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| 22 | <a href="./Home">MLton 20180207</a>\r |
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| 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">`</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">$</span><span class="w"></span>\r |
| 45 | </pre></div></div></div>\r |
| 46 | <div class="paragraph"><p>This is as syntactically concise as the <span class="monospaced">fromList</span> expression.\r |
| 47 | Furthermore, MLton, at least, will generate the efficient code as if\r |
| 48 | one had written down a use of <span class="monospaced">Array.array</span> followed by four uses of\r |
| 49 | <span class="monospaced">Array.update</span>.</p></div>\r |
| 50 | <div class="paragraph"><p>Along with <span class="monospaced">A</span> and <span class="monospaced">`</span>, one can define a constant <span class="monospaced">V</span> that makes\r |
| 51 | it possible to define vector literals with the same syntax, e.g.,</p></div>\r |
| 52 | <div class="listingblock">\r |
| 53 | <div class="content"><div class="highlight"><pre><span class="n">V</span><span class="w"> </span><span class="n">`w</span><span class="w"> </span><span class="n">`x</span><span class="w"> </span><span class="n">`y</span><span class="w"> </span><span class="n">`z</span><span class="w"> </span><span class="n">$</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">`</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">`</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 |
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