doc/guide/localhost/FunctionalRecordUpdate

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  26 <h1>FunctionalRecordUpdate</h1>
  27 </div>
  28 <div id="content">
  29 <div id="preamble">
  30 <div class="sectionbody">
  31 <div class="paragraph"><p>Functional record update is the copying of a record while replacing
  32 the values of some of the fields.  <a href="StandardML">Standard ML</a> does not
  33 have explicit syntax for functional record update.  We will show below
  34 how to implement functional record update in SML, with a little
  35 boilerplate code.</p></div>
  36 <div class="paragraph"><p>As an example, the functional update of the record</p></div>
  37 <div class="listingblock">
  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>
  39 </pre></div></div></div>
  40 <div class="paragraph"><p>with <span class="monospaced">c = 16</span> yields a new record</p></div>
  41 <div class="listingblock">
  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>
  43 </pre></div></div></div>
  44 <div class="paragraph"><p>Functional record update also makes sense with multiple simultaneous
  45 updates.  For example, the functional update of the record above with
  46 <span class="monospaced">a = 18, c = 19</span> yields a new record</p></div>
  47 <div class="listingblock">
  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>
  49 </pre></div></div></div>
  50 <div class="paragraph"><p>One could easily imagine an extension of the SML that supports
  51 functional record update.  For example</p></div>
  52 <div class="listingblock">
  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>
  54 </pre></div></div></div>
  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>
  56 replaced with <span class="monospaced">16</span> and <span class="monospaced">b</span> replaced with <span class="monospaced">17</span>.</p></div>
  57 <div class="paragraph"><p>Since there is no such syntax in SML, we now show how to implement
  58 functional record update directly.  We first give a simple
  59 implementation that has a number of problems.  We then give an
  60 advanced implementation, that, while complex underneath, is a reusable
  61 library that admits simple use.</p></div>
  62 </div>
  63 </div>
  64 <div class="sect1">
  65 <h2 id="_simple_implementation">Simple implementation</h2>
  66 <div class="sectionbody">
  67 <div class="paragraph"><p>To support functional record update on the record type</p></div>
  68 <div class="listingblock">
  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">&#39;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">&#39;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">&#39;c</span><span class="p">}</span><span class="w"></span>
  70 </pre></div></div></div>
  71 <div class="paragraph"><p>first, define an update function for each component.</p></div>
  72 <div class="listingblock">
  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>
  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>
  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>
  76 </pre></div></div></div>
  77 <div class="paragraph"><p>Then, one can express <span class="monospaced">e with {a = 16, b = 17}</span> as</p></div>
  78 <div class="listingblock">
  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>
  80 </pre></div></div></div>
  81 <div class="paragraph"><p>With infix notation</p></div>
  82 <div class="listingblock">
  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>
  84 </pre></div></div></div>
  85 <div class="paragraph"><p>the syntax is almost as concise as a language extension.</p></div>
  86 <div class="listingblock">
  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>
  88 </pre></div></div></div>
  89 <div class="paragraph"><p>This approach suffers from the fact that the amount of boilerplate
  90 code is quadratic in the number of record fields.  Furthermore,
  91 changing, adding, or deleting a field requires time proportional to
  92 the number of fields (because each <span class="monospaced">with<em>&lt;L&gt;</em></span> function must be
  93 changed).  It is also annoying to have to define a <span class="monospaced">with<em>&lt;L&gt;</em></span>
  94 function, possibly with a fixity declaration, for each field.</p></div>
  95 <div class="paragraph"><p>Fortunately, there is a solution to these problems.</p></div>
  96 </div>
  97 </div>
  98 <div class="sect1">
  99 <h2 id="_advanced_implementation">Advanced implementation</h2>
 100 <div class="sectionbody">
 101 <div class="paragraph"><p>Using <a href="Fold">Fold</a> one can define a family of <span class="monospaced">makeUpdate<em>&lt;N&gt;</em></span>
 102 functions and single <em>update</em> operator <span class="monospaced">U</span> so that one can define a
 103 functional record update function for any record type simply by
 104 specifying a (trivial) isomorphism between that type and function
 105 argument list.  For example, suppose that we would like to do
 106 functional record update on records with fields <span class="monospaced">a</span> and <span class="monospaced">b</span>.  Then one
 107 defines a function <span class="monospaced">updateAB</span> as follows.</p></div>
 108 <div class="listingblock">
 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>
 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">=&gt;</span><span class="w"></span>
 111 <span class="w">   </span><span class="k">let</span><span class="w"></span>
 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>
 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>
 114 <span class="w">   </span><span class="k">in</span><span class="w"></span>
 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>
 116 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 117 <span class="w">   </span><span class="n">z</span><span class="w"></span>
 118 </pre></div></div></div>
 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
 120 <em>to function arguements</em>) specify an isomorphism between <span class="monospaced">a</span>,<span class="monospaced">b</span>
 121 records and function arguments.  There is a second use of <span class="monospaced">from</span> to
 122 work around the lack of
 123 <a href="FirstClassPolymorphism">first-class polymorphism</a> in SML.</p></div>
 124 <div class="paragraph"><p>With the definition of <span class="monospaced">updateAB</span> in place, the following expressions
 125 are valid.</p></div>
 126 <div class="listingblock">
 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">&quot;hello&quot;</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">&quot;goodbye&quot;</span><span class="p">)</span><span class="w"> </span><span class="n">$</span><span class="w"></span>
 128 <span class="n">updateAB</span><span class="w"> </span><span class="p">{</span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">13.5</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">true</span><span class="p">}</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">b</span><span class="w"> </span><span class="n">false</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="n">set</span><span class="p">#</span><span class="n">a</span><span class="w"> </span><span class="mf">12.5</span><span class="p">)</span><span class="w"> </span><span class="n">$</span><span class="w"></span>
 129 </pre></div></div></div>
 130 <div class="paragraph"><p>As another example, suppose that we would like to do functional record
 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
 132 function <span class="monospaced">updateBCD</span> as follows.</p></div>
 133 <div class="listingblock">
 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>
 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">=&gt;</span><span class="w"></span>
 136 <span class="w">   </span><span class="k">let</span><span class="w"></span>
 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>
 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>
 139 <span class="w">   </span><span class="k">in</span><span class="w"></span>
 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>
 141 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 142 <span class="w">   </span><span class="n">z</span><span class="w"></span>
 143 </pre></div></div></div>
 144 <div class="paragraph"><p>With the definition of <span class="monospaced">updateBCD</span> in place, the following expression
 145 is valid.</p></div>
 146 <div class="listingblock">
 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>
 148 </pre></div></div></div>
 149 <div class="paragraph"><p>Note that not all fields need be updated and that the same field may
 150 be updated multiple times.  Further note that the same <span class="monospaced">set</span> operator
 151 is used for all update functions (in the above, for both <span class="monospaced">updateAB</span>
 152 and <span class="monospaced">updateBCD</span>).</p></div>
 153 <div class="paragraph"><p>In general, to define a functional-record-update function on records
 154 with fields <span class="monospaced">f1</span>, <span class="monospaced">f2</span>, &#8230;, <span class="monospaced">fN</span>, use the following template.</p></div>
 155 <div class="listingblock">
 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>
 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">=&gt;</span><span class="w"></span>
 158 <span class="w">   </span><span class="k">let</span><span class="w"></span>
 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>
 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>
 161 <span class="w">   </span><span class="k">in</span><span class="w"></span>
 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>
 163 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 164 <span class="w">   </span><span class="n">z</span><span class="w"></span>
 165 </pre></div></div></div>
 166 <div class="paragraph"><p>With this, one can update a record as follows.</p></div>
 167 <div class="listingblock">
 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>
 169 </pre></div></div></div>
 170 </div>
 171 </div>
 172 <div class="sect1">
 173 <h2 id="_the_span_class_monospaced_functionalrecordupdate_span_structure">The <span class="monospaced">FunctionalRecordUpdate</span> structure</h2>
 174 <div class="sectionbody">
 175 <div class="paragraph"><p>Here is the implementation of functional record update.</p></div>
 176 <div class="listingblock">
 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>
 178 <span class="w">   </span><span class="k">struct</span><span class="w"></span>
 179 <span class="w">      </span><span class="k">local</span><span class="w"></span>
 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>
 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>
 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>
 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>
 184
 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>
 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>
 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>
 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>
 189
 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&#39;</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>
 191 <span class="w">            </span><span class="k">let</span><span class="w"></span>
 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&#39;</span><span class="w"></span>
 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>
 194 <span class="w">            </span><span class="k">in</span><span class="w"></span>
 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">=&gt;</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>
 196 <span class="w">            </span><span class="k">end</span><span class="w"></span>
 197 <span class="w">      </span><span class="k">in</span><span class="w"></span>
 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>
 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>
 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>
 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>
 202
 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">=&gt;</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">=&gt;</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>
 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">=&gt;</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">=&gt;</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">=&gt;</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>
 205 <span class="w">      </span><span class="k">end</span><span class="w"></span>
 206 <span class="w">   </span><span class="k">end</span><span class="w"></span>
 207 </pre></div></div></div>
 208 <div class="paragraph"><p>The idea of <span class="monospaced">makeUpdate</span> is to build a record of functions which can
 209 replace the contents of one argument out of a list of arguments.  The
 210 functions <span class="monospaced">f<em>&lt;X&gt;</em></span> replace the 0th, 1st, &#8230; argument with their
 211 argument <span class="monospaced">z</span>. The <span class="monospaced">c<em>&lt;X&gt;</em></span> functions pass the first <em>X</em> <span class="monospaced">f</span>
 212 functions to the record constructor.</p></div>
 213 <div class="paragraph"><p>The <span class="monospaced">#field</span> notation of Standard ML allows us to select the map
 214 function which replaces the corresponding argument. By converting the
 215 record to an argument list, feeding that list through the selected map
 216 function and piping the list into the record constructor, functional
 217 record update is achieved.</p></div>
 218 </div>
 219 </div>
 220 <div class="sect1">
 221 <h2 id="_efficiency">Efficiency</h2>
 222 <div class="sectionbody">
 223 <div class="paragraph"><p>With MLton, the efficiency of this approach is as good as one would
 224 expect with the special syntax.  Namely a sequence of updates will be
 225 optimized into a single record construction that copies the unchanged
 226 fields and fills in the changed fields with their new values.</p></div>
 227 <div class="paragraph"><p>Before Sep 14, 2009, this page advocated an alternative implementation
 228 of <a href="FunctionalRecordUpdate">FunctionalRecordUpdate</a>.  However, the old structure caused
 229 exponentially increasing compile times.  We advise you to switch to
 230 the newer version.</p></div>
 231 </div>
 232 </div>
 233 <div class="sect1">
 234 <h2 id="_applications">Applications</h2>
 235 <div class="sectionbody">
 236 <div class="paragraph"><p>Functional record update can be used to implement labelled
 237 <a href="OptionalArguments">optional arguments</a>.</p></div>
 238 </div>
 239 </div>
 240 </div>
 241 <div id="footnotes"><hr></div>
 242 <div id="footer">
 243 <div id="footer-text">
 244 </div>
 245 <div id="footer-badges">
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