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>AdmitsEquality</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>AdmitsEquality</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 <a href="TypeConstructor">TypeConstructor</a> admits equality if whenever it is applied to\r | |
| 32 | equality types, the result is an <a href="EqualityType">EqualityType</a>. This notion enables\r | |
| 33 | one to determine whether a type constructor application yields an\r | |
| 34 | equality type solely from the application, without looking at the\r | |
| 35 | definition of the type constructor. It helps to ensure that\r | |
| 36 | <a href="PolymorphicEquality">PolymorphicEquality</a> is only applied to sensible values.</p></div>\r | |
| 37 | <div class="paragraph"><p>The definition of admits equality depends on whether the type\r | |
| 38 | constructor was declared by a <span class="monospaced">type</span> definition or a\r | |
| 39 | <span class="monospaced">datatype</span> declaration.</p></div>\r | |
| 40 | </div>\r | |
| 41 | </div>\r | |
| 42 | <div class="sect1">\r | |
| 43 | <h2 id="_type_definitions">Type definitions</h2>\r | |
| 44 | <div class="sectionbody">\r | |
| 45 | <div class="paragraph"><p>For type definition</p></div>\r | |
| 46 | <div class="listingblock">\r | |
| 47 | <div class="content"><div class="highlight"><pre><span class="k">type</span><span class="w"> </span><span class="p">(</span><span class="n">'a1</span><span class="p">,</span><span class="w"> </span><span class="p">...,</span><span class="w"> </span><span class="n">'an</span><span class="p">)</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 | |
| 48 | </pre></div></div></div>\r | |
| 49 | <div class="paragraph"><p>type constructor <span class="monospaced">t</span> admits equality if the right-hand side of the\r | |
| 50 | definition is an equality type after replacing <span class="monospaced">'a1</span>, …,\r | |
| 51 | <span class="monospaced">'an</span> by equality types (it doesn’t matter which equality types\r | |
| 52 | are chosen).</p></div>\r | |
| 53 | <div class="paragraph"><p>For a nullary type definition, this amounts to the right-hand side\r | |
| 54 | being an equality type. For example, after the definition</p></div>\r | |
| 55 | <div class="listingblock">\r | |
| 56 | <div class="content"><div class="highlight"><pre><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="n">bool</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w"></span>\r | |
| 57 | </pre></div></div></div>\r | |
| 58 | <div class="paragraph"><p>type constructor <span class="monospaced">t</span> admits equality because <span class="monospaced">bool * int</span> is\r | |
| 59 | an equality type. On the other hand, after the definition</p></div>\r | |
| 60 | <div class="listingblock">\r | |
| 61 | <div class="content"><div class="highlight"><pre><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="n">bool</span><span class="w"> </span><span class="n">*</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">real</span><span class="w"></span>\r | |
| 62 | </pre></div></div></div>\r | |
| 63 | <div class="paragraph"><p>type constructor <span class="monospaced">t</span> does not admit equality, because <span class="monospaced">real</span>\r | |
| 64 | is not an equality type.</p></div>\r | |
| 65 | <div class="paragraph"><p>For another example, after the definition</p></div>\r | |
| 66 | <div class="listingblock">\r | |
| 67 | <div class="content"><div class="highlight"><pre><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 68 | </pre></div></div></div>\r | |
| 69 | <div class="paragraph"><p>type constructor <span class="monospaced">t</span> admits equality because <span class="monospaced">bool * int</span>\r | |
| 70 | is an equality type (we could have chosen any equality type other than\r | |
| 71 | <span class="monospaced">int</span>).</p></div>\r | |
| 72 | <div class="paragraph"><p>On the other hand, after the definition</p></div>\r | |
| 73 | <div class="listingblock">\r | |
| 74 | <div class="content"><div class="highlight"><pre><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 75 | </pre></div></div></div>\r | |
| 76 | <div class="paragraph"><p>type constructor <span class="monospaced">t</span> does not admit equality because\r | |
| 77 | <span class="monospaced">real * int</span> is not equality type.</p></div>\r | |
| 78 | <div class="paragraph"><p>We can check that a type constructor admits equality using an\r | |
| 79 | <span class="monospaced">eqtype</span> specification.</p></div>\r | |
| 80 | <div class="listingblock">\r | |
| 81 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Ok</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">'a</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 | |
| 82 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 83 | <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">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 84 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 85 | </pre></div></div></div>\r | |
| 86 | <div class="listingblock">\r | |
| 87 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Bad</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">'a</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 | |
| 88 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 89 | <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">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="n">*</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>\r | |
| 90 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 91 | </pre></div></div></div>\r | |
| 92 | <div class="paragraph"><p>On <span class="monospaced">structure Bad</span>, MLton reports the following error.</p></div>\r | |
| 93 | <div class="listingblock">\r | |
| 94 | <div class="content monospaced">\r | |
| 95 | <pre>Error: z.sml 1.16-1.34.\r | |
| 96 | Type in structure disagrees with signature (admits equality): t.\r | |
| 97 | structure: type 'a t = [real] * _ * _\r | |
| 98 | defn at: z.sml 3.15-3.15\r | |
| 99 | signature: [eqtype] 'a t\r | |
| 100 | spec at: z.sml 1.30-1.30</pre>\r | |
| 101 | </div></div>\r | |
| 102 | <div class="paragraph"><p>The <span class="monospaced">structure:</span> section provides an explanation of why the type\r | |
| 103 | did not admit equality, highlighting the problematic component\r | |
| 104 | (<span class="monospaced">real</span>).</p></div>\r | |
| 105 | </div>\r | |
| 106 | </div>\r | |
| 107 | <div class="sect1">\r | |
| 108 | <h2 id="_datatype_declarations">Datatype declarations</h2>\r | |
| 109 | <div class="sectionbody">\r | |
| 110 | <div class="paragraph"><p>For a type constructor declared by a datatype declaration to admit\r | |
| 111 | equality, every <a href="Variant">variant</a> of the datatype must admit equality. For\r | |
| 112 | example, the following datatype admits equality because <span class="monospaced">bool</span> and\r | |
| 113 | <span class="monospaced">char * int</span> are equality types.</p></div>\r | |
| 114 | <div class="listingblock">\r | |
| 115 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">char</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w"></span>\r | |
| 116 | </pre></div></div></div>\r | |
| 117 | <div class="paragraph"><p>Nullary constructors trivially admit equality, so that the following\r | |
| 118 | datatype admits equality.</p></div>\r | |
| 119 | <div class="listingblock">\r | |
| 120 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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">B</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">C</span><span class="w"></span>\r | |
| 121 | </pre></div></div></div>\r | |
| 122 | <div class="paragraph"><p>For a parameterized datatype constructor to admit equality, we\r | |
| 123 | consider each <a href="Variant">variant</a> as a type definition, and require that the\r | |
| 124 | definition admit equality. For example, for the datatype</p></div>\r | |
| 125 | <div class="listingblock">\r | |
| 126 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="n">*</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 127 | </pre></div></div></div>\r | |
| 128 | <div class="paragraph"><p>the type definitions</p></div>\r | |
| 129 | <div class="listingblock">\r | |
| 130 | <div class="content"><div class="highlight"><pre><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">tA</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 131 | <span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">tB</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 132 | </pre></div></div></div>\r | |
| 133 | <div class="paragraph"><p>both admit equality. Thus, type constructor <span class="monospaced">t</span> admits equality.</p></div>\r | |
| 134 | <div class="paragraph"><p>On the other hand, the following datatype does not admit equality.</p></div>\r | |
| 135 | <div class="listingblock">\r | |
| 136 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="n">*</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 137 | </pre></div></div></div>\r | |
| 138 | <div class="paragraph"><p>As with type definitions, we can check using an <span class="monospaced">eqtype</span>\r | |
| 139 | specification.</p></div>\r | |
| 140 | <div class="listingblock">\r | |
| 141 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Bad</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">'a</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 | |
| 142 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 143 | <span class="w"> </span><span class="k">datatype</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">bool</span><span class="w"> </span><span class="n">*</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 144 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 145 | </pre></div></div></div>\r | |
| 146 | <div class="paragraph"><p>MLton reports the following error.</p></div>\r | |
| 147 | <div class="listingblock">\r | |
| 148 | <div class="content monospaced">\r | |
| 149 | <pre>Error: z.sml 1.16-1.34.\r | |
| 150 | Type in structure disagrees with signature (admits equality): t.\r | |
| 151 | structure: datatype 'a t = B of [real] * _ | ...\r | |
| 152 | defn at: z.sml 3.19-3.19\r | |
| 153 | signature: [eqtype] 'a t\r | |
| 154 | spec at: z.sml 1.30-1.30</pre>\r | |
| 155 | </div></div>\r | |
| 156 | <div class="paragraph"><p>MLton indicates the problematic constructor (<span class="monospaced">B</span>), as well as\r | |
| 157 | the problematic component of the constructor’s argument.</p></div>\r | |
| 158 | <div class="sect2">\r | |
| 159 | <h3 id="_recursive_datatypes">Recursive datatypes</h3>\r | |
| 160 | <div class="paragraph"><p>A recursive datatype like</p></div>\r | |
| 161 | <div class="listingblock">\r | |
| 162 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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">B</span><span class="w"> </span><span class="k">of</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">t</span><span class="w"></span>\r | |
| 163 | </pre></div></div></div>\r | |
| 164 | <div class="paragraph"><p>introduces a new problem, since in order to decide whether <span class="monospaced">t</span>\r | |
| 165 | admits equality, we need to know for the <span class="monospaced">B</span> <a href="Variant">variant</a> whether\r | |
| 166 | <span class="monospaced">t</span> admits equality. The <a href="DefinitionOfStandardML">Definition</a>\r | |
| 167 | answers this question by requiring a type constructor to admit\r | |
| 168 | equality if it is consistent to do so. So, in our above example, if\r | |
| 169 | we assume that <span class="monospaced">t</span> admits equality, then the <a href="Variant">variant</a>\r | |
| 170 | <span class="monospaced">B of int * t</span> admits equality. Then, since the <span class="monospaced">A</span> <a href="Variant">variant</a>\r | |
| 171 | trivially admits equality, so does the type constructor <span class="monospaced">t</span>.\r | |
| 172 | Thus, it was consistent to assume that <span class="monospaced">t</span> admits equality, and\r | |
| 173 | so, <span class="monospaced">t</span> does admit equality.</p></div>\r | |
| 174 | <div class="paragraph"><p>On the other hand, in the following declaration</p></div>\r | |
| 175 | <div class="listingblock">\r | |
| 176 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
| 177 | </pre></div></div></div>\r | |
| 178 | <div class="paragraph"><p>if we assume that <span class="monospaced">t</span> admits equality, then the <span class="monospaced">B</span> <a href="Variant">variant</a>\r | |
| 179 | does not admit equality. Hence, the type constructor <span class="monospaced">t</span> does not\r | |
| 180 | admit equality, and our assumption was inconsistent. Hence, <span class="monospaced">t</span>\r | |
| 181 | does not admit equality.</p></div>\r | |
| 182 | <div class="paragraph"><p>The same kind of reasoning applies to mutually recursive datatypes as\r | |
| 183 | well. For example, the following defines both <span class="monospaced">t</span> and <span class="monospaced">u</span> to\r | |
| 184 | admit equality.</p></div>\r | |
| 185 | <div class="listingblock">\r | |
| 186 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">u</span><span class="w"></span>\r | |
| 187 | <span class="k">and</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
| 188 | </pre></div></div></div>\r | |
| 189 | <div class="paragraph"><p>But the following defines neither <span class="monospaced">t</span> nor <span class="monospaced">u</span> to admit\r | |
| 190 | equality.</p></div>\r | |
| 191 | <div class="listingblock">\r | |
| 192 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">real</span><span class="w"></span>\r | |
| 193 | <span class="k">and</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
| 194 | </pre></div></div></div>\r | |
| 195 | <div class="paragraph"><p>As always, we can check whether a type admits equality using an\r | |
| 196 | <span class="monospaced">eqtype</span> specification.</p></div>\r | |
| 197 | <div class="listingblock">\r | |
| 198 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Bad</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">eqtype</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="k">end</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 199 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 200 | <span class="w"> </span><span class="k">datatype</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</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">B</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">real</span><span class="w"></span>\r | |
| 201 | <span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">C</span><span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">D</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
| 202 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 203 | </pre></div></div></div>\r | |
| 204 | <div class="paragraph"><p>MLton reports the following error.</p></div>\r | |
| 205 | <div class="listingblock">\r | |
| 206 | <div class="content monospaced">\r | |
| 207 | <pre>Error: z.sml 1.16-1.40.\r | |
| 208 | Type in structure disagrees with signature (admits equality): t.\r | |
| 209 | structure: datatype t = B of [_str.u] * [real] | ...\r | |
| 210 | defn at: z.sml 3.16-3.16\r | |
| 211 | signature: [eqtype] t\r | |
| 212 | spec at: z.sml 1.27-1.27\r | |
| 213 | Error: z.sml 1.16-1.40.\r | |
| 214 | Type in structure disagrees with signature (admits equality): u.\r | |
| 215 | structure: datatype u = D of [_str.t] | ...\r | |
| 216 | defn at: z.sml 4.11-4.11\r | |
| 217 | signature: [eqtype] u\r | |
| 218 | spec at: z.sml 1.36-1.36</pre>\r | |
| 219 | </div></div>\r | |
| 220 | </div>\r | |
| 221 | </div>\r | |
| 222 | </div>\r | |
| 223 | </div>\r | |
| 224 | <div id="footnotes"><hr></div>\r | |
| 225 | <div id="footer">\r | |
| 226 | <div id="footer-text">\r | |
| 227 | </div>\r | |
| 228 | <div id="footer-badges">\r | |
| 229 | </div>\r | |
| 230 | </div>\r | |
| 231 | </body>\r | |
| 232 | </html>\r |