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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>InfixingOperators</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>Fixity specifications are not part of signatures in\r | |
32 | <a href="StandardML">Standard ML</a>. When one wants to use a module that\r | |
33 | provides functions designed to be used as infix operators there are\r | |
34 | several obvious alternatives:</p></div>\r | |
35 | <div class="ulist"><ul>\r | |
36 | <li>\r | |
37 | <p>\r | |
38 | Use only prefix applications. Unfortunately there are situations\r | |
39 | where infix applications lead to considerably more readable code.\r | |
40 | </p>\r | |
41 | </li>\r | |
42 | <li>\r | |
43 | <p>\r | |
44 | Make the fixity declarations at the top-level. This may lead to\r | |
45 | collisions and may be unsustainable in a large project. Pollution of\r | |
46 | the top-level should be avoided.\r | |
47 | </p>\r | |
48 | </li>\r | |
49 | <li>\r | |
50 | <p>\r | |
51 | Make the fixity declarations at each scope where you want to use\r | |
52 | infix applications. The duplication becomes inconvenient if the\r | |
53 | operators are widely used. Duplication of code should be avoided.\r | |
54 | </p>\r | |
55 | </li>\r | |
56 | <li>\r | |
57 | <p>\r | |
58 | Use non-standard extensions, such as the <a href="MLBasis"> ML Basis system</a>\r | |
59 | to control the scope of fixity declarations. This has the obvious\r | |
60 | drawback of reduced portability.\r | |
61 | </p>\r | |
62 | </li>\r | |
63 | <li>\r | |
64 | <p>\r | |
65 | Reuse existing infix operator symbols (<span class="monospaced">^</span>, <span class="monospaced">+</span>, <span class="monospaced">-</span>, …). This\r | |
66 | can be convenient when the standard operators aren’t needed in the\r | |
67 | same scope with the new operators. On the other hand, one is limited\r | |
68 | to the standard operator symbols and the code may appear confusing.\r | |
69 | </p>\r | |
70 | </li>\r | |
71 | </ul></div>\r | |
72 | <div class="paragraph"><p>None of the obvious alternatives is best in every case. The following\r | |
73 | describes a slightly less obvious alternative that can sometimes be\r | |
74 | useful. The idea is to approximate Haskell’s special syntax for\r | |
75 | treating any identifier enclosed in grave accents (backquotes) as an\r | |
76 | infix operator. In Haskell, instead of writing the prefix application\r | |
77 | <span class="monospaced">f x y</span> one can write the infix application <span class="monospaced">x `f` y</span>.</p></div>\r | |
78 | </div>\r | |
79 | </div>\r | |
80 | <div class="sect1">\r | |
81 | <h2 id="_infixing_operators">Infixing operators</h2>\r | |
82 | <div class="sectionbody">\r | |
83 | <div class="paragraph"><p>Let’s first take a look at the definitions of the operators:</p></div>\r | |
84 | <div class="listingblock">\r | |
85 | <div class="content"><div class="highlight"><pre><span class="k">infix</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="n"><\</span><span class="w"> </span><span class="k">fun</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">f</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">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="p">(</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="cm">(* Left section *)</span><span class="w"></span>\r | |
86 | <span class="k">infix</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="n">\></span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">\></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="cm">(* Left application *)</span><span class="w"></span>\r | |
87 | <span class="k">infixr</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="n">/></span><span class="w"> </span><span class="k">fun</span><span class="w"> </span><span class="n">f</span><span class="w"> </span><span class="n">/></span><span class="w"> </span><span class="n">y</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">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">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="cm">(* Right section *)</span><span class="w"></span>\r | |
88 | <span class="k">infixr</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="n"></</span><span class="w"> </span><span class="k">fun</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">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><span class="cm">(* Right application *)</span><span class="w"></span>\r | |
89 | \r | |
90 | <span class="k">infix</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="n">o</span><span class="w"> </span><span class="cm">(* See motivation below *)</span><span class="w"></span>\r | |
91 | <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>\r | |
92 | </pre></div></div></div>\r | |
93 | <div class="paragraph"><p>The left and right sectioning operators, <span class="monospaced"><\</span> and <span class="monospaced">/></span>, are useful in\r | |
94 | SML for partial application of infix operators.\r | |
95 | <a href="References#Paulson96"> ML For the Working Programmer</a> describes curried\r | |
96 | functions <span class="monospaced">secl</span> and <span class="monospaced">secr</span> for the same purpose on pages 179-181.\r | |
97 | For example,</p></div>\r | |
98 | <div class="listingblock">\r | |
99 | <div class="content"><div class="highlight"><pre><span class="n">List</span><span class="p">.</span><span class="n">map</span><span class="w"> </span><span class="p">(</span><span class="k">op</span><span class="n">-</span><span class="w"> </span><span class="n">/></span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"></span>\r | |
100 | </pre></div></div></div>\r | |
101 | <div class="paragraph"><p>is a function for subtracting <span class="monospaced">y</span> from a list of integers and</p></div>\r | |
102 | <div class="listingblock">\r | |
103 | <div class="content"><div class="highlight"><pre><span class="n">List</span><span class="p">.</span><span class="n">exists</span><span class="w"> </span><span class="p">(</span><span class="n">x</span><span class="w"> </span><span class="n"><\</span><span class="w"> </span><span class="k">op</span><span class="p">=)</span><span class="w"></span>\r | |
104 | </pre></div></div></div>\r | |
105 | <div class="paragraph"><p>is a function for testing whether a list contains an <span class="monospaced">x</span>.</p></div>\r | |
106 | <div class="paragraph"><p>Together with the left and right application operators, <span class="monospaced">\></span> and <span class="monospaced"></</span>,\r | |
107 | the sectioning operators provide a way to treat any binary function\r | |
108 | (i.e. a function whose domain is a pair) as an infix operator. In\r | |
109 | general,</p></div>\r | |
110 | <div class="listingblock">\r | |
111 | <div class="content monospaced">\r | |
112 | <pre>x0 <\f1\> x1 <\f2\> x2 ... <\fN\> xN = fN (... f2 (f1 (x0, x1), x2) ..., xN)</pre>\r | |
113 | </div></div>\r | |
114 | <div class="paragraph"><p>and</p></div>\r | |
115 | <div class="listingblock">\r | |
116 | <div class="content monospaced">\r | |
117 | <pre>xN </fN/> ... x2 </f2/> x1 </f1/> x0 = fN (xN, ... f2 (x2, f1 (x1, x0)) ...)</pre>\r | |
118 | </div></div>\r | |
119 | <div class="sect2">\r | |
120 | <h3 id="_examples">Examples</h3>\r | |
121 | <div class="paragraph"><p>As a fairly realistic example, consider providing a function for sequencing\r | |
122 | comparisons:</p></div>\r | |
123 | <div class="listingblock">\r | |
124 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">Order</span><span class="w"> </span><span class="cm">(* ... *)</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
125 | <span class="w"> </span><span class="k">struct</span><span class="w"></span>\r | |
126 | <span class="w"> </span><span class="cm">(* ... *)</span><span class="w"></span>\r | |
127 | <span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="n">orWhenEq</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="n">EQUAL</span><span class="p">,</span><span class="w"> </span><span class="n">th</span><span class="p">)</span><span class="w"> </span><span class="p">=></span><span class="w"> </span><span class="n">th</span><span class="w"> </span><span class="p">()</span><span class="w"></span>\r | |
128 | <span class="w"> </span><span class="p">|</span><span class="w"> </span><span class="p">(</span><span class="n">other</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">other</span><span class="w"></span>\r | |
129 | <span class="w"> </span><span class="cm">(* ... *)</span><span class="w"></span>\r | |
130 | <span class="w"> </span><span class="k">end</span><span class="w"></span>\r | |
131 | </pre></div></div></div>\r | |
132 | <div class="paragraph"><p>Using <span class="monospaced">orWhenEq</span> and the infixing operators, one can write a\r | |
133 | <span class="monospaced">compare</span> function for triples as</p></div>\r | |
134 | <div class="listingblock">\r | |
135 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">compare</span><span class="w"> </span><span class="p">(</span><span class="n">fad</span><span class="p">,</span><span class="w"> </span><span class="n">fbe</span><span class="p">,</span><span class="w"> </span><span class="n">fcf</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">c</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="n">d</span><span class="p">,</span><span class="w"> </span><span class="n">e</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="w"></span>\r | |
136 | <span class="w"> </span><span class="n">fad</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">d</span><span class="p">)</span><span class="w"> </span><span class="n"><\Order</span><span class="p">.</span><span class="n">orWhenEq\></span><span class="w"> </span><span class="n">`fbe</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="p">)</span><span class="w"> </span><span class="n"><\Order</span><span class="p">.</span><span class="n">orWhenEq\></span><span class="w"> </span><span class="n">`fcf</span><span class="w"> </span><span class="p">(</span><span class="n">c</span><span class="p">,</span><span class="w"> </span><span class="n">f</span><span class="p">)</span><span class="w"></span>\r | |
137 | </pre></div></div></div>\r | |
138 | <div class="paragraph"><p>where <span class="monospaced">`</span> is defined as</p></div>\r | |
139 | <div class="listingblock">\r | |
140 | <div class="content"><div class="highlight"><pre><span class="k">fun</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="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">f</span><span class="w"> </span><span class="n">x</span><span class="w"></span>\r | |
141 | </pre></div></div></div>\r | |
142 | <div class="paragraph"><p>Although <span class="monospaced">orWhenEq</span> can be convenient (try rewriting the above without\r | |
143 | it), it is probably not useful enough to be defined at the top level\r | |
144 | as an infix operator. Fortunately we can use the infixing operators\r | |
145 | and don’t have to.</p></div>\r | |
146 | <div class="paragraph"><p>Another fairly realistic example would be to use the infixing operators with\r | |
147 | the technique described on the <a href="Printf">Printf</a> page. Assuming that you would have\r | |
148 | a <span class="monospaced">Printf</span> module binding <span class="monospaced">printf</span>, <span class="monospaced">`</span>, and formatting combinators\r | |
149 | named <span class="monospaced">int</span> and <span class="monospaced">string</span>, you could write</p></div>\r | |
150 | <div class="listingblock">\r | |
151 | <div class="content"><div class="highlight"><pre><span class="k">let</span><span class="w"> </span><span class="k">open</span><span class="w"> </span><span class="n">Printf</span><span class="w"> </span><span class="k">in</span><span class="w"></span>\r | |
152 | <span class="w"> </span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">`</span><span class="s">"Here's an int "</span><span class="n"><\int\></span><span class="s">" and a string "</span><span class="n"><\string\></span><span class="s">"."</span><span class="p">)</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="s">"foo"</span><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>without having to duplicate the fixity declarations. Alternatively, you could\r | |
155 | write</p></div>\r | |
156 | <div class="listingblock">\r | |
157 | <div class="content"><div class="highlight"><pre><span class="n">P</span><span class="p">.</span><span class="n">printf</span><span class="w"> </span><span class="p">(</span><span class="n">P</span><span class="p">.</span><span class="n">`</span><span class="s">"Here's an int "</span><span class="n"><\P</span><span class="p">.</span><span class="n">int\></span><span class="s">" and a string "</span><span class="n"><\P</span><span class="p">.</span><span class="n">string\></span><span class="s">"."</span><span class="p">)</span><span class="w"> </span><span class="mi">13</span><span class="w"> </span><span class="s">"foo"</span><span class="w"></span>\r | |
158 | </pre></div></div></div>\r | |
159 | <div class="paragraph"><p>assuming you have the made the binding</p></div>\r | |
160 | <div class="listingblock">\r | |
161 | <div class="content"><div class="highlight"><pre><span class="k">structure</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Printf</span><span class="w"></span>\r | |
162 | </pre></div></div></div>\r | |
163 | </div>\r | |
164 | </div>\r | |
165 | </div>\r | |
166 | <div class="sect1">\r | |
167 | <h2 id="_application_and_piping_operators">Application and piping operators</h2>\r | |
168 | <div class="sectionbody">\r | |
169 | <div class="paragraph"><p>The left and right application operators may also provide some notational\r | |
170 | convenience on their own. In general,</p></div>\r | |
171 | <div class="listingblock">\r | |
172 | <div class="content monospaced">\r | |
173 | <pre>f \> x1 \> ... \> xN = f x1 ... xN</pre>\r | |
174 | </div></div>\r | |
175 | <div class="paragraph"><p>and</p></div>\r | |
176 | <div class="listingblock">\r | |
177 | <div class="content monospaced">\r | |
178 | <pre>xN </ ... </ x1 </ f = f x1 ... xN</pre>\r | |
179 | </div></div>\r | |
180 | <div class="paragraph"><p>If nothing else, both of them can eliminate parentheses. For example,</p></div>\r | |
181 | <div class="listingblock">\r | |
182 | <div class="content"><div class="highlight"><pre><span class="n">foo</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">foo</span><span class="w"> </span><span class="n">\></span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">+</span><span class="w"> </span><span class="mi">2</span><span class="w"></span>\r | |
183 | </pre></div></div></div>\r | |
184 | <div class="paragraph"><p>The left and right application operators are related to operators\r | |
185 | that could be described as the right and left piping operators:</p></div>\r | |
186 | <div class="listingblock">\r | |
187 | <div class="content"><div class="highlight"><pre><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="k">val</span><span class="w"> </span><span class="k">op</span><span class="n">>|</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">op</span><span class="n"></</span><span class="w"> </span><span class="cm">(* Left pipe *)</span><span class="w"></span>\r | |
188 | <span class="k">infixr</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="n">|<</span><span class="w"> </span><span class="k">val</span><span class="w"> </span><span class="k">op</span><span class="n">|<</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="k">op</span><span class="n">\></span><span class="w"> </span><span class="cm">(* Right pipe *)</span><span class="w"></span>\r | |
189 | </pre></div></div></div>\r | |
190 | <div class="paragraph"><p>As you can see, the left and right piping operators, <span class="monospaced">>|</span> and <span class="monospaced">|<</span>,\r | |
191 | are the same as the right and left application operators,\r | |
192 | respectively, except the associativities are reversed and the binding\r | |
193 | strength is lower. They are useful for piping data through a sequence\r | |
194 | of operations. In general,</p></div>\r | |
195 | <div class="listingblock">\r | |
196 | <div class="content monospaced">\r | |
197 | <pre>x >| f1 >| ... >| fN = fN (... (f1 x) ...) = (fN o ... o f1) x</pre>\r | |
198 | </div></div>\r | |
199 | <div class="paragraph"><p>and</p></div>\r | |
200 | <div class="listingblock">\r | |
201 | <div class="content monospaced">\r | |
202 | <pre>fN |< ... |< f1 |< x = fN (... (f1 x) ...) = (fN o ... o f1) x</pre>\r | |
203 | </div></div>\r | |
204 | <div class="paragraph"><p>The right piping operator, <span class="monospaced">|<</span>, is provided by the Haskell prelude as\r | |
205 | <span class="monospaced">$</span>. It can be convenient in CPS or continuation passing style.</p></div>\r | |
206 | <div class="paragraph"><p>A use for the left piping operator is with parsing combinators. In a\r | |
207 | strict language, like SML, eta-reduction is generally unsafe. Using\r | |
208 | the left piping operator, parsing functions can be formatted\r | |
209 | conveniently as</p></div>\r | |
210 | <div class="listingblock">\r | |
211 | <div class="content"><div class="highlight"><pre><span class="k">fun</span><span class="w"> </span><span class="n">parsingFunc</span><span class="w"> </span><span class="n">input</span><span class="w"> </span><span class="p">=</span><span class="w"></span>\r | |
212 | <span class="w"> </span><span class="n">input</span><span class="w"> </span><span class="n">>|</span><span class="w"> </span><span class="cm">(* ... *)</span><span class="w"></span>\r | |
213 | <span class="w"> </span><span class="n">||</span><span class="w"> </span><span class="cm">(* ... *)</span><span class="w"></span>\r | |
214 | <span class="w"> </span><span class="n">||</span><span class="w"> </span><span class="cm">(* ... *)</span><span class="w"></span>\r | |
215 | </pre></div></div></div>\r | |
216 | <div class="paragraph"><p>where <span class="monospaced">||</span> is supposed to be a combinator provided by the parsing combinator\r | |
217 | library.</p></div>\r | |
218 | </div>\r | |
219 | </div>\r | |
220 | <div class="sect1">\r | |
221 | <h2 id="_about_precedences">About precedences</h2>\r | |
222 | <div class="sectionbody">\r | |
223 | <div class="paragraph"><p>You probably noticed that we redefined the\r | |
224 | <a href="OperatorPrecedence">precedences</a> of the function composition operator\r | |
225 | <span class="monospaced">o</span> and the assignment operator <span class="monospaced">:=</span>. Doing so is not strictly\r | |
226 | necessary, but can be convenient and should be relatively\r | |
227 | safe. Consider the following motivating examples from\r | |
228 | <a href="WesleyTerpstra"> Wesley W. Terpstra</a> relying on the redefined\r | |
229 | precedences:</p></div>\r | |
230 | <div class="listingblock">\r | |
231 | <div class="content"><div class="highlight"><pre><span class="n">Word8</span><span class="p">.</span><span class="n">fromInt</span><span class="w"> </span><span class="n">o</span><span class="w"> </span><span class="n">Char</span><span class="p">.</span><span class="n">ord</span><span class="w"> </span><span class="n">o</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="n"><\String</span><span class="p">.</span><span class="n">sub</span><span class="w"></span>\r | |
232 | <span class="cm">(* Combining sectioning and composition *)</span><span class="w"></span>\r | |
233 | \r | |
234 | <span class="n">x</span><span class="w"> </span><span class="n">:=</span><span class="w"> </span><span class="n">s</span><span class="w"> </span><span class="n"><\String</span><span class="p">.</span><span class="n">sub\></span><span class="w"> </span><span class="n">i</span><span class="w"></span>\r | |
235 | <span class="cm">(* Assigning the result of an infixed application *)</span><span class="w"></span>\r | |
236 | </pre></div></div></div>\r | |
237 | <div class="paragraph"><p>In imperative languages, assignment usually has the lowest precedence\r | |
238 | (ignoring statement separators). The precedence of <span class="monospaced">:=</span> in the\r | |
239 | <a href="BasisLibrary"> Basis Library</a> is perhaps unnecessarily high, because\r | |
240 | an expression of the form <span class="monospaced">r := x</span> always returns a unit, which makes\r | |
241 | little sense to combine with anything. Dropping <span class="monospaced">:=</span> to the lowest\r | |
242 | precedence level makes it behave more like in other imperative\r | |
243 | languages.</p></div>\r | |
244 | <div class="paragraph"><p>The case for <span class="monospaced">o</span> is different. With the exception of <span class="monospaced">before</span> and\r | |
245 | <span class="monospaced">:=</span>, it doesn’t seem to make much sense to use <span class="monospaced">o</span> with any of the\r | |
246 | operators defined by the <a href="BasisLibrary"> Basis Library</a> in an\r | |
247 | unparenthesized expression. This is simply because none of the other\r | |
248 | operators deal with functions. It would seem that the precedence of\r | |
249 | <span class="monospaced">o</span> could be chosen completely arbitrarily from the set <span class="monospaced">{1, ..., 9}</span>\r | |
250 | without having any adverse effects with respect to other infix\r | |
251 | operators defined by the <a href="BasisLibrary"> Basis Library</a>.</p></div>\r | |
252 | </div>\r | |
253 | </div>\r | |
254 | <div class="sect1">\r | |
255 | <h2 id="_design_of_the_symbols">Design of the symbols</h2>\r | |
256 | <div class="sectionbody">\r | |
257 | <div class="paragraph"><p>The closest approximation of Haskell’s <span class="monospaced">x `f` y</span> syntax\r | |
258 | achievable in Standard ML would probably be something like\r | |
259 | <span class="monospaced">x `f^ y</span>, but <span class="monospaced">^</span> is already used for string\r | |
260 | concatenation by the <a href="BasisLibrary"> Basis Library</a>. Other\r | |
261 | combinations of the characters <span class="monospaced">`</span> and <span class="monospaced">^</span> would be\r | |
262 | possible, but none seems clearly the best visually. The symbols <span class="monospaced"><\</span>,\r | |
263 | <span class="monospaced">\></span>, <span class="monospaced"></</span>, and <span class="monospaced">/></span> are reasonably concise and have a certain\r | |
264 | self-documenting appearance and symmetry, which can help to remember\r | |
265 | them. As the names suggest, the symbols of the piping operators <span class="monospaced">>|</span>\r | |
266 | and <span class="monospaced">|<</span> are inspired by Unix shell pipelines.</p></div>\r | |
267 | </div>\r | |
268 | </div>\r | |
269 | <div class="sect1">\r | |
270 | <h2 id="_also_see">Also see</h2>\r | |
271 | <div class="sectionbody">\r | |
272 | <div class="ulist"><ul>\r | |
273 | <li>\r | |
274 | <p>\r | |
275 | <a href="Utilities">Utilities</a>\r | |
276 | </p>\r | |
277 | </li>\r | |
278 | </ul></div>\r | |
279 | </div>\r | |
280 | </div>\r | |
281 | </div>\r | |
282 | <div id="footnotes"><hr></div>\r | |
283 | <div id="footer">\r | |
284 | <div id="footer-text">\r | |
285 | </div>\r | |
286 | <div id="footer-badges">\r | |
287 | </div>\r | |
288 | </div>\r | |
289 | </body>\r | |
290 | </html>\r |