HCoop / hcoop / debian / mlton.git / blame
| 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>EqualityType</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>EqualityType</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>An equality type is a type to which <a href="PolymorphicEquality">PolymorphicEquality</a> can be\r | |
| 32 | applied. The <a href="DefinitionOfStandardML">Definition</a> and the\r | |
| 33 | <a href="BasisLibrary">Basis Library</a> precisely spell out which types are\r | |
| 34 | equality types.</p></div>\r | |
| 35 | <div class="ulist"><ul>\r | |
| 36 | <li>\r | |
| 37 | <p>\r | |
| 38 | <span class="monospaced">bool</span>, <span class="monospaced">char</span>, <span class="monospaced">IntInf.int</span>, <span class="monospaced">Int<em><N></em>.int</span>, <span class="monospaced">string</span>, and <span class="monospaced">Word<em><N></em>.word</span> are equality types.\r | |
| 39 | </p>\r | |
| 40 | </li>\r | |
| 41 | <li>\r | |
| 42 | <p>\r | |
| 43 | for any <span class="monospaced">t</span>, both <span class="monospaced">t array</span> and <span class="monospaced">t ref</span> are equality types.\r | |
| 44 | </p>\r | |
| 45 | </li>\r | |
| 46 | <li>\r | |
| 47 | <p>\r | |
| 48 | if <span class="monospaced">t</span> is an equality type, then <span class="monospaced">t list</span>, and <span class="monospaced">t vector</span> are equality types.\r | |
| 49 | </p>\r | |
| 50 | </li>\r | |
| 51 | <li>\r | |
| 52 | <p>\r | |
| 53 | if <span class="monospaced">t1</span>, …, <span class="monospaced">tn</span> are equality types, then <span class="monospaced">t1 * ... * tn</span> and <span class="monospaced">{l1: t1, ..., ln: tn}</span> are equality types.\r | |
| 54 | </p>\r | |
| 55 | </li>\r | |
| 56 | <li>\r | |
| 57 | <p>\r | |
| 58 | if <span class="monospaced">t1</span>, …, <span class="monospaced">tn</span> are equality types and <span class="monospaced">t</span> <a href="AdmitsEquality">AdmitsEquality</a>, then <span class="monospaced">(t1, ..., tn) t</span> is an equality type.\r | |
| 59 | </p>\r | |
| 60 | </li>\r | |
| 61 | </ul></div>\r | |
| 62 | <div class="paragraph"><p>To check that a type t is an equality type, use the following idiom.</p></div>\r | |
| 63 | <div class="listingblock">\r | |
| 64 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">S</span><span class="p">:</span><span class="w"> </span><span class="k">sig</span><span class="w"> </span><span class="k">eqtype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="k">end</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 65 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 66 | <span class="w"> </span><span class="k">type</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">...</span><span class="w"></span>\r | |
| 67 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 68 | </pre></div></div></div>\r | |
| 69 | <div class="paragraph"><p>Notably, <span class="monospaced">exn</span> and <span class="monospaced">real</span> are not equality types. Neither is <span class="monospaced">t1 -> t2</span>, for any <span class="monospaced">t1</span> and <span class="monospaced">t2</span>.</p></div>\r | |
| 70 | <div class="paragraph"><p>Equality on arrays and ref cells is by identity, not structure.\r | |
| 71 | For example, <span class="monospaced">ref 13 = ref 13</span> is <span class="monospaced">false</span>.\r | |
| 72 | On the other hand, equality for lists, strings, and vectors is by\r | |
| 73 | structure, not identity. For example, the following equalities hold.</p></div>\r | |
| 74 | <div class="listingblock">\r | |
| 75 | <div class="content"><div class="highlight"><pre><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="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">::</span><span class="w"> </span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">]</span><span class="w"></span>\r | |
| 76 | <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="s">"foo"</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">concat</span><span class="w"> </span><span class="p">[</span><span class="s">"f"</span><span class="p">,</span><span class="w"> </span><span class="s">"o"</span><span class="p">,</span><span class="w"> </span><span class="s">"o"</span><span class="p">]</span><span class="w"></span>\r | |
| 77 | <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">Vector</span><span class="p">.</span><span class="n">fromList</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">tabulate</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">=></span><span class="w"> </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 | |
| 78 | </pre></div></div></div>\r | |
| 79 | </div>\r | |
| 80 | </div>\r | |
| 81 | </div>\r | |
| 82 | <div id="footnotes"><hr></div>\r | |
| 83 | <div id="footer">\r | |
| 84 | <div id="footer-text">\r | |
| 85 | </div>\r | |
| 86 | <div id="footer-badges">\r | |
| 87 | </div>\r | |
| 88 | </div>\r | |
| 89 | </body>\r | |
| 90 | </html>\r |