HCoop / hcoop / debian / mlton.git / blame
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|---|---|---|
| 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>ProductType</title>\r | |
| 7 | <link rel="stylesheet" href="./asciidoc.css" type="text/css">\r | |
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| 11 | <script type="text/javascript" src="./asciidoc.js"></script>\r | |
| 12 | <script type="text/javascript">\r | |
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| 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>ProductType</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> has special syntax for products (tuples). A\r | |
| 32 | product type is written as</p></div>\r | |
| 33 | <div class="listingblock">\r | |
| 34 | <div class="content"><div class="highlight"><pre><span class="n">t1</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">t2</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">tN</span><span class="w"></span>\r | |
| 35 | </pre></div></div></div>\r | |
| 36 | <div class="paragraph"><p>and a product pattern is written as</p></div>\r | |
| 37 | <div class="listingblock">\r | |
| 38 | <div class="content"><div class="highlight"><pre><span class="p">(</span><span class="n">p1</span><span class="p">,</span><span class="w"> </span><span class="n">p2</span><span class="p">,</span><span class="w"> </span><span class="p">...,</span><span class="w"> </span><span class="n">pN</span><span class="p">)</span><span class="w"></span>\r | |
| 39 | </pre></div></div></div>\r | |
| 40 | <div class="paragraph"><p>In most situations the syntax is quite convenient. However, there are\r | |
| 41 | situations where the syntax is cumbersome. There are also situations\r | |
| 42 | in which it is useful to construct and destruct n-ary products\r | |
| 43 | inductively, especially when using <a href="Fold">Fold</a>.</p></div>\r | |
| 44 | <div class="paragraph"><p>In such situations, it is useful to have a binary product datatype\r | |
| 45 | with an infix constructor defined as follows.</p></div>\r | |
| 46 | <div class="listingblock">\r | |
| 47 | <div class="content"><div class="highlight"><pre><span class="k">datatype</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">'b</span><span class="p">)</span><span class="w"> </span><span class="n">product</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'b</span><span class="w"></span>\r | |
| 48 | <span class="k">infix</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>With these definitions, one can write an n-ary product as a nested\r | |
| 51 | binary product quite conveniently.</p></div>\r | |
| 52 | <div class="listingblock">\r | |
| 53 | <div class="content"><div class="highlight"><pre><span class="n">x1</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">x2</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">xn</span><span class="w"></span>\r | |
| 54 | </pre></div></div></div>\r | |
| 55 | <div class="paragraph"><p>Because of left associativity, this is the same as</p></div>\r | |
| 56 | <div class="listingblock">\r | |
| 57 | <div class="content"><div class="highlight"><pre><span class="p">(((</span><span class="n">x1</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">x2</span><span class="p">)</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="p">...)</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">xn</span><span class="p">)</span><span class="w"></span>\r | |
| 58 | </pre></div></div></div>\r | |
| 59 | <div class="paragraph"><p>Because <span class="monospaced">&</span> is a constructor, the syntax can also be used for\r | |
| 60 | patterns.</p></div>\r | |
| 61 | <div class="paragraph"><p>The symbol <span class="monospaced">&</span> is inspired by the Curry-Howard isomorphism: the proof\r | |
| 62 | of a conjunction <span class="monospaced">(A & B)</span> is a pair of proofs <span class="monospaced">(a, b)</span>.</p></div>\r | |
| 63 | </div>\r | |
| 64 | </div>\r | |
| 65 | <div class="sect1">\r | |
| 66 | <h2 id="_example_parser_combinators">Example: parser combinators</h2>\r | |
| 67 | <div class="sectionbody">\r | |
| 68 | <div class="paragraph"><p>A typical parser combinator library provides a combinator that has a\r | |
| 69 | type of the form.</p></div>\r | |
| 70 | <div class="listingblock">\r | |
| 71 | <div class="content"><div class="highlight"><pre><span class="n">'a</span><span class="w"> </span><span class="n">parser</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="n">parser</span><span class="w"> </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">*</span><span class="w"> </span><span class="n">'b</span><span class="p">)</span><span class="w"> </span><span class="n">parser</span><span class="w"></span>\r | |
| 72 | </pre></div></div></div>\r | |
| 73 | <div class="paragraph"><p>and produces a parser for the concatenation of two parsers. When more\r | |
| 74 | than two parsers are concatenated, the result of the resulting parser\r | |
| 75 | is a nested structure of pairs</p></div>\r | |
| 76 | <div class="listingblock">\r | |
| 77 | <div class="content"><div class="highlight"><pre><span class="p">(...((</span><span class="n">p1</span><span class="p">,</span><span class="w"> </span><span class="n">p2</span><span class="p">),</span><span class="w"> </span><span class="n">p3</span><span class="p">)...,</span><span class="w"> </span><span class="n">pN</span><span class="p">)</span><span class="w"></span>\r | |
| 78 | </pre></div></div></div>\r | |
| 79 | <div class="paragraph"><p>which is somewhat cumbersome.</p></div>\r | |
| 80 | <div class="paragraph"><p>By using a product type, the type of the concatenation combinator then\r | |
| 81 | becomes</p></div>\r | |
| 82 | <div class="listingblock">\r | |
| 83 | <div class="content"><div class="highlight"><pre><span class="n">'a</span><span class="w"> </span><span class="n">parser</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="n">parser</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">'b</span><span class="p">)</span><span class="w"> </span><span class="n">product</span><span class="w"> </span><span class="n">parser</span><span class="w"></span>\r | |
| 84 | </pre></div></div></div>\r | |
| 85 | <div class="paragraph"><p>While this doesn’t stop the nesting, it makes the pattern significantly\r | |
| 86 | easier to write. Instead of</p></div>\r | |
| 87 | <div class="listingblock">\r | |
| 88 | <div class="content"><div class="highlight"><pre><span class="p">(...((</span><span class="n">p1</span><span class="p">,</span><span class="w"> </span><span class="n">p2</span><span class="p">),</span><span class="w"> </span><span class="n">p3</span><span class="p">)...,</span><span class="w"> </span><span class="n">pN</span><span class="p">)</span><span class="w"></span>\r | |
| 89 | </pre></div></div></div>\r | |
| 90 | <div class="paragraph"><p>the pattern is written as</p></div>\r | |
| 91 | <div class="listingblock">\r | |
| 92 | <div class="content"><div class="highlight"><pre><span class="n">p1</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">p2</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">p3</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">pN</span><span class="w"></span>\r | |
| 93 | </pre></div></div></div>\r | |
| 94 | <div class="paragraph"><p>which is considerably more concise.</p></div>\r | |
| 95 | </div>\r | |
| 96 | </div>\r | |
| 97 | <div class="sect1">\r | |
| 98 | <h2 id="_also_see">Also see</h2>\r | |
| 99 | <div class="sectionbody">\r | |
| 100 | <div class="ulist"><ul>\r | |
| 101 | <li>\r | |
| 102 | <p>\r | |
| 103 | <a href="VariableArityPolymorphism">VariableArityPolymorphism</a>\r | |
| 104 | </p>\r | |
| 105 | </li>\r | |
| 106 | <li>\r | |
| 107 | <p>\r | |
| 108 | <a href="Utilities">Utilities</a>\r | |
| 109 | </p>\r | |
| 110 | </li>\r | |
| 111 | </ul></div>\r | |
| 112 | </div>\r | |
| 113 | </div>\r | |
| 114 | </div>\r | |
| 115 | <div id="footnotes"><hr></div>\r | |
| 116 | <div id="footer">\r | |
| 117 | <div id="footer-text">\r | |
| 118 | </div>\r | |
| 119 | <div id="footer-badges">\r | |
| 120 | </div>\r | |
| 121 | </div>\r | |
| 122 | </body>\r | |
| 123 | </html>\r |