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| 22 | <a href="./Home">MLton 20180207</a>\r |
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| 26 | <h1>FunctionalRecordUpdate</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>Functional record update is the copying of a record while replacing\r |
| 32 | the values of some of the fields. <a href="StandardML">Standard ML</a> does not\r |
| 33 | have explicit syntax for functional record update. We will show below\r |
| 34 | how to implement functional record update in SML, with a little\r |
| 35 | boilerplate code.</p></div>\r |
| 36 | <div class="paragraph"><p>As an example, the functional update of the record</p></div>\r |
| 37 | <div class="listingblock">\r |
| 38 | <div class="content"><div class="highlight"><pre><span class="p">{</span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">13</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="mi">14</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="mi">15</span><span class="p">}</span><span class="w"></span>\r |
| 39 | </pre></div></div></div>\r |
| 40 | <div class="paragraph"><p>with <span class="monospaced">c = 16</span> yields a new record</p></div>\r |
| 41 | <div class="listingblock">\r |
| 42 | <div class="content"><div class="highlight"><pre><span class="p">{</span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">13</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="mi">14</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="mi">16</span><span class="p">}</span><span class="w"></span>\r |
| 43 | </pre></div></div></div>\r |
| 44 | <div class="paragraph"><p>Functional record update also makes sense with multiple simultaneous\r |
| 45 | updates. For example, the functional update of the record above with\r |
| 46 | <span class="monospaced">a = 18, c = 19</span> yields a new record</p></div>\r |
| 47 | <div class="listingblock">\r |
| 48 | <div class="content"><div class="highlight"><pre><span class="p">{</span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">18</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="mi">14</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="mi">19</span><span class="p">}</span><span class="w"></span>\r |
| 49 | </pre></div></div></div>\r |
| 50 | <div class="paragraph"><p>One could easily imagine an extension of the SML that supports\r |
| 51 | functional record update. For example</p></div>\r |
| 52 | <div class="listingblock">\r |
| 53 | <div class="content"><div class="highlight"><pre><span class="n">e</span><span class="w"> </span><span class="k">with</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="mi">16</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="mi">17</span><span class="p">}</span><span class="w"></span>\r |
| 54 | </pre></div></div></div>\r |
| 55 | <div class="paragraph"><p>would create a copy of the record denoted by <span class="monospaced">e</span> with field <span class="monospaced">a</span>\r |
| 56 | replaced with <span class="monospaced">16</span> and <span class="monospaced">b</span> replaced with <span class="monospaced">17</span>.</p></div>\r |
| 57 | <div class="paragraph"><p>Since there is no such syntax in SML, we now show how to implement\r |
| 58 | functional record update directly. We first give a simple\r |
| 59 | implementation that has a number of problems. We then give an\r |
| 60 | advanced implementation, that, while complex underneath, is a reusable\r |
| 61 | library that admits simple use.</p></div>\r |
| 62 | </div>\r |
| 63 | </div>\r |
| 64 | <div class="sect1">\r |
| 65 | <h2 id="_simple_implementation">Simple implementation</h2>\r |
| 66 | <div class="sectionbody">\r |
| 67 | <div class="paragraph"><p>To support functional record update on the record type</p></div>\r |
| 68 | <div class="listingblock">\r |
| 69 | <div class="content"><div class="highlight"><pre><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">b</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">c</span><span class="p">:</span><span class="w"> </span><span class="n">'c</span><span class="p">}</span><span class="w"></span>\r |
| 70 | </pre></div></div></div>\r |
| 71 | <div class="paragraph"><p>first, define an update function for each component.</p></div>\r |
| 72 | <div class="listingblock">\r |
| 73 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">withA</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="p">_,</span><span class="w"> </span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">c</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="p">{</span><span class="n">a</span><span class="w"> </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">b</span><span class="w"> </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">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">c</span><span class="p">}</span><span class="w"></span>\r |
| 74 | <span class="k">fun</span><span class="w"> </span><span class="n">withB</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="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">_,</span><span class="w"> </span><span class="n">c</span><span class="p">},</span><span class="w"> </span><span class="n">b</span><span class="p">)</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">a</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">b</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">c</span><span class="p">}</span><span class="w"></span>\r |
| 75 | <span class="k">fun</span><span class="w"> </span><span class="n">withC</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">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">_},</span><span class="w"> </span><span class="n">c</span><span class="p">)</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">a</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">b</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">c</span><span class="p">}</span><span class="w"></span>\r |
| 76 | </pre></div></div></div>\r |
| 77 | <div class="paragraph"><p>Then, one can express <span class="monospaced">e with {a = 16, b = 17}</span> as</p></div>\r |
| 78 | <div class="listingblock">\r |
| 79 | <div class="content"><div class="highlight"><pre><span class="n">withB</span><span class="w"> </span><span class="p">(</span><span class="n">withA</span><span class="w"> </span><span class="p">(</span><span class="n">e</span><span class="p">,</span><span class="w"> </span><span class="mi">16</span><span class="p">),</span><span class="w"> </span><span class="mi">17</span><span class="p">)</span><span class="w"></span>\r |
| 80 | </pre></div></div></div>\r |
| 81 | <div class="paragraph"><p>With infix notation</p></div>\r |
| 82 | <div class="listingblock">\r |
| 83 | <div class="content"><div class="highlight"><pre><span class="k">infix</span><span class="w"> </span><span class="n">withA</span><span class="w"> </span><span class="n">withB</span><span class="w"> </span><span class="n">withC</span><span class="w"></span>\r |
| 84 | </pre></div></div></div>\r |
| 85 | <div class="paragraph"><p>the syntax is almost as concise as a language extension.</p></div>\r |
| 86 | <div class="listingblock">\r |
| 87 | <div class="content"><div class="highlight"><pre><span class="n">e</span><span class="w"> </span><span class="n">withA</span><span class="w"> </span><span class="mi">16</span><span class="w"> </span><span class="n">withB</span><span class="w"> </span><span class="mi">17</span><span class="w"></span>\r |
| 88 | </pre></div></div></div>\r |
| 89 | <div class="paragraph"><p>This approach suffers from the fact that the amount of boilerplate\r |
| 90 | code is quadratic in the number of record fields. Furthermore,\r |
| 91 | changing, adding, or deleting a field requires time proportional to\r |
| 92 | the number of fields (because each <span class="monospaced">with<em><L></em></span> function must be\r |
| 93 | changed). It is also annoying to have to define a <span class="monospaced">with<em><L></em></span>\r |
| 94 | function, possibly with a fixity declaration, for each field.</p></div>\r |
| 95 | <div class="paragraph"><p>Fortunately, there is a solution to these problems.</p></div>\r |
| 96 | </div>\r |
| 97 | </div>\r |
| 98 | <div class="sect1">\r |
| 99 | <h2 id="_advanced_implementation">Advanced implementation</h2>\r |
| 100 | <div class="sectionbody">\r |
| 101 | <div class="paragraph"><p>Using <a href="Fold">Fold</a> one can define a family of <span class="monospaced">makeUpdate<em><N></em></span>\r |
| 102 | functions and single <em>update</em> operator <span class="monospaced">U</span> so that one can define a\r |
| 103 | functional record update function for any record type simply by\r |
| 104 | specifying a (trivial) isomorphism between that type and function\r |
| 105 | argument list. For example, suppose that we would like to do\r |
| 106 | functional record update on records with fields <span class="monospaced">a</span> and <span class="monospaced">b</span>. Then one\r |
| 107 | defines a function <span class="monospaced">updateAB</span> as follows.</p></div>\r |
| 108 | <div class="listingblock">\r |
| 109 | <div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">updateAB</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r |
| 110 | <span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r |
| 111 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r |
| 112 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="n">v1</span><span class="w"> </span><span class="n">v2</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">v1</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">v2</span><span class="p">}</span><span class="w"></span>\r |
| 113 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">f</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">v1</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">v2</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">v1</span><span class="w"> </span><span class="n">v2</span><span class="w"></span>\r |
| 114 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r |
| 115 | <span class="w"> </span><span class="n">makeUpdate2</span><span class="w"> </span><span class="p">(</span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">)</span><span class="w"></span>\r |
| 116 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r |
| 117 | <span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 118 | </pre></div></div></div>\r |
| 119 | <div class="paragraph"><p>The functions <span class="monospaced">from</span> (think <em>from function arguments</em>) and <span class="monospaced">to</span> (think\r |
| 120 | <em>to function arguements</em>) specify an isomorphism between <span class="monospaced">a</span>,<span class="monospaced">b</span>\r |
| 121 | records and function arguments. There is a second use of <span class="monospaced">from</span> to\r |
| 122 | work around the lack of\r |
| 123 | <a href="FirstClassPolymorphism">first-class polymorphism</a> in SML.</p></div>\r |
| 124 | <div class="paragraph"><p>With the definition of <span class="monospaced">updateAB</span> in place, the following expressions\r |
| 125 | are valid.</p></div>\r |
| 126 | <div class="listingblock">\r |
| 127 | <div class="content"><div class="highlight"><pre><span class="n">updateAB</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="mi">13</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="s">"hello"</span><span class="p">}</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">b</span><span class="w"> </span><span class="s">"goodbye"</span><span class="p">)</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r |
| 128 | <span class="n">updateAB</span><span class="w"> </span><span class="p">{</span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">13.5</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">true</span><span class="p">}</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">b</span><span class="w"> </span><span class="n">false</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">a</span><span class="w"> </span><span class="mf">12.5</span><span class="p">)</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r |
| 129 | </pre></div></div></div>\r |
| 130 | <div class="paragraph"><p>As another example, suppose that we would like to do functional record\r |
| 131 | update on records with fields <span class="monospaced">b</span>, <span class="monospaced">c</span>, and <span class="monospaced">d</span>. Then one defines a\r |
| 132 | function <span class="monospaced">updateBCD</span> as follows.</p></div>\r |
| 133 | <div class="listingblock">\r |
| 134 | <div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">updateBCD</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r |
| 135 | <span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r |
| 136 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r |
| 137 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="n">v1</span><span class="w"> </span><span class="n">v2</span><span class="w"> </span><span class="n">v3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">{</span><span class="n">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v1</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">v2</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v3</span><span class="p">}</span><span class="w"></span>\r |
| 138 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">{</span><span class="n">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v1</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">v2</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v3</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">v1</span><span class="w"> </span><span class="n">v2</span><span class="w"> </span><span class="n">v3</span><span class="w"></span>\r |
| 139 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r |
| 140 | <span class="w"> </span><span class="n">makeUpdate3</span><span class="w"> </span><span class="p">(</span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">)</span><span class="w"></span>\r |
| 141 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r |
| 142 | <span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 143 | </pre></div></div></div>\r |
| 144 | <div class="paragraph"><p>With the definition of <span class="monospaced">updateBCD</span> in place, the following expression\r |
| 145 | is valid.</p></div>\r |
| 146 | <div class="listingblock">\r |
| 147 | <div class="content"><div class="highlight"><pre><span class="n">updateBCD</span><span class="w"> </span><span class="p">{</span><span class="n">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</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="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">d</span><span class="w"> </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="n">set</span><span class="p">#</span><span class="n">c</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">c</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r |
| 148 | </pre></div></div></div>\r |
| 149 | <div class="paragraph"><p>Note that not all fields need be updated and that the same field may\r |
| 150 | be updated multiple times. Further note that the same <span class="monospaced">set</span> operator\r |
| 151 | is used for all update functions (in the above, for both <span class="monospaced">updateAB</span>\r |
| 152 | and <span class="monospaced">updateBCD</span>).</p></div>\r |
| 153 | <div class="paragraph"><p>In general, to define a functional-record-update function on records\r |
| 154 | with fields <span class="monospaced">f1</span>, <span class="monospaced">f2</span>, …, <span class="monospaced">fN</span>, use the following template.</p></div>\r |
| 155 | <div class="listingblock">\r |
| 156 | <div class="content"><div class="highlight"><pre><span class="k">val</span><span class="w"> </span><span class="n">update</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r |
| 157 | <span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r |
| 158 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r |
| 159 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="n">v1</span><span class="w"> </span><span class="n">v2</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">vn</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">{</span><span class="n">f1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v1</span><span class="p">,</span><span class="w"> </span><span class="n">f2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v2</span><span class="p">,</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="n">vn</span><span class="p">}</span><span class="w"></span>\r |
| 160 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">{</span><span class="n">f1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v1</span><span class="p">,</span><span class="w"> </span><span class="n">f2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v2</span><span class="p">,</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="n">vn</span><span class="p">}</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v1</span><span class="w"> </span><span class="n">v2</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="n">vn</span><span class="w"></span>\r |
| 161 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r |
| 162 | <span class="w"> </span><span class="n">makeUpdateN</span><span class="w"> </span><span class="p">(</span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">)</span><span class="w"></span>\r |
| 163 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r |
| 164 | <span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 165 | </pre></div></div></div>\r |
| 166 | <div class="paragraph"><p>With this, one can update a record as follows.</p></div>\r |
| 167 | <div class="listingblock">\r |
| 168 | <div class="content"><div class="highlight"><pre><span class="n">update</span><span class="w"> </span><span class="p">{</span><span class="n">f1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">v1</span><span class="p">,</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="n">vn</span><span class="p">}</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">fi1</span><span class="w"> </span><span class="n">vi1</span><span class="p">)</span><span class="w"> </span><span class="p">...</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">fim</span><span class="w"> </span><span class="n">vim</span><span class="p">)</span><span class="w"> </span><span class="n">$</span><span class="w"></span>\r |
| 169 | </pre></div></div></div>\r |
| 170 | </div>\r |
| 171 | </div>\r |
| 172 | <div class="sect1">\r |
| 173 | <h2 id="_the_span_class_monospaced_functionalrecordupdate_span_structure">The <span class="monospaced">FunctionalRecordUpdate</span> structure</h2>\r |
| 174 | <div class="sectionbody">\r |
| 175 | <div class="paragraph"><p>Here is the implementation of functional record update.</p></div>\r |
| 176 | <div class="listingblock">\r |
| 177 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">FunctionalRecordUpdate</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r |
| 178 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r |
| 179 | <span class="w"> </span><span class="k">local</span><span class="w"></span>\r |
| 180 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">next</span><span class="w"> </span><span class="n">g</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">z</span><span class="p">)</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">g</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="w"> </span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">z</span><span class="p">)</span><span class="w"></span>\r |
| 181 | <span class="w"> </span><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">f</span><span class="p">,</span><span class="w"> </span><span class="n">z</span><span class="p">)</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">f</span><span class="w"> </span><span class="p">(</span><span class="n">z</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"></span>\r |
| 182 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">f2</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">next</span><span class="w"> </span><span class="n">f1</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 183 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">f3</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">next</span><span class="w"> </span><span class="n">f2</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 184 | \r |
| 185 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">c0</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">from</span><span class="w"></span>\r |
| 186 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">c0</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="n">f1</span><span class="w"></span>\r |
| 187 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">c2</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="n">f2</span><span class="w"></span>\r |
| 188 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">c3</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">c2</span><span class="w"> </span><span class="n">from</span><span class="w"> </span><span class="n">f3</span><span class="w"></span>\r |
| 189 | \r |
| 190 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">makeUpdate</span><span class="w"> </span><span class="n">cX</span><span class="w"> </span><span class="p">(</span><span class="n">from</span><span class="p">,</span><span class="w"> </span><span class="n">from'</span><span class="p">,</span><span class="w"> </span><span class="n">to</span><span class="p">)</span><span class="w"> </span><span class="n">record</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r |
| 191 | <span class="w"> </span><span class="k">let</span><span class="w"></span>\r |
| 192 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">ops</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">cX</span><span class="w"> </span><span class="n">from'</span><span class="w"></span>\r |
| 193 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">vars</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">to</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">record</span><span class="w"></span>\r |
| 194 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r |
| 195 | <span class="w"> </span><span class="n">Fold</span><span class="p">.</span><span class="n">fold</span><span class="w"> </span><span class="p">((</span><span class="n">vars</span><span class="p">,</span><span class="w"> </span><span class="n">ops</span><span class="p">),</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">vars</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">vars</span><span class="w"> </span><span class="n">from</span><span class="p">)</span><span class="w"></span>\r |
| 196 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r |
| 197 | <span class="w"> </span><span class="k">in</span><span class="w"></span>\r |
| 198 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">makeUpdate0</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">makeUpdate</span><span class="w"> </span><span class="n">c0</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 199 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">makeUpdate1</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">makeUpdate</span><span class="w"> </span><span class="n">c1</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 200 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">makeUpdate2</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">makeUpdate</span><span class="w"> </span><span class="n">c2</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 201 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">makeUpdate3</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">makeUpdate</span><span class="w"> </span><span class="n">c3</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 202 | \r |
| 203 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">upd</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">Fold</span><span class="p">.</span><span class="n">step2</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">f</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">vars</span><span class="p">,</span><span class="w"> </span><span class="n">ops</span><span class="p">))</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">vars</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="w"> </span><span class="p">(</span><span class="n">ops</span><span class="w"> </span><span class="p">())</span><span class="w"> </span><span class="p">(</span><span class="n">out</span><span class="p">,</span><span class="w"> </span><span class="n">f</span><span class="p">)),</span><span class="w"> </span><span class="n">ops</span><span class="p">))</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 204 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">set</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">Fold</span><span class="p">.</span><span class="n">step2</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">v</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">vars</span><span class="p">,</span><span class="w"> </span><span class="n">ops</span><span class="p">))</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">out</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">vars</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="w"> </span><span class="p">(</span><span class="n">ops</span><span class="w"> </span><span class="p">())</span><span class="w"> </span><span class="p">(</span><span class="n">out</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">v</span><span class="p">)),</span><span class="w"> </span><span class="n">ops</span><span class="p">))</span><span class="w"> </span><span class="n">z</span><span class="w"></span>\r |
| 205 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r |
| 206 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r |
| 207 | </pre></div></div></div>\r |
| 208 | <div class="paragraph"><p>The idea of <span class="monospaced">makeUpdate</span> is to build a record of functions which can\r |
| 209 | replace the contents of one argument out of a list of arguments. The\r |
| 210 | functions <span class="monospaced">f<em><X></em></span> replace the 0th, 1st, … argument with their\r |
| 211 | argument <span class="monospaced">z</span>. The <span class="monospaced">c<em><X></em></span> functions pass the first <em>X</em> <span class="monospaced">f</span>\r |
| 212 | functions to the record constructor.</p></div>\r |
| 213 | <div class="paragraph"><p>The <span class="monospaced">#field</span> notation of Standard ML allows us to select the map\r |
| 214 | function which replaces the corresponding argument. By converting the\r |
| 215 | record to an argument list, feeding that list through the selected map\r |
| 216 | function and piping the list into the record constructor, functional\r |
| 217 | record update is achieved.</p></div>\r |
| 218 | </div>\r |
| 219 | </div>\r |
| 220 | <div class="sect1">\r |
| 221 | <h2 id="_efficiency">Efficiency</h2>\r |
| 222 | <div class="sectionbody">\r |
| 223 | <div class="paragraph"><p>With MLton, the efficiency of this approach is as good as one would\r |
| 224 | expect with the special syntax. Namely a sequence of updates will be\r |
| 225 | optimized into a single record construction that copies the unchanged\r |
| 226 | fields and fills in the changed fields with their new values.</p></div>\r |
| 227 | <div class="paragraph"><p>Before Sep 14, 2009, this page advocated an alternative implementation\r |
| 228 | of <a href="FunctionalRecordUpdate">FunctionalRecordUpdate</a>. However, the old structure caused\r |
| 229 | exponentially increasing compile times. We advise you to switch to\r |
| 230 | the newer version.</p></div>\r |
| 231 | </div>\r |
| 232 | </div>\r |
| 233 | <div class="sect1">\r |
| 234 | <h2 id="_applications">Applications</h2>\r |
| 235 | <div class="sectionbody">\r |
| 236 | <div class="paragraph"><p>Functional record update can be used to implement labelled\r |
| 237 | <a href="OptionalArguments">optional arguments</a>.</p></div>\r |
| 238 | </div>\r |
| 239 | </div>\r |
| 240 | </div>\r |
| 241 | <div id="footnotes"><hr></div>\r |
| 242 | <div id="footer">\r |
| 243 | <div id="footer-text">\r |
| 244 | </div>\r |
| 245 | <div id="footer-badges">\r |
| 246 | </div>\r |
| 247 | </div>\r |
| 248 | </body>\r |
| 249 | </html>\r |