HCoop / hcoop / debian / mlton.git / blame
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| 6 | <title>UniversalType</title>\r | |
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| 19 | <body class="article">\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>UniversalType</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 universal type is a type into which all other types can be embedded.\r | |
| 32 | Here’s a <a href="StandardML">Standard ML</a> signature for a universal type.</p></div>\r | |
| 33 | <div class="listingblock">\r | |
| 34 | <div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">UNIVERSAL_TYPE</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 35 | <span class="w"> </span><span class="k">sig</span><span class="w"></span>\r | |
| 36 | <span class="w"> </span><span class="k">type</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
| 37 | \r | |
| 38 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">embed</span><span class="p">:</span><span class="w"> </span><span class="n">unit</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="p">-></span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="p">(</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="n">option</span><span class="p">)</span><span class="w"></span>\r | |
| 39 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 40 | </pre></div></div></div>\r | |
| 41 | <div class="paragraph"><p>The idea is that <span class="monospaced">type t</span> is the universal type and that each call to\r | |
| 42 | <span class="monospaced">embed</span> returns a new pair of functions <span class="monospaced">(inject, project)</span>, where\r | |
| 43 | <span class="monospaced">inject</span> embeds a value into the universal type and <span class="monospaced">project</span> extracts\r | |
| 44 | the value from the universal type. A pair <span class="monospaced">(inject, project)</span>\r | |
| 45 | returned by <span class="monospaced">embed</span> works together in that <span class="monospaced">project u</span> will return\r | |
| 46 | <span class="monospaced">SOME v</span> if and only if <span class="monospaced">u</span> was created by <span class="monospaced">inject v</span>. If <span class="monospaced">u</span> was\r | |
| 47 | created by a different function <span class="monospaced">inject'</span>, then <span class="monospaced">project</span> returns\r | |
| 48 | <span class="monospaced">NONE</span>.</p></div>\r | |
| 49 | <div class="paragraph"><p>Here’s an example embedding integers and reals into a universal type.</p></div>\r | |
| 50 | <div class="listingblock">\r | |
| 51 | <div class="content"><div class="highlight"><pre><span class="k">functor</span><span class="w"> </span><span class="n">Test</span><span class="w"> </span><span class="p">(</span><span class="n">U</span><span class="p">:</span><span class="w"> </span><span class="n">UNIVERSAL_TYPE</span><span class="p">):</span><span class="w"> </span><span class="k">sig</span><span class="w"> </span><span class="k">end</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 52 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 53 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="p">(</span><span class="n">intIn</span><span class="p">:</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">U</span><span class="p">.</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="n">intOut</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">U</span><span class="p">.</span><span class="n">embed</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
| 54 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">U</span><span class="p">.</span><span class="n">t</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="p">(</span><span class="n">intIn</span><span class="w"> </span><span class="mi">13</span><span class="p">)</span><span class="w"></span>\r | |
| 55 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">s1</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 56 | <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="n">intOut</span><span class="w"> </span><span class="p">(</span><span class="n">!r</span><span class="p">)</span><span class="w"> </span><span class="k">of</span><span class="w"></span>\r | |
| 57 | <span class="w"> </span><span class="n">NONE</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="s">"NONE"</span><span class="w"></span>\r | |
| 58 | <span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">SOME</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">Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">i</span><span class="w"></span>\r | |
| 59 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="p">(</span><span class="n">realIn</span><span class="p">:</span><span class="w"> </span><span class="n">real</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">U</span><span class="p">.</span><span class="n">t</span><span class="p">,</span><span class="w"> </span><span class="n">realOut</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">U</span><span class="p">.</span><span class="n">embed</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
| 60 | <span class="w"> </span><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">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">realIn</span><span class="w"> </span><span class="mf">13.0</span><span class="w"></span>\r | |
| 61 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">s2</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 62 | <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="n">intOut</span><span class="w"> </span><span class="p">(</span><span class="n">!r</span><span class="p">)</span><span class="w"> </span><span class="k">of</span><span class="w"></span>\r | |
| 63 | <span class="w"> </span><span class="n">NONE</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="s">"NONE"</span><span class="w"></span>\r | |
| 64 | <span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">SOME</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">Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">i</span><span class="w"></span>\r | |
| 65 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">s3</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 66 | <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="n">realOut</span><span class="w"> </span><span class="p">(</span><span class="n">!r</span><span class="p">)</span><span class="w"> </span><span class="k">of</span><span class="w"></span>\r | |
| 67 | <span class="w"> </span><span class="n">NONE</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="s">"NONE"</span><span class="w"></span>\r | |
| 68 | <span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">Real</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
| 69 | <span class="w"> </span><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">print</span><span class="w"> </span><span class="p">(</span><span class="n">concat</span><span class="w"> </span><span class="p">[</span><span class="n">s1</span><span class="p">,</span><span class="w"> </span><span class="s">" "</span><span class="p">,</span><span class="w"> </span><span class="n">s2</span><span class="p">,</span><span class="w"> </span><span class="s">" "</span><span class="p">,</span><span class="w"> </span><span class="n">s3</span><span class="p">,</span><span class="w"> </span><span class="s">"</span><span class="se">\n</span><span class="s">"</span><span class="p">])</span><span class="w"></span>\r | |
| 70 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 71 | </pre></div></div></div>\r | |
| 72 | <div class="paragraph"><p>Applying <span class="monospaced">Test</span> to an appropriate implementation will print</p></div>\r | |
| 73 | <div class="listingblock">\r | |
| 74 | <div class="content monospaced">\r | |
| 75 | <pre>13 NONE 13.0</pre>\r | |
| 76 | </div></div>\r | |
| 77 | <div class="paragraph"><p>Note that two different calls to embed on the same type return\r | |
| 78 | different embeddings.</p></div>\r | |
| 79 | <div class="paragraph"><p>Standard ML does not have explicit support for universal types;\r | |
| 80 | however, there are at least two ways to implement them.</p></div>\r | |
| 81 | </div>\r | |
| 82 | </div>\r | |
| 83 | <div class="sect1">\r | |
| 84 | <h2 id="_implementation_using_exceptions">Implementation Using Exceptions</h2>\r | |
| 85 | <div class="sectionbody">\r | |
| 86 | <div class="paragraph"><p>While the intended use of SML exceptions is for exception handling, an\r | |
| 87 | accidental feature of their design is that the <span class="monospaced">exn</span> type is a\r | |
| 88 | universal type. The implementation relies on being able to declare\r | |
| 89 | exceptions locally to a function and on the fact that exceptions are\r | |
| 90 | <a href="GenerativeException">generative</a>.</p></div>\r | |
| 91 | <div class="listingblock">\r | |
| 92 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">U</span><span class="p">:></span><span class="w"> </span><span class="n">UNIVERSAL_TYPE</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 93 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 94 | <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="n">exn</span><span class="w"></span>\r | |
| 95 | \r | |
| 96 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">embed</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 97 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 98 | <span class="w"> </span><span class="k">exception</span><span class="w"> </span><span class="n">E</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
| 99 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">project</span><span class="w"> </span><span class="p">(</span><span class="n">e</span><span class="p">:</span><span class="w"> </span><span class="n">t</span><span class="p">):</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 100 | <span class="w"> </span><span class="k">case</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="k">of</span><span class="w"></span>\r | |
| 101 | <span class="w"> </span><span class="n">E</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">SOME</span><span class="w"> </span><span class="n">a</span><span class="w"></span>\r | |
| 102 | <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="w"> </span><span class="n">NONE</span><span class="w"></span>\r | |
| 103 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 104 | <span class="w"> </span><span class="p">(</span><span class="n">E</span><span class="p">,</span><span class="w"> </span><span class="n">project</span><span class="p">)</span><span class="w"></span>\r | |
| 105 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 106 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 107 | </pre></div></div></div>\r | |
| 108 | </div>\r | |
| 109 | </div>\r | |
| 110 | <div class="sect1">\r | |
| 111 | <h2 id="_implementation_using_functions_and_references">Implementation Using Functions and References</h2>\r | |
| 112 | <div class="sectionbody">\r | |
| 113 | <div class="listingblock">\r | |
| 114 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">U</span><span class="p">:></span><span class="w"> </span><span class="n">UNIVERSAL_TYPE</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 115 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 116 | <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">T</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="p">{</span><span class="n">clear</span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">unit</span><span class="p">,</span><span class="w"></span>\r | |
| 117 | <span class="w"> </span><span class="n">store</span><span class="p">:</span><span class="w"> </span><span class="n">unit</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">unit</span><span class="p">}</span><span class="w"></span>\r | |
| 118 | \r | |
| 119 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">embed</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 120 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 121 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="n">NONE</span><span class="w"></span>\r | |
| 122 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">inject</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">'a</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>\r | |
| 123 | <span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">{</span><span class="n">clear</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">NONE</span><span class="p">,</span><span class="w"></span>\r | |
| 124 | <span class="w"> </span><span class="n">store</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="n">a</span><span class="p">}</span><span class="w"></span>\r | |
| 125 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">project</span><span class="w"> </span><span class="p">(</span><span class="n">T</span><span class="w"> </span><span class="p">{</span><span class="n">clear</span><span class="p">,</span><span class="w"> </span><span class="n">store</span><span class="p">}):</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 126 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 127 | <span class="w"> </span><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">store</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
| 128 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">!r</span><span class="w"></span>\r | |
| 129 | <span class="w"> </span><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">clear</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
| 130 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 131 | <span class="w"> </span><span class="n">res</span><span class="w"></span>\r | |
| 132 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 133 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 134 | <span class="w"> </span><span class="p">(</span><span class="n">inject</span><span class="p">,</span><span class="w"> </span><span class="n">project</span><span class="p">)</span><span class="w"></span>\r | |
| 135 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 136 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 137 | </pre></div></div></div>\r | |
| 138 | <div class="paragraph"><p>Note that due to the use of a shared ref cell, the above\r | |
| 139 | implementation is not thread safe.</p></div>\r | |
| 140 | <div class="paragraph"><p>One could try to simplify the above implementation by eliminating the\r | |
| 141 | <span class="monospaced">clear</span> function, making <span class="monospaced">type t = unit -> unit</span>.</p></div>\r | |
| 142 | <div class="listingblock">\r | |
| 143 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">U</span><span class="p">:></span><span class="w"> </span><span class="n">UNIVERSAL_TYPE</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 144 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
| 145 | <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="n">unit</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">unit</span><span class="w"></span>\r | |
| 146 | \r | |
| 147 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">embed</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
| 148 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r | |
| 149 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">r</span><span class="p">:</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ref</span><span class="w"> </span><span class="n">NONE</span><span class="w"></span>\r | |
| 150 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">inject</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">'a</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="k">fn</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">SOME</span><span class="w"> </span><span class="n">a</span><span class="w"></span>\r | |
| 151 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">project</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="p">:</span><span class="w"> </span><span class="n">t</span><span class="p">):</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">option</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">NONE</span><span class="p">;</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">();</span><span class="w"> </span><span class="n">!r</span><span class="p">)</span><span class="w"></span>\r | |
| 152 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
| 153 | <span class="w"> </span><span class="p">(</span><span class="n">inject</span><span class="p">,</span><span class="w"> </span><span class="n">project</span><span class="p">)</span><span class="w"></span>\r | |
| 154 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 155 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
| 156 | </pre></div></div></div>\r | |
| 157 | <div class="paragraph"><p>While correct, this approach keeps the contents of the ref cell alive\r | |
| 158 | longer than necessary, which could cause a space leak. The problem is\r | |
| 159 | in <span class="monospaced">project</span>, where the call to <span class="monospaced">f</span> stores some value in some ref cell\r | |
| 160 | <span class="monospaced">r'</span>. Perhaps <span class="monospaced">r'</span> is the same ref cell as <span class="monospaced">r</span>, but perhaps not. If\r | |
| 161 | we do not clear <span class="monospaced">r'</span> before returning from <span class="monospaced">project</span>, then <span class="monospaced">r'</span> will\r | |
| 162 | keep the value alive, even though it is useless.</p></div>\r | |
| 163 | </div>\r | |
| 164 | </div>\r | |
| 165 | <div class="sect1">\r | |
| 166 | <h2 id="_also_see">Also see</h2>\r | |
| 167 | <div class="sectionbody">\r | |
| 168 | <div class="ulist"><ul>\r | |
| 169 | <li>\r | |
| 170 | <p>\r | |
| 171 | <a href="PropertyList">PropertyList</a>: Lisp-style property lists implemented with a universal type\r | |
| 172 | </p>\r | |
| 173 | </li>\r | |
| 174 | </ul></div>\r | |
| 175 | </div>\r | |
| 176 | </div>\r | |
| 177 | </div>\r | |
| 178 | <div id="footnotes"><hr></div>\r | |
| 179 | <div id="footer">\r | |
| 180 | <div id="footer-text">\r | |
| 181 | </div>\r | |
| 182 | <div id="footer-badges">\r | |
| 183 | </div>\r | |
| 184 | </div>\r | |
| 185 | </body>\r | |
| 186 | </html>\r |