[hcoop/debian/mlton.git] / doc / guide / localhost / ArrayLiteral

<!DOCTYPE html>\r
<html lang="en">\r
<head>\r
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">\r
<meta name="generator" content="AsciiDoc 8.6.9">\r
<title>ArrayLiteral</title>\r
<link rel="stylesheet" href="./asciidoc.css" type="text/css">\r
<link rel="stylesheet" href="./pygments.css" type="text/css">\r
\r
\r
<script type="text/javascript" src="./asciidoc.js"></script>\r
<script type="text/javascript">\r
/*<![CDATA[*/\r
asciidoc.install();\r
/*]]>*/\r
</script>\r
<link rel="stylesheet" href="./mlton.css" type="text/css">\r
</head>\r
<body class="article">\r
<div id="banner">\r
<div id="banner-home">\r
<a href="./Home">MLton 20180207</a>\r
</div>\r
</div>\r
<div id="header">\r
<h1>ArrayLiteral</h1>\r
</div>\r
<div id="content">\r
<div id="preamble">\r
<div class="sectionbody">\r
<div class="paragraph"><p><a href="StandardML">Standard ML</a> does not have a syntax for array literals or\r
vector literals.  The only way to write down an array is like</p></div>\r
<div class="listingblock">\r
<div class="content"><div class="highlight"><pre><span class="n">Array</span><span class="p">.</span><span class="n">fromList</span><span class="w"> </span><span class="p">[</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">,</span><span class="w"> </span><span class="n">z</span><span class="p">]</span><span class="w"></span>\r
</pre></div></div></div>\r
<div class="paragraph"><p>No SML compiler produces efficient code for the above expression.  The\r
generated code allocates a list and then converts it to an array.  To\r
alleviate this, one could write down the same array using\r
<span class="monospaced">Array.tabulate</span>, or even using <span class="monospaced">Array.array</span> and <span class="monospaced">Array.update</span>, but\r
that is syntactically unwieldy.</p></div>\r
<div class="paragraph"><p>Fortunately, using <a href="Fold">Fold</a>, it is possible to define constants <span class="monospaced">A</span>,\r
and <span class="monospaced">&grave;</span> so that one can write down an array like:</p></div>\r
<div class="listingblock">\r
<div class="content"><div class="highlight"><pre><span class="n">A</span><span class="w"> </span><span class="n">`w</span><span class="w"> </span><span class="n">`x</span><span class="w"> </span><span class="n">`y</span><span class="w"> </span><span class="n">`z</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r
</pre></div></div></div>\r
<div class="paragraph"><p>This is as syntactically concise as the <span class="monospaced">fromList</span> expression.\r
Furthermore, MLton, at least, will generate the efficient code as if\r
one had written down a use of <span class="monospaced">Array.array</span> followed by four uses of\r
<span class="monospaced">Array.update</span>.</p></div>\r
<div class="paragraph"><p>Along with <span class="monospaced">A</span> and <span class="monospaced">&grave;</span>, one can define a constant <span class="monospaced">V</span> that makes\r
it possible to define vector literals with the same syntax, e.g.,</p></div>\r
<div class="listingblock">\r
<div class="content"><div class="highlight"><pre><span class="n">V</span><span class="w"> </span><span class="n">`w</span><span class="w"> </span><span class="n">`x</span><span class="w"> </span><span class="n">`y</span><span class="w"> </span><span class="n">`z</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r
</pre></div></div></div>\r
<div class="paragraph"><p>Note that the same element indicator, <span class="monospaced">&grave;</span>, serves for both array\r
and vector literals.  Of course, the <span class="monospaced">$</span> is the end-of-arguments\r
marker always used with <a href="Fold">Fold</a>.  The only difference between an\r
array literal and vector literal is the <span class="monospaced">A</span> or <span class="monospaced">V</span> at the beginning.</p></div>\r
<div class="paragraph"><p>Here is the implementation of <span class="monospaced">A</span>, <span class="monospaced">V</span>, and <span class="monospaced">&grave;</span>.  We place them\r
in a structure and use signature abstraction to hide the type of the\r
accumulator.  See <a href="Fold">Fold</a> for more on this technique.</p></div>\r
<div class="listingblock">\r
<div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Literal</span><span class="p">:&gt;</span><span class="w"></span>\r
<span class="w">   </span><span class="k">sig</span><span class="w"></span>\r
<span class="w">      </span><span class="k">type</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">array</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;d</span><span class="p">)</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">t</span><span class="w"></span>\r
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">V</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">vector</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;d</span><span class="p">)</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">t</span><span class="w"></span>\r
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;b</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;c</span><span class="p">,</span><span class="w"> </span><span class="n">&#39;d</span><span class="p">)</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">step1</span><span class="w"></span>\r
<span class="w">   </span><span class="k">end</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r
<span class="w">   </span><span class="k">struct</span><span class="w"></span>\r
<span class="w">      </span><span class="k">type</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">&#39;a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">(</span><span class="n">&#39;a</span><span class="w"> </span><span class="n">array</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"></span>\r
\r
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r
<span class="w">         </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>\r
<span class="w">         </span><span class="n">Fold</span><span class="p">.</span><span class="n">fold</span><span class="w"></span>\r
<span class="w">         </span><span class="p">((</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">NONE</span><span class="p">,</span><span class="w"> </span><span class="n">ignore</span><span class="p">),</span><span class="w"></span>\r
<span class="w">          </span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">opt</span><span class="p">,</span><span class="w"> </span><span class="n">fill</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>\r
<span class="w">          </span><span class="k">case</span><span class="w"> </span><span class="n">opt</span><span class="w"> </span><span class="k">of</span><span class="w"></span>\r
<span class="w">             </span><span class="n">NONE</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>\r
<span class="w">                </span><span class="n">Array</span><span class="p">.</span><span class="n">tabulate</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="n">Fail</span><span class="w"> </span><span class="s">&quot;array0&quot;</span><span class="p">)</span><span class="w"></span>\r
<span class="w">           </span><span class="p">|</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>\r
<span class="w">                </span><span class="k">let</span><span class="w"></span>\r
<span class="w">                   </span><span class="k">val</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">array</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"></span>\r
<span class="w">                   </span><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">fill</span><span class="w"> </span><span class="n">a</span><span class="w"></span>\r
<span class="w">                </span><span class="k">in</span><span class="w"></span>\r
<span class="w">                   </span><span class="n">a</span><span class="w"></span>\r
<span class="w">                </span><span class="k">end</span><span class="p">)</span><span class="w"></span>\r
<span class="w">         </span><span class="n">z</span><span class="w"></span>\r
\r
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">V</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">post</span><span class="w"> </span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">vector</span><span class="p">)</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r
\r
<span class="w">      </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r
<span class="w">         </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>\r
<span class="w">         </span><span class="n">Fold</span><span class="p">.</span><span class="n">step1</span><span class="w"></span>\r
<span class="w">         </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">opt</span><span class="p">,</span><span class="w"> </span><span class="n">fill</span><span class="p">))</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"></span>\r
<span class="w">          </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"></span>\r
<span class="w">           </span><span class="n">SOME</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"></span>\r
<span class="w">           </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="p">(</span><span class="n">Array</span><span class="p">.</span><span class="n">update</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="n">fill</span><span class="w"> </span><span class="n">a</span><span class="p">)))</span><span class="w"></span>\r
<span class="w">         </span><span class="n">z</span><span class="w"></span>\r
<span class="w">   </span><span class="k">end</span><span class="w"></span>\r
</pre></div></div></div>\r
<div class="paragraph"><p>The idea of the code is for the fold to accumulate a count of the\r
number of elements, a sample element, and a function that fills in all\r
the elements.  When the fold is complete, the finishing function\r
allocates the array, applies the fill function, and returns the array.\r
The only difference between <span class="monospaced">A</span> and <span class="monospaced">V</span> is at the very end; <span class="monospaced">A</span> just\r
returns the array, while <span class="monospaced">V</span> converts it to a vector using\r
post-composition, which is further described on the <a href="Fold">Fold</a> page.</p></div>\r
</div>\r
</div>\r
</div>\r
<div id="footnotes"><hr></div>\r
<div id="footer">\r
<div id="footer-text">\r
</div>\r
<div id="footer-badges">\r
</div>\r
</div>\r
</body>\r
</html>\r
Commit	Line	Data
7f918cf1 CE	1	<!DOCTYPE html>\r
	2	<html lang="en">\r
	3	<head>\r
	4	<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">\r
	5	<meta name="generator" content="AsciiDoc 8.6.9">\r
	6	<title>ArrayLiteral</title>\r
	7	<link rel="stylesheet" href="./asciidoc.css" type="text/css">\r
	8	<link rel="stylesheet" href="./pygments.css" type="text/css">\r
	9	\r
	10	\r
	11	<script type="text/javascript" src="./asciidoc.js"></script>\r
	12	<script type="text/javascript">\r
	13	/<![CDATA[/\r
	14	asciidoc.install();\r
	15	/]]>/\r
	16	</script>\r
	17	<link rel="stylesheet" href="./mlton.css" type="text/css">\r
	18	</head>\r
	19	<body class="article">\r
	20	<div id="banner">\r
	21	<div id="banner-home">\r
	22	<a href="./Home">MLton 20180207</a>\r
	23	</div>\r
	24	</div>\r
	25	<div id="header">\r
	26	<h1>ArrayLiteral</h1>\r
	27	</div>\r
	28	<div id="content">\r
	29	<div id="preamble">\r
	30	<div class="sectionbody">\r
	31	<div class="paragraph"><p><a href="StandardML">Standard ML</a> does not have a syntax for array literals or\r
	32	vector literals. The only way to write down an array is like</p></div>\r
	33	<div class="listingblock">\r
	34	<div class="content"><div class="highlight"><pre><span class="n">Array</span><span class="p">.</span><span class="n">fromList</span><span class="w"> </span><span class="p">[</span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">,</span><span class="w"> </span><span class="n">z</span><span class="p">]</span><span class="w"></span>\r
	35	</pre></div></div></div>\r
	36	<div class="paragraph"><p>No SML compiler produces efficient code for the above expression. The\r
	37	generated code allocates a list and then converts it to an array. To\r
	38	alleviate this, one could write down the same array using\r
	39	<span class="monospaced">Array.tabulate</span>, or even using <span class="monospaced">Array.array</span> and <span class="monospaced">Array.update</span>, but\r
	40	that is syntactically unwieldy.</p></div>\r
	41	<div class="paragraph"><p>Fortunately, using <a href="Fold">Fold</a>, it is possible to define constants <span class="monospaced">A</span>,\r
	42	and <span class="monospaced">&grave;</span> so that one can write down an array like:</p></div>\r
	43	<div class="listingblock">\r
	44	<div class="content"><div class="highlight"><pre><span class="n">A</span><span class="w"> </span><span class="n">`w</span><span class="w"> </span><span class="n">`x</span><span class="w"> </span><span class="n">`y</span><span class="w"> </span><span class="n">`z</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r
	45	</pre></div></div></div>\r
	46	<div class="paragraph"><p>This is as syntactically concise as the <span class="monospaced">fromList</span> expression.\r
	47	Furthermore, MLton, at least, will generate the efficient code as if\r
	48	one had written down a use of <span class="monospaced">Array.array</span> followed by four uses of\r
	49	<span class="monospaced">Array.update</span>.</p></div>\r
	50	<div class="paragraph"><p>Along with <span class="monospaced">A</span> and <span class="monospaced">&grave;</span>, one can define a constant <span class="monospaced">V</span> that makes\r
	51	it possible to define vector literals with the same syntax, e.g.,</p></div>\r
	52	<div class="listingblock">\r
	53	<div class="content"><div class="highlight"><pre><span class="n">V</span><span class="w"> </span><span class="n">`w</span><span class="w"> </span><span class="n">`x</span><span class="w"> </span><span class="n">`y</span><span class="w"> </span><span class="n">`z</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r
	54	</pre></div></div></div>\r
	55	<div class="paragraph"><p>Note that the same element indicator, <span class="monospaced">&grave;</span>, serves for both array\r
	56	and vector literals. Of course, the <span class="monospaced">$</span> is the end-of-arguments\r
	57	marker always used with <a href="Fold">Fold</a>. The only difference between an\r
	58	array literal and vector literal is the <span class="monospaced">A</span> or <span class="monospaced">V</span> at the beginning.</p></div>\r
	59	<div class="paragraph"><p>Here is the implementation of <span class="monospaced">A</span>, <span class="monospaced">V</span>, and <span class="monospaced">&grave;</span>. We place them\r
	60	in a structure and use signature abstraction to hide the type of the\r
	61	accumulator. See <a href="Fold">Fold</a> for more on this technique.</p></div>\r
	62	<div class="listingblock">\r
	63	<div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Literal</span><span class="p">:></span><span class="w"></span>\r
	64	<span class="w"> </span><span class="k">sig</span><span class="w"></span>\r
65	<span class="w"> </span><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r
66	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">A</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">array</span><span class="p">,</span><span class="w"> </span><span class="n">'d</span><span class="p">)</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">t</span><span class="w"></span>\r
67	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">V</span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">vector</span><span class="p">,</span><span class="w"> </span><span class="n">'d</span><span class="p">)</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">t</span><span class="w"></span>\r
68	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="p">,</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="p">,</span><span class="w"> </span><span class="n">'b</span><span class="p">,</span><span class="w"> </span><span class="n">'c</span><span class="p">,</span><span class="w"> </span><span class="n">'d</span><span class="p">)</span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">step1</span><span class="w"></span>\r
69	<span class="w"> </span><span class="k">end</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r
70	<span class="w"> </span><span class="k">struct</span><span class="w"></span>\r
71	<span class="w"> </span><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n"></span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="n"></span><span class="w"> </span><span class="p">(</span><span class="n">'a</span><span class="w"> </span><span class="n">array</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">unit</span><span class="p">)</span><span class="w"></span>\r
72	\r
73	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r
74	<span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r
75	<span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">fold</span><span class="w"></span>\r
76	<span class="w"> </span><span class="p">((</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">NONE</span><span class="p">,</span><span class="w"> </span><span class="n">ignore</span><span class="p">),</span><span class="w"></span>\r
77	<span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">opt</span><span class="p">,</span><span class="w"> </span><span class="n">fill</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r
78	<span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="n">opt</span><span class="w"> </span><span class="k">of</span><span class="w"></span>\r
79	<span class="w"> </span><span class="n">NONE</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r
80	<span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">tabulate</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="n">Fail</span><span class="w"> </span><span class="s">"array0"</span><span class="p">)</span><span class="w"></span>\r
81	<span class="w"> </span><span class="p">\|</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r
82	<span class="w"> </span><span class="k">let</span><span class="w"></span>\r
83	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">array</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"></span>\r
84	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">fill</span><span class="w"> </span><span class="n">a</span><span class="w"></span>\r
85	<span class="w"> </span><span class="k">in</span><span class="w"></span>\r
86	<span class="w"> </span><span class="n">a</span><span class="w"></span>\r
87	<span class="w"> </span><span class="k">end</span><span class="p">)</span><span class="w"></span>\r
88	<span class="w"> </span><span class="n">z</span><span class="w"></span>\r
89	\r
90	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">V</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">post</span><span class="w"> </span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">vector</span><span class="p">)</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r
91	\r
92	<span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r
93	<span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r
94	<span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">step1</span><span class="w"></span>\r
95	<span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">opt</span><span class="p">,</span><span class="w"> </span><span class="n">fill</span><span class="p">))</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r
96	<span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"></span>\r
97	<span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"></span>\r
98	<span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="p">(</span><span class="n">Array</span><span class="p">.</span><span class="n">update</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="p">);</span><span class="w"> </span><span class="n">fill</span><span class="w"> </span><span class="n">a</span><span class="p">)))</span><span class="w"></span>\r
99	<span class="w"> </span><span class="n">z</span><span class="w"></span>\r
100	<span class="w"> </span><span class="k">end</span><span class="w"></span>\r
101	</pre></div></div></div>\r
102	<div class="paragraph"><p>The idea of the code is for the fold to accumulate a count of the\r
103	number of elements, a sample element, and a function that fills in all\r
104	the elements. When the fold is complete, the finishing function\r
105	allocates the array, applies the fill function, and returns the array.\r
106	The only difference between <span class="monospaced">A</span> and <span class="monospaced">V</span> is at the very end; <span class="monospaced">A</span> just\r
107	returns the array, while <span class="monospaced">V</span> converts it to a vector using\r
108	post-composition, which is further described on the <a href="Fold">Fold</a> page.</p></div>\r
109	</div>\r
110	</div>\r
111	</div>\r
112	<div id="footnotes"><hr></div>\r
113	<div id="footer">\r
114	<div id="footer-text">\r
115	</div>\r
116	<div id="footer-badges">\r
117	</div>\r
118	</div>\r
119	</body>\r
120	</html>\r