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- <div class="section" id="the-four-fundamental-operations-of-definite-action">
+ <section id="the-four-fundamental-operations-of-definite-action">
<h1>The Four Fundamental Operations of Definite Action<a class="headerlink" href="#the-four-fundamental-operations-of-definite-action" title="Permalink to this headline">¶</a></h1>
<p>All definite actions (computer program) can be defined by four
fundamental patterns of combination:</p>
<ol class="arabic simple">
-<li>Sequence</li>
-<li>Branch</li>
-<li>Loop</li>
-<li>Parallel</li>
+<li><p>Sequence</p></li>
+<li><p>Branch</p></li>
+<li><p>Loop</p></li>
+<li><p>Parallel</p></li>
</ol>
-<div class="section" id="sequence">
+<section id="sequence">
<h2>Sequence<a class="headerlink" href="#sequence" title="Permalink to this headline">¶</a></h2>
<p>Do one thing after another. In joy this is represented by putting two
symbols together, juxtaposition:</p>
</div>
<p>Operations have inputs and outputs. The outputs of <code class="docutils literal notranslate"><span class="pre">foo</span></code> must be
compatible in “arity”, type, and shape with the inputs of <code class="docutils literal notranslate"><span class="pre">bar</span></code>.</p>
-</div>
-<div class="section" id="branch">
+</section>
+<section id="branch">
<h2>Branch<a class="headerlink" href="#branch" title="Permalink to this headline">¶</a></h2>
<p>Do one thing or another.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">boolean</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
<span class="n">foo</span> <span class="n">T</span> <span class="n">bar</span>
</pre></div>
</div>
-<div class="section" id="ifte">
+<section id="ifte">
<h3><code class="docutils literal notranslate"><span class="pre">ifte</span></code><a class="headerlink" href="#ifte" title="Permalink to this headline">¶</a></h3>
<p>Often it will be easier on the programmer to write branching code with
the predicate specified in a quote. The <code class="docutils literal notranslate"><span class="pre">ifte</span></code> combinator provides
of <code class="docutils literal notranslate"><span class="pre">branch</span></code>, it will only accept Boolean values, and in the definition
of <code class="docutils literal notranslate"><span class="pre">ifte</span></code> above by including <code class="docutils literal notranslate"><span class="pre">not</span></code> in the quote, which also has the
effect that the subject quotes are in the proper order for <code class="docutils literal notranslate"><span class="pre">branch</span></code>.)</p>
-</div>
-</div>
-<div class="section" id="loop">
+</section>
+</section>
+<section id="loop">
<h2>Loop<a class="headerlink" href="#loop" title="Permalink to this headline">¶</a></h2>
<p>Do one thing zero or more times.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">boolean</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
<span class="n">G</span> <span class="n">G</span> <span class="n">G</span>
</pre></div>
</div>
-<div class="section" id="while">
+<section id="while">
<h3><code class="docutils literal notranslate"><span class="pre">while</span></code><a class="headerlink" href="#while" title="Permalink to this headline">¶</a></h3>
<p>Keep doing <code class="docutils literal notranslate"><span class="pre">B</span></code> <em>while</em> some predicate <code class="docutils literal notranslate"><span class="pre">P</span></code> is true. This is
convenient as the predicate function is made nullary automatically and
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span> <span class="p">[</span><span class="n">B</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">loop</span>
</pre></div>
</div>
-</div>
-</div>
-<div class="section" id="parallel">
+</section>
+</section>
+<section id="parallel">
<h2>Parallel<a class="headerlink" href="#parallel" title="Permalink to this headline">¶</a></h2>
<p>The <em>parallel</em> operation indicates that two (or more) functions <em>do not
interfere</em> with each other and so can run in parallel. The main
(“join” or “wait”) of the results of the functions after they finish.</p>
<p>The current implementaions and the following definitions <em>are not
actually parallel</em> (yet), but there is no reason they couldn’t be
-reimplemented in terms of e.g. Python threads. I am not concerned with
+reimplemented in terms of e.g. Python threads. I am not concerned with
performance of the system just yet, only the elegance of the code it
allows us to write.</p>
-<div class="section" id="cleave">
+<section id="cleave">
<h3><code class="docutils literal notranslate"><span class="pre">cleave</span></code><a class="headerlink" href="#cleave" title="Permalink to this headline">¶</a></h3>
<p>Joy has a few parallel combinators, the main one being <code class="docutils literal notranslate"><span class="pre">cleave</span></code>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">A</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">cleave</span>
<p>Just a thought, if you <code class="docutils literal notranslate"><span class="pre">cleave</span></code> two jobs and one requires more time to
finish than the other you’d like to be able to assign resources
accordingly so that they both finish at the same time.</p>
-</div>
-<div class="section" id="apply-functions">
+</section>
+<section id="apply-functions">
<h3>“Apply” Functions<a class="headerlink" href="#apply-functions" title="Permalink to this headline">¶</a></h3>
<p>There are also <code class="docutils literal notranslate"><span class="pre">app2</span></code> and <code class="docutils literal notranslate"><span class="pre">app3</span></code> which run a single quote on more
than one value:</p>
<span class="n">a</span> <span class="n">b</span>
</pre></div>
</div>
-</div>
-<div class="section" id="map">
+</section>
+<section id="map">
<h3><code class="docutils literal notranslate"><span class="pre">map</span></code><a class="headerlink" href="#map" title="Permalink to this headline">¶</a></h3>
<p>The common <code class="docutils literal notranslate"><span class="pre">map</span></code> function in Joy should also be though of as a
<em>parallel</em> operator:</p>
</pre></div>
</div>
<p>There is no reason why the implementation of <code class="docutils literal notranslate"><span class="pre">map</span></code> couldn’t distribute
-the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g. a pool of worker CPUs.</p>
-</div>
-<div class="section" id="pam">
+the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g. a pool of worker CPUs.</p>
+</section>
+<section id="pam">
<h3><code class="docutils literal notranslate"><span class="pre">pam</span></code><a class="headerlink" href="#pam" title="Permalink to this headline">¶</a></h3>
<p>One of my favorite combinators, the <code class="docutils literal notranslate"><span class="pre">pam</span></code> combinator is just:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pam</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="nb">map</span>
<span class="p">[</span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">...</span><span class="p">]</span>
</pre></div>
</div>
-</div>
-<div class="section" id="handling-other-kinds-of-join">
+</section>
+<section id="handling-other-kinds-of-join">
<h3>Handling Other Kinds of Join<a class="headerlink" href="#handling-other-kinds-of-join" title="Permalink to this headline">¶</a></h3>
<p>The <code class="docutils literal notranslate"><span class="pre">cleave</span></code> operators and others all have pretty brutal join
semantics: everything works and we always wait for every
sub-computation. We can imagine a few different potentially useful
patterns of “joining” results from parallel combinators.</p>
-<div class="section" id="first-to-finish">
+<section id="first-to-finish">
<h4>first-to-finish<a class="headerlink" href="#first-to-finish" title="Permalink to this headline">¶</a></h4>
<p>Thinking about variations of <code class="docutils literal notranslate"><span class="pre">pam</span></code> there could be one that only
returns the first result of the first-to-finish sub-program, or the
stack could be replaced by its output stack.</p>
<p>The other sub-programs would be cancelled.</p>
-</div>
-<div class="section" id="fulminators">
+</section>
+<section id="fulminators">
<h4>“Fulminators”<a class="headerlink" href="#fulminators" title="Permalink to this headline">¶</a></h4>
<p>Also known as “Futures” or “Promises” (by <em>everybody</em> else. “Fulinators”
is what I was going to call them when I was thinking about implementing
sort of thing works perfectly in Joy code I’m not going to worry about
it. (And I think the Categories can deal with it anyhow? Incremental
evaluation, yeah?)</p>
-</div>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
+</section>
</div>
+
</div>
</div>
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- <h3><a href="../index.html">Table Of Contents</a></h3>
- <ul>
-<li><a class="reference internal" href="#">The Four Fundamental Operations of Definite Action</a><ul>
-<li><a class="reference internal" href="#sequence">Sequence</a></li>
-<li><a class="reference internal" href="#branch">Branch</a><ul>
-<li><a class="reference internal" href="#ifte"><code class="docutils literal notranslate"><span class="pre">ifte</span></code></a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#loop">Loop</a><ul>
-<li><a class="reference internal" href="#while"><code class="docutils literal notranslate"><span class="pre">while</span></code></a></li>
-</ul>
-</li>
-<li><a class="reference internal" href="#parallel">Parallel</a><ul>
-<li><a class="reference internal" href="#cleave"><code class="docutils literal notranslate"><span class="pre">cleave</span></code></a></li>
-<li><a class="reference internal" href="#apply-functions">“Apply” Functions</a></li>
-<li><a class="reference internal" href="#map"><code class="docutils literal notranslate"><span class="pre">map</span></code></a></li>
-<li><a class="reference internal" href="#pam"><code class="docutils literal notranslate"><span class="pre">pam</span></code></a></li>
-<li><a class="reference internal" href="#handling-other-kinds-of-join">Handling Other Kinds of Join</a><ul>
-<li><a class="reference internal" href="#first-to-finish">first-to-finish</a></li>
-<li><a class="reference internal" href="#fulminators">“Fulminators”</a></li>
-</ul>
-</li>
-</ul>
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