HCoop / hcoop / debian / mlton.git / blame
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| 5 | <meta name="generator" content="AsciiDoc 8.6.9">\r | |
| 6 | <title>Monomorphise</title>\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>Monomorphise</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="Monomorphise">Monomorphise</a> is a translation pass from the <a href="XML">XML</a>\r | |
| 32 | <a href="IntermediateLanguage">IntermediateLanguage</a> to the <a href="SXML">SXML</a> <a href="IntermediateLanguage">IntermediateLanguage</a>.</p></div>\r | |
| 33 | </div>\r | |
| 34 | </div>\r | |
| 35 | <div class="sect1">\r | |
| 36 | <h2 id="_description">Description</h2>\r | |
| 37 | <div class="sectionbody">\r | |
| 38 | <div class="paragraph"><p>Monomorphisation eliminates polymorphic values and datatype\r | |
| 39 | declarations by duplicating them for each type at which they are used.</p></div>\r | |
| 40 | <div class="paragraph"><p>Consider the following <a href="XML">XML</a> program.</p></div>\r | |
| 41 | <div class="listingblock">\r | |
| 42 | <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">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 43 | <span class="k">fun</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">f</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">'a</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 44 | <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">f</span><span class="w"> </span><span class="mi">1</span><span class="w"></span>\r | |
| 45 | <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="n">f</span><span class="w"> </span><span class="mi">2</span><span class="w"></span>\r | |
| 46 | <span class="k">val</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">f</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"></span>\r | |
| 47 | </pre></div></div></div>\r | |
| 48 | <div class="paragraph"><p>The result of monomorphising this program is the following <a href="SXML">SXML</a> program:</p></div>\r | |
| 49 | <div class="listingblock">\r | |
| 50 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T1</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">int</span><span class="w"></span>\r | |
| 51 | <span class="k">datatype</span><span class="w"> </span><span class="n">t2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T2</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">int</span><span class="w"></span>\r | |
| 52 | <span class="k">fun</span><span class="w"> </span><span class="n">f1</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">int</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T1</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 53 | <span class="k">fun</span><span class="w"> </span><span class="n">f2</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">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">T2</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 54 | <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">f1</span><span class="w"> </span><span class="mi">1</span><span class="w"></span>\r | |
| 55 | <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="n">f1</span><span class="w"> </span><span class="mi">2</span><span class="w"></span>\r | |
| 56 | <span class="k">val</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">f2</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"></span>\r | |
| 57 | </pre></div></div></div>\r | |
| 58 | </div>\r | |
| 59 | </div>\r | |
| 60 | <div class="sect1">\r | |
| 61 | <h2 id="_implementation">Implementation</h2>\r | |
| 62 | <div class="sectionbody">\r | |
| 63 | <div class="ulist"><ul>\r | |
| 64 | <li>\r | |
| 65 | <p>\r | |
| 66 | <a href="https://github.com/MLton/mlton/blob/master/mlton/xml/monomorphise.sig"><span class="monospaced">monomorphise.sig</span></a>\r | |
| 67 | </p>\r | |
| 68 | </li>\r | |
| 69 | <li>\r | |
| 70 | <p>\r | |
| 71 | <a href="https://github.com/MLton/mlton/blob/master/mlton/xml/monomorphise.fun"><span class="monospaced">monomorphise.fun</span></a>\r | |
| 72 | </p>\r | |
| 73 | </li>\r | |
| 74 | </ul></div>\r | |
| 75 | </div>\r | |
| 76 | </div>\r | |
| 77 | <div class="sect1">\r | |
| 78 | <h2 id="_details_and_notes">Details and Notes</h2>\r | |
| 79 | <div class="sectionbody">\r | |
| 80 | <div class="paragraph"><p>The monomorphiser works by making one pass over the entire program.\r | |
| 81 | On the way down, it creates a cache for each variable declared in a\r | |
| 82 | polymorphic declaration that maps a lists of type arguments to a new\r | |
| 83 | variable name. At a variable reference, it consults the cache (based\r | |
| 84 | on the types the variable is applied to). If there is already an\r | |
| 85 | entry in the cache, it is used. If not, a new entry is created. On\r | |
| 86 | the way up, the monomorphiser duplicates a variable declaration for\r | |
| 87 | each entry in the cache.</p></div>\r | |
| 88 | <div class="paragraph"><p>As with variables, the monomorphiser records all of the type at which\r | |
| 89 | constructors are used. After the entire program is processed, the\r | |
| 90 | monomorphiser duplicates each datatype declaration and its associated\r | |
| 91 | constructors.</p></div>\r | |
| 92 | <div class="paragraph"><p>The monomorphiser duplicates all of the functions declared in a\r | |
| 93 | <span class="monospaced">fun</span> declaration as a unit. Consider the following program</p></div>\r | |
| 94 | <div class="listingblock">\r | |
| 95 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">f</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">'a</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 96 | <span class="k">and</span><span class="w"> </span><span class="n">g</span><span class="w"> </span><span class="p">(</span><span class="n">y</span><span class="p">:</span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">y</span><span class="w"></span>\r | |
| 97 | <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">f</span><span class="w"> </span><span class="mi">13</span><span class="w"></span>\r | |
| 98 | <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="n">g</span><span class="w"> </span><span class="mi">14</span><span class="w"></span>\r | |
| 99 | <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="n">f</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>\r | |
| 100 | </pre></div></div></div>\r | |
| 101 | <div class="paragraph"><p>and its monomorphisation</p></div>\r | |
| 102 | <div class="listingblock">\r | |
| 103 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">f1</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">int</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">g1</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 104 | <span class="k">and</span><span class="w"> </span><span class="n">g1</span><span class="w"> </span><span class="p">(</span><span class="n">y</span><span class="p">:</span><span class="w"> </span><span class="n">int</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f1</span><span class="w"> </span><span class="n">y</span><span class="w"></span>\r | |
| 105 | <span class="k">fun</span><span class="w"> </span><span class="n">f2</span><span class="w"> </span><span class="p">(</span><span class="n">x</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">int</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">g2</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 106 | <span class="k">and</span><span class="w"> </span><span class="n">g2</span><span class="w"> </span><span class="p">(</span><span class="n">y</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">int</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f2</span><span class="w"> </span><span class="n">y</span><span class="w"></span>\r | |
| 107 | <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">f1</span><span class="w"> </span><span class="mi">13</span><span class="w"></span>\r | |
| 108 | <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="n">g1</span><span class="w"> </span><span class="mi">14</span><span class="w"></span>\r | |
| 109 | <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="n">f2</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>\r | |
| 110 | </pre></div></div></div>\r | |
| 111 | </div>\r | |
| 112 | </div>\r | |
| 113 | <div class="sect1">\r | |
| 114 | <h2 id="_pathological_datatype_declarations">Pathological datatype declarations</h2>\r | |
| 115 | <div class="sectionbody">\r | |
| 116 | <div class="paragraph"><p>SML allows a pathological polymorphic datatype declaration in which\r | |
| 117 | recursive uses of the defined type constructor are applied to\r | |
| 118 | different type arguments than the definition. This has been\r | |
| 119 | disallowed by others on type theoretic grounds. A canonical example\r | |
| 120 | is the following.</p></div>\r | |
| 121 | <div class="listingblock">\r | |
| 122 | <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">'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="p">(</span><span class="n">'a</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="p">)</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
| 123 | <span class="k">val</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">t</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="n">B</span><span class="w"> </span><span class="p">(</span><span class="n">A</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="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">))))</span><span class="w"></span>\r | |
| 124 | </pre></div></div></div>\r | |
| 125 | <div class="paragraph"><p>The presence of the recursion in the datatype declaration might appear\r | |
| 126 | to cause the need for the monomorphiser to create an infinite number\r | |
| 127 | of types. However, due to the absence of polymorphic recursion in\r | |
| 128 | SML, there are in fact only a finite number of instances of such types\r | |
| 129 | in any given program. The monomorphiser translates the above program\r | |
| 130 | to the following one.</p></div>\r | |
| 131 | <div class="listingblock">\r | |
| 132 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">t1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">B1</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">t2</span><span class="w"></span>\r | |
| 133 | <span class="k">datatype</span><span class="w"> </span><span class="n">t2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">B2</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">t3</span><span class="w"></span>\r | |
| 134 | <span class="k">datatype</span><span class="w"> </span><span class="n">t3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">A3</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="p">)</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">(</span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="p">)</span><span class="w"></span>\r | |
| 135 | <span class="k">val</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">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">B1</span><span class="w"> </span><span class="p">(</span><span class="n">B2</span><span class="w"> </span><span class="p">(</span><span class="n">A3</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="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">))))</span><span class="w"></span>\r | |
| 136 | </pre></div></div></div>\r | |
| 137 | <div class="paragraph"><p>It is crucial that the monomorphiser be allowed to drop unused\r | |
| 138 | constructors from datatype declarations in order for the translation\r | |
| 139 | to terminate.</p></div>\r | |
| 140 | </div>\r | |
| 141 | </div>\r | |
| 142 | </div>\r | |
| 143 | <div id="footnotes"><hr></div>\r | |
| 144 | <div id="footer">\r | |
| 145 | <div id="footer-text">\r | |
| 146 | </div>\r | |
| 147 | <div id="footer-badges">\r | |
| 148 | </div>\r | |
| 149 | </div>\r | |
| 150 | </body>\r | |
| 151 | </html>\r |