li>
</ul>
<p>What we just did is a <em>demonstration</em> that probably the most important rule of logical deduction - the infamous <em>modus ponens</em> - is a natural interpretation of applying a function to a value in a (typed) lambda-calculus.</p>
<p>Amusingly, such a “proof” is already present in e.g. Ocaml:</p>
<pre><code class="language-ocaml">(fun v -&gt; (fun f -&gt; f v))
- : 'a -&gt; ('a -&gt; 'b) -&gt; 'b = &lt;fun&gt;
</code></pre>
<p>For the trained mind, this reads: "from a value of type 