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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>ForLoops</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 <span class="monospaced">for</span>-loop is typically used to iterate over a range of consecutive\r | |
32 | integers that denote indices of some sort. For example, in <a href="OCaml">OCaml</a>\r | |
33 | a <span class="monospaced">for</span>-loop takes either the form</p></div>\r | |
34 | <div class="listingblock">\r | |
35 | <div class="content monospaced">\r | |
36 | <pre>for <name> = <lower> to <upper> do <body> done</pre>\r | |
37 | </div></div>\r | |
38 | <div class="paragraph"><p>or the form</p></div>\r | |
39 | <div class="listingblock">\r | |
40 | <div class="content monospaced">\r | |
41 | <pre>for <name> = <upper> downto <lower> do <body> done</pre>\r | |
42 | </div></div>\r | |
43 | <div class="paragraph"><p>Some languages provide considerably more flexible <span class="monospaced">for</span>-loop or\r | |
44 | <span class="monospaced">foreach</span>-constructs.</p></div>\r | |
45 | <div class="paragraph"><p>A bit surprisingly, <a href="StandardML">Standard ML</a> provides special syntax\r | |
46 | for <span class="monospaced">while</span>-loops, but not for <span class="monospaced">for</span>-loops. Indeed, in SML, many uses\r | |
47 | of <span class="monospaced">for</span>-loops are better expressed using <span class="monospaced">app</span>, <span class="monospaced">foldl</span>/<span class="monospaced">foldr</span>,\r | |
48 | <span class="monospaced">map</span> and many other higher-order functions provided by the\r | |
49 | <a href="BasisLibrary">Basis Library</a> for manipulating lists, vectors and\r | |
50 | arrays. However, the Basis Library does not provide a function for\r | |
51 | iterating over a range of integer values. Fortunately, it is very\r | |
52 | easy to write one.</p></div>\r | |
53 | </div>\r | |
54 | </div>\r | |
55 | <div class="sect1">\r | |
56 | <h2 id="_a_fairly_simple_design">A fairly simple design</h2>\r | |
57 | <div class="sectionbody">\r | |
58 | <div class="paragraph"><p>The following implementation imitates both the syntax and semantics of\r | |
59 | the OCaml <span class="monospaced">for</span>-loop.</p></div>\r | |
60 | <div class="listingblock">\r | |
61 | <div class="content"><div class="highlight"><pre><span class="k">datatype</span><span class="w"> </span><span class="n">for</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w"></span>\r | |
62 | <span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w"></span>\r | |
63 | \r | |
64 | <span class="k">infix</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">downto</span><span class="w"></span>\r | |
65 | \r | |
66 | <span class="k">val</span><span class="w"> </span><span class="n">for</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
67 | <span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r | |
68 | <span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="k">let</span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">loop</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="n">></span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="k">then</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
69 | <span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="w"> </span><span class="n">lo</span><span class="p">;</span><span class="w"> </span><span class="n">loop</span><span class="w"> </span><span class="p">(</span><span class="n">lo+</span><span class="mi">1</span><span class="p">))</span><span class="w"></span>\r | |
70 | <span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">loop</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="k">end</span><span class="p">)</span><span class="w"></span>\r | |
71 | <span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r | |
72 | <span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="k">let</span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">loop</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="n"><</span><span class="w"> </span><span class="n">lo</span><span class="w"> </span><span class="k">then</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
73 | <span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="w"> </span><span class="n">up</span><span class="p">;</span><span class="w"> </span><span class="n">loop</span><span class="w"> </span><span class="p">(</span><span class="n">up-</span><span class="mi">1</span><span class="p">))</span><span class="w"></span>\r | |
74 | <span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">loop</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="k">end</span><span class="p">)</span><span class="w"></span>\r | |
75 | </pre></div></div></div>\r | |
76 | <div class="paragraph"><p>For example,</p></div>\r | |
77 | <div class="listingblock">\r | |
78 | <div class="content"><div class="highlight"><pre><span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="mi">9</span><span class="p">)</span><span class="w"></span>\r | |
79 | <span class="w"> </span><span class="p">(</span><span class="k">fn</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">print</span><span class="w"> </span><span class="p">(</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="p">))</span><span class="w"></span>\r | |
80 | </pre></div></div></div>\r | |
81 | <div class="paragraph"><p>would print <span class="monospaced">123456789</span> and</p></div>\r | |
82 | <div class="listingblock">\r | |
83 | <div class="content"><div class="highlight"><pre><span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="mi">9</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"></span>\r | |
84 | <span class="w"> </span><span class="p">(</span><span class="k">fn</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">print</span><span class="w"> </span><span class="p">(</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="p">))</span><span class="w"></span>\r | |
85 | </pre></div></div></div>\r | |
86 | <div class="paragraph"><p>would print <span class="monospaced">987654321</span>.</p></div>\r | |
87 | <div class="paragraph"><p>Straightforward formatting of nested loops</p></div>\r | |
88 | <div class="listingblock">\r | |
89 | <div class="content"><div class="highlight"><pre><span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"></span>\r | |
90 | <span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r | |
91 | <span class="w"> </span><span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">d</span><span class="p">)</span><span class="w"></span>\r | |
92 | <span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r | |
93 | <span class="w"> </span><span class="p">...))</span><span class="w"></span>\r | |
94 | </pre></div></div></div>\r | |
95 | <div class="paragraph"><p>is fairly readable, but tends to cause the body of the loop to be\r | |
96 | indented quite deeply.</p></div>\r | |
97 | </div>\r | |
98 | </div>\r | |
99 | <div class="sect1">\r | |
100 | <h2 id="_off_by_one">Off-by-one</h2>\r | |
101 | <div class="sectionbody">\r | |
102 | <div class="paragraph"><p>The above design has an annoying feature. In practice, the upper\r | |
103 | bound of the iterated range is almost always excluded and most loops\r | |
104 | would subtract one from the upper bound:</p></div>\r | |
105 | <div class="listingblock">\r | |
106 | <div class="content"><div class="highlight"><pre><span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">n-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">...</span><span class="w"></span>\r | |
107 | <span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="n">n-</span><span class="mi">1</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">...</span><span class="w"></span>\r | |
108 | </pre></div></div></div>\r | |
109 | <div class="paragraph"><p>It is probably better to break convention and exclude the upper bound\r | |
110 | by default, because it leads to more concise code and becomes\r | |
111 | idiomatic with very little practice. The iterator combinators\r | |
112 | described below exclude the upper bound by default.</p></div>\r | |
113 | </div>\r | |
114 | </div>\r | |
115 | <div class="sect1">\r | |
116 | <h2 id="_iterator_combinators">Iterator combinators</h2>\r | |
117 | <div class="sectionbody">\r | |
118 | <div class="paragraph"><p>While the simple <span class="monospaced">for</span>-function described in the previous section is\r | |
119 | probably good enough for many uses, it is a bit cumbersome when one\r | |
120 | needs to iterate over a Cartesian product. One might also want to\r | |
121 | iterate over more than just consecutive integers. It turns out that\r | |
122 | one can provide a library of iterator combinators that allow one to\r | |
123 | implement iterators more flexibly.</p></div>\r | |
124 | <div class="paragraph"><p>Since the types of the combinators may be a bit difficult to infer\r | |
125 | from their implementations, let’s first take a look at a signature of\r | |
126 | the iterator combinator library:</p></div>\r | |
127 | <div class="listingblock">\r | |
128 | <div class="content"><div class="highlight"><pre><span class="k">signature</span><span class="w"> </span><span class="n">ITER</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
129 | <span class="w"> </span><span class="k">sig</span><span class="w"></span>\r | |
130 | <span class="w"> </span><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">'a</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><span class="p">-></span><span class="w"> </span><span class="n">unit</span><span class="w"></span>\r | |
131 | \r | |
132 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">return</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
133 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">>>=</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">t</span><span class="w"> </span><span class="n">*</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">'b</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
134 | \r | |
135 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">none</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">t</span><span class="w"></span>\r | |
136 | \r | |
137 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
138 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">int</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
139 | \r | |
140 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">inList</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">list</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">t</span><span class="w"></span>\r | |
141 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">inVector</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">vector</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">t</span><span class="w"></span>\r | |
142 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">inArray</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">array</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">t</span><span class="w"></span>\r | |
143 | \r | |
144 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">using</span><span class="w"> </span><span class="p">:</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">StringCvt</span><span class="p">.</span><span class="n">reader</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
145 | \r | |
146 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">when</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">t</span><span class="w"> </span><span class="n">*</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">bool</span><span class="p">)</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">t</span><span class="w"></span>\r | |
147 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">by</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">t</span><span class="w"> </span><span class="n">*</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">'b</span><span class="p">)</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
148 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">@@</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">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
149 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">**</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">t</span><span class="w"> </span><span class="n">*</span><span class="w"> </span><span class="n">'b</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="p">(</span><span class="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">product</span><span class="w"> </span><span class="n">t</span><span class="w"></span>\r | |
150 | \r | |
151 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">for</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="p">-></span><span class="w"> </span><span class="n">'a</span><span class="w"></span>\r | |
152 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
153 | </pre></div></div></div>\r | |
154 | <div class="paragraph"><p>Several of the above combinators are meant to be used as infix\r | |
155 | operators. Here is a set of suitable infix declarations:</p></div>\r | |
156 | <div class="listingblock">\r | |
157 | <div class="content"><div class="highlight"><pre><span class="k">infix</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">downto</span><span class="w"></span>\r | |
158 | <span class="k">infix</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">@@</span><span class="w"> </span><span class="n">when</span><span class="w"> </span><span class="n">by</span><span class="w"></span>\r | |
159 | <span class="k">infix</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="n">>>=</span><span class="w"> </span><span class="n">**</span><span class="w"></span>\r | |
160 | </pre></div></div></div>\r | |
161 | <div class="paragraph"><p>A few notes are in order:</p></div>\r | |
162 | <div class="ulist"><ul>\r | |
163 | <li>\r | |
164 | <p>\r | |
165 | The <span class="monospaced">'a t</span> type constructor with the <span class="monospaced">return</span> and <span class="monospaced">>>=</span> operators forms a monad.\r | |
166 | </p>\r | |
167 | </li>\r | |
168 | <li>\r | |
169 | <p>\r | |
170 | The <span class="monospaced">to</span> and <span class="monospaced">downto</span> combinators will omit the upper bound of the range.\r | |
171 | </p>\r | |
172 | </li>\r | |
173 | <li>\r | |
174 | <p>\r | |
175 | <span class="monospaced">for</span> is the identity function. It is purely for syntactic sugar and is not strictly required.\r | |
176 | </p>\r | |
177 | </li>\r | |
178 | <li>\r | |
179 | <p>\r | |
180 | The <span class="monospaced">@@</span> combinator produces an iterator for the concatenation of the given iterators.\r | |
181 | </p>\r | |
182 | </li>\r | |
183 | <li>\r | |
184 | <p>\r | |
185 | The <span class="monospaced">**</span> combinator produces an iterator for the Cartesian product of the given iterators.\r | |
186 | </p>\r | |
187 | <div class="ulist"><ul>\r | |
188 | <li>\r | |
189 | <p>\r | |
190 | See <a href="ProductType">ProductType</a> for the type constructor <span class="monospaced">('a, 'b) product</span> used in the type of the iterator produced by <span class="monospaced">**</span>.\r | |
191 | </p>\r | |
192 | </li>\r | |
193 | </ul></div>\r | |
194 | </li>\r | |
195 | <li>\r | |
196 | <p>\r | |
197 | The <span class="monospaced">using</span> combinator allows one to iterate over slices, streams and many other kinds of sequences.\r | |
198 | </p>\r | |
199 | </li>\r | |
200 | <li>\r | |
201 | <p>\r | |
202 | <span class="monospaced">when</span> is the filtering combinator. The name <span class="monospaced">when</span> is inspired by <a href="OCaml">OCaml</a>'s guard clauses.\r | |
203 | </p>\r | |
204 | </li>\r | |
205 | <li>\r | |
206 | <p>\r | |
207 | <span class="monospaced">by</span> is the mapping combinator.\r | |
208 | </p>\r | |
209 | </li>\r | |
210 | </ul></div>\r | |
211 | <div class="paragraph"><p>The below implementation of the <span class="monospaced">ITER</span>-signature makes use of the\r | |
212 | following basic combinators:</p></div>\r | |
213 | <div class="listingblock">\r | |
214 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">const</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="p">_</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
215 | <span class="k">fun</span><span class="w"> </span><span class="n">flip</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
216 | <span class="k">fun</span><span class="w"> </span><span class="n">id</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">x</span><span class="w"></span>\r | |
217 | <span class="k">fun</span><span class="w"> </span><span class="n">opt</span><span class="w"> </span><span class="n">fno</span><span class="w"> </span><span class="n">fso</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">NONE</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">fno</span><span class="w"> </span><span class="p">()</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">?</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">fso</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
218 | <span class="k">fun</span><span class="w"> </span><span class="n">pass</span><span class="w"> </span><span class="n">x</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">f</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
219 | </pre></div></div></div>\r | |
220 | <div class="paragraph"><p>Here is an implementation the <span class="monospaced">ITER</span>-signature:</p></div>\r | |
221 | <div class="listingblock">\r | |
222 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Iter</span><span class="w"> </span><span class="p">:></span><span class="w"> </span><span class="n">ITER</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
223 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
224 | <span class="w"> </span><span class="k">type</span><span class="w"> </span><span class="n">'a</span><span class="w"> </span><span class="n">t</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="n">'a</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><span class="p">-></span><span class="w"> </span><span class="n">unit</span><span class="w"></span>\r | |
225 | \r | |
226 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">return</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">pass</span><span class="w"></span>\r | |
227 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">iA</span><span class="w"> </span><span class="n">>>=</span><span class="w"> </span><span class="n">a2iB</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">iA</span><span class="w"> </span><span class="p">(</span><span class="n">flip</span><span class="w"> </span><span class="n">a2iB</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"></span>\r | |
228 | \r | |
229 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">none</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ignore</span><span class="w"></span>\r | |
230 | \r | |
231 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">u</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="k">let</span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">`l</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l<u</span><span class="w"> </span><span class="k">then</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="w"> </span><span class="n">l</span><span class="p">;</span><span class="w"> </span><span class="n">`</span><span class="p">(</span><span class="n">l+</span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">`l</span><span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
232 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">u</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="n">l</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="k">let</span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">`u</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">u>l</span><span class="w"> </span><span class="k">then</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="n">u-</span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="n">`</span><span class="p">(</span><span class="n">u-</span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">()</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">`u</span><span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
233 | \r | |
234 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">inList</span><span class="w"> </span><span class="n">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">flip</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">app</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
235 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">inVector</span><span class="w"> </span><span class="n">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">flip</span><span class="w"> </span><span class="n">Vector</span><span class="p">.</span><span class="n">app</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
236 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">inArray</span><span class="w"> </span><span class="n">?</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">flip</span><span class="w"> </span><span class="n">Array</span><span class="p">.</span><span class="n">app</span><span class="w"> </span><span class="n">?</span><span class="w"></span>\r | |
237 | \r | |
238 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">using</span><span class="w"> </span><span class="n">get</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">let</span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">`s</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">opt</span><span class="w"> </span><span class="p">(</span><span class="n">const</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="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="p">=></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">`s</span><span class="p">))</span><span class="w"> </span><span class="p">(</span><span class="n">get</span><span class="w"> </span><span class="n">s</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">`s</span><span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
239 | \r | |
240 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">iA</span><span class="w"> </span><span class="n">when</span><span class="w"> </span><span class="n">p</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">iA</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">then</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">())</span><span class="w"></span>\r | |
241 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">iA</span><span class="w"> </span><span class="n">by</span><span class="w"> </span><span class="n">g</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">iA</span><span class="w"> </span><span class="p">(</span><span class="n">f</span><span class="w"> </span><span class="n">o</span><span class="w"> </span><span class="n">g</span><span class="p">)</span><span class="w"></span>\r | |
242 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">iA</span><span class="w"> </span><span class="n">@@</span><span class="w"> </span><span class="n">iB</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="p">(</span><span class="n">iA</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">unit</span><span class="p">;</span><span class="w"> </span><span class="n">iB</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"></span>\r | |
243 | <span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="p">(</span><span class="n">iA</span><span class="w"> </span><span class="n">**</span><span class="w"> </span><span class="n">iB</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">iA</span><span class="w"> </span><span class="p">(</span><span class="k">fn</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">iB</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="p">(</span><span class="n">a</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">b</span><span class="p">)))</span><span class="w"></span>\r | |
244 | \r | |
245 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">for</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">id</span><span class="w"></span>\r | |
246 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
247 | </pre></div></div></div>\r | |
248 | <div class="paragraph"><p>Note that some of the above combinators (e.g. <span class="monospaced">**</span>) could be expressed\r | |
249 | in terms of the other combinators, most notably <span class="monospaced">return</span> and <span class="monospaced">>>=</span>.\r | |
250 | Another implementation issue worth mentioning is that <span class="monospaced">downto</span> is\r | |
251 | written specifically to avoid computing <span class="monospaced">l-1</span>, which could cause an\r | |
252 | <span class="monospaced">Overflow</span>.</p></div>\r | |
253 | <div class="paragraph"><p>To use the above combinators the <span class="monospaced">Iter</span>-structure needs to be opened</p></div>\r | |
254 | <div class="listingblock">\r | |
255 | <div class="content"><div class="highlight"><pre><span class="k">open</span><span class="w"> </span><span class="n">Iter</span><span class="w"></span>\r | |
256 | </pre></div></div></div>\r | |
257 | <div class="paragraph"><p>and one usually also wants to declare the infix status of the\r | |
258 | operators as shown earlier.</p></div>\r | |
259 | <div class="paragraph"><p>Here is an example that illustrates some of the features:</p></div>\r | |
260 | <div class="listingblock">\r | |
261 | <div class="content"><div class="highlight"><pre><span class="n">for</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="n">when</span><span class="w"> </span><span class="p">(</span><span class="k">fn</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">x</span><span class="w"> </span><span class="n">mod</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="n"><></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="n">**</span><span class="w"> </span><span class="n">inList</span><span class="w"> </span><span class="p">[</span><span class="s">"a"</span><span class="p">,</span><span class="w"> </span><span class="s">"b"</span><span class="p">]</span><span class="w"> </span><span class="n">**</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="n">downto</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">by</span><span class="w"> </span><span class="n">real</span><span class="p">)</span><span class="w"></span>\r | |
262 | <span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">x</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="n">&</span><span class="w"> </span><span class="n">z</span><span class="w"> </span><span class="p">=></span><span class="w"></span>\r | |
263 | <span class="w"> </span><span class="n">print</span><span class="w"> </span><span class="p">(</span><span class="s">"("</span><span class="n">^Int</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">x^</span><span class="s">", </span><span class="se">\"</span><span class="s">"</span><span class="n">^y^</span><span class="s">"</span><span class="se">\"</span><span class="s">, "</span><span class="n">^Real</span><span class="p">.</span><span class="n">toString</span><span class="w"> </span><span class="n">z^</span><span class="s">")</span><span class="se">\n</span><span class="s">"</span><span class="p">))</span><span class="w"></span>\r | |
264 | </pre></div></div></div>\r | |
265 | <div class="paragraph"><p>Using the <span class="monospaced">Iter</span> combinators one can easily produce more complicated\r | |
266 | iterators. For example, here is an iterator over a "triangle":</p></div>\r | |
267 | <div class="listingblock">\r | |
268 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">triangle</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">u</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="n">>>=</span><span class="w"> </span><span class="p">(</span><span class="k">fn</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">i</span><span class="w"> </span><span class="n">to</span><span class="w"> </span><span class="n">u</span><span class="w"> </span><span class="n">>>=</span><span class="w"> </span><span class="p">(</span><span class="k">fn</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">)))</span><span class="w"></span>\r | |
269 | </pre></div></div></div>\r | |
270 | </div>\r | |
271 | </div>\r | |
272 | </div>\r | |
273 | <div id="footnotes"><hr></div>\r | |
274 | <div id="footer">\r | |
275 | <div id="footer-text">\r | |
276 | </div>\r | |
277 | <div id="footer-badges">\r | |
278 | </div>\r | |
279 | </div>\r | |
280 | </body>\r | |
281 | </html>\r |