HCoop / hcoop / debian / mlton.git / blame
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| 6 | <title>NumericLiteral</title>\r | |
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| 22 | <a href="./Home">MLton 20180207</a>\r | |
| 23 | </div>\r | |
| 24 | </div>\r | |
| 25 | <div id="header">\r | |
| 26 | <h1>NumericLiteral</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>Numeric literals in <a href="StandardML">Standard ML</a> can be written in either\r | |
| 32 | decimal or hexadecimal notation. Sometimes it can be convenient to\r | |
| 33 | write numbers down in other bases. Fortunately, using <a href="Fold">Fold</a>, it is\r | |
| 34 | possible to define a concise syntax for numeric literals that allows\r | |
| 35 | one to write numeric constants in any base and of various types\r | |
| 36 | (<span class="monospaced">int</span>, <span class="monospaced">IntInf.int</span>, <span class="monospaced">word</span>, and more).</p></div>\r | |
| 37 | <div class="paragraph"><p>We will define constants <span class="monospaced">I</span>, <span class="monospaced">II</span>, <span class="monospaced">W</span>, and <span class="monospaced">`</span> so\r | |
| 38 | that, for example,</p></div>\r | |
| 39 | <div class="listingblock">\r | |
| 40 | <div class="content"><div class="highlight"><pre><span class="n">I</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="n">`</span><span class="mi">1</span><span class="n">`</span><span class="mi">2</span><span class="n">`</span><span class="mi">3</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r | |
| 41 | </pre></div></div></div>\r | |
| 42 | <div class="paragraph"><p>denotes <span class="monospaced">123:int</span> in base 10, while</p></div>\r | |
| 43 | <div class="listingblock">\r | |
| 44 | <div class="content"><div class="highlight"><pre><span class="n">II</span><span class="w"> </span><span class="mi">8</span><span class="w"> </span><span class="n">`</span><span class="mi">2</span><span class="n">`</span><span class="mi">3</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r | |
| 45 | </pre></div></div></div>\r | |
| 46 | <div class="paragraph"><p>denotes <span class="monospaced">19:IntInf.int</span> in base 8, and</p></div>\r | |
| 47 | <div class="listingblock">\r | |
| 48 | <div class="content"><div class="highlight"><pre><span class="n">W</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="n">`</span><span class="mi">1</span><span class="n">`</span><span class="mi">1</span><span class="n">`</span><span class="mi">0</span><span class="n">`</span><span class="mi">1</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r | |
| 49 | </pre></div></div></div>\r | |
| 50 | <div class="paragraph"><p>denotes <span class="monospaced">0w13: word</span>.</p></div>\r | |
| 51 | <div class="paragraph"><p>Here is the code.</p></div>\r | |
| 52 | <div class="listingblock">\r | |
| 53 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Num</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 54 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 55 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="p">(</span><span class="k">op</span><span class="w"> </span><span class="n">*</span><span class="p">,</span><span class="w"> </span><span class="k">op</span><span class="w"> </span><span class="n">+</span><span class="p">,</span><span class="w"> </span><span class="n">i2x</span><span class="p">)</span><span class="w"> </span><span class="n">iBase</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 56 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 57 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">xBase</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">i2x</span><span class="w"> </span><span class="n">iBase</span><span class="w"></span>\r | |
| 58 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 59 | <span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">fold</span><span class="w"></span>\r | |
| 60 | <span class="w"> </span><span class="p">((</span><span class="n">i2x</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"></span>\r | |
| 61 | <span class="w"> </span><span class="k">fn</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">x</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r | |
| 62 | <span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="n"><=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">andalso</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="n"><</span><span class="w"> </span><span class="n">iBase</span><span class="w"> </span><span class="k">then</span><span class="w"></span>\r | |
| 63 | <span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">xBase</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="n">i2x</span><span class="w"> </span><span class="n">i</span><span class="w"></span>\r | |
| 64 | <span class="w"> </span><span class="k">else</span><span class="w"></span>\r | |
| 65 | <span class="w"> </span><span class="k">raise</span><span class="w"> </span><span class="n">Fail</span><span class="w"> </span><span class="p">(</span><span class="n">concat</span><span class="w"></span>\r | |
| 66 | <span class="w"> </span><span class="p">[</span><span class="s">"Num: "</span><span class="p">,</span><span class="w"> </span><span class="n">Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"></span>\r | |
| 67 | <span class="w"> </span><span class="s">" is not a valid\</span>\r | |
| 68 | <span class="s"> \ digit in base "</span><span class="p">,</span><span class="w"></span>\r | |
| 69 | <span class="w"> </span><span class="n">Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">iBase</span><span class="p">])),</span><span class="w"></span>\r | |
| 70 | <span class="w"> </span><span class="n">fst</span><span class="p">)</span><span class="w"></span>\r | |
| 71 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 72 | \r | |
| 73 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">I</span><span class="w"> </span><span class="n">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="p">(</span><span class="k">op</span><span class="w"> </span><span class="n">*</span><span class="p">,</span><span class="w"> </span><span class="k">op</span><span class="w"> </span><span class="n">+</span><span class="p">,</span><span class="w"> </span><span class="n">id</span><span class="p">)</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
| 74 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">II</span><span class="w"> </span><span class="n">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="p">(</span><span class="k">op</span><span class="w"> </span><span class="n">*</span><span class="p">,</span><span class="w"> </span><span class="k">op</span><span class="w"> </span><span class="n">+</span><span class="p">,</span><span class="w"> </span><span class="n">IntInf</span><span class="p">.</span><span class="n">fromInt</span><span class="p">)</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
| 75 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">W</span><span class="w"> </span><span class="n">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">make</span><span class="w"> </span><span class="p">(</span><span class="k">op</span><span class="w"> </span><span class="n">*</span><span class="p">,</span><span class="w"> </span><span class="k">op</span><span class="w"> </span><span class="n">+</span><span class="p">,</span><span class="w"> </span><span class="n">Word</span><span class="p">.</span><span class="n">fromInt</span><span class="p">)</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
| 76 | \r | |
| 77 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">`</span><span class="w"> </span><span class="n">?</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">step1</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">step</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="p">(</span><span class="n">step</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">x</span><span class="p">),</span><span class="w"> </span><span class="n">step</span><span class="p">))</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
| 79 | \r | |
| 80 | <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="mi">10</span><span class="w"></span>\r | |
| 81 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">11</span><span class="w"></span>\r | |
| 82 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">12</span><span class="w"></span>\r | |
| 83 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">13</span><span class="w"></span>\r | |
| 84 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">14</span><span class="w"></span>\r | |
| 85 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">15</span><span class="w"></span>\r | |
| 86 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 87 | </pre></div></div></div>\r | |
| 88 | <div class="paragraph"><p>where</p></div>\r | |
| 89 | <div class="listingblock">\r | |
| 90 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">fst</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="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 91 | </pre></div></div></div>\r | |
| 92 | <div class="paragraph"><p>The idea is for the fold to start with zero and to construct the\r | |
| 93 | result one digit at a time, with each stepper multiplying the previous\r | |
| 94 | result by the base and adding the next digit. The code is abstracted\r | |
| 95 | in two different ways for extra generality. First, the <span class="monospaced">make</span>\r | |
| 96 | function abstracts over the various primitive operations (addition,\r | |
| 97 | multiplication, etc) that are needed to construct a number. This\r | |
| 98 | allows the same code to be shared for constants <span class="monospaced">I</span>, <span class="monospaced">II</span>, <span class="monospaced">W</span> used to\r | |
| 99 | write down the various numeric types. It also allows users to add new\r | |
| 100 | constants for additional numeric types, by supplying the necessary\r | |
| 101 | arguments to make.</p></div>\r | |
| 102 | <div class="paragraph"><p>Second, the step function, <span class="monospaced">`</span>, is abstracted over the actual\r | |
| 103 | construction operation, which is created by make, and passed along the\r | |
| 104 | fold. This allows the same constant, <span class="monospaced">`</span>, to be used for all\r | |
| 105 | numeric types. The alternative approach, having a different step\r | |
| 106 | function for each numeric type, would be more painful to use.</p></div>\r | |
| 107 | <div class="paragraph"><p>On the surface, it appears that the code checks the digits dynamically\r | |
| 108 | to ensure they are valid for the base. However, MLton will simplify\r | |
| 109 | everything away at compile time, leaving just the final numeric\r | |
| 110 | constant.</p></div>\r | |
| 111 | </div>\r | |
| 112 | </div>\r | |
| 113 | </div>\r | |
| 114 | <div id="footnotes"><hr></div>\r | |
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