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<title>Implementing Prolog</title>
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<body>
<div class="reveal">
<div class="slides">
<section id="title-slide">
<h1 class="title">Implementing Prolog</h1>
<p class="subtitle">A λ-Nantes Workshop</p>
<p class="author">arnaud@pankzsoft.com - <span class="citation"
data-cites="abailly.bsky.social">@abailly.bsky.social</span></p>
<p class="date">2025-12-10</p>
</section>
<section>
<section id="usage" class="title-slide slide level1">
<h1>Usage</h1>
<p><img data-src="star-wars.jpg" /></p>
</section>
<section id="example" class="slide level2">
<h2>Example</h2>
<p>A <em>program</em> about Star Wars characters (including the crappy
recent ones)</p>
</section>
<section id="example---facts" class="slide level2">
<h2>Example - Facts</h2>
<p>Simple facts asserting the gender of some characters.</p>
<div class="sourceCode" id="cb1"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>female(leia)<span class="kw">.</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>male(vader)<span class="kw">.</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>male(luke)<span class="kw">.</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>male(kylo)<span class="kw">.</span></span></code></pre></div>
</section>
<section id="example---facts-1" class="slide level2">
<h2>Example - Facts</h2>
<p>More complex facts asserting a <code>child</code>hood
<em>relation</em> between some characters.</p>
<div class="sourceCode" id="cb2"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>child(luke<span class="kw">,</span> vader)<span class="kw">.</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>child(leia<span class="kw">,</span> vader)<span class="kw">.</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>child(kylo<span class="kw">,</span> leia)<span class="kw">.</span></span></code></pre></div>
</section>
<section id="example---rules" class="slide level2">
<h2>Example - Rules</h2>
<p><em>Rules</em> (or <em>Clauses</em>) allowing to infer some relation
from other relations.</p>
<div class="sourceCode" id="cb3"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>son(<span class="dt">X</span><span class="kw">,</span><span class="dt">Y</span>) <span class="kw">:-</span> male(<span class="dt">X</span>)<span class="kw">,</span> child(<span class="dt">X</span><span class="kw">,</span><span class="dt">Y</span>)<span class="kw">.</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>daughter(<span class="dt">X</span><span class="kw">,</span><span class="dt">Y</span>) <span class="kw">:-</span> female(<span class="dt">X</span>)<span class="kw">,</span> child(<span class="dt">X</span><span class="kw">,</span><span class="dt">Y</span>)<span class="kw">.</span></span></code></pre></div>
</section>
<section id="example---rules-1" class="slide level2">
<h2>Example - Rules</h2>
<p>More complex rules asserting a transitive relation</p>
<div class="sourceCode" id="cb4"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>grandchild(<span class="dt">X</span><span class="kw">,</span><span class="dt">Z</span>) <span class="kw">:-</span> child(<span class="dt">X</span><span class="kw">,</span><span class="dt">Y</span>)<span class="kw">,</span> child(<span class="dt">Y</span><span class="kw">,</span><span class="dt">Z</span>)<span class="kw">.</span></span></code></pre></div>
</section>
<section id="example---query" class="slide level2">
<h2>Example - Query</h2>
<p>We can <em>query</em> this program, for example asking who is a
grandchild of Darth Vader</p>
<div class="sourceCode" id="cb5"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="dt">></span> <span class="fu">?-</span> grandchild(<span class="dt">X</span><span class="er">,</span> vader)<span class="kw">.</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>success<span class="kw">.</span> <span class="dt">Type</span> [<span class="dt">Enter</span>] to list solutions<span class="kw">.</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="dt">></span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="er">[</span><span class="dt">X</span> <span class="kw">-></span> kylo<span class="er">]</span></span></code></pre></div>
</section>
<section id="example---query-1" class="slide level2">
<h2>Example - Query</h2>
<p>A Prolog query can have several answers:</p>
<div class="sourceCode" id="cb6"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="dt">></span> <span class="fu">?-</span> child(<span class="dt">X</span><span class="er">,</span> vader)<span class="kw">.</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>success<span class="kw">.</span> <span class="dt">Type</span> [<span class="dt">Enter</span>] to list solutions<span class="kw">.</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="dt">></span></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="er">[</span><span class="dt">X</span> <span class="kw">-></span> luke<span class="er">]</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="dt">></span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a><span class="er">[</span><span class="dt">X</span> <span class="kw">-></span> leia<span class="er">]</span></span></code></pre></div>
</section>
<section id="example---query-2" class="slide level2">
<h2>Example - Query</h2>
<p>Or no answer:</p>
<div class="sourceCode" id="cb7"><pre
class="sourceCode prolog"><code class="sourceCode prolog"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="dt">></span> <span class="fu">?-</span> grandchild(leia<span class="er">,</span> <span class="dt">X</span>)<span class="kw">.</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>failure</span></code></pre></div>
</section></section>
<section>
<section id="implementation" class="title-slide slide level1">
<h1>Implementation</h1>
</section>
<section id="terms" class="slide level2">
<h2>Terms</h2>
<ul>
<li class="fragment">variables start with upper casae: <code>X</code>,
<code>Y</code>…</li>
<li class="fragment">symbols start with lower case: <code>s</code>,
<code>z</code>, <code>child</code>, …</li>
<li class="fragment">symbols have 0 or more arguments, e.g an
<em>arity</em> : <code>bob</code>, <code>child(X, Y)</code>,
<code>father(bob, Z)</code>…</li>
</ul>
</section>
<section id="clauses" class="slide level2">
<h2>Clauses</h2>
<ul>
<li class="fragment"><em>head</em>: a single term</li>
<li class="fragment"><em>premises</em>: a (possibly empty) list of
terms</li>
<li class="fragment">a <em>data set</em> (or a <em>program</em>) is a
list of clauses or <em>facts</em></li>
<li class="fragment">a <em>query</em> is a term introduced with
<code>?-</code></li>
</ul>
</section>
<section id="basic-algorithm" class="slide level2">
<h2>Basic algorithm</h2>
<p>Given a query and a set of clauses, a Prolog interpreter loop goes
like:</p>
<ol type="1">
<li class="fragment">Push <em>query</em> on its goal stack</li>
<li class="fragment">Pop up current <em>goal</em> from the stack</li>
<li class="fragment">Try to match <em>goal</em> with each
<em>clause</em>:
<ol type="a">
<li class="fragment"><em>Unify</em> goal with the <em>head</em> of
<em>clause</em> with <em>fresh</em> variables</li>
<li class="fragment">If unification succeeds, push <em>premises</em> of
clause onto goals stack</li>
</ol></li>
<li class="fragment">Query succeeds if stack is empty with a successful
match</li>
</ol>
</section>
<section id="unification" class="slide level2">
<h2>Unification</h2>
<p>Given two terms <span
class="math inline"><em>t</em><sub>1</sub></span> and <span
class="math inline"><em>t</em><sub>2</sub></span> with <em>free
variables</em> <span
class="math inline"><em>f</em><em>v</em>(<em>t</em><sub>1</sub>)</span>,
<span
class="math inline"><em>f</em><em>v</em>(<em>t</em><sub>2</sub>)</span>,
unification is the process of defining a <em>substitution</em> between
variables and <em>terms</em></p>
<p><span
class="math display"><em>σ</em> : <em>f</em><em>v</em>(<em>t</em><sub>1</sub>) ∪ <em>f</em><em>v</em>(<em>t</em><sub>2</sub>) → <em>T</em></span></p>
</section>
<section id="unification-1" class="slide level2">
<h2>Unification</h2>
<ul>
<li class="fragment">Two variables unify with each other</li>
<li class="fragment">A variable unifies with a term if not already
mapped</li>
<li class="fragment">Two relations unify with each other iff
<ul>
<li class="fragment">Their symbol is the same</li>
<li class="fragment">Their arguments unify with each other</li>
</ul></li>
</ul>
</section>
<section id="unification-2" class="slide level2">
<h2>Unification</h2>
<ul>
<li class="fragment"><span
class="math inline"><em>σ</em>(<em>X</em>, <em>Y</em>) = {<em>X</em> ↦ <em>Y</em>}</span></li>
<li class="fragment"><span
class="math inline"><em>σ</em>(<em>X</em>, <em>f</em><em>o</em><em>o</em>) = {<em>X</em> ↦ <em>f</em><em>o</em><em>o</em>}</span></li>
<li class="fragment"><span
class="math inline"><em>σ</em>(<em>f</em><em>o</em><em>o</em>, <em>X</em>) = {<em>X</em> ↦ <em>f</em><em>o</em><em>o</em>}</span></li>
<li class="fragment"><span
class="math inline"><em>σ</em>(<em>f</em><em>o</em><em>o</em>(<em>b</em><em>a</em><em>r</em>, <em>Y</em>), <em>f</em><em>o</em><em>o</em>(<em>X</em>, <em>Z</em>)) = {<em>X</em> ↦ <em>b</em><em>a</em><em>r</em>, <em>Y</em> ↦ <em>Z</em>}</span></li>
</ul>
</section></section>
<section>
<section id="practice" class="title-slide slide level1">
<h1>Practice</h1>
<p><img data-src="workbench.jpg" /></p>
</section>
<section id="references" class="slide level2">
<h2>References</h2>
<ul>
<li class="fragment"><a
href="https://github.com/norm2782/NanoProlog">NanoProlog</a></li>
<li class="fragment"><a
href="https://github.com/abailly/hslogic">hslogic</a></li>
<li class="fragment"><a
href="https://github.com/andrejbauer/plzoo/tree/master/src/miniprolog">miniprolog</a></li>
</ul>
</section></section>
</div>
</div>
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// Use this method for navigation when auto-sliding
autoSlideMethod: null,
// Specify the average time in seconds that you think you will spend
// presenting each slide. This is used to show a pacing timer in the
// speaker view
defaultTiming: null,
// Enable slide navigation via mouse wheel
mouseWheel: false,
// The display mode that will be used to show slides
display: 'block',
// Hide cursor if inactive
hideInactiveCursor: true,
// Time before the cursor is hidden (in ms)
hideCursorTime: 5000,
// Opens links in an iframe preview overlay
previewLinks: false,
// Transition style (none/fade/slide/convex/concave/zoom)
transition: 'slide',
// Transition speed (default/fast/slow)
transitionSpeed: 'default',
// Transition style for full page slide backgrounds
// (none/fade/slide/convex/concave/zoom)
backgroundTransition: 'fade',
// Number of slides away from the current that are visible
viewDistance: 3,
// Number of slides away from the current that are visible on mobile
// devices. It is advisable to set this to a lower number than
// viewDistance in order to save resources.
mobileViewDistance: 2,
// reveal.js plugins
plugins: [
RevealNotes,
RevealSearch,
RevealZoom
]
});
</script>
</body>
</html>
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