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<div id="content" class="content">
<h1 class="title">the un i blog</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#orgb8f5d7f">1. Referential transparency</a>
<ul>
<li><a href="#orgbc3f2fa">1.1. Let transparency</a></li>
<li><a href="#org08b103d">1.2. Soft let transparency</a></li>
<li><a href="#org4328a10">1.3. Softest let transparency</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgb8f5d7f" class="outline-2">
<h2 id="orgb8f5d7f"><span class="section-number-2">1.</span> Referential transparency</h2>
<div class="outline-text-2" id="text-1">
<p>
There’s a couple of variations of the notion of referential transparency that seem quite useful in expressing properties of some functional languages:
</p>
</div>
<div id="outline-container-orgbc3f2fa" class="outline-3">
<h3 id="orgbc3f2fa"><span class="section-number-3">1.1.</span> Let transparency</h3>
<div class="outline-text-3" id="text-1-1">
<p>
Call a language <i>let-transparent</i> if for all well-typed terms , such that does not appear freely in , the terms
and behave identically. In particular, this property implies lazy evaluation for .
</p>
</div>
</div>
<div id="outline-container-org08b103d" class="outline-3">
<h3 id="org08b103d"><span class="section-number-3">1.2.</span> Soft let transparency</h3>
<div class="outline-text-3" id="text-1-2">
<p>
Call a language <i>soft let-transparent</i> if for all well-typed terms (or int, or any sufficiently ,,pure’’ type), such that does not appear freely in <i>and has a normal form</i> the terms
and behave identically. This still implies somewhat lazy if your language allows for non-terminating programs, but this laziness does not have to hold for side-effect-inducing terms assuming some kind of type coloring.
</p>
</div>
</div>
<div id="outline-container-org4328a10" class="outline-3">
<h3 id="org4328a10"><span class="section-number-3">1.3.</span> Softest let transparency</h3>
<div class="outline-text-3" id="text-1-3">
<p>
Call a language <i>softest let-transparent</i> if for all well-typed terms (or int, or any sufficiently ,,pure’’ type), such that does not appear freely in <i>and , both have normal forms</i> the terms
and behave identically. This does not imply lazy evaluation in any case!
</p>
<p>
idk really what these notions are useful for but i came up with them last night when trying to sleep so idk
</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="date">Date: 2024-06-06 Do 00:00</p>
<p class="author">Author: Uni</p>
<p class="date">Created: 2024-07-14 So 15:58</p>
</div>
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