda y . x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&#10;and &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;False = \lambda x. \lambda y . y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. In plain English: If the value is true, the first function is called, if&#10;the value is false, the second function will be called instead.&lt;/p&gt;&#10;&lt;p&gt;We also know that we need to store some state here, so we need a second struct to hold it. We will&#10;name each function that carries state for its parent function with the same name as the parent&#10;function, followed by an underscore, so we’ll know it represents a partial computation. When&#10;implemented, this logic would look like this:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Copy, Clone)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;True&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Copy, Clone)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;True_&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;True&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;eval&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;: &lt;span class="nc"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;True_&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;True_&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;eval&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;U&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;: &lt;span class="nc"&gt;U&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;The same (just in reverse) is also true for our &lt;code&gt;False&lt;/code&gt; implementation. As you can see, the only&#10;thing we are doing in these functions is either creating a type or returning a type. The return&#10;type of &lt;code&gt;True_&amp;lt;T&amp;gt;&lt;/code&gt; will always be &lt;code&gt;T&lt;/code&gt; which will be known at compile-time. So no matter which two&#10;values we initially put into &lt;code&gt;True&lt;/code&gt;, the resulting type will be known at compile-time.&lt;/p&gt;&#10;&lt;p&gt;With our boolean values in place, let’s do some logic with logical or and and. If we write them out&#10;in lambda calculus, the implementation will also be immediately clear: &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;lor = \lambda x . \lambda y . x\ x\ y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. If&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; is true, then we can return &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; knowing that it’s true, otherwise the operation can only be&#10;true if &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; is true, so we return &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. The same goes for logical and: &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;land = \lambda x . \lambda y . x\ y\ x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. If&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; is false, we can return &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;, if it’s true, then the expression is true if and only if &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; is&#10;true. Lastly to have a full logic system we’re missing the not operator, which is probably the&#10;simplest to understand: &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;F&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lambda x . x\ False\ True&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;, if it’s true, return false, else return true.&lt;/p&gt;&#10;&lt;p&gt;When implemented, it would look something like:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lor&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;eval&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;: &lt;span class="nc"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lor_&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lor_&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;eval&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;U&lt;/span&gt;: &lt;span class="nc"&gt;Lambda&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;: &lt;span class="nc"&gt;U&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Lambda&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;first&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;first&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;first&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lambda&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;And similarly for &lt;code&gt;Land&lt;/code&gt; and &lt;code&gt;Not&lt;/code&gt;.&lt;/p&gt;&#10;&lt;p&gt;The attentive ones of you might have noticed that the &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;lor&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; implementation is actually overly&#10;complex. Since we can just partially apply functions, we can reduce the implementation to&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lambda x . x\ x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; if we so choose. This will return a function with the first field bound, and it can&#10;equally be applied to the next function. In Haskell this is also called point-free programming.&lt;/p&gt;&#10;&lt;h2 id="helper-functions"&gt;Helper Functions&lt;/h2&gt;&#10;&lt;p&gt;Now we want to actually get our hands on the result of the calculations we’ve performed so far.&#10;Since the structs / types ARE our data, we can simply print out the type name of the final value&#10;to get our answers. Rust provides the &lt;code&gt;std::any::type_name()&lt;/code&gt; function to get the string for a&#10;type. However to get that, we would have to know that type, which we explicitly don’t want to know&#10;ourselves. We can easily build around this though by creating a helper function that does the job&#10;for us:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;type_name&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nc"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nb"&gt;&amp;#39;static&lt;/span&gt; &lt;span class="kt"&gt;str&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;any&lt;/span&gt;::&lt;span class="n"&gt;type_name&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;size_of&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;_&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nc"&gt;T&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="kt"&gt;usize&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;mem&lt;/span&gt;::&lt;span class="n"&gt;size_of&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;println!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&lt;/span&gt;&lt;span class="si"&gt;{}&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;type_name&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;Lor&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;True&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;False&lt;/span&gt;&lt;span class="p"&gt;)));&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;With this we delegate the work to actually know the type we want to print out to the compiler. We&#10;can do the same to check the size of the type so we know how much memory it occupies.&lt;/p&gt;&#10;&lt;h2 id="church-numerals"&gt;Church Numerals&lt;/h2&gt;&#10;&lt;p&gt;The last thing I want to touch on are numbers. How can we represent numbers in this system? In a&#10;system where all you can do is apply functions to other functions, numbers can be represented as a&#10;number of function applications. Zero obviously applies the function zero times. This could also be&#10;defined as &lt;code&gt;False&lt;/code&gt;, e.g. return the last parameter ignoring the first, or as Zero returning the&#10;identity function &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;zero = \lambda x . id&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. Each function greater than zero is then represented as the&#10;successor to the previous number. So one is the successor of zero and two is the successor of one&#10;(or, the successor of the successor of zero).&lt;/p&gt;&#10;&lt;p&gt;The application of successor is then a bit more involved: &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;succ = \lambda x . \lambda y . \lambda z . y\ (x\ y\ z)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;, i.e.&#10;we apply the function &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; once to the result of &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; applications of &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; to &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;z&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. So each successor&#10;applies the function once until it hits zero which does not apply the function, but returns its&#10;initial value.&lt;/p&gt;&#10;&lt;p&gt;Addition then can be defined as the repeated application of the successor function to a value:&#10;&lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;λ&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;add = \lambda x . \lambda y . x\ succ\ y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;. So we are basically adding one &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; times to &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; which is functionally&#10;the same as &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;x + y&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;.&lt;/p&gt;&#10;&lt;p&gt;Remember the size_of function from before? Now let’s see how much memory our church numeral takes&#10;up if we, for example calculate &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;2 + 3&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-rust" data-lang="rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;two&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Succ&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Succ&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Zero&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;three&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Succ&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Succ&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Succ&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Zero&lt;/span&gt;&lt;span class="p"&gt;)));&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Add&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;three&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;eval&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;two&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;println!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&lt;/span&gt;&lt;span class="si"&gt;{}&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;type_name&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="c1"&gt;// Succ_&amp;lt;Succ_&amp;lt;Succ_&amp;lt;Succ_&amp;lt;Succ_&amp;lt;Zero&amp;gt;&amp;gt;&amp;gt;&amp;gt;&amp;gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;println!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&lt;/span&gt;&lt;span class="si"&gt;{}&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;size_of&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="c1"&gt;// 0&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Yes, that’s right. Our church numeral does not take up any memory at all! It’s all just type&#10;information at compile-time. And the addition we have defined is just type resolution at&#10;compile-time. If we execute &lt;code&gt;$ strings&lt;/code&gt; on our final binary, we can even see the result of the type&#10;name already lying there. So theoretically we have created the perfect program. It computes&#10;everything in 0 seconds (not counting compile-time). However, all information must also be known at&#10;compile-time, and we have no further control at runtime, so it’s probably not the most flexible&#10;program ever written.&lt;/p&gt;&#10;</description></item><item><title>Static Field Validation in Serde</title><link>https://blog.hestia.gay/post/serde-static-field-validation.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/serde-static-field-validation.md/</guid><pubDate>Mon, 05 Jun 2023 00:00:00 +0000</pubDate><category>rust</category><description>&lt;p&gt;I recently had to parse the JSON-RPC 2.0 standard and ran into the following problem: The standard&#10;requires the field &lt;code&gt;&amp;quot;jsonrpc&amp;quot;: &amp;quot;2.0&amp;quot;&lt;/code&gt; in the JSON itself, and I wanted to validate that with Serde&#10;to ensure the message conforms to the standard. On the other hand I don’t need the field in the&#10;actual struct, since once it’s validated it won’t ever and should never change.&lt;/p&gt;&#10;&lt;p&gt;&lt;em&gt;Edit:&lt;/em&gt; I now know of the existence of &lt;a href="https://github.com/dtolnay/monostate"&gt;the crate monostate&lt;/a&gt;&#10;by the creator of serde, David Tolnay. I think it&amp;rsquo;s still interesting to explore this problem a bit.&lt;/p&gt;&#10;&lt;h2 id="serde-tag"&gt;Serde Tag&lt;/h2&gt;&#10;&lt;p&gt;My first idea was to use the &lt;code&gt;tag&lt;/code&gt; feature of Serde:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde&lt;/span&gt;::&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Deserialize&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Serialize&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde_json&lt;/span&gt;::&lt;span class="n"&gt;Value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Serialize, Deserialize)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Debug, Eq, PartialEq)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[serde(tag = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;jsonrpc&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;, rename = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;2.0&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;: &lt;span class="nb"&gt;String&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(skip_serializing_if = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Option::is_none&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;params&lt;/span&gt;: &lt;span class="nb"&gt;Option&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Value&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(skip_serializing_if = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Option::is_none&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;: &lt;span class="nb"&gt;Option&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;usize&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;so let’s try it out:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;jsonrpc&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;: &lt;span class="s"&gt;&amp;#34;my_method&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;to_owned&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;params&lt;/span&gt;: &lt;span class="nb"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;: &lt;span class="nb"&gt;None&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde_json&lt;/span&gt;::&lt;span class="n"&gt;to_string&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;jsonrpc&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;unwrap&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;assert_eq!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="sa"&gt;r&lt;/span&gt;&lt;span class="s"&gt;#&amp;#34;{&amp;#34;jsonrpc&amp;#34;:&amp;#34;2.0&amp;#34;,&amp;#34;method&amp;#34;:&amp;#34;my_method&amp;#34;}&amp;#34;#&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Wonderful! As expected it adds the jsonrpc tag to the message! Now let’s try de-serializing:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="sa"&gt;r&lt;/span&gt;&lt;span class="s"&gt;#&amp;#34;{&amp;#34;jsonrpc&amp;#34;:&amp;#34;2.0&amp;#34;,&amp;#34;method&amp;#34;:&amp;#34;my_method&amp;#34;}&amp;#34;#&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expected&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;: &lt;span class="s"&gt;&amp;#34;my_method&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;to_owned&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;params&lt;/span&gt;: &lt;span class="nb"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;: &lt;span class="nb"&gt;None&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;: &lt;span class="nc"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde_json&lt;/span&gt;::&lt;span class="n"&gt;from_str&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;unwrap&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;assert_eq!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expected&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Till now everything worked great and I was optimistic. But what we really want is to fail if the&#10;jsonrpc field isn’t given, as that’s what the specification demands. So let’s try that:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="sa"&gt;r&lt;/span&gt;&lt;span class="s"&gt;#&amp;#34;{&amp;#34;method&amp;#34;:&amp;#34;my_method&amp;#34;}&amp;#34;#&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expected&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;: &lt;span class="s"&gt;&amp;#34;my_method&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;to_owned&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;params&lt;/span&gt;: &lt;span class="nb"&gt;None&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;: &lt;span class="nb"&gt;None&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;: &lt;span class="nc"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde_json&lt;/span&gt;::&lt;span class="n"&gt;from_str&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;message&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;unwrap&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;assert_eq!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;expected&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Serde will still de-serialize this! Which is bad, actually, because I wanted to use it for&#10;validation. This path was obviously a dead end, so I went back to the drawing board.&lt;/p&gt;&#10;&lt;h2 id="abusing-enums"&gt;(Ab)using enums&lt;/h2&gt;&#10;&lt;p&gt;Now what if the tag actually means something? What if it’s actually an enum variant and therefore&#10;is needed for de-serialization? So I constructed my second attempt:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Serialize, Deserialize)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Debug, Eq, PartialEq)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[serde(tag = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;jsonrpc&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;enum&lt;/span&gt; &lt;span class="nc"&gt;JsonRpcEnum&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(rename = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;2.0&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;JsonRpc&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;: &lt;span class="nb"&gt;String&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(skip_serializing_if = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Option::is_none&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;params&lt;/span&gt;: &lt;span class="nb"&gt;Option&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Value&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(skip_serializing_if = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Option::is_none&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;: &lt;span class="nb"&gt;Option&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;usize&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Running all the previous tests showed that this works! It serializes what it should and more&#10;importantly, doesn’t de-serialize what it shouldn’t. Even better, the Rust compiler is smart enough&#10;to see that the enum has only one possible variant, and it therefore optimized away the 8-byte tags&#10;that are normally associated with an enum.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="fm"&gt;assert_eq!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;mem&lt;/span&gt;::&lt;span class="n"&gt;size_of&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;JsonRpcTagged&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;mem&lt;/span&gt;::&lt;span class="n"&gt;size_of&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;JsonRpcEnum&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Now I should be happy right? I have achieved what I initially set out to do. But my perfectionism&#10;wouldn’t let me stop there. First of all, the type looks a bit weird, but more dramatically, we&#10;can’t access the fields in an easy way. The easiest way to access the contents of this enum is&#10;pretty ugly:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kd"&gt;let&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;JsonRpcEnum&lt;/span&gt;::&lt;span class="n"&gt;JsonRpc&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="k"&gt;ref&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;..&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;some_jsonrpc&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;It’s cool to see that Rust actually lets you compile a monstrosity like that, but it’s definitely&#10;not something for the weak-spirited. While I try not to judge people based on their appearances, I&#10;will judge code for that. So back to the drawing board I went one last time.&lt;/p&gt;&#10;&lt;h2 id="using-custom-de-serialization"&gt;Using Custom De-serialization&lt;/h2&gt;&#10;&lt;p&gt;First I tried implementing both Serialize and De-serialize for an empty struct:&#10;&lt;code&gt;struct JsonRpcVersion;&lt;/code&gt;, but that meant for all other derives I’d have to add them to both the&#10;JsonRpc struct and this empty struct. Furthermore this was not very reusable as I’d need replicate&#10;the whole logic the next time I needed something similar.&lt;/p&gt;&#10;&lt;p&gt;Enter the empty tuple. One of my favorite Rust features is that it allows some cool code trickery&#10;and compiler optimizations. Look at the implementation of the HashSet if you have some time, or&#10;read some of the many other great blog posts. It solves my first problem of running (after&#10;validation) structs for all derive macros I want to use. It’s also zero-size, meaning we’re not&#10;wasting memory space or compute time.&lt;/p&gt;&#10;&lt;p&gt;The other savior of my soul was the &lt;code&gt;#[serde(with = &amp;quot;Validator&amp;quot;)]&lt;/code&gt; attribute. It lets you specify a&#10;validator that handles both serialization and de-serialization by calling &lt;code&gt;Validator::serialize(..)&lt;/code&gt;&#10;and &lt;code&gt;Validator::deserialize(..)&lt;/code&gt; on it respectively. Now all I need is a validator struct that&#10;implements it, and a trait that does the implementation for me.&lt;/p&gt;&#10;&lt;p&gt;So let’s take a look at the Trait I came up with:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde&lt;/span&gt;::&lt;span class="n"&gt;de&lt;/span&gt;::&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Error&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Unexpected&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Visitor&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serde&lt;/span&gt;::&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Deserializer&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Serializer&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;fmt&lt;/span&gt;::&lt;span class="n"&gt;Formatter&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;use&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;marker&lt;/span&gt;::&lt;span class="n"&gt;PhantomData&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;pub&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;trait&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Validator&lt;/span&gt;: &lt;span class="nb"&gt;Sized&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;EXPECTED_VALUE&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nb"&gt;&amp;#39;static&lt;/span&gt; &lt;span class="kt"&gt;str&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;serialize&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;S&lt;/span&gt;: &lt;span class="nc"&gt;Serializer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;_version&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serializer&lt;/span&gt;: &lt;span class="nc"&gt;S&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;S&lt;/span&gt;::&lt;span class="nb"&gt;Ok&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;S&lt;/span&gt;::&lt;span class="n"&gt;Error&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;serializer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;serialize_str&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;Self&lt;/span&gt;::&lt;span class="no"&gt;EXPECTED_VALUE&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;deserialize&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;de&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;D&lt;/span&gt;: &lt;span class="nc"&gt;Deserializer&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;de&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;deserializer&lt;/span&gt;: &lt;span class="nc"&gt;D&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;D&lt;/span&gt;::&lt;span class="n"&gt;Error&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;deserializer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;deserialize_str&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ValidatorVisitor&lt;/span&gt;::&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="bp"&gt;Self&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;phantom_data&lt;/span&gt;: &lt;span class="nc"&gt;PhantomData&lt;/span&gt;::&lt;span class="n"&gt;default&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Default)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;ValidatorVisitor&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Validator&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;phantom_data&lt;/span&gt;: &lt;span class="nc"&gt;PhantomData&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;de&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;: &lt;span class="nc"&gt;Validator&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Visitor&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;de&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;ValidatorVisitor&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="nc"&gt;Value&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;expecting&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;formatter&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nc"&gt;mut&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Formatter&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nc"&gt;std&lt;/span&gt;::&lt;span class="n"&gt;fmt&lt;/span&gt;::&lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;formatter&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;write_str&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;::&lt;span class="no"&gt;EXPECTED_VALUE&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;visit_borrowed_str&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;E&lt;/span&gt;: &lt;span class="nc"&gt;Error&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="bp"&gt;self&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="na"&gt;&amp;#39;de&lt;/span&gt; &lt;span class="kt"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;-&amp;gt; &lt;span class="nb"&gt;Result&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="bp"&gt;Self&lt;/span&gt;::&lt;span class="n"&gt;Value&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;E&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;if&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;::&lt;span class="no"&gt;EXPECTED_VALUE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;Ok&lt;/span&gt;&lt;span class="p"&gt;(())&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="nb"&gt;Err&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;E&lt;/span&gt;::&lt;span class="n"&gt;invalid_value&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Unexpected&lt;/span&gt;::&lt;span class="n"&gt;Str&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;::&lt;span class="no"&gt;EXPECTED_VALUE&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;It’s a bit of code, but it’s worth understanding, so let me guide you through it.&lt;/p&gt;&#10;&lt;p&gt;The trait itself implements the serialize and de-serialize functions that will later be called by&#10;Serde. The value for it is provided as an associated constant value. Shout-out to &lt;a href="https://users.rust-lang.org/u/SkiFire13"&gt;u/SkiFire13&lt;/a&gt;&#10;on the Rust user forum for making me aware of that feature. It provides whatever data we need to&#10;parse the value later on. For the serialization, we can simply write the string to the formatter.&#10;But de-serialization gets a bit more complicated.&lt;/p&gt;&#10;&lt;p&gt;To de-serialize data, I need a Visitor. My first instinct was to implement the Visitor for all&#10;arbitrary types &lt;code&gt;T: Validator&lt;/code&gt; to get quick access to the string slice in the trait bound. Sadly&#10;the compiler doesn’t allow blanket implementations of traits that aren’t defined in this crate so&#10;I had to create a wrapper type.&lt;/p&gt;&#10;&lt;p&gt;The ValidatorVisitor is a zero-sized struct that does nothing but hold the type &lt;code&gt;T&lt;/code&gt; for the Visitor&#10;to access. Since the compiler doesn’t allow you to compile a struct with an unused generic&#10;argument, we need to add one field to the visitor: some phantom data that consumes that type in the&#10;background and does some compiler magic that allows this implementation to actually compile.&lt;/p&gt;&#10;&lt;p&gt;In the implementation body of the trait we then simply provide the function &lt;code&gt;visit_borrowed_str(..)&lt;/code&gt;&#10;that returns an empty tuple if it receives the correct value; otherwise it returns an error.&lt;/p&gt;&#10;&lt;p&gt;Now what does the final implementation of my JsonRpc struct actually look like? The Validators are just four LOC:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;JsonRpcVersionValidator&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;impl&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;Validator&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;JsonRpcVersionValidator&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="no"&gt;EXPECTED_VALUE&lt;/span&gt;: &lt;span class="kp"&gt;&amp;amp;&lt;/span&gt;&lt;span class="nb"&gt;&amp;#39;static&lt;/span&gt; &lt;span class="kt"&gt;str&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;2.0&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;That’s what I’m talking about! That’s what clean code should look like! We have one point that&#10;statically controls the value, and it’s very re-usable. After we’ve defined the Validator, we can&#10;simply use it in the struct as follows:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-Rust" data-lang="Rust"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="cp"&gt;#[derive(Serialize, Deserialize, Debug, Eq, PartialEq)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;JsonRpcValidated&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(with = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;JsonRpcVersionValidator&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;, rename = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;jsonrpc&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;version&lt;/span&gt;: &lt;span class="p"&gt;(),&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;method&lt;/span&gt;: &lt;span class="nb"&gt;String&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(skip_serializing_if = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Option::is_none&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;params&lt;/span&gt;: &lt;span class="nb"&gt;Option&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Value&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="cp"&gt;#[serde(skip_serializing_if = &lt;/span&gt;&lt;span class="s"&gt;&amp;#34;Option::is_none&amp;#34;&lt;/span&gt;&lt;span class="cp"&gt;)]&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;: &lt;span class="nb"&gt;Option&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;usize&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;And with that we have a struct that matches all the criteria I originally set out. It serializes&#10;correctly, it de-serializes what it should, and doesn’t what it shouldn’t. It’s easy to use and&#10;reuse and doesn’t waste any space or computation time.&lt;/p&gt;&#10;</description></item><item><title>About Set Theory, the N-queens Problem, and SQL</title><link>https://blog.hestia.gay/post/sql-n-queens-problem.md/</link><guid isPermaLink="true">https://blog.hestia.gay/post/sql-n-queens-problem.md/</guid><pubDate>Mon, 05 Jun 2023 00:00:00 +0000</pubDate><category>beginner</category><category>sql</category><description>&lt;p&gt;The n-queens problem is a common exercise in computer science. Legend has it that a mathematician&#10;once declared that women are like the queens in chess, you can’t put eight of them in a room&#10;without them trying to kill each other. This obviously isn’t true, and since I’m a feminist, but&#10;also a nerd, we will disprove him today in an unconventional way: with an SQL query.&lt;/p&gt;&#10;&lt;h2 id="let-me-give-you-a-quick-overview-of-the-problem"&gt;Let me give you a quick overview of the problem:&lt;/h2&gt;&#10;&lt;p&gt;In chess the queen can move any number of squares vertically, horizontally or diagonally. This&#10;means, if two queens are in the same row, the same column or diagonal to one another, they can&#10;attack each other. The problem requires us to place n queens on a n-by-n board without any of them&#10;being able to attack each other, or in more technical terms, we are looking for the set of all sets&#10;with cardinality n such that no two queens in that set can attack each other. If that set is&#10;non-empty, then we have disproven the claim.&lt;/p&gt;&#10;&lt;h2 id="modeling-the-problem"&gt;Modeling the problem&lt;/h2&gt;&#10;&lt;p&gt;Normally this problem would be solved iteratively with an algorithm, however this is not possible&#10;in SQL. Therefore we have to reach back to set theory to model the problem in a language that&#10;translates well to SQL.&lt;/p&gt;&#10;&lt;p&gt;First we need a set of all positions a queen can be in. For that we model a queen as a tuple of two&#10;coordinates in the n-by-n grid:&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy="false"&gt;{&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi mathvariant="normal"&gt;∣&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo stretchy="false"&gt;[&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy="false"&gt;]&lt;/mo&gt;&lt;mo stretchy="false"&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;&#10;possible\ positions = \lbrace ( x, y )\ |\ x, y \in [ 1 , n ] \rbrace&#10;&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;After that we need a set of all combinations with queens. This set of possible positions grows&#10;quadratically with the length of the board, described by the function &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;!&lt;/mo&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;!&lt;/mo&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mi mathvariant="normal"&gt;/&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy="false"&gt;!&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;((n^2!) / ( n^2 - n )! ) / n!&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;.&#10;That’s because we have &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo stretchy="false"&gt;!&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;n^2!&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; possible combinations of queen positions on the board without&#10;stacking any on top of each other. However &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;!&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;(n^2-n)!&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; of those are sets with more than n queens on the&#10;board. After that we have all combinations duplicated &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo stretchy="false"&gt;!&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;n!&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt; times as permutations of each other. We&#10;are, however, only interested in single solutions without considering those permutations. With this&#10;we find there exist 1,820 possible combinations for a 4-by-4 board, which is the smallest board&#10;with a solution. On a standard 8-by-8 board this number rises to 4,426,165,368.&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;msub&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo fence="true" stretchy="true" minsize="1.8em" maxsize="1.8em"&gt;{&lt;/mo&gt;&lt;mo fence="true" stretchy="true" minsize="1.2em" maxsize="1.2em"&gt;{&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mi mathvariant="normal"&gt;.&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo fence="true" stretchy="true" minsize="1.2em" maxsize="1.2em"&gt;}&lt;/mo&gt;&lt;mi mathvariant="normal"&gt;∣&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo fence="true" stretchy="true" minsize="1.8em" maxsize="1.8em"&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;&#10;boards_n = \Bigl\{ \bigl\{ (x_1, y_1), (x_2, y_2) .. (x_n, y_n) \bigr\} | (x, y) \in possible\ positions \Bigr\}&#10;&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;Now that we have that set, we need to filter out all sets that contain queens that can attack each&#10;other. To check if they are in the same column or row is trivial. We just have to check if the x or&#10;y coordinates of the tuple are equal. However for the diagonals we have to use a trick.&lt;/p&gt;&#10;&lt;p&gt;Let’s first list the diagonal fields from the top left to the bottom right out so we get a feel for&#10;the data: (1,1), (2,2) .. (8,8). As we can see, in this diagonal both the x and y coordinates grow&#10;at the same rate. With that information we can guarantee that the difference between x and y in the&#10;same diagonal also stays the same: 1 – 1 = 0, 2 – 2 = 0 .. 8 – 8 = 0. We can use that difference to&#10;check weather two queens are in the same diagonal or not.&lt;/p&gt;&#10;&lt;p&gt;We can use a similar trick for the other diagonal as well. Let’s list the fields from the top right&#10;to the bottom left first: (8,1), (7,2) .. (1,8). Here the x coordinate decreases at the same rate&#10;that y increases. Therefore the sum of the coordinates in this diagonal stays the same: 8 + 1 = 9,&#10;7 + 2 = 9 .. 1 + 8 = 9.&lt;/p&gt;&#10;&lt;p&gt;With this we now have all our conditions for which queens can attack each other, and we only need&#10;to plug them into our final formula to get the expression:&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;{&lt;/mo&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\lbrace\ &lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;&#10;&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mspace width="1.4226em"/&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi mathvariant="normal"&gt;∣&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\hspace{5mm} board \in boards\ |&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;&#10;&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mspace width="1.4226em"/&gt;&lt;mi mathvariant="normal"&gt;∀&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi mathvariant="normal"&gt;∄&lt;/mi&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo separator="true"&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\hspace{5mm} \forall (x_1, y_1) \in board\ :\ \nexists (x_2, y_2) \in ( board \setminus (x_1, y_1))&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;&#10;&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mspace width="1.4226em"/&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mtext&gt; &lt;/mtext&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;∨&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;∨&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;∨&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\hspace{5mm} such\ that\ (x_1=x_2) \lor (y_1=y_1) \lor (x_1-y_1=x_2-y_2) \lor (x_1+y_1) = (x_2+y_2)&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;&#10;&lt;/p&gt;&#10;&lt;div class="math-block"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML" display="block"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;\rbrace&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/div&gt;&lt;p&gt;We create the set of all sets of queens with cardinality &lt;span class="math-inline"&gt;&lt;span class="katex"&gt;&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;annotation encoding="application/x-tex"&gt;n&lt;/annotation&gt;&lt;/semantics&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;, for which it holds that for all queens&#10;in that set there does not exist another queen such that they could attack each other horizontally,&#10;vertically or diagonally.&lt;/p&gt;&#10;&lt;p&gt;Or in plain English: All sets with n queens in them and no two queens can attack one another.&lt;/p&gt;&#10;&lt;h2 id="translating-this-to-sql"&gt;Translating this to SQL&lt;/h2&gt;&#10;&lt;p&gt;While at first it seems like this logic could be mapped fairly well to SQL, we quickly run into our&#10;first problems: this logic works on sets of sets of tuples, however SQL works on sets of tuples.&#10;Therefore we have to flatten the sets down to a larger tuple.&lt;/p&gt;&#10;&lt;p&gt;However this structure also gives us distinct advantages: We can make assumptions about our data&#10;and with that decrease the amount of work that has to be done and stop computation for partial&#10;results, if they already don’t fit our criteria.&lt;/p&gt;&#10;&lt;p&gt;I will implement the logic here for the smallest board with solutions: the 4-by-4 board, since the&#10;implementation get increasingly verbose. However this model can theoretically be increased for all&#10;sizes.&lt;/p&gt;&#10;&lt;p&gt;But first we need a set of columns on which we can place. We use a recursive common table&#10;expression (rCTE) for this to save ourselves a bit work:&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-SQL" data-lang="SQL"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WITH&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;RECURSIVE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;UNION&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;Now we could theoretically create a table for all positions of queens on the board with nested&#10;common table expressions to get a set of all possible positions for a queen on a chess board.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-SQL" data-lang="SQL"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WITH&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;RECURSIVE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_positions&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WITH&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;RECURSIVE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;UNION&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_row&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;UNION&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_row&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_row&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;new_columns&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;queen_column&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_positions&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;new_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_row&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen_positions&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;After n cross joins of this table with itself, we would then get a set of all boards with exactly n&#10;queens on them, even the boards with queens stacked on top of each other. However this would also&#10;result in a lot of wasted work by including many solutions that obviously don’t work. Furthermore&#10;it would duplicate all solutions by a factor of n! since the tuple is sorted and therefore all&#10;mutations of the same result appear different. This is a tradeoff we have to stomach by mapping the&#10;set of tuples, which would avoid such cases, to a tuple that can be processed by an SQL query. The&#10;query to filter out duplicates would grow very quickly and would be much more verbose that doing&#10;the join by hand. However, by writing the query by hand, we have an alternative.&lt;/p&gt;&#10;&lt;p&gt;We can save a lot of work by making assumptions about our data. Remember how I previously mentioned&#10;that we have 1,820 possible combinations of queen positions for this board? We know that&#10;combinations with queens in the same row can never be in the final result, because they already&#10;violate one of the rules. Therefore we can leave them out of the initial set by adding each new&#10;queen in a new row. The new set with this simple assumption will still grow exponentially with the&#10;function &lt;code&gt;n^n&lt;/code&gt;, which is a huge space to search, but it’s still far less than what’s needed by the&#10;brute-force approach. By including that assumption in our query (and making it a bit more verbose),&#10;this query will only return 256 results, saving the computer a lot of time and resources, especially&#10;for larger boards.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-SQL" data-lang="SQL"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WITH&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;RECURSIVE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;UNION&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen4&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;After this we only need to apply our rules to the query, and filter out all sets that contain queens&#10;that attack each other. Here we can make another assumption about our data: While it would be&#10;easiest to add a where-clause for all restrictions to the end of the query, we can optimize by&#10;throwing out partial results that already violate our rules. We check after each join if it clashes&#10;with any of the previous queens and only keep those that don’t, reducing the joins that need to be&#10;carried out for the remaining queens. For example, after joining in the second queen, we already&#10;check if she can attack the first queen. If that’s possible, we can already ignore that without&#10;taking any further queens into account. After the third queen, we check if there are clashes with&#10;queens one and two and so on.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-SQL" data-lang="SQL"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WITH&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;RECURSIVE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;UNION&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;With this, we have at last constructed the final query! Now the only thing remaining is to format&#10;our output to get actual chess positions, so that the chess players here won’t hunt me down later.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-SQL" data-lang="SQL"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;[..]&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[..]&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;The final result is a set with two possible solutions. After a quick check on Wikipedia we can see&#10;that we actually found the correct solutions for a 4-by-4 board through a simple SQL query.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;+--------+--------+--------+--------+&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;| queen1 | queen2 | queen3 | queen4 |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;+--------+--------+--------+--------+&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;| A2 | B4 | C1 | D3 |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;| A3 | B1 | C4 | D2 |&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;+--------+--------+--------+--------+&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;&lt;p&gt;And to answer the question from above, here’s the query for eight queens. We get 92 results, firmly&#10;disproving this mathematician of legends.&lt;/p&gt;&#10;&lt;figure class="code"&gt;&#10; &lt;figcaption&gt;&lt;span class="dots" aria-hidden="true"&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;i&gt;&lt;/i&gt;&lt;/span&gt;&lt;/figcaption&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-SQL" data-lang="SQL"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WITH&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;RECURSIVE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;UNION&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen7&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;CONCAT&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;CHAR&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;64&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;as&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen1&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nqueens_columns&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;queen8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;NOT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y1&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y2&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y3&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y4&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y5&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y6&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;OR&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y7&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;x8&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;y8&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10;&lt;/figure&gt;&#10;</description></item></channel></rss>