Clarify parsing infelicity.
[ghc.git] / docs / users_guide / glasgow_exts.xml
1 <?xml version="1.0" encoding="iso-8859-1"?>
2 <para>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They can all be enabled or disabled by command line flags
7 or language pragmas. By default GHC understands the most recent Haskell
8 version it supports, plus a handful of extensions.
9 </para>
10
11 <para>
12 Some of the Glasgow extensions serve to give you access to the
13 underlying facilities with which we implement Haskell. Thus, you can
14 get at the Raw Iron, if you are willing to write some non-portable
15 code at a more primitive level. You need not be &ldquo;stuck&rdquo;
16 on performance because of the implementation costs of Haskell's
17 &ldquo;high-level&rdquo; features&mdash;you can always code
18 &ldquo;under&rdquo; them. In an extreme case, you can write all your
19 time-critical code in C, and then just glue it together with Haskell!
20 </para>
21
22 <para>
23 Before you get too carried away working at the lowest level (e.g.,
24 sloshing <literal>MutableByteArray&num;</literal>s around your
25 program), you may wish to check if there are libraries that provide a
26 &ldquo;Haskellised veneer&rdquo; over the features you want. The
27 separate <ulink url="../libraries/index.html">libraries
28 documentation</ulink> describes all the libraries that come with GHC.
29 </para>
30
31 <!-- LANGUAGE OPTIONS -->
32 <sect1 id="options-language">
33 <title>Language options</title>
34
35 <indexterm><primary>language</primary><secondary>option</secondary>
36 </indexterm>
37 <indexterm><primary>options</primary><secondary>language</secondary>
38 </indexterm>
39 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
40 </indexterm>
41
42 <para>The language option flags control what variation of the language are
43 permitted.</para>
44
45 <para>Language options can be controlled in two ways:
46 <itemizedlist>
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
50 <listitem><para>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
53 </listitem>
54 </itemizedlist></para>
55
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 &what_glasgow_exts_does;
60 Enabling these options is the <emphasis>only</emphasis>
61 effect of <option>-fglasgow-exts</option>.
62 We are trying to move away from this portmanteau flag,
63 and towards enabling features individually.</para>
64
65 </sect1>
66
67 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
68 <sect1 id="primitives">
69 <title>Unboxed types and primitive operations</title>
70
71 <para>GHC is built on a raft of primitive data types and operations;
72 "primitive" in the sense that they cannot be defined in Haskell itself.
73 While you really can use this stuff to write fast code,
74 we generally find it a lot less painful, and more satisfying in the
75 long run, to use higher-level language features and libraries. With
76 any luck, the code you write will be optimised to the efficient
77 unboxed version in any case. And if it isn't, we'd like to know
78 about it.</para>
79
80 <para>All these primitive data types and operations are exported by the
81 library <literal>GHC.Prim</literal>, for which there is
82 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
83 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
84 </para>
85
86 <para>
87 If you want to mention any of the primitive data types or operations in your
88 program, you must first import <literal>GHC.Prim</literal> to bring them
89 into scope. Many of them have names ending in "&num;", and to mention such
90 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
91 </para>
92
93 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
94 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
95 we briefly summarise here. </para>
96
97 <sect2 id="glasgow-unboxed">
98 <title>Unboxed types</title>
99
100 <para>
101 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
102 </para>
103
104 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
105 that values of that type are represented by a pointer to a heap
106 object. The representation of a Haskell <literal>Int</literal>, for
107 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
108 type, however, is represented by the value itself, no pointers or heap
109 allocation are involved.
110 </para>
111
112 <para>
113 Unboxed types correspond to the &ldquo;raw machine&rdquo; types you
114 would use in C: <literal>Int&num;</literal> (long int),
115 <literal>Double&num;</literal> (double), <literal>Addr&num;</literal>
116 (void *), etc. The <emphasis>primitive operations</emphasis>
117 (PrimOps) on these types are what you might expect; e.g.,
118 <literal>(+&num;)</literal> is addition on
119 <literal>Int&num;</literal>s, and is the machine-addition that we all
120 know and love&mdash;usually one instruction.
121 </para>
122
123 <para>
124 Primitive (unboxed) types cannot be defined in Haskell, and are
125 therefore built into the language and compiler. Primitive types are
126 always unlifted; that is, a value of a primitive type cannot be
127 bottom. We use the convention (but it is only a convention)
128 that primitive types, values, and
129 operations have a <literal>&num;</literal> suffix (see <xref linkend="magic-hash"/>).
130 For some primitive types we have special syntax for literals, also
131 described in the <link linkend="magic-hash">same section</link>.
132 </para>
133
134 <para>
135 Primitive values are often represented by a simple bit-pattern, such
136 as <literal>Int&num;</literal>, <literal>Float&num;</literal>,
137 <literal>Double&num;</literal>. But this is not necessarily the case:
138 a primitive value might be represented by a pointer to a
139 heap-allocated object. Examples include
140 <literal>Array&num;</literal>, the type of primitive arrays. A
141 primitive array is heap-allocated because it is too big a value to fit
142 in a register, and would be too expensive to copy around; in a sense,
143 it is accidental that it is represented by a pointer. If a pointer
144 represents a primitive value, then it really does point to that value:
145 no unevaluated thunks, no indirections&hellip;nothing can be at the
146 other end of the pointer than the primitive value.
147 A numerically-intensive program using unboxed types can
148 go a <emphasis>lot</emphasis> faster than its &ldquo;standard&rdquo;
149 counterpart&mdash;we saw a threefold speedup on one example.
150 </para>
151
152 <para>
153 There are some restrictions on the use of primitive types:
154 <itemizedlist>
155 <listitem><para>The main restriction
156 is that you can't pass a primitive value to a polymorphic
157 function or store one in a polymorphic data type. This rules out
158 things like <literal>[Int&num;]</literal> (i.e. lists of primitive
159 integers). The reason for this restriction is that polymorphic
160 arguments and constructor fields are assumed to be pointers: if an
161 unboxed integer is stored in one of these, the garbage collector would
162 attempt to follow it, leading to unpredictable space leaks. Or a
163 <function>seq</function> operation on the polymorphic component may
164 attempt to dereference the pointer, with disastrous results. Even
165 worse, the unboxed value might be larger than a pointer
166 (<literal>Double&num;</literal> for instance).
167 </para>
168 </listitem>
169 <listitem><para> You cannot define a newtype whose representation type
170 (the argument type of the data constructor) is an unboxed type. Thus,
171 this is illegal:
172 <programlisting>
173 newtype A = MkA Int#
174 </programlisting>
175 </para></listitem>
176 <listitem><para> You cannot bind a variable with an unboxed type
177 in a <emphasis>top-level</emphasis> binding.
178 </para></listitem>
179 <listitem><para> You cannot bind a variable with an unboxed type
180 in a <emphasis>recursive</emphasis> binding.
181 </para></listitem>
182 <listitem><para> You may bind unboxed variables in a (non-recursive,
183 non-top-level) pattern binding, but you must make any such pattern-match
184 strict. For example, rather than:
185 <programlisting>
186 data Foo = Foo Int Int#
187
188 f x = let (Foo a b, w) = ..rhs.. in ..body..
189 </programlisting>
190 you must write:
191 <programlisting>
192 data Foo = Foo Int Int#
193
194 f x = let !(Foo a b, w) = ..rhs.. in ..body..
195 </programlisting>
196 since <literal>b</literal> has type <literal>Int#</literal>.
197 </para>
198 </listitem>
199 </itemizedlist>
200 </para>
201
202 </sect2>
203
204 <sect2 id="unboxed-tuples">
205 <title>Unboxed tuples</title>
206
207 <para>
208 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>;
209 they are a syntactic extension enabled by the language flag <option>-XUnboxedTuples</option>. An
210 unboxed tuple looks like this:
211 </para>
212
213 <para>
214
215 <programlisting>
216 (# e_1, ..., e_n #)
217 </programlisting>
218
219 </para>
220
221 <para>
222 where <literal>e&lowbar;1..e&lowbar;n</literal> are expressions of any
223 type (primitive or non-primitive). The type of an unboxed tuple looks
224 the same.
225 </para>
226
227 <para>
228 Note that when unboxed tuples are enabled,
229 <literal>(#</literal> is a single lexeme, so for example when using
230 operators like <literal>#</literal> and <literal>#-</literal> you need
231 to write <literal>( # )</literal> and <literal>( #- )</literal> rather than
232 <literal>(#)</literal> and <literal>(#-)</literal>.
233 </para>
234
235 <para>
236 Unboxed tuples are used for functions that need to return multiple
237 values, but they avoid the heap allocation normally associated with
238 using fully-fledged tuples. When an unboxed tuple is returned, the
239 components are put directly into registers or on the stack; the
240 unboxed tuple itself does not have a composite representation. Many
241 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
242 tuples.
243 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
244 tuples to avoid unnecessary allocation during sequences of operations.
245 </para>
246
247 <para>
248 There are some restrictions on the use of unboxed tuples:
249 <itemizedlist>
250
251 <listitem>
252 <para>
253 Values of unboxed tuple types are subject to the same restrictions as
254 other unboxed types; i.e. they may not be stored in polymorphic data
255 structures or passed to polymorphic functions.
256 </para>
257 </listitem>
258
259 <listitem>
260 <para>
261 The typical use of unboxed tuples is simply to return multiple values,
262 binding those multiple results with a <literal>case</literal> expression, thus:
263 <programlisting>
264 f x y = (# x+1, y-1 #)
265 g x = case f x x of { (# a, b #) -&#62; a + b }
266 </programlisting>
267 You can have an unboxed tuple in a pattern binding, thus
268 <programlisting>
269 f x = let (# p,q #) = h x in ..body..
270 </programlisting>
271 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
272 the resulting binding is lazy like any other Haskell pattern binding. The
273 above example desugars like this:
274 <programlisting>
275 f x = let t = case h x of { (# p,q #) -> (p,q) }
276 p = fst t
277 q = snd t
278 in ..body..
279 </programlisting>
280 Indeed, the bindings can even be recursive.
281 </para>
282 </listitem>
283 </itemizedlist>
284
285 </para>
286
287 </sect2>
288 </sect1>
289
290
291 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
292
293 <sect1 id="syntax-extns">
294 <title>Syntactic extensions</title>
295
296 <sect2 id="unicode-syntax">
297 <title>Unicode syntax</title>
298 <para>The language
299 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
300 enables Unicode characters to be used to stand for certain ASCII
301 character sequences. The following alternatives are provided:</para>
302
303 <informaltable>
304 <tgroup cols="2" align="left" colsep="1" rowsep="1">
305 <thead>
306 <row>
307 <entry>ASCII</entry>
308 <entry>Unicode alternative</entry>
309 <entry>Code point</entry>
310 <entry>Name</entry>
311 </row>
312 </thead>
313
314 <!--
315 to find the DocBook entities for these characters, find
316 the Unicode code point (e.g. 0x2237), and grep for it in
317 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
318 your system. Some of these Unicode code points don't have
319 equivalent DocBook entities.
320 -->
321
322 <tbody>
323 <row>
324 <entry><literal>::</literal></entry>
325 <entry>&#x2237;</entry>
326 <entry>0x2237</entry>
327 <entry>PROPORTION</entry>
328 </row>
329 </tbody>
330 <tbody>
331 <row>
332 <entry><literal>=&gt;</literal></entry>
333 <entry>&rArr;</entry>
334 <entry>0x21D2</entry>
335 <entry>RIGHTWARDS DOUBLE ARROW</entry>
336 </row>
337 </tbody>
338 <tbody>
339 <row>
340 <entry><literal>forall</literal></entry>
341 <entry>&forall;</entry>
342 <entry>0x2200</entry>
343 <entry>FOR ALL</entry>
344 </row>
345 </tbody>
346 <tbody>
347 <row>
348 <entry><literal>-&gt;</literal></entry>
349 <entry>&rarr;</entry>
350 <entry>0x2192</entry>
351 <entry>RIGHTWARDS ARROW</entry>
352 </row>
353 </tbody>
354 <tbody>
355 <row>
356 <entry><literal>&lt;-</literal></entry>
357 <entry>&larr;</entry>
358 <entry>0x2190</entry>
359 <entry>LEFTWARDS ARROW</entry>
360 </row>
361 </tbody>
362
363 <tbody>
364 <row>
365 <entry>-&lt;</entry>
366 <entry>&#x2919;</entry>
367 <entry>0x2919</entry>
368 <entry>LEFTWARDS ARROW-TAIL</entry>
369 </row>
370 </tbody>
371
372 <tbody>
373 <row>
374 <entry>&gt;-</entry>
375 <entry>&#x291A;</entry>
376 <entry>0x291A</entry>
377 <entry>RIGHTWARDS ARROW-TAIL</entry>
378 </row>
379 </tbody>
380
381 <tbody>
382 <row>
383 <entry>-&lt;&lt;</entry>
384 <entry>&#x291B;</entry>
385 <entry>0x291B</entry>
386 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
387 </row>
388 </tbody>
389
390 <tbody>
391 <row>
392 <entry>&gt;&gt;-</entry>
393 <entry>&#x291C;</entry>
394 <entry>0x291C</entry>
395 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
396 </row>
397 </tbody>
398
399 <tbody>
400 <row>
401 <entry>*</entry>
402 <entry>&starf;</entry>
403 <entry>0x2605</entry>
404 <entry>BLACK STAR</entry>
405 </row>
406 </tbody>
407
408 </tgroup>
409 </informaltable>
410 </sect2>
411
412 <sect2 id="magic-hash">
413 <title>The magic hash</title>
414 <para>The language extension <option>-XMagicHash</option> allows "&num;" as a
415 postfix modifier to identifiers. Thus, "x&num;" is a valid variable, and "T&num;" is
416 a valid type constructor or data constructor.</para>
417
418 <para>The hash sign does not change semantics at all. We tend to use variable
419 names ending in "&num;" for unboxed values or types (e.g. <literal>Int&num;</literal>),
420 but there is no requirement to do so; they are just plain ordinary variables.
421 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
422 For example, to bring <literal>Int&num;</literal> into scope you must
423 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
424 the <option>-XMagicHash</option> extension
425 then allows you to <emphasis>refer</emphasis> to the <literal>Int&num;</literal>
426 that is now in scope. Note that with this option, the meaning of <literal>x&num;y = 0</literal>
427 is changed: it defines a function <literal>x&num;</literal> taking a single argument <literal>y</literal>;
428 to define the operator <literal>&num;</literal>, put a space: <literal>x &num; y = 0</literal>.
429
430 </para>
431 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
432 <itemizedlist>
433 <listitem><para> <literal>'x'&num;</literal> has type <literal>Char&num;</literal></para> </listitem>
434 <listitem><para> <literal>&quot;foo&quot;&num;</literal> has type <literal>Addr&num;</literal></para> </listitem>
435 <listitem><para> <literal>3&num;</literal> has type <literal>Int&num;</literal>. In general,
436 any Haskell integer lexeme followed by a <literal>&num;</literal> is an <literal>Int&num;</literal> literal, e.g.
437 <literal>-0x3A&num;</literal> as well as <literal>32&num;</literal>.</para></listitem>
438 <listitem><para> <literal>3&num;&num;</literal> has type <literal>Word&num;</literal>. In general,
439 any non-negative Haskell integer lexeme followed by <literal>&num;&num;</literal>
440 is a <literal>Word&num;</literal>. </para> </listitem>
441 <listitem><para> <literal>3.2&num;</literal> has type <literal>Float&num;</literal>.</para> </listitem>
442 <listitem><para> <literal>3.2&num;&num;</literal> has type <literal>Double&num;</literal></para> </listitem>
443 </itemizedlist>
444 </para>
445 </sect2>
446
447 <sect2 id="negative-literals">
448 <title>Negative literals</title>
449 <para>
450 The literal <literal>-123</literal> is, according to
451 Haskell98 and Haskell 2010, desugared as
452 <literal>negate (fromInteger 123)</literal>.
453 The language extension <option>-XNegativeLiterals</option>
454 means that it is instead desugared as
455 <literal>fromInteger (-123)</literal>.
456 </para>
457
458 <para>
459 This can make a difference when the positive and negative range of
460 a numeric data type don't match up. For example,
461 in 8-bit arithmetic -128 is representable, but +128 is not.
462 So <literal>negate (fromInteger 128)</literal> will elicit an
463 unexpected integer-literal-overflow message.
464 </para>
465 </sect2>
466
467 <sect2 id="num-decimals">
468 <title>Fractional looking integer literals</title>
469 <para>
470 Haskell 2010 and Haskell 98 define floating literals with
471 the syntax <literal>1.2e6</literal>. These literals have the
472 type <literal>Fractional a => a</literal>.
473 </para>
474
475 <para>
476 The language extension <option>-XNumDecimals</option> allows
477 you to also use the floating literal syntax for instances of
478 <literal>Integral</literal>, and have values like
479 <literal>(1.2e6 :: Num a => a)</literal>
480 </para>
481 </sect2>
482
483 <sect2 id="binary-literals">
484 <title>Binary integer literals</title>
485 <para>
486 Haskell 2010 and Haskell 98 allows for integer literals to
487 be given in decimal, octal (prefixed by
488 <literal>0o</literal> or <literal>0O</literal>), or
489 hexadecimal notation (prefixed by <literal>0x</literal> or
490 <literal>0X</literal>).
491 </para>
492
493 <para>
494 The language extension <option>-XBinaryLiterals</option>
495 adds support for expressing integer literals in binary
496 notation with the prefix <literal>0b</literal> or
497 <literal>0B</literal>. For instance, the binary integer
498 literal <literal>0b11001001</literal> will be desugared into
499 <literal>fromInteger 201</literal> when
500 <option>-XBinaryLiterals</option> is enabled.
501 </para>
502 </sect2>
503
504 <!-- ====================== HIERARCHICAL MODULES ======================= -->
505
506
507 <sect2 id="hierarchical-modules">
508 <title>Hierarchical Modules</title>
509
510 <para>GHC supports a small extension to the syntax of module
511 names: a module name is allowed to contain a dot
512 <literal>&lsquo;.&rsquo;</literal>. This is also known as the
513 &ldquo;hierarchical module namespace&rdquo; extension, because
514 it extends the normally flat Haskell module namespace into a
515 more flexible hierarchy of modules.</para>
516
517 <para>This extension has very little impact on the language
518 itself; modules names are <emphasis>always</emphasis> fully
519 qualified, so you can just think of the fully qualified module
520 name as <quote>the module name</quote>. In particular, this
521 means that the full module name must be given after the
522 <literal>module</literal> keyword at the beginning of the
523 module; for example, the module <literal>A.B.C</literal> must
524 begin</para>
525
526 <programlisting>module A.B.C</programlisting>
527
528
529 <para>It is a common strategy to use the <literal>as</literal>
530 keyword to save some typing when using qualified names with
531 hierarchical modules. For example:</para>
532
533 <programlisting>
534 import qualified Control.Monad.ST.Strict as ST
535 </programlisting>
536
537 <para>For details on how GHC searches for source and interface
538 files in the presence of hierarchical modules, see <xref
539 linkend="search-path"/>.</para>
540
541 <para>GHC comes with a large collection of libraries arranged
542 hierarchically; see the accompanying <ulink
543 url="../libraries/index.html">library
544 documentation</ulink>. More libraries to install are available
545 from <ulink
546 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
547 </sect2>
548
549 <!-- ====================== PATTERN GUARDS ======================= -->
550
551 <sect2 id="pattern-guards">
552 <title>Pattern guards</title>
553
554 <para>
555 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
556 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
557 </para>
558
559 <para>
560 Suppose we have an abstract data type of finite maps, with a
561 lookup operation:
562
563 <programlisting>
564 lookup :: FiniteMap -> Int -> Maybe Int
565 </programlisting>
566
567 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
568 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
569 </para>
570
571 <programlisting>
572 clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
573 | otherwise = var1 + var2
574 where
575 m1 = lookup env var1
576 m2 = lookup env var2
577 ok1 = maybeToBool m1
578 ok2 = maybeToBool m2
579 val1 = expectJust m1
580 val2 = expectJust m2
581 </programlisting>
582
583 <para>
584 The auxiliary functions are
585 </para>
586
587 <programlisting>
588 maybeToBool :: Maybe a -&gt; Bool
589 maybeToBool (Just x) = True
590 maybeToBool Nothing = False
591
592 expectJust :: Maybe a -&gt; a
593 expectJust (Just x) = x
594 expectJust Nothing = error "Unexpected Nothing"
595 </programlisting>
596
597 <para>
598 What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
599 ok2</literal> checks that both lookups succeed, using
600 <function>maybeToBool</function> to convert the <function>Maybe</function>
601 types to booleans. The (lazily evaluated) <function>expectJust</function>
602 calls extract the values from the results of the lookups, and binds the
603 returned values to <varname>val1</varname> and <varname>val2</varname>
604 respectively. If either lookup fails, then clunky takes the
605 <literal>otherwise</literal> case and returns the sum of its arguments.
606 </para>
607
608 <para>
609 This is certainly legal Haskell, but it is a tremendously verbose and
610 un-obvious way to achieve the desired effect. Arguably, a more direct way
611 to write clunky would be to use case expressions:
612 </para>
613
614 <programlisting>
615 clunky env var1 var2 = case lookup env var1 of
616 Nothing -&gt; fail
617 Just val1 -&gt; case lookup env var2 of
618 Nothing -&gt; fail
619 Just val2 -&gt; val1 + val2
620 where
621 fail = var1 + var2
622 </programlisting>
623
624 <para>
625 This is a bit shorter, but hardly better. Of course, we can rewrite any set
626 of pattern-matching, guarded equations as case expressions; that is
627 precisely what the compiler does when compiling equations! The reason that
628 Haskell provides guarded equations is because they allow us to write down
629 the cases we want to consider, one at a time, independently of each other.
630 This structure is hidden in the case version. Two of the right-hand sides
631 are really the same (<function>fail</function>), and the whole expression
632 tends to become more and more indented.
633 </para>
634
635 <para>
636 Here is how I would write clunky:
637 </para>
638
639 <programlisting>
640 clunky env var1 var2
641 | Just val1 &lt;- lookup env var1
642 , Just val2 &lt;- lookup env var2
643 = val1 + val2
644 ...other equations for clunky...
645 </programlisting>
646
647 <para>
648 The semantics should be clear enough. The qualifiers are matched in order.
649 For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
650 right hand side is evaluated and matched against the pattern on the left.
651 If the match fails then the whole guard fails and the next equation is
652 tried. If it succeeds, then the appropriate binding takes place, and the
653 next qualifier is matched, in the augmented environment. Unlike list
654 comprehensions, however, the type of the expression to the right of the
655 <literal>&lt;-</literal> is the same as the type of the pattern to its
656 left. The bindings introduced by pattern guards scope over all the
657 remaining guard qualifiers, and over the right hand side of the equation.
658 </para>
659
660 <para>
661 Just as with list comprehensions, boolean expressions can be freely mixed
662 with among the pattern guards. For example:
663 </para>
664
665 <programlisting>
666 f x | [y] &lt;- x
667 , y > 3
668 , Just z &lt;- h y
669 = ...
670 </programlisting>
671
672 <para>
673 Haskell's current guards therefore emerge as a special case, in which the
674 qualifier list has just one element, a boolean expression.
675 </para>
676 </sect2>
677
678 <!-- ===================== View patterns =================== -->
679
680 <sect2 id="view-patterns">
681 <title>View patterns
682 </title>
683
684 <para>
685 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
686 More information and examples of view patterns can be found on the
687 <ulink url="http://ghc.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
688 page</ulink>.
689 </para>
690
691 <para>
692 View patterns are somewhat like pattern guards that can be nested inside
693 of other patterns. They are a convenient way of pattern-matching
694 against values of abstract types. For example, in a programming language
695 implementation, we might represent the syntax of the types of the
696 language as follows:
697
698 <programlisting>
699 type Typ
700
701 data TypView = Unit
702 | Arrow Typ Typ
703
704 view :: Typ -> TypView
705
706 -- additional operations for constructing Typ's ...
707 </programlisting>
708
709 The representation of Typ is held abstract, permitting implementations
710 to use a fancy representation (e.g., hash-consing to manage sharing).
711
712 Without view patterns, using this signature a little inconvenient:
713 <programlisting>
714 size :: Typ -> Integer
715 size t = case view t of
716 Unit -> 1
717 Arrow t1 t2 -> size t1 + size t2
718 </programlisting>
719
720 It is necessary to iterate the case, rather than using an equational
721 function definition. And the situation is even worse when the matching
722 against <literal>t</literal> is buried deep inside another pattern.
723 </para>
724
725 <para>
726 View patterns permit calling the view function inside the pattern and
727 matching against the result:
728 <programlisting>
729 size (view -> Unit) = 1
730 size (view -> Arrow t1 t2) = size t1 + size t2
731 </programlisting>
732
733 That is, we add a new form of pattern, written
734 <replaceable>expression</replaceable> <literal>-></literal>
735 <replaceable>pattern</replaceable> that means "apply the expression to
736 whatever we're trying to match against, and then match the result of
737 that application against the pattern". The expression can be any Haskell
738 expression of function type, and view patterns can be used wherever
739 patterns are used.
740 </para>
741
742 <para>
743 The semantics of a pattern <literal>(</literal>
744 <replaceable>exp</replaceable> <literal>-></literal>
745 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
746
747 <itemizedlist>
748
749 <listitem> Scoping:
750
751 <para>The variables bound by the view pattern are the variables bound by
752 <replaceable>pat</replaceable>.
753 </para>
754
755 <para>
756 Any variables in <replaceable>exp</replaceable> are bound occurrences,
757 but variables bound "to the left" in a pattern are in scope. This
758 feature permits, for example, one argument to a function to be used in
759 the view of another argument. For example, the function
760 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
761 written using view patterns as follows:
762
763 <programlisting>
764 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
765 ...other equations for clunky...
766 </programlisting>
767 </para>
768
769 <para>
770 More precisely, the scoping rules are:
771 <itemizedlist>
772 <listitem>
773 <para>
774 In a single pattern, variables bound by patterns to the left of a view
775 pattern expression are in scope. For example:
776 <programlisting>
777 example :: Maybe ((String -> Integer,Integer), String) -> Bool
778 example Just ((f,_), f -> 4) = True
779 </programlisting>
780
781 Additionally, in function definitions, variables bound by matching earlier curried
782 arguments may be used in view pattern expressions in later arguments:
783 <programlisting>
784 example :: (String -> Integer) -> String -> Bool
785 example f (f -> 4) = True
786 </programlisting>
787 That is, the scoping is the same as it would be if the curried arguments
788 were collected into a tuple.
789 </para>
790 </listitem>
791
792 <listitem>
793 <para>
794 In mutually recursive bindings, such as <literal>let</literal>,
795 <literal>where</literal>, or the top level, view patterns in one
796 declaration may not mention variables bound by other declarations. That
797 is, each declaration must be self-contained. For example, the following
798 program is not allowed:
799 <programlisting>
800 let {(x -> y) = e1 ;
801 (y -> x) = e2 } in x
802 </programlisting>
803
804 (For some amplification on this design choice see
805 <ulink url="http://ghc.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
806
807 </para>
808 </listitem>
809 </itemizedlist>
810
811 </para>
812 </listitem>
813
814 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
815 <replaceable>T1</replaceable> <literal>-></literal>
816 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
817 a <replaceable>T2</replaceable>, then the whole view pattern matches a
818 <replaceable>T1</replaceable>.
819 </para></listitem>
820
821 <listitem><para> Matching: To the equations in Section 3.17.3 of the
822 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
823 Report</ulink>, add the following:
824 <programlisting>
825 case v of { (e -> p) -> e1 ; _ -> e2 }
826 =
827 case (e v) of { p -> e1 ; _ -> e2 }
828 </programlisting>
829 That is, to match a variable <replaceable>v</replaceable> against a pattern
830 <literal>(</literal> <replaceable>exp</replaceable>
831 <literal>-></literal> <replaceable>pat</replaceable>
832 <literal>)</literal>, evaluate <literal>(</literal>
833 <replaceable>exp</replaceable> <replaceable> v</replaceable>
834 <literal>)</literal> and match the result against
835 <replaceable>pat</replaceable>.
836 </para></listitem>
837
838 <listitem><para> Efficiency: When the same view function is applied in
839 multiple branches of a function definition or a case expression (e.g.,
840 in <literal>size</literal> above), GHC makes an attempt to collect these
841 applications into a single nested case expression, so that the view
842 function is only applied once. Pattern compilation in GHC follows the
843 matrix algorithm described in Chapter 4 of <ulink
844 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
845 Implementation of Functional Programming Languages</ulink>. When the
846 top rows of the first column of a matrix are all view patterns with the
847 "same" expression, these patterns are transformed into a single nested
848 case. This includes, for example, adjacent view patterns that line up
849 in a tuple, as in
850 <programlisting>
851 f ((view -> A, p1), p2) = e1
852 f ((view -> B, p3), p4) = e2
853 </programlisting>
854 </para>
855
856 <para> The current notion of when two view pattern expressions are "the
857 same" is very restricted: it is not even full syntactic equality.
858 However, it does include variables, literals, applications, and tuples;
859 e.g., two instances of <literal>view ("hi", "there")</literal> will be
860 collected. However, the current implementation does not compare up to
861 alpha-equivalence, so two instances of <literal>(x, view x ->
862 y)</literal> will not be coalesced.
863 </para>
864
865 </listitem>
866
867 </itemizedlist>
868 </para>
869
870 </sect2>
871
872 <!-- ===================== Pattern synonyms =================== -->
873
874 <sect2 id="pattern-synonyms">
875 <title>Pattern synonyms
876 </title>
877
878 <para>
879 Pattern synonyms are enabled by the flag
880 <literal>-XPatternSynonyms</literal>, which is required for defining
881 them, but <emphasis>not</emphasis> for using them. More information
882 and examples of view patterns can be found on the <ulink
883 url="http://ghc.haskell.org/trac/ghc/wiki/PatternSynonyms">Wiki
884 page</ulink>.
885 </para>
886
887 <para>
888 Pattern synonyms enable giving names to parametrized pattern
889 schemes. They can also be thought of as abstract constructors that
890 don't have a bearing on data representation. For example, in a
891 programming language implementation, we might represent types of the
892 language as follows:
893 </para>
894
895 <programlisting>
896 data Type = App String [Type]
897 </programlisting>
898
899 <para>
900 Here are some examples of using said representation.
901 Consider a few types of the <literal>Type</literal> universe encoded
902 like this:
903 </para>
904
905 <programlisting>
906 App "->" [t1, t2] -- t1 -> t2
907 App "Int" [] -- Int
908 App "Maybe" [App "Int" []] -- Maybe Int
909 </programlisting>
910
911 <para>
912 This representation is very generic in that no types are given special
913 treatment. However, some functions might need to handle some known
914 types specially, for example the following two functions collect all
915 argument types of (nested) arrow types, and recognize the
916 <literal>Int</literal> type, respectively:
917 </para>
918
919 <programlisting>
920 collectArgs :: Type -> [Type]
921 collectArgs (App "->" [t1, t2]) = t1 : collectArgs t2
922 collectArgs _ = []
923
924 isInt :: Type -> Bool
925 isInt (App "Int" []) = True
926 isInt _ = False
927 </programlisting>
928
929 <para>
930 Matching on <literal>App</literal> directly is both hard to read and
931 error prone to write. And the situation is even worse when the
932 matching is nested:
933 </para>
934
935 <programlisting>
936 isIntEndo :: Type -> Bool
937 isIntEndo (App "->" [App "Int" [], App "Int" []]) = True
938 isIntEndo _ = False
939 </programlisting>
940
941 <para>
942 Pattern synonyms permit abstracting from the representation to expose
943 matchers that behave in a constructor-like manner with respect to
944 pattern matching. We can create pattern synonyms for the known types
945 we care about, without committing the representation to them (note
946 that these don't have to be defined in the same module as the
947 <literal>Type</literal> type):
948 </para>
949
950 <programlisting>
951 pattern Arrow t1 t2 = App "->" [t1, t2]
952 pattern Int = App "Int" []
953 pattern Maybe t = App "Maybe" [t]
954 </programlisting>
955
956 <para>
957 Which enables us to rewrite our functions in a much cleaner style:
958 </para>
959
960 <programlisting>
961 collectArgs :: Type -> [Type]
962 collectArgs (Arrow t1 t2) = t1 : collectArgs t2
963 collectArgs _ = []
964
965 isInt :: Type -> Bool
966 isInt Int = True
967 isInt _ = False
968
969 isIntEndo :: Type -> Bool
970 isIntEndo (Arrow Int Int) = True
971 isIntEndo _ = False
972 </programlisting>
973
974 <para>
975 Note that in this example, the pattern synonyms
976 <literal>Int</literal> and <literal>Arrow</literal> can also be used
977 as expressions (they are <emphasis>bidirectional</emphasis>). This
978 is not necessarily the case: <emphasis>unidirectional</emphasis>
979 pattern synonyms can also be declared with the following syntax:
980 </para>
981
982 <programlisting>
983 pattern Head x &lt;- x:xs
984 </programlisting>
985
986 <para>
987 In this case, <literal>Head</literal> <replaceable>x</replaceable>
988 cannot be used in expressions, only patterns, since it wouldn't
989 specify a value for the <replaceable>xs</replaceable> on the
990 right-hand side. We can give an explicit inversion of a pattern
991 synonym using the following syntax:
992 </para>
993
994 <programlisting>
995 pattern Head x &lt;- x:xs where
996 Head x = [x]
997 </programlisting>
998
999 <para>
1000 The syntax and semantics of pattern synonyms are elaborated in the
1001 following subsections.
1002 See the <ulink
1003 url="http://ghc.haskell.org/trac/ghc/wiki/PatternSynonyms">Wiki
1004 page</ulink> for more details.
1005 </para>
1006
1007 <sect3> <title>Syntax and scoping of pattern synonyms</title>
1008 <para>
1009 A pattern synonym declaration can be either unidirectional or
1010 bidirectional. The syntax for unidirectional pattern synonyms is:
1011 <programlisting>
1012 pattern Name args &lt;- pat
1013 </programlisting>
1014 and the syntax for bidirectional pattern synonyms is:
1015 <programlisting>
1016 pattern Name args = pat
1017 </programlisting> or
1018 <programlisting>
1019 pattern Name args &lt;- pat where
1020 Name args = expr
1021 </programlisting>
1022 Either prefix or infix syntax can be
1023 used.
1024 </para>
1025 <para>
1026 Pattern synonym declarations can only occur in the top level of a
1027 module. In particular, they are not allowed as local
1028 definitions.
1029 </para>
1030 <para>
1031 The variables in the left-hand side of the definition are bound by
1032 the pattern on the right-hand side. For implicitly bidirectional
1033 pattern synonyms, all the variables of the right-hand side must also
1034 occur on the left-hand side; also, wildcard patterns and view
1035 patterns are not allowed. For unidirectional and
1036 explicitly-bidirectional pattern synonyms, there is no restriction
1037 on the right-hand side pattern.
1038 </para>
1039
1040 <para>
1041 Pattern synonyms cannot be defined recursively.
1042 </para>
1043 </sect3>
1044
1045 <sect3 id="patsyn-impexp"> <title>Import and export of pattern synonyms</title>
1046
1047 <para>
1048 The name of the pattern synonym itself is in the same namespace as
1049 proper data constructors. In an export or import specification,
1050 you must prefix pattern
1051 names with the <literal>pattern</literal> keyword, e.g.:
1052 <programlisting>
1053 module Example (pattern Single) where
1054 pattern Single x = [x]
1055 </programlisting>
1056 Without the <literal>pattern</literal> prefix, <literal>Single</literal> would
1057 be interpreted as a type constructor in the export list.
1058 </para>
1059 <para>
1060 You may also use the <literal>pattern</literal> keyword in an import/export
1061 specification to import or export an ordinary data constructor. For example:
1062 <programlisting>
1063 import Data.Maybe( pattern Just )
1064 </programlisting>
1065 would bring into scope the data constructor <literal>Just</literal> from the
1066 <literal>Maybe</literal> type, without also bringing the type constructor
1067 <literal>Maybe</literal> into scope.
1068 </para>
1069 </sect3>
1070
1071 <sect3> <title>Typing of pattern synonyms</title>
1072
1073 <para>
1074 Given a pattern synonym definition of the form
1075 <programlisting>
1076 pattern P var1 var2 ... varN &lt;- pat
1077 </programlisting>
1078 it is assigned a <emphasis>pattern type</emphasis> of the form
1079 <programlisting>
1080 pattern P :: CProv => CReq => t1 -> t2 -> ... -> tN -> t
1081 </programlisting>
1082 where <replaceable>CProv</replaceable> and
1083 <replaceable>CReq</replaceable> are type contexts, and
1084 <replaceable>t1</replaceable>, <replaceable>t2</replaceable>, ...,
1085 <replaceable>tN</replaceable> and <replaceable>t</replaceable> are
1086 types.
1087 Notice the unusual form of the type, with two contexts <replaceable>CProv</replaceable> and <replaceable>CReq</replaceable>:
1088 <itemizedlist>
1089 <listitem><para><replaceable>CReq</replaceable> are the constraints <emphasis>required</emphasis> to match the pattern.</para></listitem>
1090 <listitem><para><replaceable>CProv</replaceable> are the constraints <emphasis>made available (provided)</emphasis>
1091 by a successful pattern match.</para></listitem>
1092 </itemizedlist>
1093 For example, consider
1094 <programlisting>
1095 data T a where
1096 MkT :: (Show b) => a -> b -> T a
1097
1098 f1 :: (Eq a, Num a) => T a -> String
1099 f1 (MkT 42 x) = show x
1100
1101 pattern ExNumPat :: (Show b) => (Num a, Eq a) => b -> T a
1102 pattern ExNumPat x = MkT 42 x
1103
1104 f2 :: (Eq a, Num a) => T a -> String
1105 f2 (ExNumPat x) = show x
1106 </programlisting>
1107 Here <literal>f1</literal> does not use pattern synonyms. To match against the
1108 numeric pattern <literal>42</literal> <emphasis>requires</emphasis> the caller to
1109 satisfy the constraints <literal>(Num a, Eq a)</literal>,
1110 so they appear in <literal>f1</literal>'s type. The call to <literal>show</literal> generates a <literal>(Show b)</literal>
1111 constraint, where <literal>b</literal> is an existentially type variable bound by the pattern match
1112 on <literal>MkT</literal>. But the same pattern match also <emphasis>provides</emphasis> the constraint
1113 <literal>(Show b)</literal> (see <literal>MkT</literal>'s type), and so all is well.
1114 </para>
1115 <para>
1116 Exactly the same reasoning applies to <literal>ExNumPat</literal>:
1117 matching against <literal>ExNumPat</literal> <emphasis>requires</emphasis>
1118 the constraints <literal>(Num a, Eq a)</literal>, and <emphasis>provides</emphasis>
1119 the constraint <literal>(Show b)</literal>.
1120 </para>
1121 <para>
1122 Note also the following points
1123 <itemizedlist>
1124 <listitem><para>
1125 In the common case where <replaceable>CReq</replaceable> is empty,
1126 <literal>()</literal>, it can be omitted altogether.
1127 </para> </listitem>
1128
1129 <listitem><para>
1130 You may specify an explicit <emphasis>pattern signature</emphasis>, as
1131 we did for <literal>ExNumPat</literal> above, to specify the type of a pattern,
1132 just as you can for a function. As usual, the type signature can be less polymorphic
1133 than the inferred type. For example
1134 <programlisting>
1135 -- Inferred type would be 'a -> [a]'
1136 pattern SinglePair :: (a, a) -> [(a, a)]
1137 pattern SinglePair x = [x]
1138 </programlisting>
1139 </para> </listitem>
1140
1141 <listitem><para>
1142 The GHCi <literal>:info</literal> command shows pattern types in this format.
1143 </para> </listitem>
1144
1145 <listitem><para>
1146 For a bidirectional pattern synonym, a use of the pattern synonym as an expression has the type
1147 <programlisting>
1148 (CProv, CReq) => t1 -> t2 -> ... -> tN -> t
1149 </programlisting>
1150 So in the previous example, when used in an expression, <literal>ExNumPat</literal> has type
1151 <programlisting>
1152 ExNumPat :: (Show b, Num a, Eq a) => b -> T t
1153 </programlisting>
1154 Notice that this is a tiny bit more restrictive than the expression <literal>MkT 42 x</literal>
1155 which would not require <literal>(Eq a)</literal>.
1156 </para> </listitem>
1157
1158 <listitem><para>
1159 Consider these two pattern synonyms:
1160 <programlisting>
1161 data S a where
1162 S1 :: Bool -> S Bool
1163
1164 pattern P1 b = Just b -- P1 :: Bool -> Maybe Bool
1165 pattern P2 b = S1 b -- P2 :: (b~Bool) => Bool -> S b
1166
1167 f :: Maybe a -> String
1168 f (P1 x) = "no no no" -- Type-incorrect
1169
1170 g :: S a -> String
1171 g (P2 b) = "yes yes yes" -- Fine
1172 </programlisting>
1173 Pattern <literal>P1</literal> can only match against a value of type <literal>Maybe Bool</literal>,
1174 so function <literal>f</literal> is rejected because the type signature is <literal>Maybe a</literal>.
1175 (To see this, imagine expanding the pattern synonym.)
1176 </para>
1177 <para>
1178 On the other hand, function <literal>g</literal> works fine, because matching against <literal>P2</literal>
1179 (which wraps the GADT <literal>S</literal>) provides the local equality <literal>(a~Bool)</literal>.
1180 If you were to give an explicit pattern signature <literal>P2 :: Bool -> S Bool</literal>, then <literal>P2</literal>
1181 would become less polymorphic, and would behave exactly like <literal>P1</literal> so that <literal>g</literal>
1182 would then be rejected.
1183 </para>
1184 <para>
1185 In short, if you want GADT-like behaviour for pattern synonyms,
1186 then (unlike unlike concrete data constructors like <literal>S1</literal>)
1187 you must write its type with explicit provided equalities.
1188 For a concrete data constructor like <literal>S1</literal> you can write
1189 its type signature as either <literal>S1 :: Bool -> S Bool</literal> or
1190 <literal>S1 :: (b~Bool) => Bool -> S b</literal>; the two are equivalent.
1191 Not so for pattern synonyms: the two forms are different, in order to
1192 distinguish the two cases above. (See <ulink url="https://ghc.haskell.org/trac/ghc/ticket/9953">Trac #9953</ulink> for
1193 discussion of this choice.)
1194 </para></listitem>
1195 </itemizedlist>
1196 </para>
1197 </sect3>
1198
1199 <sect3><title>Matching of pattern synonyms</title>
1200
1201 <para>
1202 A pattern synonym occurrence in a pattern is evaluated by first
1203 matching against the pattern synonym itself, and then on the argument
1204 patterns. For example, in the following program, <literal>f</literal>
1205 and <literal>f'</literal> are equivalent:
1206 </para>
1207
1208 <programlisting>
1209 pattern Pair x y &lt;- [x, y]
1210
1211 f (Pair True True) = True
1212 f _ = False
1213
1214 f' [x, y] | True &lt;- x, True &lt;- y = True
1215 f' _ = False
1216 </programlisting>
1217
1218 <para>
1219 Note that the strictness of <literal>f</literal> differs from that
1220 of <literal>g</literal> defined below:
1221 <programlisting>
1222 g [True, True] = True
1223 g _ = False
1224
1225 *Main> f (False:undefined)
1226 *** Exception: Prelude.undefined
1227 *Main> g (False:undefined)
1228 False
1229 </programlisting>
1230 </para>
1231 </sect3>
1232
1233 </sect2>
1234
1235 <!-- ===================== n+k patterns =================== -->
1236
1237 <sect2 id="n-k-patterns">
1238 <title>n+k patterns</title>
1239 <indexterm><primary><option>-XNPlusKPatterns</option></primary></indexterm>
1240
1241 <para>
1242 <literal>n+k</literal> pattern support is disabled by default. To enable
1243 it, you can use the <option>-XNPlusKPatterns</option> flag.
1244 </para>
1245
1246 </sect2>
1247
1248 <!-- ===================== Traditional record syntax =================== -->
1249
1250 <sect2 id="traditional-record-syntax">
1251 <title>Traditional record syntax</title>
1252 <indexterm><primary><option>-XNoTraditionalRecordSyntax</option></primary></indexterm>
1253
1254 <para>
1255 Traditional record syntax, such as <literal>C {f = x}</literal>, is enabled by default.
1256 To disable it, you can use the <option>-XNoTraditionalRecordSyntax</option> flag.
1257 </para>
1258
1259 </sect2>
1260
1261 <!-- ===================== Recursive do-notation =================== -->
1262
1263 <sect2 id="recursive-do-notation">
1264 <title>The recursive do-notation
1265 </title>
1266
1267 <para>
1268 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
1269 that is, the variables bound in a do-expression are visible only in the textually following
1270 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
1271 group.
1272 </para>
1273
1274 <para>
1275 It turns out that such recursive bindings do indeed make sense for a variety of monads, but
1276 not all. In particular, recursion in this sense requires a fixed-point operator for the underlying
1277 monad, captured by the <literal>mfix</literal> method of the <literal>MonadFix</literal> class, defined in <literal>Control.Monad.Fix</literal> as follows:
1278 <programlisting>
1279 class Monad m => MonadFix m where
1280 mfix :: (a -> m a) -> m a
1281 </programlisting>
1282 Haskell's
1283 <literal>Maybe</literal>, <literal>[]</literal> (list), <literal>ST</literal> (both strict and lazy versions),
1284 <literal>IO</literal>, and many other monads have <literal>MonadFix</literal> instances. On the negative
1285 side, the continuation monad, with the signature <literal>(a -> r) -> r</literal>, does not.
1286 </para>
1287
1288 <para>
1289 For monads that do belong to the <literal>MonadFix</literal> class, GHC provides
1290 an extended version of the do-notation that allows recursive bindings.
1291 The <option>-XRecursiveDo</option> (language pragma: <literal>RecursiveDo</literal>)
1292 provides the necessary syntactic support, introducing the keywords <literal>mdo</literal> and
1293 <literal>rec</literal> for higher and lower levels of the notation respectively. Unlike
1294 bindings in a <literal>do</literal> expression, those introduced by <literal>mdo</literal> and <literal>rec</literal>
1295 are recursively defined, much like in an ordinary let-expression. Due to the new
1296 keyword <literal>mdo</literal>, we also call this notation the <emphasis>mdo-notation</emphasis>.
1297 </para>
1298
1299 <para>
1300 Here is a simple (albeit contrived) example:
1301 <programlisting>
1302 {-# LANGUAGE RecursiveDo #-}
1303 justOnes = mdo { xs &lt;- Just (1:xs)
1304 ; return (map negate xs) }
1305 </programlisting>
1306 or equivalently
1307 <programlisting>
1308 {-# LANGUAGE RecursiveDo #-}
1309 justOnes = do { rec { xs &lt;- Just (1:xs) }
1310 ; return (map negate xs) }
1311 </programlisting>
1312 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
1313 </para>
1314
1315 <para>
1316 GHC's implementation the mdo-notation closely follows the original translation as described in the paper
1317 <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for Haskell</ulink>, which
1318 in turn is based on the work <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion
1319 in Monadic Computations</ulink>. Furthermore, GHC extends the syntax described in the former paper
1320 with a lower level syntax flagged by the <literal>rec</literal> keyword, as we describe next.
1321 </para>
1322
1323 <sect3>
1324 <title>Recursive binding groups</title>
1325
1326 <para>
1327 The flag <option>-XRecursiveDo</option> also introduces a new keyword <literal>rec</literal>, which wraps a
1328 mutually-recursive group of monadic statements inside a <literal>do</literal> expression, producing a single statement.
1329 Similar to a <literal>let</literal> statement inside a <literal>do</literal>, variables bound in
1330 the <literal>rec</literal> are visible throughout the <literal>rec</literal> group, and below it. For example, compare
1331 <programlisting>
1332 do { a &lt;- getChar do { a &lt;- getChar
1333 ; let { r1 = f a r2 ; rec { r1 &lt;- f a r2
1334 ; ; r2 = g r1 } ; ; r2 &lt;- g r1 }
1335 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
1336 </programlisting>
1337 In both cases, <literal>r1</literal> and <literal>r2</literal> are available both throughout
1338 the <literal>let</literal> or <literal>rec</literal> block, and in the statements that follow it.
1339 The difference is that <literal>let</literal> is non-monadic, while <literal>rec</literal> is monadic.
1340 (In Haskell <literal>let</literal> is really <literal>letrec</literal>, of course.)
1341 </para>
1342
1343 <para>
1344 The semantics of <literal>rec</literal> is fairly straightforward. Whenever GHC finds a <literal>rec</literal>
1345 group, it will compute its set of bound variables, and will introduce an appropriate call
1346 to the underlying monadic value-recursion operator <literal>mfix</literal>, belonging to the
1347 <literal>MonadFix</literal> class. Here is an example:
1348 <programlisting>
1349 rec { b &lt;- f a c ===> (b,c) &lt;- mfix (\ ~(b,c) -> do { b &lt;- f a c
1350 ; c &lt;- f b a } ; c &lt;- f b a
1351 ; return (b,c) })
1352 </programlisting>
1353 As usual, the meta-variables <literal>b</literal>, <literal>c</literal> etc., can be arbitrary patterns.
1354 In general, the statement <literal>rec <replaceable>ss</replaceable></literal> is desugared to the statement
1355 <programlisting>
1356 <replaceable>vs</replaceable> &lt;- mfix (\ ~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
1357 </programlisting>
1358 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
1359 </para>
1360
1361 <para>
1362 Note in particular that the translation for a <literal>rec</literal> block only involves wrapping a call
1363 to <literal>mfix</literal>: it performs no other analysis on the bindings. The latter is the task
1364 for the <literal>mdo</literal> notation, which is described next.
1365 </para>
1366 </sect3>
1367
1368 <sect3>
1369 <title>The <literal>mdo</literal> notation</title>
1370
1371 <para>
1372 A <literal>rec</literal>-block tells the compiler where precisely the recursive knot should be tied. It turns out that
1373 the placement of the recursive knots can be rather delicate: in particular, we would like the knots to be wrapped
1374 around as minimal groups as possible. This process is known as <emphasis>segmentation</emphasis>, and is described
1375 in detail in Section 3.2 of <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for
1376 Haskell</ulink>. Segmentation improves polymorphism and reduces the size of the recursive knot. Most importantly, it avoids
1377 unnecessary interference caused by a fundamental issue with the so-called <emphasis>right-shrinking</emphasis>
1378 axiom for monadic recursion. In brief, most monads of interest (IO, strict state, etc.) do <emphasis>not</emphasis>
1379 have recursion operators that satisfy this axiom, and thus not performing segmentation can cause unnecessary
1380 interference, changing the termination behavior of the resulting translation.
1381 (Details can be found in Sections 3.1 and 7.2.2 of
1382 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.)
1383 </para>
1384
1385 <para>
1386 The <literal>mdo</literal> notation removes the burden of placing
1387 explicit <literal>rec</literal> blocks in the code. Unlike an
1388 ordinary <literal>do</literal> expression, in which variables bound by
1389 statements are only in scope for later statements, variables bound in
1390 an <literal>mdo</literal> expression are in scope for all statements
1391 of the expression. The compiler then automatically identifies minimal
1392 mutually recursively dependent segments of statements, treating them as
1393 if the user had wrapped a <literal>rec</literal> qualifier around them.
1394 </para>
1395
1396 <para>
1397 The definition is syntactic:
1398 </para>
1399 <itemizedlist>
1400 <listitem>
1401 <para>
1402 A generator <replaceable>g</replaceable>
1403 <emphasis>depends</emphasis> on a textually following generator
1404 <replaceable>g'</replaceable>, if
1405 </para>
1406 <itemizedlist>
1407 <listitem>
1408 <para>
1409 <replaceable>g'</replaceable> defines a variable that
1410 is used by <replaceable>g</replaceable>, or
1411 </para>
1412 </listitem>
1413 <listitem>
1414 <para>
1415 <replaceable>g'</replaceable> textually appears between
1416 <replaceable>g</replaceable> and
1417 <replaceable>g''</replaceable>, where <replaceable>g</replaceable>
1418 depends on <replaceable>g''</replaceable>.
1419 </para>
1420 </listitem>
1421 </itemizedlist>
1422 </listitem>
1423 <listitem>
1424 <para>
1425 A <emphasis>segment</emphasis> of a given
1426 <literal>mdo</literal>-expression is a minimal sequence of generators
1427 such that no generator of the sequence depends on an outside
1428 generator. As a special case, although it is not a generator,
1429 the final expression in an <literal>mdo</literal>-expression is
1430 considered to form a segment by itself.
1431 </para>
1432 </listitem>
1433 </itemizedlist>
1434 <para>
1435 Segments in this sense are
1436 related to <emphasis>strongly-connected components</emphasis> analysis,
1437 with the exception that bindings in a segment cannot be reordered and
1438 must be contiguous.
1439 </para>
1440
1441 <para>
1442 Here is an example <literal>mdo</literal>-expression, and its translation to <literal>rec</literal> blocks:
1443 <programlisting>
1444 mdo { a &lt;- getChar ===> do { a &lt;- getChar
1445 ; b &lt;- f a c ; rec { b &lt;- f a c
1446 ; c &lt;- f b a ; ; c &lt;- f b a }
1447 ; z &lt;- h a b ; z &lt;- h a b
1448 ; d &lt;- g d e ; rec { d &lt;- g d e
1449 ; e &lt;- g a z ; ; e &lt;- g a z }
1450 ; putChar c } ; putChar c }
1451 </programlisting>
1452 Note that a given <literal>mdo</literal> expression can cause the creation of multiple <literal>rec</literal> blocks.
1453 If there are no recursive dependencies, <literal>mdo</literal> will introduce no <literal>rec</literal> blocks. In this
1454 latter case an <literal>mdo</literal> expression is precisely the same as a <literal>do</literal> expression, as one
1455 would expect.
1456 </para>
1457
1458 <para>
1459 In summary, given an <literal>mdo</literal> expression, GHC first performs segmentation, introducing
1460 <literal>rec</literal> blocks to wrap over minimal recursive groups. Then, each resulting
1461 <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal> as described
1462 in the previous section. The original <literal>mdo</literal>-expression typechecks exactly when the desugared
1463 version would do so.
1464 </para>
1465
1466 <para>
1467 Here are some other important points in using the recursive-do notation:
1468
1469 <itemizedlist>
1470 <listitem>
1471 <para>
1472 It is enabled with the flag <literal>-XRecursiveDo</literal>, or the <literal>LANGUAGE RecursiveDo</literal>
1473 pragma. (The same flag enables both <literal>mdo</literal>-notation, and the use of <literal>rec</literal>
1474 blocks inside <literal>do</literal> expressions.)
1475 </para>
1476 </listitem>
1477 <listitem>
1478 <para>
1479 <literal>rec</literal> blocks can also be used inside <literal>mdo</literal>-expressions, which will be
1480 treated as a single statement. However, it is good style to either use <literal>mdo</literal> or
1481 <literal>rec</literal> blocks in a single expression.
1482 </para>
1483 </listitem>
1484 <listitem>
1485 <para>
1486 If recursive bindings are required for a monad, then that monad must be declared an instance of
1487 the <literal>MonadFix</literal> class.
1488 </para>
1489 </listitem>
1490 <listitem>
1491 <para>
1492 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1493 Furthermore, the <literal>Control.Monad.ST</literal> and <literal>Control.Monad.ST.Lazy</literal>
1494 modules provide the instances of the <literal>MonadFix</literal> class for Haskell's internal
1495 state monad (strict and lazy, respectively).
1496 </para>
1497 </listitem>
1498 <listitem>
1499 <para>
1500 Like <literal>let</literal> and <literal>where</literal> bindings, name shadowing is not allowed within
1501 an <literal>mdo</literal>-expression or a <literal>rec</literal>-block; that is, all the names bound in
1502 a single <literal>rec</literal> must be distinct. (GHC will complain if this is not the case.)
1503 </para>
1504 </listitem>
1505 </itemizedlist>
1506 </para>
1507 </sect3>
1508 </sect2>
1509
1510 <sect2 id="applicative-do">
1511 <title>Applicative do-notation</title>
1512 <indexterm><primary>Applicative do-notation</primary>
1513 </indexterm>
1514 <indexterm><primary>do-notation</primary><secondary>Applicative</secondary>
1515 </indexterm>
1516
1517 <para>
1518 The language option
1519 <option>-XApplicativeDo</option><indexterm><primary><option>-XApplicativeDo</option></primary></indexterm>
1520 enables an alternative translation for the do-notation, which
1521 uses the operators <literal>&lt;&dollar;&gt;</literal>,
1522 <literal>&lt;*&gt;</literal>, along with
1523 <literal>join</literal>, as far as possible. There are two main
1524 reasons for wanting to do this:
1525 </para>
1526
1527 <itemizedlist>
1528 <listitem>
1529 <para>
1530 We can use do-notation with types that are an instance of
1531 <literal>Applicative</literal> and
1532 <literal>Functor</literal>, but not
1533 <literal>Monad</literal>.
1534 </para>
1535 </listitem>
1536 <listitem>
1537 <para>
1538 In some monads, using the applicative operators is more
1539 efficient than monadic bind. For example, it may enable
1540 more parallelism.
1541 </para>
1542 </listitem>
1543 </itemizedlist>
1544
1545 <para>
1546 Applicative do-notation desugaring preserves the original
1547 semantics, provided that the <literal>Applicative</literal>
1548 instance satisfies <literal>&lt;*&gt; = ap</literal> and
1549 <literal>pure = return</literal> (these are true of all the
1550 common monadic types). Thus, you can normally turn on
1551 <option>-XApplicativeDo</option> without fear of breaking your
1552 program. There is one pitfall to watch out for; see <xref
1553 linkend="applicative-do-pitfall" />.
1554 </para>
1555
1556 <para>
1557 There are no syntactic changes with
1558 <option>-XApplicativeDo</option>. The only way it shows up at
1559 the source level is that you can have a <literal>do</literal>
1560 expression that doesn't require a <literal>Monad</literal>
1561 constraint. For example, in GHCi:
1562 </para>
1563
1564 <programlisting>
1565 Prelude&gt; :set -XApplicativeDo
1566 Prelude&gt; :t \m -&gt; do { x &lt;- m; return (not x) }
1567 \m -&gt; do { x &lt;- m; return (not x) }
1568 :: Functor f =&gt; f Bool -&gt; f Bool
1569 </programlisting>
1570
1571 <para>
1572 This example only requires <literal>Functor</literal>, because it
1573 is translated into <literal>(\x -&gt; not x) &lt;$&gt; m</literal>. A
1574 more complex example requires <literal>Applicative</literal>:
1575
1576 <programlisting>
1577 Prelude&gt; :t \m -&gt; do { x &lt;- m 'a'; y &lt;- m 'b'; return (x || y) }
1578 \m -&gt; do { x &lt;- m 'a'; y &lt;- m 'b'; return (x || y) }
1579 :: Applicative f =&gt; (Char -&gt; f Bool) -&gt; f Bool
1580 </programlisting>
1581 </para>
1582
1583 <para>
1584 Here GHC has translated the expression into
1585
1586 <programlisting>
1587 (\x y -&gt; x || y) &lt;$&gt; m 'a' &lt;*&gt; m 'b'
1588 </programlisting>
1589
1590 It is possible to see the actual translation by using
1591 <option>-ddump-ds</option>, but be warned, the output is quite
1592 verbose.
1593 </para>
1594
1595 <para>
1596 Note that if the expression can't be translated into uses of
1597 <literal>&lt;&dollar;&gt;</literal>, <literal>&lt;*&gt;</literal>
1598 only, then it will incur a <literal>Monad</literal> constraint as
1599 usual. This happens when there is a dependency on a value
1600 produced by an earlier statement in the do-block:
1601
1602 <programlisting>
1603 Prelude&gt; :t \m -&gt; do { x &lt;- m True; y &lt;- m x; return (x || y) }
1604 \m -&gt; do { x &lt;- m True; y &lt;- m x; return (x || y) }
1605 :: Monad m =&gt; (Bool -&gt; m Bool) -&gt; m Bool
1606 </programlisting>
1607
1608 Here, <literal>m x</literal> depends on the value of
1609 <literal>x</literal> produced by the first statement, so the
1610 expression cannot be translated using <literal>&lt;*&gt;</literal>.
1611 </para>
1612
1613 <para>In general, the rule for when a <literal>do</literal>
1614 statement incurs a <literal>Monad</literal> constraint is as
1615 follows. If the do-expression has the following form:
1616
1617 <programlisting>
1618 do p1 &lt;- E1; ...; pn &lt;- En; return E
1619 </programlisting>
1620
1621 where none of the variables defined by <literal>p1...pn</literal>
1622 are mentioned in <literal>E1...En</literal>, then the expression
1623 will only require <literal>Applicative</literal>. Otherwise, the
1624 expression will require <literal>Monad</literal>.
1625 </para>
1626
1627 <sect3 id="applicative-do-pitfall">
1628 <title>Things to watch out for</title>
1629
1630 <para>
1631 Your code should just work as before when
1632 <option>-XApplicativeDo</option> is enabled, provided you use
1633 conventional <literal>Applicative</literal> instances. However, if
1634 you define a <literal>Functor</literal> or
1635 <literal>Applicative</literal> instance using do-notation, then
1636 it will likely get turned into an infinite loop by GHC. For
1637 example, if you do this:
1638
1639 <programlisting>
1640 instance Functor MyType where
1641 fmap f m = do x &lt;- m; return (f x)
1642 </programlisting>
1643
1644 Then applicative desugaring will turn it into
1645
1646 <programlisting>
1647 instance Functor MyType where
1648 fmap f m = fmap (\x -&gt; f x) m
1649 </programlisting>
1650
1651 And the program will loop at runtime. Similarly, an
1652 <literal>Applicative</literal> instance like this
1653
1654 <programlisting>
1655 instance Applicative MyType where
1656 pure = return
1657 x &lt;*&gt; y = do f &lt;- x; a &lt;- y; return (f a)
1658 </programlisting>
1659 will result in an infinte loop when <literal>&lt;*&gt;</literal>
1660 is called.
1661 </para>
1662
1663 <para>Just as you wouldn't define a <literal>Monad</literal>
1664 instance using the do-notation, you shouldn't define
1665 <literal>Functor</literal> or <literal>Applicative</literal>
1666 instance using do-notation (when using
1667 <literal>ApplicativeDo</literal>) either. The correct way to
1668 define these instances in terms of <literal>Monad</literal> is to
1669 use the <literal>Monad</literal> operations directly, e.g.
1670
1671 <programlisting>
1672 instance Functor MyType where
1673 fmap f m = m &gt;&gt;= return . f
1674
1675 instance Applicative MyType where
1676 pure = return
1677 (&lt;*&gt;) = ap
1678 </programlisting>
1679 </para>
1680 </sect3>
1681
1682 </sect2>
1683
1684
1685 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1686
1687 <sect2 id="parallel-list-comprehensions">
1688 <title>Parallel List Comprehensions</title>
1689 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1690 </indexterm>
1691 <indexterm><primary>parallel list comprehensions</primary>
1692 </indexterm>
1693
1694 <para>Parallel list comprehensions are a natural extension to list
1695 comprehensions. List comprehensions can be thought of as a nice
1696 syntax for writing maps and filters. Parallel comprehensions
1697 extend this to include the <literal>zipWith</literal> family.</para>
1698
1699 <para>A parallel list comprehension has multiple independent
1700 branches of qualifier lists, each separated by a `|' symbol. For
1701 example, the following zips together two lists:</para>
1702
1703 <programlisting>
1704 [ (x, y) | x &lt;- xs | y &lt;- ys ]
1705 </programlisting>
1706
1707 <para>The behaviour of parallel list comprehensions follows that of
1708 zip, in that the resulting list will have the same length as the
1709 shortest branch.</para>
1710
1711 <para>We can define parallel list comprehensions by translation to
1712 regular comprehensions. Here's the basic idea:</para>
1713
1714 <para>Given a parallel comprehension of the form: </para>
1715
1716 <programlisting>
1717 [ e | p1 &lt;- e11, p2 &lt;- e12, ...
1718 | q1 &lt;- e21, q2 &lt;- e22, ...
1719 ...
1720 ]
1721 </programlisting>
1722
1723 <para>This will be translated to: </para>
1724
1725 <programlisting>
1726 [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
1727 [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
1728 ...
1729 ]
1730 </programlisting>
1731
1732 <para>where `zipN' is the appropriate zip for the given number of
1733 branches.</para>
1734
1735 </sect2>
1736
1737 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1738
1739 <sect2 id="generalised-list-comprehensions">
1740 <title>Generalised (SQL-Like) List Comprehensions</title>
1741 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1742 </indexterm>
1743 <indexterm><primary>extended list comprehensions</primary>
1744 </indexterm>
1745 <indexterm><primary>group</primary></indexterm>
1746 <indexterm><primary>sql</primary></indexterm>
1747
1748
1749 <para>Generalised list comprehensions are a further enhancement to the
1750 list comprehension syntactic sugar to allow operations such as sorting
1751 and grouping which are familiar from SQL. They are fully described in the
1752 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1753 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1754 except that the syntax we use differs slightly from the paper.</para>
1755 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1756 <para>Here is an example:
1757 <programlisting>
1758 employees = [ ("Simon", "MS", 80)
1759 , ("Erik", "MS", 100)
1760 , ("Phil", "Ed", 40)
1761 , ("Gordon", "Ed", 45)
1762 , ("Paul", "Yale", 60)]
1763
1764 output = [ (the dept, sum salary)
1765 | (name, dept, salary) &lt;- employees
1766 , then group by dept using groupWith
1767 , then sortWith by (sum salary)
1768 , then take 5 ]
1769 </programlisting>
1770 In this example, the list <literal>output</literal> would take on
1771 the value:
1772
1773 <programlisting>
1774 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1775 </programlisting>
1776 </para>
1777 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1778 (The functions <literal>sortWith</literal> and <literal>groupWith</literal> are not keywords; they are ordinary
1779 functions that are exported by <literal>GHC.Exts</literal>.)</para>
1780
1781 <para>There are five new forms of comprehension qualifier,
1782 all introduced by the (existing) keyword <literal>then</literal>:
1783 <itemizedlist>
1784 <listitem>
1785
1786 <programlisting>
1787 then f
1788 </programlisting>
1789
1790 This statement requires that <literal>f</literal> have the type <literal>
1791 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1792 motivating example, as this form is used to apply <literal>take 5</literal>.
1793
1794 </listitem>
1795
1796
1797 <listitem>
1798 <para>
1799 <programlisting>
1800 then f by e
1801 </programlisting>
1802
1803 This form is similar to the previous one, but allows you to create a function
1804 which will be passed as the first argument to f. As a consequence f must have
1805 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1806 from the type, this function lets f &quot;project out&quot; some information
1807 from the elements of the list it is transforming.</para>
1808
1809 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1810 is supplied with a function that lets it find out the <literal>sum salary</literal>
1811 for any item in the list comprehension it transforms.</para>
1812
1813 </listitem>
1814
1815
1816 <listitem>
1817
1818 <programlisting>
1819 then group by e using f
1820 </programlisting>
1821
1822 <para>This is the most general of the grouping-type statements. In this form,
1823 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1824 As with the <literal>then f by e</literal> case above, the first argument
1825 is a function supplied to f by the compiler which lets it compute e on every
1826 element of the list being transformed. However, unlike the non-grouping case,
1827 f additionally partitions the list into a number of sublists: this means that
1828 at every point after this statement, binders occurring before it in the comprehension
1829 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1830 this, let's look at an example:</para>
1831
1832 <programlisting>
1833 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1834 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1835 groupRuns f = groupBy (\x y -> f x == f y)
1836
1837 output = [ (the x, y)
1838 | x &lt;- ([1..3] ++ [1..2])
1839 , y &lt;- [4..6]
1840 , then group by x using groupRuns ]
1841 </programlisting>
1842
1843 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1844
1845 <programlisting>
1846 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1847 </programlisting>
1848
1849 <para>Note that we have used the <literal>the</literal> function to change the type
1850 of x from a list to its original numeric type. The variable y, in contrast, is left
1851 unchanged from the list form introduced by the grouping.</para>
1852
1853 </listitem>
1854
1855 <listitem>
1856
1857 <programlisting>
1858 then group using f
1859 </programlisting>
1860
1861 <para>With this form of the group statement, f is required to simply have the type
1862 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1863 comprehension so far directly. An example of this form is as follows:</para>
1864
1865 <programlisting>
1866 output = [ x
1867 | y &lt;- [1..5]
1868 , x &lt;- "hello"
1869 , then group using inits]
1870 </programlisting>
1871
1872 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1873
1874 <programlisting>
1875 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1876 </programlisting>
1877
1878 </listitem>
1879 </itemizedlist>
1880 </para>
1881 </sect2>
1882
1883 <!-- ===================== MONAD COMPREHENSIONS ===================== -->
1884
1885 <sect2 id="monad-comprehensions">
1886 <title>Monad comprehensions</title>
1887 <indexterm><primary>monad comprehensions</primary></indexterm>
1888
1889 <para>
1890 Monad comprehensions generalise the list comprehension notation,
1891 including parallel comprehensions
1892 (<xref linkend="parallel-list-comprehensions"/>) and
1893 transform comprehensions (<xref linkend="generalised-list-comprehensions"/>)
1894 to work for any monad.
1895 </para>
1896
1897 <para>Monad comprehensions support:</para>
1898
1899 <itemizedlist>
1900 <listitem>
1901 <para>
1902 Bindings:
1903 </para>
1904
1905 <programlisting>
1906 [ x + y | x &lt;- Just 1, y &lt;- Just 2 ]
1907 </programlisting>
1908
1909 <para>
1910 Bindings are translated with the <literal>(&gt;&gt;=)</literal> and
1911 <literal>return</literal> functions to the usual do-notation:
1912 </para>
1913
1914 <programlisting>
1915 do x &lt;- Just 1
1916 y &lt;- Just 2
1917 return (x+y)
1918 </programlisting>
1919
1920 </listitem>
1921 <listitem>
1922 <para>
1923 Guards:
1924 </para>
1925
1926 <programlisting>
1927 [ x | x &lt;- [1..10], x &lt;= 5 ]
1928 </programlisting>
1929
1930 <para>
1931 Guards are translated with the <literal>guard</literal> function,
1932 which requires a <literal>MonadPlus</literal> instance:
1933 </para>
1934
1935 <programlisting>
1936 do x &lt;- [1..10]
1937 guard (x &lt;= 5)
1938 return x
1939 </programlisting>
1940
1941 </listitem>
1942 <listitem>
1943 <para>
1944 Transform statements (as with <literal>-XTransformListComp</literal>):
1945 </para>
1946
1947 <programlisting>
1948 [ x+y | x &lt;- [1..10], y &lt;- [1..x], then take 2 ]
1949 </programlisting>
1950
1951 <para>
1952 This translates to:
1953 </para>
1954
1955 <programlisting>
1956 do (x,y) &lt;- take 2 (do x &lt;- [1..10]
1957 y &lt;- [1..x]
1958 return (x,y))
1959 return (x+y)
1960 </programlisting>
1961
1962 </listitem>
1963 <listitem>
1964 <para>
1965 Group statements (as with <literal>-XTransformListComp</literal>):
1966 </para>
1967
1968 <programlisting>
1969 [ x | x &lt;- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
1970 [ x | x &lt;- [1,1,2,2,3], then group using myGroup ]
1971 </programlisting>
1972
1973 </listitem>
1974 <listitem>
1975 <para>
1976 Parallel statements (as with <literal>-XParallelListComp</literal>):
1977 </para>
1978
1979 <programlisting>
1980 [ (x+y) | x &lt;- [1..10]
1981 | y &lt;- [11..20]
1982 ]
1983 </programlisting>
1984
1985 <para>
1986 Parallel statements are translated using the
1987 <literal>mzip</literal> function, which requires a
1988 <literal>MonadZip</literal> instance defined in
1989 <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
1990 </para>
1991
1992 <programlisting>
1993 do (x,y) &lt;- mzip (do x &lt;- [1..10]
1994 return x)
1995 (do y &lt;- [11..20]
1996 return y)
1997 return (x+y)
1998 </programlisting>
1999
2000 </listitem>
2001 </itemizedlist>
2002
2003 <para>
2004 All these features are enabled by default if the
2005 <literal>MonadComprehensions</literal> extension is enabled. The types
2006 and more detailed examples on how to use comprehensions are explained
2007 in the previous chapters <xref
2008 linkend="generalised-list-comprehensions"/> and <xref
2009 linkend="parallel-list-comprehensions"/>. In general you just have
2010 to replace the type <literal>[a]</literal> with the type
2011 <literal>Monad m => m a</literal> for monad comprehensions.
2012 </para>
2013
2014 <para>
2015 Note: Even though most of these examples are using the list monad,
2016 monad comprehensions work for any monad.
2017 The <literal>base</literal> package offers all necessary instances for
2018 lists, which make <literal>MonadComprehensions</literal> backward
2019 compatible to built-in, transform and parallel list comprehensions.
2020 </para>
2021 <para> More formally, the desugaring is as follows. We write <literal>D[ e | Q]</literal>
2022 to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
2023 <programlisting>
2024 Expressions: e
2025 Declarations: d
2026 Lists of qualifiers: Q,R,S
2027
2028 -- Basic forms
2029 D[ e | ] = return e
2030 D[ e | p &lt;- e, Q ] = e &gt;&gt;= \p -&gt; D[ e | Q ]
2031 D[ e | e, Q ] = guard e &gt;&gt; \p -&gt; D[ e | Q ]
2032 D[ e | let d, Q ] = let d in D[ e | Q ]
2033
2034 -- Parallel comprehensions (iterate for multiple parallel branches)
2035 D[ e | (Q | R), S ] = mzip D[ Qv | Q ] D[ Rv | R ] &gt;&gt;= \(Qv,Rv) -&gt; D[ e | S ]
2036
2037 -- Transform comprehensions
2038 D[ e | Q then f, R ] = f D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
2039
2040 D[ e | Q then f by b, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
2041
2042 D[ e | Q then group using f, R ] = f D[ Qv | Q ] &gt;&gt;= \ys -&gt;
2043 case (fmap selQv1 ys, ..., fmap selQvn ys) of
2044 Qv -&gt; D[ e | R ]
2045
2046 D[ e | Q then group by b using f, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \ys -&gt;
2047 case (fmap selQv1 ys, ..., fmap selQvn ys) of
2048 Qv -&gt; D[ e | R ]
2049
2050 where Qv is the tuple of variables bound by Q (and used subsequently)
2051 selQvi is a selector mapping Qv to the ith component of Qv
2052
2053 Operator Standard binding Expected type
2054 --------------------------------------------------------------------
2055 return GHC.Base t1 -&gt; m t2
2056 (&gt;&gt;=) GHC.Base m1 t1 -&gt; (t2 -&gt; m2 t3) -&gt; m3 t3
2057 (&gt;&gt;) GHC.Base m1 t1 -&gt; m2 t2 -&gt; m3 t3
2058 guard Control.Monad t1 -&gt; m t2
2059 fmap GHC.Base forall a b. (a-&gt;b) -&gt; n a -&gt; n b
2060 mzip Control.Monad.Zip forall a b. m a -&gt; m b -&gt; m (a,b)
2061 </programlisting>
2062 The comprehension should typecheck when its desugaring would typecheck,
2063 except that (as discussed in <xref linkend="generalised-list-comprehensions"/>)
2064 in the "then f" and "then group using f" clauses,
2065 when the "by b" qualifier is omitted, argument f should have a polymorphic type.
2066 In particular, "then Data.List.sort" and
2067 "then group using Data.List.group" are insufficiently polymorphic.
2068 </para>
2069 <para>
2070 Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
2071 Without rebindable
2072 syntax, the operators from the "standard binding" module are used; with
2073 rebindable syntax, the operators are looked up in the current lexical scope.
2074 For example, parallel comprehensions will be typechecked and desugared
2075 using whatever "<literal>mzip</literal>" is in scope.
2076 </para>
2077 <para>
2078 The rebindable operators must have the "Expected type" given in the
2079 table above. These types are surprisingly general. For example, you can
2080 use a bind operator with the type
2081 <programlisting>
2082 (>>=) :: T x y a -> (a -> T y z b) -> T x z b
2083 </programlisting>
2084 In the case of transform comprehensions, notice that the groups are
2085 parameterised over some arbitrary type <literal>n</literal> (provided it
2086 has an <literal>fmap</literal>, as well as
2087 the comprehension being over an arbitrary monad.
2088 </para>
2089 </sect2>
2090
2091 <!-- ===================== REBINDABLE SYNTAX =================== -->
2092
2093 <sect2 id="rebindable-syntax">
2094 <title>Rebindable syntax and the implicit Prelude import</title>
2095
2096 <para><indexterm><primary>-XNoImplicitPrelude
2097 option</primary></indexterm> GHC normally imports
2098 <filename>Prelude.hi</filename> files for you. If you'd
2099 rather it didn't, then give it a
2100 <option>-XNoImplicitPrelude</option> option. The idea is
2101 that you can then import a Prelude of your own. (But don't
2102 call it <literal>Prelude</literal>; the Haskell module
2103 namespace is flat, and you must not conflict with any
2104 Prelude module.)</para>
2105
2106 <para>Suppose you are importing a Prelude of your own
2107 in order to define your own numeric class
2108 hierarchy. It completely defeats that purpose if the
2109 literal "1" means "<literal>Prelude.fromInteger
2110 1</literal>", which is what the Haskell Report specifies.
2111 So the <option>-XRebindableSyntax</option>
2112 flag causes
2113 the following pieces of built-in syntax to refer to
2114 <emphasis>whatever is in scope</emphasis>, not the Prelude
2115 versions:
2116 <itemizedlist>
2117 <listitem>
2118 <para>An integer literal <literal>368</literal> means
2119 "<literal>fromInteger (368::Integer)</literal>", rather than
2120 "<literal>Prelude.fromInteger (368::Integer)</literal>".
2121 </para> </listitem>
2122
2123 <listitem><para>Fractional literals are handed in just the same way,
2124 except that the translation is
2125 <literal>fromRational (3.68::Rational)</literal>.
2126 </para> </listitem>
2127
2128 <listitem><para>The equality test in an overloaded numeric pattern
2129 uses whatever <literal>(==)</literal> is in scope.
2130 </para> </listitem>
2131
2132 <listitem><para>The subtraction operation, and the
2133 greater-than-or-equal test, in <literal>n+k</literal> patterns
2134 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
2135 </para></listitem>
2136
2137 <listitem>
2138 <para>Negation (e.g. "<literal>- (f x)</literal>")
2139 means "<literal>negate (f x)</literal>", both in numeric
2140 patterns, and expressions.
2141 </para></listitem>
2142
2143 <listitem>
2144 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
2145 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
2146 </para></listitem>
2147
2148 <listitem>
2149 <para>"Do" notation is translated using whatever
2150 functions <literal>(>>=)</literal>,
2151 <literal>(>>)</literal>, and <literal>fail</literal>,
2152 are in scope (not the Prelude
2153 versions). List comprehensions, <literal>mdo</literal>
2154 (<xref linkend="recursive-do-notation"/>), and parallel array
2155 comprehensions, are unaffected. </para></listitem>
2156
2157 <listitem>
2158 <para>Arrow
2159 notation (see <xref linkend="arrow-notation"/>)
2160 uses whatever <literal>arr</literal>,
2161 <literal>(>>>)</literal>, <literal>first</literal>,
2162 <literal>app</literal>, <literal>(|||)</literal> and
2163 <literal>loop</literal> functions are in scope. But unlike the
2164 other constructs, the types of these functions must match the
2165 Prelude types very closely. Details are in flux; if you want
2166 to use this, ask!
2167 </para></listitem>
2168 </itemizedlist>
2169 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
2170 </para>
2171 <para>
2172 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
2173 even if that is a little unexpected. For example, the
2174 static semantics of the literal <literal>368</literal>
2175 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
2176 <literal>fromInteger</literal> to have any of the types:
2177 <programlisting>
2178 fromInteger :: Integer -> Integer
2179 fromInteger :: forall a. Foo a => Integer -> a
2180 fromInteger :: Num a => a -> Integer
2181 fromInteger :: Integer -> Bool -> Bool
2182 </programlisting>
2183 </para>
2184
2185 <para>Be warned: this is an experimental facility, with
2186 fewer checks than usual. Use <literal>-dcore-lint</literal>
2187 to typecheck the desugared program. If Core Lint is happy
2188 you should be all right.</para>
2189
2190 </sect2>
2191
2192 <sect2 id="postfix-operators">
2193 <title>Postfix operators</title>
2194
2195 <para>
2196 The <option>-XPostfixOperators</option> flag enables a small
2197 extension to the syntax of left operator sections, which allows you to
2198 define postfix operators. The extension is this: the left section
2199 <programlisting>
2200 (e !)
2201 </programlisting>
2202 is equivalent (from the point of view of both type checking and execution) to the expression
2203 <programlisting>
2204 ((!) e)
2205 </programlisting>
2206 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
2207 The strict Haskell 98 interpretation is that the section is equivalent to
2208 <programlisting>
2209 (\y -> (!) e y)
2210 </programlisting>
2211 That is, the operator must be a function of two arguments. GHC allows it to
2212 take only one argument, and that in turn allows you to write the function
2213 postfix.
2214 </para>
2215 <para>The extension does not extend to the left-hand side of function
2216 definitions; you must define such a function in prefix form.</para>
2217
2218 </sect2>
2219
2220 <sect2 id="tuple-sections">
2221 <title>Tuple sections</title>
2222
2223 <para>
2224 The <option>-XTupleSections</option> flag enables Python-style partially applied
2225 tuple constructors. For example, the following program
2226 <programlisting>
2227 (, True)
2228 </programlisting>
2229 is considered to be an alternative notation for the more unwieldy alternative
2230 <programlisting>
2231 \x -> (x, True)
2232 </programlisting>
2233 You can omit any combination of arguments to the tuple, as in the following
2234 <programlisting>
2235 (, "I", , , "Love", , 1337)
2236 </programlisting>
2237 which translates to
2238 <programlisting>
2239 \a b c d -> (a, "I", b, c, "Love", d, 1337)
2240 </programlisting>
2241 </para>
2242
2243 <para>
2244 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
2245 will also be available for them, like so
2246 <programlisting>
2247 (# , True #)
2248 </programlisting>
2249 Because there is no unboxed unit tuple, the following expression
2250 <programlisting>
2251 (# #)
2252 </programlisting>
2253 continues to stand for the unboxed singleton tuple data constructor.
2254 </para>
2255
2256 </sect2>
2257
2258 <sect2 id="lambda-case">
2259 <title>Lambda-case</title>
2260 <para>
2261 The <option>-XLambdaCase</option> flag enables expressions of the form
2262 <programlisting>
2263 \case { p1 -> e1; ...; pN -> eN }
2264 </programlisting>
2265 which is equivalent to
2266 <programlisting>
2267 \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }
2268 </programlisting>
2269 Note that <literal>\case</literal> starts a layout, so you can write
2270 <programlisting>
2271 \case
2272 p1 -> e1
2273 ...
2274 pN -> eN
2275 </programlisting>
2276 </para>
2277 </sect2>
2278
2279 <sect2 id="empty-case">
2280 <title>Empty case alternatives</title>
2281 <para>
2282 The <option>-XEmptyCase</option> flag enables
2283 case expressions, or lambda-case expressions, that have no alternatives,
2284 thus:
2285 <programlisting>
2286 case e of { } -- No alternatives
2287 or
2288 \case { } -- -XLambdaCase is also required
2289 </programlisting>
2290 This can be useful when you know that the expression being scrutinised
2291 has no non-bottom values. For example:
2292 <programlisting>
2293 data Void
2294 f :: Void -> Int
2295 f x = case x of { }
2296 </programlisting>
2297 With dependently-typed features it is more useful
2298 (see <ulink url="http://ghc.haskell.org/trac/ghc/ticket/2431">Trac</ulink>).
2299 For example, consider these two candidate definitions of <literal>absurd</literal>:
2300 <programlisting>
2301 data a :==: b where
2302 Refl :: a :==: a
2303
2304 absurd :: True :~: False -> a
2305 absurd x = error "absurd" -- (A)
2306 absurd x = case x of {} -- (B)
2307 </programlisting>
2308 We much prefer (B). Why? Because GHC can figure out that <literal>(True :~: False)</literal>
2309 is an empty type. So (B) has no partiality and GHC should be able to compile with
2310 <option>-fwarn-incomplete-patterns</option>. (Though the pattern match checking is not
2311 yet clever enough to do that.)
2312 On the other hand (A) looks dangerous, and GHC doesn't check to make
2313 sure that, in fact, the function can never get called.
2314 </para>
2315 </sect2>
2316
2317 <sect2 id="multi-way-if">
2318 <title>Multi-way if-expressions</title>
2319 <para>
2320 With <option>-XMultiWayIf</option> flag GHC accepts conditional expressions
2321 with multiple branches:
2322 <programlisting>
2323 if | guard1 -> expr1
2324 | ...
2325 | guardN -> exprN
2326 </programlisting>
2327 which is roughly equivalent to
2328 <programlisting>
2329 case () of
2330 _ | guard1 -> expr1
2331 ...
2332 _ | guardN -> exprN
2333 </programlisting>
2334 </para>
2335
2336 <para>Multi-way if expressions introduce a new layout context. So the
2337 example above is equivalent to:
2338 <programlisting>
2339 if { | guard1 -> expr1
2340 ; | ...
2341 ; | guardN -> exprN
2342 }
2343 </programlisting>
2344 The following behaves as expected:
2345 <programlisting>
2346 if | guard1 -> if | guard2 -> expr2
2347 | guard3 -> expr3
2348 | guard4 -> expr4
2349 </programlisting>
2350 because layout translates it as
2351 <programlisting>
2352 if { | guard1 -> if { | guard2 -> expr2
2353 ; | guard3 -> expr3
2354 }
2355 ; | guard4 -> expr4
2356 }
2357 </programlisting>
2358 Layout with multi-way if works in the same way as other layout
2359 contexts, except that the semi-colons between guards in a multi-way if
2360 are optional. So it is not necessary to line up all the guards at the
2361 same column; this is consistent with the way guards work in function
2362 definitions and case expressions.
2363 </para>
2364 </sect2>
2365
2366 <sect2 id="disambiguate-fields">
2367 <title>Record field disambiguation</title>
2368 <para>
2369 In record construction and record pattern matching
2370 it is entirely unambiguous which field is referred to, even if there are two different
2371 data types in scope with a common field name. For example:
2372 <programlisting>
2373 module M where
2374 data S = MkS { x :: Int, y :: Bool }
2375
2376 module Foo where
2377 import M
2378
2379 data T = MkT { x :: Int }
2380
2381 ok1 (MkS { x = n }) = n+1 -- Unambiguous
2382 ok2 n = MkT { x = n+1 } -- Unambiguous
2383
2384 bad1 k = k { x = 3 } -- Ambiguous
2385 bad2 k = x k -- Ambiguous
2386 </programlisting>
2387 Even though there are two <literal>x</literal>'s in scope,
2388 it is clear that the <literal>x</literal> in the pattern in the
2389 definition of <literal>ok1</literal> can only mean the field
2390 <literal>x</literal> from type <literal>S</literal>. Similarly for
2391 the function <literal>ok2</literal>. However, in the record update
2392 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
2393 it is not clear which of the two types is intended.
2394 </para>
2395 <para>
2396 Haskell 98 regards all four as ambiguous, but with the
2397 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
2398 the former two. The rules are precisely the same as those for instance
2399 declarations in Haskell 98, where the method names on the left-hand side
2400 of the method bindings in an instance declaration refer unambiguously
2401 to the method of that class (provided they are in scope at all), even
2402 if there are other variables in scope with the same name.
2403 This reduces the clutter of qualified names when you import two
2404 records from different modules that use the same field name.
2405 </para>
2406 <para>
2407 Some details:
2408 <itemizedlist>
2409 <listitem><para>
2410 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For example:
2411 <programlisting>
2412 module Foo where
2413 import M
2414 x=True
2415 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
2416 </programlisting>
2417 </para></listitem>
2418
2419 <listitem><para>
2420 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualified</emphasis>
2421 field names even if the corresponding selector is only in scope <emphasis>qualified</emphasis>
2422 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
2423 <programlisting>
2424 module Foo where
2425 import qualified M -- Note qualified
2426
2427 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
2428 </programlisting>
2429 Since the constructor <literal>MkS</literal> is only in scope qualified, you must
2430 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
2431 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
2432 is not. (In effect, it is qualified by the constructor.)
2433 </para></listitem>
2434 </itemizedlist>
2435 </para>
2436
2437 </sect2>
2438
2439 <!-- ===================== Record puns =================== -->
2440
2441 <sect2 id="record-puns">
2442 <title>Record puns
2443 </title>
2444
2445 <para>
2446 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
2447 </para>
2448
2449 <para>
2450 When using records, it is common to write a pattern that binds a
2451 variable with the same name as a record field, such as:
2452
2453 <programlisting>
2454 data C = C {a :: Int}
2455 f (C {a = a}) = a
2456 </programlisting>
2457 </para>
2458
2459 <para>
2460 Record punning permits the variable name to be elided, so one can simply
2461 write
2462
2463 <programlisting>
2464 f (C {a}) = a
2465 </programlisting>
2466
2467 to mean the same pattern as above. That is, in a record pattern, the
2468 pattern <literal>a</literal> expands into the pattern <literal>a =
2469 a</literal> for the same name <literal>a</literal>.
2470 </para>
2471
2472 <para>
2473 Note that:
2474 <itemizedlist>
2475 <listitem><para>
2476 Record punning can also be used in an expression, writing, for example,
2477 <programlisting>
2478 let a = 1 in C {a}
2479 </programlisting>
2480 instead of
2481 <programlisting>
2482 let a = 1 in C {a = a}
2483 </programlisting>
2484 The expansion is purely syntactic, so the expanded right-hand side
2485 expression refers to the nearest enclosing variable that is spelled the
2486 same as the field name.
2487 </para></listitem>
2488
2489 <listitem><para>
2490 Puns and other patterns can be mixed in the same record:
2491 <programlisting>
2492 data C = C {a :: Int, b :: Int}
2493 f (C {a, b = 4}) = a
2494 </programlisting>
2495 </para></listitem>
2496
2497 <listitem><para>
2498 Puns can be used wherever record patterns occur (e.g. in
2499 <literal>let</literal> bindings or at the top-level).
2500 </para></listitem>
2501
2502 <listitem><para>
2503 A pun on a qualified field name is expanded by stripping off the module qualifier.
2504 For example:
2505 <programlisting>
2506 f (C {M.a}) = a
2507 </programlisting>
2508 means
2509 <programlisting>
2510 f (M.C {M.a = a}) = a
2511 </programlisting>
2512 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
2513 is only in scope in qualified form.)
2514 </para></listitem>
2515 </itemizedlist>
2516 </para>
2517
2518
2519 </sect2>
2520
2521 <!-- ===================== Record wildcards =================== -->
2522
2523 <sect2 id="record-wildcards">
2524 <title>Record wildcards
2525 </title>
2526
2527 <para>
2528 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
2529 This flag implies <literal>-XDisambiguateRecordFields</literal>.
2530 </para>
2531
2532 <para>
2533 For records with many fields, it can be tiresome to write out each field
2534 individually in a record pattern, as in
2535 <programlisting>
2536 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
2537 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
2538 </programlisting>
2539 </para>
2540
2541 <para>
2542 Record wildcard syntax permits a "<literal>..</literal>" in a record
2543 pattern, where each elided field <literal>f</literal> is replaced by the
2544 pattern <literal>f = f</literal>. For example, the above pattern can be
2545 written as
2546 <programlisting>
2547 f (C {a = 1, ..}) = b + c + d
2548 </programlisting>
2549 </para>
2550
2551 <para>
2552 More details:
2553 <itemizedlist>
2554 <listitem><para>
2555 Record wildcards in patterns can be mixed with other patterns, including puns
2556 (<xref linkend="record-puns"/>); for example, in a pattern <literal>(C {a
2557 = 1, b, ..})</literal>. Additionally, record wildcards can be used
2558 wherever record patterns occur, including in <literal>let</literal>
2559 bindings and at the top-level. For example, the top-level binding
2560 <programlisting>
2561 C {a = 1, ..} = e
2562 </programlisting>
2563 defines <literal>b</literal>, <literal>c</literal>, and
2564 <literal>d</literal>.
2565 </para></listitem>
2566
2567 <listitem><para>
2568 Record wildcards can also be used in an expression, when constructing a record. For example,
2569 <programlisting>
2570 let {a = 1; b = 2; c = 3; d = 4} in C {..}
2571 </programlisting>
2572 in place of
2573 <programlisting>
2574 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
2575 </programlisting>
2576 The expansion is purely syntactic, so the record wildcard
2577 expression refers to the nearest enclosing variables that are spelled
2578 the same as the omitted field names.
2579 </para></listitem>
2580
2581 <listitem><para>
2582 Record wildcards may <emphasis>not</emphasis> be used in record <emphasis>updates</emphasis>. For example this
2583 is illegal:
2584 <programlisting>
2585 f r = r { x = 3, .. }
2586 </programlisting>
2587 </para></listitem>
2588
2589 <listitem><para>
2590 For both pattern and expression wildcards, the "<literal>..</literal>" expands to the missing
2591 <emphasis>in-scope</emphasis> record fields.
2592 Specifically the expansion of "<literal>C {..}</literal>" includes
2593 <literal>f</literal> if and only if:
2594 <itemizedlist>
2595 <listitem><para>
2596 <literal>f</literal> is a record field of constructor <literal>C</literal>.
2597 </para></listitem>
2598 <listitem><para>
2599 The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
2600 </para></listitem>
2601 <listitem><para>
2602 In the case of expressions (but not patterns),
2603 the variable <literal>f</literal> is in scope unqualified,
2604 apart from the binding of the record selector itself.
2605 </para></listitem>
2606 </itemizedlist>
2607 These rules restrict record wildcards to the situations in which the user
2608 could have written the expanded version.
2609 For example
2610 <programlisting>
2611 module M where
2612 data R = R { a,b,c :: Int }
2613 module X where
2614 import M( R(a,c) )
2615 f b = R { .. }
2616 </programlisting>
2617 The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
2618 omitting <literal>b</literal> since the record field is not in scope,
2619 and omitting <literal>c</literal> since the variable <literal>c</literal>
2620 is not in scope (apart from the binding of the
2621 record selector <literal>c</literal>, of course).
2622 </para></listitem>
2623
2624 <listitem><para>
2625 Record wildcards cannot be used (a) in a record update construct, and (b) for data
2626 constructors that are not declared with record fields. For example:
2627 <programlisting>
2628 f x = x { v=True, .. } -- Illegal (a)
2629
2630 data T = MkT Int Bool
2631 g = MkT { .. } -- Illegal (b)
2632 h (MkT { .. }) = True -- Illegal (b)
2633 </programlisting>
2634 </para></listitem>
2635 </itemizedlist>
2636 </para>
2637
2638 </sect2>
2639
2640 <!-- ===================== Local fixity declarations =================== -->
2641
2642 <sect2 id="local-fixity-declarations">
2643 <title>Local Fixity Declarations
2644 </title>
2645
2646 <para>A careful reading of the Haskell 98 Report reveals that fixity
2647 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
2648 <literal>infixr</literal>) are permitted to appear inside local bindings
2649 such those introduced by <literal>let</literal> and
2650 <literal>where</literal>. However, the Haskell Report does not specify
2651 the semantics of such bindings very precisely.
2652 </para>
2653
2654 <para>In GHC, a fixity declaration may accompany a local binding:
2655 <programlisting>
2656 let f = ...
2657 infixr 3 `f`
2658 in
2659 ...
2660 </programlisting>
2661 and the fixity declaration applies wherever the binding is in scope.
2662 For example, in a <literal>let</literal>, it applies in the right-hand
2663 sides of other <literal>let</literal>-bindings and the body of the
2664 <literal>let</literal>C. Or, in recursive <literal>do</literal>
2665 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
2666 declarations of a <literal>let</literal> statement scope over other
2667 statements in the group, just as the bound name does.
2668 </para>
2669
2670 <para>
2671 Moreover, a local fixity declaration *must* accompany a local binding of
2672 that name: it is not possible to revise the fixity of name bound
2673 elsewhere, as in
2674 <programlisting>
2675 let infixr 9 $ in ...
2676 </programlisting>
2677
2678 Because local fixity declarations are technically Haskell 98, no flag is
2679 necessary to enable them.
2680 </para>
2681 </sect2>
2682
2683 <sect2 id="package-imports">
2684 <title>Import and export extensions</title>
2685
2686 <sect3>
2687 <title>Hiding things the imported module doesn't export</title>
2688
2689 <para>
2690 Technically in Haskell 2010 this is illegal:
2691 <programlisting>
2692 module A( f ) where
2693 f = True
2694
2695 module B where
2696 import A hiding( g ) -- A does not export g
2697 g = f
2698 </programlisting>
2699 The <literal>import A hiding( g )</literal> in module <literal>B</literal>
2700 is technically an error (<ulink url="http://www.haskell.org/onlinereport/haskell2010/haskellch5.html#x11-1020005.3.1">Haskell Report, 5.3.1</ulink>)
2701 because <literal>A</literal> does not export <literal>g</literal>.
2702 However GHC allows it, in the interests of supporting backward compatibility; for example, a newer version of
2703 <literal>A</literal> might export <literal>g</literal>, and you want <literal>B</literal> to work
2704 in either case.
2705 </para>
2706 <para>
2707 The warning <literal>-fwarn-dodgy-imports</literal>, which is off by default but included with <literal>-W</literal>,
2708 warns if you hide something that the imported module does not export.
2709 </para>
2710 </sect3>
2711
2712 <sect3>
2713 <title id="package-qualified-imports">Package-qualified imports</title>
2714
2715 <para>With the <option>-XPackageImports</option> flag, GHC allows
2716 import declarations to be qualified by the package name that the
2717 module is intended to be imported from. For example:</para>
2718
2719 <programlisting>
2720 import "network" Network.Socket
2721 </programlisting>
2722
2723 <para>would import the module <literal>Network.Socket</literal> from
2724 the package <literal>network</literal> (any version). This may
2725 be used to disambiguate an import when the same module is
2726 available from multiple packages, or is present in both the
2727 current package being built and an external package.</para>
2728
2729 <para>The special package name <literal>this</literal> can be used to
2730 refer to the current package being built.</para>
2731
2732 <para>Note: you probably don't need to use this feature, it was
2733 added mainly so that we can build backwards-compatible versions of
2734 packages when APIs change. It can lead to fragile dependencies in
2735 the common case: modules occasionally move from one package to
2736 another, rendering any package-qualified imports broken.
2737 See also <xref linkend="package-thinning-and-renaming" /> for
2738 an alternative way of disambiguating between module names.</para>
2739 </sect3>
2740
2741 <sect3 id="safe-imports-ext">
2742 <title>Safe imports</title>
2743
2744 <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
2745 and <option>-XUnsafe</option> language flags, GHC extends
2746 the import declaration syntax to take an optional <literal>safe</literal>
2747 keyword after the <literal>import</literal> keyword. This feature
2748 is part of the Safe Haskell GHC extension. For example:</para>
2749
2750 <programlisting>
2751 import safe qualified Network.Socket as NS
2752 </programlisting>
2753
2754 <para>would import the module <literal>Network.Socket</literal>
2755 with compilation only succeeding if Network.Socket can be
2756 safely imported. For a description of when a import is
2757 considered safe see <xref linkend="safe-haskell"/></para>
2758
2759 </sect3>
2760
2761 <sect3 id="explicit-namespaces">
2762 <title>Explicit namespaces in import/export</title>
2763
2764 <para> In an import or export list, such as
2765 <programlisting>
2766 module M( f, (++) ) where ...
2767 import N( f, (++) )
2768 ...
2769 </programlisting>
2770 the entities <literal>f</literal> and <literal>(++)</literal> are <emphasis>values</emphasis>.
2771 However, with type operators (<xref linkend="type-operators"/>) it becomes possible
2772 to declare <literal>(++)</literal> as a <emphasis>type constructor</emphasis>. In that
2773 case, how would you export or import it?
2774 </para>
2775 <para>
2776 The <option>-XExplicitNamespaces</option> extension allows you to prefix the name of
2777 a type constructor in an import or export list with "<literal>type</literal>" to
2778 disambiguate this case, thus:
2779 <programlisting>
2780 module M( f, type (++) ) where ...
2781 import N( f, type (++) )
2782 ...
2783 module N( f, type (++) ) where
2784 data family a ++ b = L a | R b
2785 </programlisting>
2786 The extension <option>-XExplicitNamespaces</option>
2787 is implied by <option>-XTypeOperators</option> and (for some reason) by <option>-XTypeFamilies</option>.
2788 </para>
2789 <para>
2790 In addition, with <option>-XPatternSynonyms</option> you can prefix the name of
2791 a data constructor in an import or export list with the keyword <literal>pattern</literal>,
2792 to allow the import or export of a data constructor without its parent type constructor
2793 (see <xref linkend="patsyn-impexp"/>).
2794 </para>
2795 </sect3>
2796
2797 </sect2>
2798
2799 <sect2 id="syntax-stolen">
2800 <title>Summary of stolen syntax</title>
2801
2802 <para>Turning on an option that enables special syntax
2803 <emphasis>might</emphasis> cause working Haskell 98 code to fail
2804 to compile, perhaps because it uses a variable name which has
2805 become a reserved word. This section lists the syntax that is
2806 "stolen" by language extensions.
2807 We use
2808 notation and nonterminal names from the Haskell 98 lexical syntax
2809 (see the Haskell 98 Report).
2810 We only list syntax changes here that might affect
2811 existing working programs (i.e. "stolen" syntax). Many of these
2812 extensions will also enable new context-free syntax, but in all
2813 cases programs written to use the new syntax would not be
2814 compilable without the option enabled.</para>
2815
2816 <para>There are two classes of special
2817 syntax:
2818
2819 <itemizedlist>
2820 <listitem>
2821 <para>New reserved words and symbols: character sequences
2822 which are no longer available for use as identifiers in the
2823 program.</para>
2824 </listitem>
2825 <listitem>
2826 <para>Other special syntax: sequences of characters that have
2827 a different meaning when this particular option is turned
2828 on.</para>
2829 </listitem>
2830 </itemizedlist>
2831
2832 The following syntax is stolen:
2833
2834 <variablelist>
2835 <varlistentry>
2836 <term>
2837 <literal>forall</literal>
2838 <indexterm><primary><literal>forall</literal></primary></indexterm>
2839 </term>
2840 <listitem><para>
2841 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
2842 <option>-XScopedTypeVariables</option>,
2843 <option>-XLiberalTypeSynonyms</option>,
2844 <option>-XRankNTypes</option>,
2845 <option>-XExistentialQuantification</option>
2846 </para></listitem>
2847 </varlistentry>
2848
2849 <varlistentry>
2850 <term>
2851 <literal>mdo</literal>
2852 <indexterm><primary><literal>mdo</literal></primary></indexterm>
2853 </term>
2854 <listitem><para>
2855 Stolen by: <option>-XRecursiveDo</option>
2856 </para></listitem>
2857 </varlistentry>
2858
2859 <varlistentry>
2860 <term>
2861 <literal>foreign</literal>
2862 <indexterm><primary><literal>foreign</literal></primary></indexterm>
2863 </term>
2864 <listitem><para>
2865 Stolen by: <option>-XForeignFunctionInterface</option>
2866 </para></listitem>
2867 </varlistentry>
2868
2869 <varlistentry>
2870 <term>
2871 <literal>rec</literal>,
2872 <literal>proc</literal>, <literal>-&lt;</literal>,
2873 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
2874 <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
2875 <literal>|)</literal> brackets
2876 <indexterm><primary><literal>proc</literal></primary></indexterm>
2877 </term>
2878 <listitem><para>
2879 Stolen by: <option>-XArrows</option>
2880 </para></listitem>
2881 </varlistentry>
2882
2883 <varlistentry>
2884 <term>
2885 <literal>?<replaceable>varid</replaceable></literal>
2886 <indexterm><primary>implicit parameters</primary></indexterm>
2887 </term>
2888 <listitem><para>
2889 Stolen by: <option>-XImplicitParams</option>
2890 </para></listitem>
2891 </varlistentry>
2892
2893 <varlistentry>
2894 <term>
2895 <literal>[|</literal>,
2896 <literal>[e|</literal>, <literal>[p|</literal>,
2897 <literal>[d|</literal>, <literal>[t|</literal>,
2898 <literal>$(</literal>,
2899 <literal>$$(</literal>,
2900 <literal>[||</literal>,
2901 <literal>[e||</literal>,
2902 <literal>$<replaceable>varid</replaceable></literal>,
2903 <literal>$$<replaceable>varid</replaceable></literal>
2904 <indexterm><primary>Template Haskell</primary></indexterm>
2905 </term>
2906 <listitem><para>
2907 Stolen by: <option>-XTemplateHaskell</option>
2908 </para></listitem>
2909 </varlistentry>
2910
2911 <varlistentry>
2912 <term>
2913 <literal>[<replaceable>varid</replaceable>|</literal>
2914 <indexterm><primary>quasi-quotation</primary></indexterm>
2915 </term>
2916 <listitem><para>
2917 Stolen by: <option>-XQuasiQuotes</option>
2918 </para></listitem>
2919 </varlistentry>
2920
2921 <varlistentry>
2922 <term>
2923 <replaceable>varid</replaceable>{<literal>&num;</literal>},
2924 <replaceable>char</replaceable><literal>&num;</literal>,
2925 <replaceable>string</replaceable><literal>&num;</literal>,
2926 <replaceable>integer</replaceable><literal>&num;</literal>,
2927 <replaceable>float</replaceable><literal>&num;</literal>,
2928 <replaceable>float</replaceable><literal>&num;&num;</literal>
2929 </term>
2930 <listitem><para>
2931 Stolen by: <option>-XMagicHash</option>
2932 </para></listitem>
2933 </varlistentry>
2934
2935 <varlistentry>
2936 <term>
2937 <literal>(&num;</literal>, <literal>&num;)</literal>
2938 </term>
2939 <listitem><para>
2940 Stolen by: <option>-XUnboxedTuples</option>
2941 </para></listitem>
2942 </varlistentry>
2943
2944 <varlistentry>
2945 <term>
2946 <replaceable>varid</replaceable><literal>!</literal><replaceable>varid</replaceable>
2947 </term>
2948 <listitem><para>
2949 Stolen by: <option>-XBangPatterns</option>
2950 </para></listitem>
2951 </varlistentry>
2952
2953 <varlistentry>
2954 <term>
2955 <literal>pattern</literal>
2956 </term>
2957 <listitem><para>
2958 Stolen by: <option>-XPatternSynonyms</option>
2959 </para></listitem>
2960 </varlistentry>
2961 </variablelist>
2962 </para>
2963 </sect2>
2964 </sect1>
2965
2966
2967 <!-- TYPE SYSTEM EXTENSIONS -->
2968 <sect1 id="data-type-extensions">
2969 <title>Extensions to data types and type synonyms</title>
2970
2971 <sect2 id="nullary-types">
2972 <title>Data types with no constructors</title>
2973
2974 <para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
2975 GHC lets you declare a data type with no constructors. For example:</para>
2976
2977 <programlisting>
2978 data S -- S :: *
2979 data T a -- T :: * -> *
2980 </programlisting>
2981
2982 <para>Syntactically, the declaration lacks the "= constrs" part. The
2983 type can be parameterised over types of any kind, but if the kind is
2984 not <literal>*</literal> then an explicit kind annotation must be used
2985 (see <xref linkend="kinding"/>).</para>
2986
2987 <para>Such data types have only one value, namely bottom.
2988 Nevertheless, they can be useful when defining "phantom types".</para>
2989 </sect2>
2990
2991 <sect2 id="datatype-contexts">
2992 <title>Data type contexts</title>
2993
2994 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2995
2996 <programlisting>
2997 data Eq a => Set a = NilSet | ConsSet a (Set a)
2998 </programlisting>
2999
3000 <para>give constructors with types:</para>
3001
3002 <programlisting>
3003 NilSet :: Set a
3004 ConsSet :: Eq a => a -> Set a -> Set a
3005 </programlisting>
3006
3007 <para>This is widely considered a misfeature, and is going to be removed from
3008 the language. In GHC, it is controlled by the deprecated extension
3009 <literal>DatatypeContexts</literal>.</para>
3010 </sect2>
3011
3012 <sect2 id="infix-tycons">
3013 <title>Infix type constructors, classes, and type variables</title>
3014
3015 <para>
3016 GHC allows type constructors, classes, and type variables to be operators, and
3017 to be written infix, very much like expressions. More specifically:
3018 <itemizedlist>
3019 <listitem><para>
3020 A type constructor or class can be any non-reserved operator.
3021 Symbols used in types are always like capitalized identifiers; they
3022 are never variables. Note that this is different from the lexical
3023 syntax of data constructors, which are required to begin with a
3024 <literal>:</literal>.
3025 </para></listitem>
3026 <listitem><para>
3027 Data type and type-synonym declarations can be written infix, parenthesised
3028 if you want further arguments. E.g.
3029 <screen>
3030 data a :*: b = Foo a b
3031 type a :+: b = Either a b
3032 class a :=: b where ...
3033
3034 data (a :**: b) x = Baz a b x
3035 type (a :++: b) y = Either (a,b) y
3036 </screen>
3037 </para></listitem>
3038 <listitem><para>
3039 Types, and class constraints, can be written infix. For example
3040 <screen>
3041 x :: Int :*: Bool
3042 f :: (a :=: b) => a -> b
3043 </screen>
3044 </para></listitem>
3045 <listitem><para>
3046 Back-quotes work
3047 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
3048 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
3049 </para></listitem>
3050 <listitem><para>
3051 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
3052 one cannot distinguish between the two in a fixity declaration; a fixity declaration
3053 sets the fixity for a data constructor and the corresponding type constructor. For example:
3054 <screen>
3055 infixl 7 T, :*:
3056 </screen>
3057 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
3058 and similarly for <literal>:*:</literal>.
3059 <literal>Int `a` Bool</literal>.
3060 </para></listitem>
3061 <listitem><para>
3062 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
3063 </para></listitem>
3064
3065 </itemizedlist>
3066 </para>
3067 </sect2>
3068
3069 <sect2 id="type-operators">
3070 <title>Type operators</title>
3071 <para>
3072 In types, an operator symbol like <literal>(+)</literal> is normally treated as a type
3073 <emphasis>variable</emphasis>, just like <literal>a</literal>. Thus in Haskell 98 you can say
3074 <programlisting>
3075 type T (+) = ((+), (+))
3076 -- Just like: type T a = (a,a)
3077
3078 f :: T Int -> Int
3079 f (x,y)= x
3080 </programlisting>
3081 As you can see, using operators in this way is not very useful, and Haskell 98 does not even
3082 allow you to write them infix.
3083 </para>
3084 <para>
3085 The language <option>-XTypeOperators</option> changes this behaviour:
3086 <itemizedlist>
3087 <listitem><para>
3088 Operator symbols become type <emphasis>constructors</emphasis> rather than
3089 type <emphasis>variables</emphasis>.
3090 </para></listitem>
3091 <listitem><para>
3092 Operator symbols in types can be written infix, both in definitions and uses.
3093 for example:
3094 <programlisting>
3095 data a + b = Plus a b
3096 type Foo = Int + Bool
3097 </programlisting>
3098 </para></listitem>
3099 <listitem><para>
3100 There is now some potential ambiguity in import and export lists; for example
3101 if you write <literal>import M( (+) )</literal> do you mean the
3102 <emphasis>function</emphasis> <literal>(+)</literal> or the
3103 <emphasis>type constructor</emphasis> <literal>(+)</literal>?
3104 The default is the former, but with <option>-XExplicitNamespaces</option> (which is implied
3105 by <option>-XTypeOperators</option>) GHC allows you to specify the latter
3106 by preceding it with the keyword <literal>type</literal>, thus:
3107 <programlisting>
3108 import M( type (+) )
3109 </programlisting>
3110 See <xref linkend="explicit-namespaces"/>.
3111 </para></listitem>
3112 <listitem><para>
3113 The fixity of a type operator may be set using the usual fixity declarations
3114 but, as in <xref linkend="infix-tycons"/>, the function and type constructor share
3115 a single fixity.
3116 </para></listitem>
3117 </itemizedlist>
3118 </para>
3119 </sect2>
3120
3121 <sect2 id="type-synonyms">
3122 <title>Liberalised type synonyms</title>
3123
3124 <para>
3125 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
3126 on individual synonym declarations.
3127 With the <option>-XLiberalTypeSynonyms</option> extension,
3128 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
3129 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
3130
3131 <itemizedlist>
3132 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
3133 in a type synonym, thus:
3134 <programlisting>
3135 type Discard a = forall b. Show b => a -> b -> (a, String)
3136
3137 f :: Discard a
3138 f x y = (x, show y)
3139
3140 g :: Discard Int -> (Int,String) -- A rank-2 type
3141 g f = f 3 True
3142 </programlisting>
3143 </para>
3144 </listitem>
3145
3146 <listitem><para>
3147 If you also use <option>-XUnboxedTuples</option>,
3148 you can write an unboxed tuple in a type synonym:
3149 <programlisting>
3150 type Pr = (# Int, Int #)
3151
3152 h :: Int -> Pr
3153 h x = (# x, x #)
3154 </programlisting>
3155 </para></listitem>
3156
3157 <listitem><para>
3158 You can apply a type synonym to a forall type:
3159 <programlisting>
3160 type Foo a = a -> a -> Bool
3161
3162 f :: Foo (forall b. b->b)
3163 </programlisting>
3164 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
3165 <programlisting>
3166 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
3167 </programlisting>
3168 </para></listitem>
3169
3170 <listitem><para>
3171 You can apply a type synonym to a partially applied type synonym:
3172 <programlisting>
3173 type Generic i o = forall x. i x -> o x
3174 type Id x = x
3175
3176 foo :: Generic Id []
3177 </programlisting>
3178 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
3179 <programlisting>
3180 foo :: forall x. x -> [x]
3181 </programlisting>
3182 </para></listitem>
3183
3184 </itemizedlist>
3185 </para>
3186
3187 <para>
3188 GHC currently does kind checking before expanding synonyms (though even that
3189 could be changed.)
3190 </para>
3191 <para>
3192 After expanding type synonyms, GHC does validity checking on types, looking for
3193 the following mal-formedness which isn't detected simply by kind checking:
3194 <itemizedlist>
3195 <listitem><para>
3196 Type constructor applied to a type involving for-alls (if <literal>XImpredicativeTypes</literal>
3197 is off)
3198 </para></listitem>
3199 <listitem><para>
3200 Partially-applied type synonym.
3201 </para></listitem>
3202 </itemizedlist>
3203 So, for example, this will be rejected:
3204 <programlisting>
3205 type Pr = forall a. a
3206
3207 h :: [Pr]
3208 h = ...
3209 </programlisting>
3210 because GHC does not allow type constructors applied to for-all types.
3211 </para>
3212 </sect2>
3213
3214
3215 <sect2 id="existential-quantification">
3216 <title>Existentially quantified data constructors
3217 </title>
3218
3219 <para>
3220 The idea of using existential quantification in data type declarations
3221 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
3222 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
3223 London, 1991). It was later formalised by Laufer and Odersky
3224 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
3225 TOPLAS, 16(5), pp1411-1430, 1994).
3226 It's been in Lennart
3227 Augustsson's <command>hbc</command> Haskell compiler for several years, and
3228 proved very useful. Here's the idea. Consider the declaration:
3229 </para>
3230
3231 <para>
3232
3233 <programlisting>
3234 data Foo = forall a. MkFoo a (a -> Bool)
3235 | Nil
3236 </programlisting>
3237
3238 </para>
3239
3240 <para>
3241 The data type <literal>Foo</literal> has two constructors with types:
3242 </para>
3243
3244 <para>
3245
3246 <programlisting>
3247 MkFoo :: forall a. a -> (a -> Bool) -> Foo
3248 Nil :: Foo
3249 </programlisting>
3250
3251 </para>
3252
3253 <para>
3254 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
3255 does not appear in the data type itself, which is plain <literal>Foo</literal>.
3256 For example, the following expression is fine:
3257 </para>
3258
3259 <para>
3260
3261 <programlisting>
3262 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
3263 </programlisting>
3264
3265 </para>
3266
3267 <para>
3268 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
3269 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
3270 isUpper</function> packages a character with a compatible function. These
3271 two things are each of type <literal>Foo</literal> and can be put in a list.
3272 </para>
3273
3274 <para>
3275 What can we do with a value of type <literal>Foo</literal>?. In particular,
3276 what happens when we pattern-match on <function>MkFoo</function>?
3277 </para>
3278
3279 <para>
3280
3281 <programlisting>
3282 f (MkFoo val fn) = ???
3283 </programlisting>
3284
3285 </para>
3286
3287 <para>
3288 Since all we know about <literal>val</literal> and <function>fn</function> is that they
3289 are compatible, the only (useful) thing we can do with them is to
3290 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
3291 </para>
3292
3293 <para>
3294
3295 <programlisting>
3296 f :: Foo -> Bool
3297 f (MkFoo val fn) = fn val
3298 </programlisting>
3299
3300 </para>
3301
3302 <para>
3303 What this allows us to do is to package heterogeneous values
3304 together with a bunch of functions that manipulate them, and then treat
3305 that collection of packages in a uniform manner. You can express
3306 quite a bit of object-oriented-like programming this way.
3307 </para>
3308
3309 <sect3 id="existential">
3310 <title>Why existential?
3311 </title>
3312
3313 <para>
3314 What has this to do with <emphasis>existential</emphasis> quantification?
3315 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
3316 </para>
3317
3318 <para>
3319
3320 <programlisting>
3321 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
3322 </programlisting>
3323
3324 </para>
3325
3326 <para>
3327 But Haskell programmers can safely think of the ordinary
3328 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
3329 adding a new existential quantification construct.
3330 </para>
3331
3332 </sect3>
3333
3334 <sect3 id="existential-with-context">
3335 <title>Existentials and type classes</title>
3336
3337 <para>
3338 An easy extension is to allow
3339 arbitrary contexts before the constructor. For example:
3340 </para>
3341
3342 <para>
3343
3344 <programlisting>
3345 data Baz = forall a. Eq a => Baz1 a a
3346 | forall b. Show b => Baz2 b (b -> b)
3347 </programlisting>
3348
3349 </para>
3350
3351 <para>
3352 The two constructors have the types you'd expect:
3353 </para>
3354
3355 <para>
3356
3357 <programlisting>
3358 Baz1 :: forall a. Eq a => a -> a -> Baz
3359 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
3360 </programlisting>
3361
3362 </para>
3363
3364 <para>
3365 But when pattern matching on <function>Baz1</function> the matched values can be compared
3366 for equality, and when pattern matching on <function>Baz2</function> the first matched
3367 value can be converted to a string (as well as applying the function to it).
3368 So this program is legal:
3369 </para>
3370
3371 <para>
3372
3373 <programlisting>
3374 f :: Baz -> String
3375 f (Baz1 p q) | p == q = "Yes"
3376 | otherwise = "No"
3377 f (Baz2 v fn) = show (fn v)
3378 </programlisting>
3379
3380 </para>
3381
3382 <para>
3383 Operationally, in a dictionary-passing implementation, the
3384 constructors <function>Baz1</function> and <function>Baz2</function> must store the
3385 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
3386 extract it on pattern matching.
3387 </para>
3388
3389 </sect3>
3390
3391 <sect3 id="existential-records">
3392 <title>Record Constructors</title>
3393
3394 <para>
3395 GHC allows existentials to be used with records syntax as well. For example:
3396
3397 <programlisting>
3398 data Counter a = forall self. NewCounter
3399 { _this :: self
3400 , _inc :: self -> self
3401 , _display :: self -> IO ()
3402 , tag :: a
3403 }
3404 </programlisting>
3405 Here <literal>tag</literal> is a public field, with a well-typed selector
3406 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
3407 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
3408 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
3409 compile-time error. In other words, <emphasis>GHC defines a record selector function
3410 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
3411 (This example used an underscore in the fields for which record selectors
3412 will not be defined, but that is only programming style; GHC ignores them.)
3413 </para>
3414
3415 <para>
3416 To make use of these hidden fields, we need to create some helper functions:
3417
3418 <programlisting>
3419 inc :: Counter a -> Counter a
3420 inc (NewCounter x i d t) = NewCounter
3421 { _this = i x, _inc = i, _display = d, tag = t }
3422
3423 display :: Counter a -> IO ()
3424 display NewCounter{ _this = x, _display = d } = d x
3425 </programlisting>
3426
3427 Now we can define counters with different underlying implementations:
3428
3429 <programlisting>
3430 counterA :: Counter String
3431 counterA = NewCounter
3432 { _this = 0, _inc = (1+), _display = print, tag = "A" }
3433
3434 counterB :: Counter String
3435 counterB = NewCounter
3436 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
3437
3438 main = do
3439 display (inc counterA) -- prints "1"
3440 display (inc (inc counterB)) -- prints "##"
3441 </programlisting>
3442
3443 Record update syntax is supported for existentials (and GADTs):
3444 <programlisting>
3445 setTag :: Counter a -> a -> Counter a
3446 setTag obj t = obj{ tag = t }
3447 </programlisting>
3448 The rule for record update is this: <emphasis>
3449 the types of the updated fields may
3450 mention only the universally-quantified type variables
3451 of the data constructor. For GADTs, the field may mention only types
3452 that appear as a simple type-variable argument in the constructor's result
3453 type</emphasis>. For example:
3454 <programlisting>
3455 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
3456 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
3457 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
3458 -- existentially quantified)
3459
3460 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
3461 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
3462 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
3463 -- type-variable argument in G1's result type)
3464 </programlisting>
3465 </para>
3466
3467 </sect3>
3468
3469
3470 <sect3>
3471 <title>Restrictions</title>
3472
3473 <para>
3474 There are several restrictions on the ways in which existentially-quantified
3475 constructors can be use.
3476 </para>
3477
3478 <para>
3479
3480 <itemizedlist>
3481 <listitem>
3482
3483 <para>
3484 When pattern matching, each pattern match introduces a new,
3485 distinct, type for each existential type variable. These types cannot
3486 be unified with any other type, nor can they escape from the scope of
3487 the pattern match. For example, these fragments are incorrect:
3488
3489
3490 <programlisting>
3491 f1 (MkFoo a f) = a
3492 </programlisting>
3493
3494
3495 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
3496 is the result of <function>f1</function>. One way to see why this is wrong is to
3497 ask what type <function>f1</function> has:
3498
3499
3500 <programlisting>
3501 f1 :: Foo -> a -- Weird!
3502 </programlisting>
3503
3504
3505 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
3506 this:
3507
3508
3509 <programlisting>
3510 f1 :: forall a. Foo -> a -- Wrong!
3511 </programlisting>
3512
3513
3514 The original program is just plain wrong. Here's another sort of error
3515
3516
3517 <programlisting>
3518 f2 (Baz1 a b) (Baz1 p q) = a==q
3519 </programlisting>
3520
3521
3522 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
3523 <literal>a==q</literal> is wrong because it equates the two distinct types arising
3524 from the two <function>Baz1</function> constructors.
3525
3526
3527 </para>
3528 </listitem>
3529 <listitem>
3530
3531 <para>
3532 You can't pattern-match on an existentially quantified
3533 constructor in a <literal>let</literal> or <literal>where</literal> group of
3534 bindings. So this is illegal:
3535
3536
3537 <programlisting>
3538 f3 x = a==b where { Baz1 a b = x }
3539 </programlisting>
3540
3541 Instead, use a <literal>case</literal> expression:
3542
3543 <programlisting>
3544 f3 x = case x of Baz1 a b -> a==b
3545 </programlisting>
3546
3547 In general, you can only pattern-match
3548 on an existentially-quantified constructor in a <literal>case</literal> expression or
3549 in the patterns of a function definition.
3550
3551 The reason for this restriction is really an implementation one.
3552 Type-checking binding groups is already a nightmare without
3553 existentials complicating the picture. Also an existential pattern
3554 binding at the top level of a module doesn't make sense, because it's
3555 not clear how to prevent the existentially-quantified type "escaping".
3556 So for now, there's a simple-to-state restriction. We'll see how
3557 annoying it is.
3558
3559 </para>
3560 </listitem>
3561 <listitem>
3562
3563 <para>
3564 You can't use existential quantification for <literal>newtype</literal>
3565 declarations. So this is illegal:
3566
3567
3568 <programlisting>
3569 newtype T = forall a. Ord a => MkT a
3570 </programlisting>
3571
3572
3573 Reason: a value of type <literal>T</literal> must be represented as a
3574 pair of a dictionary for <literal>Ord t</literal> and a value of type
3575 <literal>t</literal>. That contradicts the idea that
3576 <literal>newtype</literal> should have no concrete representation.
3577 You can get just the same efficiency and effect by using
3578 <literal>data</literal> instead of <literal>newtype</literal>. If
3579 there is no overloading involved, then there is more of a case for
3580 allowing an existentially-quantified <literal>newtype</literal>,
3581 because the <literal>data</literal> version does carry an
3582 implementation cost, but single-field existentially quantified
3583 constructors aren't much use. So the simple restriction (no
3584 existential stuff on <literal>newtype</literal>) stands, unless there
3585 are convincing reasons to change it.
3586
3587
3588 </para>
3589 </listitem>
3590 <listitem>
3591
3592 <para>
3593 You can't use <literal>deriving</literal> to define instances of a
3594 data type with existentially quantified data constructors.
3595
3596 Reason: in most cases it would not make sense. For example:;
3597
3598 <programlisting>
3599 data T = forall a. MkT [a] deriving( Eq )
3600 </programlisting>
3601
3602 To derive <literal>Eq</literal> in the standard way we would need to have equality
3603 between the single component of two <function>MkT</function> constructors:
3604
3605 <programlisting>
3606 instance Eq T where
3607 (MkT a) == (MkT b) = ???
3608 </programlisting>
3609
3610 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
3611 It's just about possible to imagine examples in which the derived instance
3612 would make sense, but it seems altogether simpler simply to prohibit such
3613 declarations. Define your own instances!
3614 </para>
3615 </listitem>
3616
3617 </itemizedlist>
3618
3619 </para>
3620
3621 </sect3>
3622 </sect2>
3623
3624 <!-- ====================== Generalised algebraic data types ======================= -->
3625
3626 <sect2 id="gadt-style">
3627 <title>Declaring data types with explicit constructor signatures</title>
3628
3629 <para>When the <literal>GADTSyntax</literal> extension is enabled,
3630 GHC allows you to declare an algebraic data type by
3631 giving the type signatures of constructors explicitly. For example:
3632 <programlisting>
3633 data Maybe a where
3634 Nothing :: Maybe a
3635 Just :: a -> Maybe a
3636 </programlisting>
3637 The form is called a "GADT-style declaration"
3638 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
3639 can only be declared using this form.</para>
3640 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
3641 For example, these two declarations are equivalent:
3642 <programlisting>
3643 data Foo = forall a. MkFoo a (a -> Bool)
3644 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
3645 </programlisting>
3646 </para>
3647 <para>Any data type that can be declared in standard Haskell-98 syntax
3648 can also be declared using GADT-style syntax.
3649 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
3650 they treat class constraints on the data constructors differently.
3651 Specifically, if the constructor is given a type-class context, that
3652 context is made available by pattern matching. For example:
3653 <programlisting>
3654 data Set a where
3655 MkSet :: Eq a => [a] -> Set a
3656
3657 makeSet :: Eq a => [a] -> Set a
3658 makeSet xs = MkSet (nub xs)
3659
3660 insert :: a -> Set a -> Set a
3661 insert a (MkSet as) | a `elem` as = MkSet as
3662 | otherwise = MkSet (a:as)
3663 </programlisting>
3664 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
3665 gives rise to a <literal>(Eq a)</literal>
3666 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
3667 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
3668 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
3669 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
3670 when pattern-matching that dictionary becomes available for the right-hand side of the match.
3671 In the example, the equality dictionary is used to satisfy the equality constraint
3672 generated by the call to <literal>elem</literal>, so that the type of
3673 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
3674 </para>
3675 <para>
3676 For example, one possible application is to reify dictionaries:
3677 <programlisting>
3678 data NumInst a where
3679 MkNumInst :: Num a => NumInst a
3680
3681 intInst :: NumInst Int
3682 intInst = MkNumInst
3683
3684 plus :: NumInst a -> a -> a -> a
3685 plus MkNumInst p q = p + q
3686 </programlisting>
3687 Here, a value of type <literal>NumInst a</literal> is equivalent
3688 to an explicit <literal>(Num a)</literal> dictionary.
3689 </para>
3690 <para>
3691 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
3692 For example, the <literal>NumInst</literal> data type above could equivalently be declared
3693 like this:
3694 <programlisting>
3695 data NumInst a
3696 = Num a => MkNumInst (NumInst a)
3697 </programlisting>
3698 Notice that, unlike the situation when declaring an existential, there is
3699 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
3700 data type's universally quantified type variable <literal>a</literal>.
3701 A constructor may have both universal and existential type variables: for example,
3702 the following two declarations are equivalent:
3703 <programlisting>
3704 data T1 a
3705 = forall b. (Num a, Eq b) => MkT1 a b
3706 data T2 a where
3707 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
3708 </programlisting>
3709 </para>
3710 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
3711 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
3712 In Haskell 98 the definition
3713 <programlisting>
3714 data Eq a => Set' a = MkSet' [a]
3715 </programlisting>
3716 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
3717 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
3718 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
3719 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
3720 GHC's behaviour is much more useful, as well as much more intuitive.
3721 </para>
3722
3723 <para>
3724 The rest of this section gives further details about GADT-style data
3725 type declarations.
3726
3727 <itemizedlist>
3728 <listitem><para>
3729 The result type of each data constructor must begin with the type constructor being defined.
3730 If the result type of all constructors
3731 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
3732 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
3733 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
3734 </para></listitem>
3735
3736 <listitem><para>
3737 As with other type signatures, you can give a single signature for several data constructors.
3738 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
3739 <programlisting>
3740 data T a where
3741 T1,T2 :: a -> T a
3742 T3 :: T a
3743 </programlisting>
3744 </para></listitem>
3745
3746 <listitem><para>
3747 The type signature of
3748 each constructor is independent, and is implicitly universally quantified as usual.
3749 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
3750 have no scope, and different constructors may have different universally-quantified type variables:
3751 <programlisting>
3752 data T a where -- The 'a' has no scope
3753 T1,T2 :: b -> T b -- Means forall b. b -> T b
3754 T3 :: T a -- Means forall a. T a
3755 </programlisting>
3756 </para></listitem>
3757
3758 <listitem><para>
3759 A constructor signature may mention type class constraints, which can differ for
3760 different constructors. For example, this is fine:
3761 <programlisting>
3762 data T a where
3763 T1 :: Eq b => b -> b -> T b
3764 T2 :: (Show c, Ix c) => c -> [c] -> T c
3765 </programlisting>
3766 When pattern matching, these constraints are made available to discharge constraints
3767 in the body of the match. For example:
3768 <programlisting>
3769 f :: T a -> String
3770 f (T1 x y) | x==y = "yes"
3771 | otherwise = "no"
3772 f (T2 a b) = show a
3773 </programlisting>
3774 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
3775 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
3776 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
3777 </para></listitem>
3778
3779 <listitem><para>
3780 Unlike a Haskell-98-style
3781 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
3782 have no scope. Indeed, one can write a kind signature instead:
3783 <programlisting>
3784 data Set :: * -> * where ...
3785 </programlisting>
3786 or even a mixture of the two:
3787 <programlisting>
3788 data Bar a :: (* -> *) -> * where ...
3789 </programlisting>
3790 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3791 like this:
3792 <programlisting>
3793 data Bar a (b :: * -> *) where ...
3794 </programlisting>
3795 </para></listitem>
3796
3797
3798 <listitem><para>
3799 You can use strictness annotations, in the obvious places
3800 in the constructor type:
3801 <programlisting>
3802 data Term a where
3803 Lit :: !Int -> Term Int
3804 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3805 Pair :: Term a -> Term b -> Term (a,b)
3806 </programlisting>
3807 </para></listitem>
3808
3809 <listitem><para>
3810 You can use a <literal>deriving</literal> clause on a GADT-style data type
3811 declaration. For example, these two declarations are equivalent
3812 <programlisting>
3813 data Maybe1 a where {
3814 Nothing1 :: Maybe1 a ;
3815 Just1 :: a -> Maybe1 a
3816 } deriving( Eq, Ord )
3817
3818 data Maybe2 a = Nothing2 | Just2 a
3819 deriving( Eq, Ord )
3820 </programlisting>
3821 </para></listitem>
3822
3823 <listitem><para>
3824 The type signature may have quantified type variables that do not appear
3825 in the result type:
3826 <programlisting>
3827 data Foo where
3828 MkFoo :: a -> (a->Bool) -> Foo
3829 Nil :: Foo
3830 </programlisting>
3831 Here the type variable <literal>a</literal> does not appear in the result type
3832 of either constructor.
3833 Although it is universally quantified in the type of the constructor, such
3834 a type variable is often called "existential".
3835 Indeed, the above declaration declares precisely the same type as
3836 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
3837 </para><para>
3838 The type may contain a class context too, of course:
3839 <programlisting>
3840 data Showable where
3841 MkShowable :: Show a => a -> Showable
3842 </programlisting>
3843 </para></listitem>
3844
3845 <listitem><para>
3846 You can use record syntax on a GADT-style data type declaration:
3847
3848 <programlisting>
3849 data Person where
3850 Adult :: { name :: String, children :: [Person] } -> Person
3851 Child :: Show a => { name :: !String, funny :: a } -> Person
3852 </programlisting>
3853 As usual, for every constructor that has a field <literal>f</literal>, the type of
3854 field <literal>f</literal> must be the same (modulo alpha conversion).
3855 The <literal>Child</literal> constructor above shows that the signature
3856 may have a context, existentially-quantified variables, and strictness annotations,
3857 just as in the non-record case. (NB: the "type" that follows the double-colon
3858 is not really a type, because of the record syntax and strictness annotations.
3859 A "type" of this form can appear only in a constructor signature.)
3860 </para></listitem>
3861
3862 <listitem><para>
3863 Record updates are allowed with GADT-style declarations,
3864 only fields that have the following property: the type of the field
3865 mentions no existential type variables.
3866 </para></listitem>
3867
3868 <listitem><para>
3869 As in the case of existentials declared using the Haskell-98-like record syntax
3870 (<xref linkend="existential-records"/>),
3871 record-selector functions are generated only for those fields that have well-typed
3872 selectors.
3873 Here is the example of that section, in GADT-style syntax:
3874 <programlisting>
3875 data Counter a where
3876 NewCounter :: { _this :: self
3877 , _inc :: self -> self
3878 , _display :: self -> IO ()
3879 , tag :: a
3880 } -> Counter a
3881 </programlisting>
3882 As before, only one selector function is generated here, that for <literal>tag</literal>.
3883 Nevertheless, you can still use all the field names in pattern matching and record construction.
3884 </para></listitem>
3885
3886 <listitem><para>
3887 In a GADT-style data type declaration there is no obvious way to specify that a data constructor
3888 should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
3889 (Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
3890 So GHC implements the following design: a data constructor declared in a GADT-style data type
3891 declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
3892 (b) it has two arguments, (c) it has a programmer-supplied fixity declaration. For example
3893 <programlisting>
3894 infix 6 (:--:)
3895 data T a where
3896 (:--:) :: Int -> Bool -> T Int
3897 </programlisting>
3898 </para></listitem>
3899 </itemizedlist></para>
3900 </sect2>
3901
3902 <sect2 id="gadt">
3903 <title>Generalised Algebraic Data Types (GADTs)</title>
3904
3905 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
3906 by allowing constructors to have richer return types. Here is an example:
3907 <programlisting>
3908 data Term a where
3909 Lit :: Int -> Term Int
3910 Succ :: Term Int -> Term Int
3911 IsZero :: Term Int -> Term Bool
3912 If :: Term Bool -> Term a -> Term a -> Term a
3913 Pair :: Term a -> Term b -> Term (a,b)
3914 </programlisting>
3915 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3916 case with ordinary data types. This generality allows us to
3917 write a well-typed <literal>eval</literal> function
3918 for these <literal>Terms</literal>:
3919 <programlisting>
3920 eval :: Term a -> a
3921 eval (Lit i) = i
3922 eval (Succ t) = 1 + eval t
3923 eval (IsZero t) = eval t == 0
3924 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3925 eval (Pair e1 e2) = (eval e1, eval e2)
3926 </programlisting>
3927 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
3928 For example, in the right hand side of the equation
3929 <programlisting>
3930 eval :: Term a -> a
3931 eval (Lit i) = ...
3932 </programlisting>
3933 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
3934 A precise specification of the type rules is beyond what this user manual aspires to,
3935 but the design closely follows that described in
3936 the paper <ulink
3937 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
3938 unification-based type inference for GADTs</ulink>,
3939 (ICFP 2006).
3940 The general principle is this: <emphasis>type refinement is only carried out
3941 based on user-supplied type annotations</emphasis>.
3942 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
3943 and lots of obscure error messages will
3944 occur. However, the refinement is quite general. For example, if we had:
3945 <programlisting>
3946 eval :: Term a -> a -> a
3947 eval (Lit i) j = i+j
3948 </programlisting>
3949 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3950 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
3951 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3952 </para>
3953 <para>
3954 These and many other examples are given in papers by Hongwei Xi, and
3955 Tim Sheard. There is a longer introduction
3956 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3957 and Ralf Hinze's
3958 <ulink url="http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
3959 may use different notation to that implemented in GHC.
3960 </para>
3961 <para>
3962 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
3963 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XGADTSyntax</option>
3964 and <option>-XMonoLocalBinds</option>.
3965 <itemizedlist>
3966 <listitem><para>
3967 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
3968 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
3969 The result type of each constructor must begin with the type constructor being defined,
3970 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
3971 For example, in the <literal>Term</literal> data
3972 type above, the type of each constructor must end with <literal>Term ty</literal>, but
3973 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
3974 constructor).
3975 </para></listitem>
3976
3977 <listitem><para>
3978 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
3979 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
3980 whose result type is not just <literal>T a b</literal>.
3981 </para></listitem>
3982
3983 <listitem><para>
3984 You cannot use a <literal>deriving</literal> clause for a GADT; only for
3985 an ordinary data type.
3986 </para></listitem>
3987
3988 <listitem><para>
3989 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
3990 For example:
3991 <programlisting>
3992 data Term a where
3993 Lit :: { val :: Int } -> Term Int
3994 Succ :: { num :: Term Int } -> Term Int
3995 Pred :: { num :: Term Int } -> Term Int
3996 IsZero :: { arg :: Term Int } -> Term Bool
3997 Pair :: { arg1 :: Term a
3998 , arg2 :: Term b
3999 } -> Term (a,b)
4000 If :: { cnd :: Term Bool
4001 , tru :: Term a
4002 , fls :: Term a
4003 } -> Term a
4004 </programlisting>
4005 However, for GADTs there is the following additional constraint:
4006 every constructor that has a field <literal>f</literal> must have
4007 the same result type (modulo alpha conversion)
4008 Hence, in the above example, we cannot merge the <literal>num</literal>
4009 and <literal>arg</literal> fields above into a
4010 single name. Although their field types are both <literal>Term Int</literal>,
4011 their selector functions actually have different types:
4012
4013 <programlisting>
4014 num :: Term Int -> Term Int
4015 arg :: Term Bool -> Term Int
4016 </programlisting>
4017 </para></listitem>
4018
4019 <listitem><para>
4020 When pattern-matching against data constructors drawn from a GADT,
4021 for example in a <literal>case</literal> expression, the following rules apply:
4022 <itemizedlist>
4023 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
4024 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
4025 <listitem><para>The type of any free variable mentioned in any of
4026 the <literal>case</literal> alternatives must be rigid.</para></listitem>
4027 </itemizedlist>
4028 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
4029 way to ensure that a variable a rigid type is to give it a type signature.
4030 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
4031 Simple unification-based type inference for GADTs
4032 </ulink>. The criteria implemented by GHC are given in the Appendix.
4033
4034 </para></listitem>
4035
4036 </itemizedlist>
4037 </para>
4038
4039 </sect2>
4040 </sect1>
4041
4042 <!-- ====================== End of Generalised algebraic data types ======================= -->
4043
4044 <sect1 id="deriving">
4045 <title>Extensions to the "deriving" mechanism</title>
4046
4047 <sect2 id="deriving-inferred">
4048 <title>Inferred context for deriving clauses</title>
4049
4050 <para>
4051 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
4052 legal. For example:
4053 <programlisting>
4054 data T0 f a = MkT0 a deriving( Eq )
4055 data T1 f a = MkT1 (f a) deriving( Eq )
4056 data T2 f a = MkT2 (f (f a)) deriving( Eq )
4057 </programlisting>
4058 The natural generated <literal>Eq</literal> code would result in these instance declarations:
4059 <programlisting>
4060 instance Eq a => Eq (T0 f a) where ...
4061 instance Eq (f a) => Eq (T1 f a) where ...
4062 instance Eq (f (f a)) => Eq (T2 f a) where ...
4063 </programlisting>
4064 The first of these is obviously fine. The second is still fine, although less obviously.
4065 The third is not Haskell 98, and risks losing termination of instances.
4066 </para>
4067 <para>
4068 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
4069 each constraint in the inferred instance context must consist only of type variables,
4070 with no repetitions.
4071 </para>
4072 <para>
4073 This rule is applied regardless of flags. If you want a more exotic context, you can write
4074 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
4075 </para>
4076 </sect2>
4077
4078 <sect2 id="stand-alone-deriving">
4079 <title>Stand-alone deriving declarations</title>
4080
4081 <para>
4082 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
4083 <programlisting>
4084 data Foo a = Bar a | Baz String
4085
4086 deriving instance Eq a => Eq (Foo a)
4087 </programlisting>
4088 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
4089 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
4090 </para>
4091 <para>
4092 However, standalone deriving differs from a <literal>deriving</literal> clause in a number
4093 of important ways:
4094 <itemizedlist>
4095 <listitem><para>The standalone deriving declaration does not need to be in the
4096 same module as the data type declaration. (But be aware of the dangers of
4097 orphan instances (<xref linkend="orphan-modules&