Improve documentation of overloaded lists
[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 commandline 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 Unboxed tuples are used for functions that need to return multiple
229 values, but they avoid the heap allocation normally associated with
230 using fully-fledged tuples. When an unboxed tuple is returned, the
231 components are put directly into registers or on the stack; the
232 unboxed tuple itself does not have a composite representation. Many
233 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
234 tuples.
235 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
236 tuples to avoid unnecessary allocation during sequences of operations.
237 </para>
238
239 <para>
240 There are some restrictions on the use of unboxed tuples:
241 <itemizedlist>
242
243 <listitem>
244 <para>
245 Values of unboxed tuple types are subject to the same restrictions as
246 other unboxed types; i.e. they may not be stored in polymorphic data
247 structures or passed to polymorphic functions.
248 </para>
249 </listitem>
250
251 <listitem>
252 <para>
253 The typical use of unboxed tuples is simply to return multiple values,
254 binding those multiple results with a <literal>case</literal> expression, thus:
255 <programlisting>
256 f x y = (# x+1, y-1 #)
257 g x = case f x x of { (# a, b #) -&#62; a + b }
258 </programlisting>
259 You can have an unboxed tuple in a pattern binding, thus
260 <programlisting>
261 f x = let (# p,q #) = h x in ..body..
262 </programlisting>
263 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
264 the resulting binding is lazy like any other Haskell pattern binding. The
265 above example desugars like this:
266 <programlisting>
267 f x = let t = case h x o f{ (# p,q #) -> (p,q)
268 p = fst t
269 q = snd t
270 in ..body..
271 </programlisting>
272 Indeed, the bindings can even be recursive.
273 </para>
274 </listitem>
275 </itemizedlist>
276
277 </para>
278
279 </sect2>
280 </sect1>
281
282
283 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
284
285 <sect1 id="syntax-extns">
286 <title>Syntactic extensions</title>
287
288 <sect2 id="unicode-syntax">
289 <title>Unicode syntax</title>
290 <para>The language
291 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
292 enables Unicode characters to be used to stand for certain ASCII
293 character sequences. The following alternatives are provided:</para>
294
295 <informaltable>
296 <tgroup cols="2" align="left" colsep="1" rowsep="1">
297 <thead>
298 <row>
299 <entry>ASCII</entry>
300 <entry>Unicode alternative</entry>
301 <entry>Code point</entry>
302 <entry>Name</entry>
303 </row>
304 </thead>
305
306 <!--
307 to find the DocBook entities for these characters, find
308 the Unicode code point (e.g. 0x2237), and grep for it in
309 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
310 your system. Some of these Unicode code points don't have
311 equivalent DocBook entities.
312 -->
313
314 <tbody>
315 <row>
316 <entry><literal>::</literal></entry>
317 <entry>::</entry> <!-- no special char, apparently -->
318 <entry>0x2237</entry>
319 <entry>PROPORTION</entry>
320 </row>
321 </tbody>
322 <tbody>
323 <row>
324 <entry><literal>=&gt;</literal></entry>
325 <entry>&rArr;</entry>
326 <entry>0x21D2</entry>
327 <entry>RIGHTWARDS DOUBLE ARROW</entry>
328 </row>
329 </tbody>
330 <tbody>
331 <row>
332 <entry><literal>forall</literal></entry>
333 <entry>&forall;</entry>
334 <entry>0x2200</entry>
335 <entry>FOR ALL</entry>
336 </row>
337 </tbody>
338 <tbody>
339 <row>
340 <entry><literal>-&gt;</literal></entry>
341 <entry>&rarr;</entry>
342 <entry>0x2192</entry>
343 <entry>RIGHTWARDS ARROW</entry>
344 </row>
345 </tbody>
346 <tbody>
347 <row>
348 <entry><literal>&lt;-</literal></entry>
349 <entry>&larr;</entry>
350 <entry>0x2190</entry>
351 <entry>LEFTWARDS ARROW</entry>
352 </row>
353 </tbody>
354
355 <tbody>
356 <row>
357 <entry>-&lt;</entry>
358 <entry>&larrtl;</entry>
359 <entry>0x2919</entry>
360 <entry>LEFTWARDS ARROW-TAIL</entry>
361 </row>
362 </tbody>
363
364 <tbody>
365 <row>
366 <entry>&gt;-</entry>
367 <entry>&rarrtl;</entry>
368 <entry>0x291A</entry>
369 <entry>RIGHTWARDS ARROW-TAIL</entry>
370 </row>
371 </tbody>
372
373 <tbody>
374 <row>
375 <entry>-&lt;&lt;</entry>
376 <entry></entry>
377 <entry>0x291B</entry>
378 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
379 </row>
380 </tbody>
381
382 <tbody>
383 <row>
384 <entry>&gt;&gt;-</entry>
385 <entry></entry>
386 <entry>0x291C</entry>
387 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
388 </row>
389 </tbody>
390
391 <tbody>
392 <row>
393 <entry>*</entry>
394 <entry>&starf;</entry>
395 <entry>0x2605</entry>
396 <entry>BLACK STAR</entry>
397 </row>
398 </tbody>
399
400 </tgroup>
401 </informaltable>
402 </sect2>
403
404 <sect2 id="magic-hash">
405 <title>The magic hash</title>
406 <para>The language extension <option>-XMagicHash</option> allows "&num;" as a
407 postfix modifier to identifiers. Thus, "x&num;" is a valid variable, and "T&num;" is
408 a valid type constructor or data constructor.</para>
409
410 <para>The hash sign does not change semantics at all. We tend to use variable
411 names ending in "&num;" for unboxed values or types (e.g. <literal>Int&num;</literal>),
412 but there is no requirement to do so; they are just plain ordinary variables.
413 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
414 For example, to bring <literal>Int&num;</literal> into scope you must
415 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
416 the <option>-XMagicHash</option> extension
417 then allows you to <emphasis>refer</emphasis> to the <literal>Int&num;</literal>
418 that is now in scope.</para>
419 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
420 <itemizedlist>
421 <listitem><para> <literal>'x'&num;</literal> has type <literal>Char&num;</literal></para> </listitem>
422 <listitem><para> <literal>&quot;foo&quot;&num;</literal> has type <literal>Addr&num;</literal></para> </listitem>
423 <listitem><para> <literal>3&num;</literal> has type <literal>Int&num;</literal>. In general,
424 any Haskell integer lexeme followed by a <literal>&num;</literal> is an <literal>Int&num;</literal> literal, e.g.
425 <literal>-0x3A&num;</literal> as well as <literal>32&num;</literal></para>.</listitem>
426 <listitem><para> <literal>3&num;&num;</literal> has type <literal>Word&num;</literal>. In general,
427 any non-negative Haskell integer lexeme followed by <literal>&num;&num;</literal>
428 is a <literal>Word&num;</literal>. </para> </listitem>
429 <listitem><para> <literal>3.2&num;</literal> has type <literal>Float&num;</literal>.</para> </listitem>
430 <listitem><para> <literal>3.2&num;&num;</literal> has type <literal>Double&num;</literal></para> </listitem>
431 </itemizedlist>
432 </para>
433 </sect2>
434
435 <!-- ====================== HIERARCHICAL MODULES ======================= -->
436
437
438 <sect2 id="hierarchical-modules">
439 <title>Hierarchical Modules</title>
440
441 <para>GHC supports a small extension to the syntax of module
442 names: a module name is allowed to contain a dot
443 <literal>&lsquo;.&rsquo;</literal>. This is also known as the
444 &ldquo;hierarchical module namespace&rdquo; extension, because
445 it extends the normally flat Haskell module namespace into a
446 more flexible hierarchy of modules.</para>
447
448 <para>This extension has very little impact on the language
449 itself; modules names are <emphasis>always</emphasis> fully
450 qualified, so you can just think of the fully qualified module
451 name as <quote>the module name</quote>. In particular, this
452 means that the full module name must be given after the
453 <literal>module</literal> keyword at the beginning of the
454 module; for example, the module <literal>A.B.C</literal> must
455 begin</para>
456
457 <programlisting>module A.B.C</programlisting>
458
459
460 <para>It is a common strategy to use the <literal>as</literal>
461 keyword to save some typing when using qualified names with
462 hierarchical modules. For example:</para>
463
464 <programlisting>
465 import qualified Control.Monad.ST.Strict as ST
466 </programlisting>
467
468 <para>For details on how GHC searches for source and interface
469 files in the presence of hierarchical modules, see <xref
470 linkend="search-path"/>.</para>
471
472 <para>GHC comes with a large collection of libraries arranged
473 hierarchically; see the accompanying <ulink
474 url="../libraries/index.html">library
475 documentation</ulink>. More libraries to install are available
476 from <ulink
477 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
478 </sect2>
479
480 <!-- ====================== PATTERN GUARDS ======================= -->
481
482 <sect2 id="pattern-guards">
483 <title>Pattern guards</title>
484
485 <para>
486 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
487 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.)
488 </para>
489
490 <para>
491 Suppose we have an abstract data type of finite maps, with a
492 lookup operation:
493
494 <programlisting>
495 lookup :: FiniteMap -> Int -> Maybe Int
496 </programlisting>
497
498 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
499 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
500 </para>
501
502 <programlisting>
503 clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
504 | otherwise = var1 + var2
505 where
506 m1 = lookup env var1
507 m2 = lookup env var2
508 ok1 = maybeToBool m1
509 ok2 = maybeToBool m2
510 val1 = expectJust m1
511 val2 = expectJust m2
512 </programlisting>
513
514 <para>
515 The auxiliary functions are
516 </para>
517
518 <programlisting>
519 maybeToBool :: Maybe a -&gt; Bool
520 maybeToBool (Just x) = True
521 maybeToBool Nothing = False
522
523 expectJust :: Maybe a -&gt; a
524 expectJust (Just x) = x
525 expectJust Nothing = error "Unexpected Nothing"
526 </programlisting>
527
528 <para>
529 What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
530 ok2</literal> checks that both lookups succeed, using
531 <function>maybeToBool</function> to convert the <function>Maybe</function>
532 types to booleans. The (lazily evaluated) <function>expectJust</function>
533 calls extract the values from the results of the lookups, and binds the
534 returned values to <varname>val1</varname> and <varname>val2</varname>
535 respectively. If either lookup fails, then clunky takes the
536 <literal>otherwise</literal> case and returns the sum of its arguments.
537 </para>
538
539 <para>
540 This is certainly legal Haskell, but it is a tremendously verbose and
541 un-obvious way to achieve the desired effect. Arguably, a more direct way
542 to write clunky would be to use case expressions:
543 </para>
544
545 <programlisting>
546 clunky env var1 var2 = case lookup env var1 of
547 Nothing -&gt; fail
548 Just val1 -&gt; case lookup env var2 of
549 Nothing -&gt; fail
550 Just val2 -&gt; val1 + val2
551 where
552 fail = var1 + var2
553 </programlisting>
554
555 <para>
556 This is a bit shorter, but hardly better. Of course, we can rewrite any set
557 of pattern-matching, guarded equations as case expressions; that is
558 precisely what the compiler does when compiling equations! The reason that
559 Haskell provides guarded equations is because they allow us to write down
560 the cases we want to consider, one at a time, independently of each other.
561 This structure is hidden in the case version. Two of the right-hand sides
562 are really the same (<function>fail</function>), and the whole expression
563 tends to become more and more indented.
564 </para>
565
566 <para>
567 Here is how I would write clunky:
568 </para>
569
570 <programlisting>
571 clunky env var1 var2
572 | Just val1 &lt;- lookup env var1
573 , Just val2 &lt;- lookup env var2
574 = val1 + val2
575 ...other equations for clunky...
576 </programlisting>
577
578 <para>
579 The semantics should be clear enough. The qualifiers are matched in order.
580 For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
581 right hand side is evaluated and matched against the pattern on the left.
582 If the match fails then the whole guard fails and the next equation is
583 tried. If it succeeds, then the appropriate binding takes place, and the
584 next qualifier is matched, in the augmented environment. Unlike list
585 comprehensions, however, the type of the expression to the right of the
586 <literal>&lt;-</literal> is the same as the type of the pattern to its
587 left. The bindings introduced by pattern guards scope over all the
588 remaining guard qualifiers, and over the right hand side of the equation.
589 </para>
590
591 <para>
592 Just as with list comprehensions, boolean expressions can be freely mixed
593 with among the pattern guards. For example:
594 </para>
595
596 <programlisting>
597 f x | [y] &lt;- x
598 , y > 3
599 , Just z &lt;- h y
600 = ...
601 </programlisting>
602
603 <para>
604 Haskell's current guards therefore emerge as a special case, in which the
605 qualifier list has just one element, a boolean expression.
606 </para>
607 </sect2>
608
609 <!-- ===================== View patterns =================== -->
610
611 <sect2 id="view-patterns">
612 <title>View patterns
613 </title>
614
615 <para>
616 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
617 More information and examples of view patterns can be found on the
618 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
619 page</ulink>.
620 </para>
621
622 <para>
623 View patterns are somewhat like pattern guards that can be nested inside
624 of other patterns. They are a convenient way of pattern-matching
625 against values of abstract types. For example, in a programming language
626 implementation, we might represent the syntax of the types of the
627 language as follows:
628
629 <programlisting>
630 type Typ
631
632 data TypView = Unit
633 | Arrow Typ Typ
634
635 view :: Typ -> TypView
636
637 -- additional operations for constructing Typ's ...
638 </programlisting>
639
640 The representation of Typ is held abstract, permitting implementations
641 to use a fancy representation (e.g., hash-consing to manage sharing).
642
643 Without view patterns, using this signature a little inconvenient:
644 <programlisting>
645 size :: Typ -> Integer
646 size t = case view t of
647 Unit -> 1
648 Arrow t1 t2 -> size t1 + size t2
649 </programlisting>
650
651 It is necessary to iterate the case, rather than using an equational
652 function definition. And the situation is even worse when the matching
653 against <literal>t</literal> is buried deep inside another pattern.
654 </para>
655
656 <para>
657 View patterns permit calling the view function inside the pattern and
658 matching against the result:
659 <programlisting>
660 size (view -> Unit) = 1
661 size (view -> Arrow t1 t2) = size t1 + size t2
662 </programlisting>
663
664 That is, we add a new form of pattern, written
665 <replaceable>expression</replaceable> <literal>-></literal>
666 <replaceable>pattern</replaceable> that means "apply the expression to
667 whatever we're trying to match against, and then match the result of
668 that application against the pattern". The expression can be any Haskell
669 expression of function type, and view patterns can be used wherever
670 patterns are used.
671 </para>
672
673 <para>
674 The semantics of a pattern <literal>(</literal>
675 <replaceable>exp</replaceable> <literal>-></literal>
676 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
677
678 <itemizedlist>
679
680 <listitem> Scoping:
681
682 <para>The variables bound by the view pattern are the variables bound by
683 <replaceable>pat</replaceable>.
684 </para>
685
686 <para>
687 Any variables in <replaceable>exp</replaceable> are bound occurrences,
688 but variables bound "to the left" in a pattern are in scope. This
689 feature permits, for example, one argument to a function to be used in
690 the view of another argument. For example, the function
691 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
692 written using view patterns as follows:
693
694 <programlisting>
695 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
696 ...other equations for clunky...
697 </programlisting>
698 </para>
699
700 <para>
701 More precisely, the scoping rules are:
702 <itemizedlist>
703 <listitem>
704 <para>
705 In a single pattern, variables bound by patterns to the left of a view
706 pattern expression are in scope. For example:
707 <programlisting>
708 example :: Maybe ((String -> Integer,Integer), String) -> Bool
709 example Just ((f,_), f -> 4) = True
710 </programlisting>
711
712 Additionally, in function definitions, variables bound by matching earlier curried
713 arguments may be used in view pattern expressions in later arguments:
714 <programlisting>
715 example :: (String -> Integer) -> String -> Bool
716 example f (f -> 4) = True
717 </programlisting>
718 That is, the scoping is the same as it would be if the curried arguments
719 were collected into a tuple.
720 </para>
721 </listitem>
722
723 <listitem>
724 <para>
725 In mutually recursive bindings, such as <literal>let</literal>,
726 <literal>where</literal>, or the top level, view patterns in one
727 declaration may not mention variables bound by other declarations. That
728 is, each declaration must be self-contained. For example, the following
729 program is not allowed:
730 <programlisting>
731 let {(x -> y) = e1 ;
732 (y -> x) = e2 } in x
733 </programlisting>
734
735 (For some amplification on this design choice see
736 <ulink url="http://hackage.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
737
738 </para>
739 </listitem>
740 </itemizedlist>
741
742 </para>
743 </listitem>
744
745 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
746 <replaceable>T1</replaceable> <literal>-></literal>
747 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
748 a <replaceable>T2</replaceable>, then the whole view pattern matches a
749 <replaceable>T1</replaceable>.
750 </para></listitem>
751
752 <listitem><para> Matching: To the equations in Section 3.17.3 of the
753 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
754 Report</ulink>, add the following:
755 <programlisting>
756 case v of { (e -> p) -> e1 ; _ -> e2 }
757 =
758 case (e v) of { p -> e1 ; _ -> e2 }
759 </programlisting>
760 That is, to match a variable <replaceable>v</replaceable> against a pattern
761 <literal>(</literal> <replaceable>exp</replaceable>
762 <literal>-></literal> <replaceable>pat</replaceable>
763 <literal>)</literal>, evaluate <literal>(</literal>
764 <replaceable>exp</replaceable> <replaceable> v</replaceable>
765 <literal>)</literal> and match the result against
766 <replaceable>pat</replaceable>.
767 </para></listitem>
768
769 <listitem><para> Efficiency: When the same view function is applied in
770 multiple branches of a function definition or a case expression (e.g.,
771 in <literal>size</literal> above), GHC makes an attempt to collect these
772 applications into a single nested case expression, so that the view
773 function is only applied once. Pattern compilation in GHC follows the
774 matrix algorithm described in Chapter 4 of <ulink
775 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
776 Implementation of Functional Programming Languages</ulink>. When the
777 top rows of the first column of a matrix are all view patterns with the
778 "same" expression, these patterns are transformed into a single nested
779 case. This includes, for example, adjacent view patterns that line up
780 in a tuple, as in
781 <programlisting>
782 f ((view -> A, p1), p2) = e1
783 f ((view -> B, p3), p4) = e2
784 </programlisting>
785 </para>
786
787 <para> The current notion of when two view pattern expressions are "the
788 same" is very restricted: it is not even full syntactic equality.
789 However, it does include variables, literals, applications, and tuples;
790 e.g., two instances of <literal>view ("hi", "there")</literal> will be
791 collected. However, the current implementation does not compare up to
792 alpha-equivalence, so two instances of <literal>(x, view x ->
793 y)</literal> will not be coalesced.
794 </para>
795
796 </listitem>
797
798 </itemizedlist>
799 </para>
800
801 </sect2>
802
803 <!-- ===================== n+k patterns =================== -->
804
805 <sect2 id="n-k-patterns">
806 <title>n+k patterns</title>
807 <indexterm><primary><option>-XNPlusKPatterns</option></primary></indexterm>
808
809 <para>
810 <literal>n+k</literal> pattern support is disabled by default. To enable
811 it, you can use the <option>-XNPlusKPatterns</option> flag.
812 </para>
813
814 </sect2>
815
816 <!-- ===================== Traditional record syntax =================== -->
817
818 <sect2 id="traditional-record-syntax">
819 <title>Traditional record syntax</title>
820 <indexterm><primary><option>-XNoTraditionalRecordSyntax</option></primary></indexterm>
821
822 <para>
823 Traditional record syntax, such as <literal>C {f = x}</literal>, is enabled by default.
824 To disable it, you can use the <option>-XNoTraditionalRecordSyntax</option> flag.
825 </para>
826
827 </sect2>
828
829 <!-- ===================== Recursive do-notation =================== -->
830
831 <sect2 id="recursive-do-notation">
832 <title>The recursive do-notation
833 </title>
834
835 <para>
836 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
837 that is, the variables bound in a do-expression are visible only in the textually following
838 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
839 group.
840 </para>
841
842 <para>
843 It turns out that such recursive bindings do indeed make sense for a variety of monads, but
844 not all. In particular, recursion in this sense requires a fixed-point operator for the underlying
845 monad, captured by the <literal>mfix</literal> method of the <literal>MonadFix</literal> class, defined in <literal>Control.Monad.Fix</literal> as follows:
846 <programlisting>
847 class Monad m => MonadFix m where
848 mfix :: (a -> m a) -> m a
849 </programlisting>
850 Haskell's
851 <literal>Maybe</literal>, <literal>[]</literal> (list), <literal>ST</literal> (both strict and lazy versions),
852 <literal>IO</literal>, and many other monads have <literal>MonadFix</literal> instances. On the negative
853 side, the continuation monad, with the signature <literal>(a -> r) -> r</literal>, does not.
854 </para>
855
856 <para>
857 For monads that do belong to the <literal>MonadFix</literal> class, GHC provides
858 an extended version of the do-notation that allows recursive bindings.
859 The <option>-XRecursiveDo</option> (language pragma: <literal>RecursiveDo</literal>)
860 provides the necessary syntactic support, introducing the keywords <literal>mdo</literal> and
861 <literal>rec</literal> for higher and lower levels of the notation respectively. Unlike
862 bindings in a <literal>do</literal> expression, those introduced by <literal>mdo</literal> and <literal>rec</literal>
863 are recursively defined, much like in an ordinary let-expression. Due to the new
864 keyword <literal>mdo</literal>, we also call this notation the <emphasis>mdo-notation</emphasis>.
865 </para>
866
867 <para>
868 Here is a simple (albeit contrived) example:
869 <programlisting>
870 {-# LANGUAGE RecursiveDo #-}
871 justOnes = mdo { xs &lt;- Just (1:xs)
872 ; return (map negate xs) }
873 </programlisting>
874 or equivalently
875 <programlisting>
876 {-# LANGUAGE RecursiveDo #-}
877 justOnes = do { rec { xs &lt;- Just (1:xs) }
878 ; return (map negate xs) }
879 </programlisting>
880 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
881 </para>
882
883 <para>
884 GHC's implementation the mdo-notation closely follows the original translation as described in the paper
885 <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for Haskell</ulink>, which
886 in turn is based on the work <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion
887 in Monadic Computations</ulink>. Furthermore, GHC extends the syntax described in the former paper
888 with a lower level syntax flagged by the <literal>rec</literal> keyword, as we describe next.
889 </para>
890
891 <sect3>
892 <title>Recursive binding groups</title>
893
894 <para>
895 The flag <option>-XRecursiveDo</option> also introduces a new keyword <literal>rec</literal>, which wraps a
896 mutually-recursive group of monadic statements inside a <literal>do</literal> expression, producing a single statement.
897 Similar to a <literal>let</literal> statement inside a <literal>do</literal>, variables bound in
898 the <literal>rec</literal> are visible throughout the <literal>rec</literal> group, and below it. For example, compare
899 <programlisting>
900 do { a &lt;- getChar do { a &lt;- getChar
901 ; let { r1 = f a r2 ; rec { r1 &lt;- f a r2
902 ; ; r2 = g r1 } ; ; r2 &lt;- g r1 }
903 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
904 </programlisting>
905 In both cases, <literal>r1</literal> and <literal>r2</literal> are available both throughout
906 the <literal>let</literal> or <literal>rec</literal> block, and in the statements that follow it.
907 The difference is that <literal>let</literal> is non-monadic, while <literal>rec</literal> is monadic.
908 (In Haskell <literal>let</literal> is really <literal>letrec</literal>, of course.)
909 </para>
910
911 <para>
912 The semantics of <literal>rec</literal> is fairly straightforward. Whenever GHC finds a <literal>rec</literal>
913 group, it will compute its set of bound variables, and will introduce an appropriate call
914 to the underlying monadic value-recursion operator <literal>mfix</literal>, belonging to the
915 <literal>MonadFix</literal> class. Here is an example:
916 <programlisting>
917 rec { b &lt;- f a c ===> (b,c) &lt;- mfix (\~(b,c) -> do { b &lt;- f a c
918 ; c &lt;- f b a } ; c &lt;- f b a
919 ; return (b,c) })
920 </programlisting>
921 As usual, the meta-variables <literal>b</literal>, <literal>c</literal> etc., can be arbitrary patterns.
922 In general, the statement <literal>rec <replaceable>ss</replaceable></literal> is desugared to the statement
923 <programlisting>
924 <replaceable>vs</replaceable> &lt;- mfix (\~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
925 </programlisting>
926 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
927 </para>
928
929 <para>
930 Note in particular that the translation for a <literal>rec</literal> block only involves wrapping a call
931 to <literal>mfix</literal>: it performs no other analysis on the bindings. The latter is the task
932 for the <literal>mdo</literal> notation, which is described next.
933 </para>
934 </sect3>
935
936 <sect3>
937 <title>The <literal>mdo</literal> notation</title>
938
939 <para>
940 A <literal>rec</literal>-block tells the compiler where precisely the recursive knot should be tied. It turns out that
941 the placement of the recursive knots can be rather delicate: in particular, we would like the knots to be wrapped
942 around as minimal groups as possible. This process is known as <emphasis>segmentation</emphasis>, and is described
943 in detail in Secton 3.2 of <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for
944 Haskell</ulink>. Segmentation improves polymorphism and reduces the size of the recursive knot. Most importantly, it avoids
945 unnecessary interference caused by a fundamental issue with the so-called <emphasis>right-shrinking</emphasis>
946 axiom for monadic recursion. In brief, most monads of interest (IO, strict state, etc.) do <emphasis>not</emphasis>
947 have recursion operators that satisfy this axiom, and thus not performing segmentation can cause unnecessary
948 interference, changing the termination behavior of the resulting translation.
949 (Details can be found in Sections 3.1 and 7.2.2 of
950 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.)
951 </para>
952
953 <para>
954 The <literal>mdo</literal> notation removes the burden of placing
955 explicit <literal>rec</literal> blocks in the code. Unlike an
956 ordinary <literal>do</literal> expression, in which variables bound by
957 statements are only in scope for later statements, variables bound in
958 an <literal>mdo</literal> expression are in scope for all statements
959 of the expression. The compiler then automatically identifies minimal
960 mutually recursively dependent segments of statements, treating them as
961 if the user had wrapped a <literal>rec</literal> qualifier around them.
962 </para>
963
964 <para>
965 The definition is syntactic:
966 </para>
967 <itemizedlist>
968 <listitem>
969 <para>
970 A generator <replaceable>g</replaceable>
971 <emphasis>depends</emphasis> on a textually following generator
972 <replaceable>g'</replaceable>, if
973 </para>
974 <itemizedlist>
975 <listitem>
976 <para>
977 <replaceable>g'</replaceable> defines a variable that
978 is used by <replaceable>g</replaceable>, or
979 </para>
980 </listitem>
981 <listitem>
982 <para>
983 <replaceable>g'</replaceable> textually appears between
984 <replaceable>g</replaceable> and
985 <replaceable>g''</replaceable>, where <replaceable>g</replaceable>
986 depends on <replaceable>g''</replaceable>.
987 </para>
988 </listitem>
989 </itemizedlist>
990 </listitem>
991 <listitem>
992 <para>
993 A <emphasis>segment</emphasis> of a given
994 <literal>mdo</literal>-expression is a minimal sequence of generators
995 such that no generator of the sequence depends on an outside
996 generator. As a special case, although it is not a generator,
997 the final expression in an <literal>mdo</literal>-expression is
998 considered to form a segment by itself.
999 </para>
1000 </listitem>
1001 </itemizedlist>
1002 <para>
1003 Segments in this sense are
1004 related to <emphasis>strongly-connected components</emphasis> analysis,
1005 with the exception that bindings in a segment cannot be reordered and
1006 must be contiguous.
1007 </para>
1008
1009 <para>
1010 Here is an example <literal>mdo</literal>-expression, and its translation to <literal>rec</literal> blocks:
1011 <programlisting>
1012 mdo { a &lt;- getChar ===> do { a &lt;- getChar
1013 ; b &lt;- f a c ; rec { b &lt;- f a c
1014 ; c &lt;- f b a ; ; c &lt;- f b a }
1015 ; z &lt;- h a b ; z &lt;- h a b
1016 ; d &lt;- g d e ; rec { d &lt;- g d e
1017 ; e &lt;- g a z ; ; e &lt;- g a z }
1018 ; putChar c } ; putChar c }
1019 </programlisting>
1020 Note that a given <literal>mdo</literal> expression can cause the creation of multiple <literal>rec</literal> blocks.
1021 If there are no recursive dependencies, <literal>mdo</literal> will introduce no <literal>rec</literal> blocks. In this
1022 latter case an <literal>mdo</literal> expression is precisely the same as a <literal>do</literal> expression, as one
1023 would expect.
1024 </para>
1025
1026 <para>
1027 In summary, given an <literal>mdo</literal> expression, GHC first performs segmentation, introducing
1028 <literal>rec</literal> blocks to wrap over minimal recursive groups. Then, each resulting
1029 <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal> as described
1030 in the previous section. The original <literal>mdo</literal>-expression typechecks exactly when the desugared
1031 version would do so.
1032 </para>
1033
1034 <para>
1035 Here are some other important points in using the recursive-do notation:
1036
1037 <itemizedlist>
1038 <listitem>
1039 <para>
1040 It is enabled with the flag <literal>-XRecursiveDo</literal>, or the <literal>LANGUAGE RecursiveDo</literal>
1041 pragma. (The same flag enables both <literal>mdo</literal>-notation, and the use of <literal>rec</literal>
1042 blocks inside <literal>do</literal> expressions.)
1043 </para>
1044 </listitem>
1045 <listitem>
1046 <para>
1047 <literal>rec</literal> blocks can also be used inside <literal>mdo</literal>-expressions, which will be
1048 treated as a single statement. However, it is good style to either use <literal>mdo</literal> or
1049 <literal>rec</literal> blocks in a single expression.
1050 </para>
1051 </listitem>
1052 <listitem>
1053 <para>
1054 If recursive bindings are required for a monad, then that monad must be declared an instance of
1055 the <literal>MonadFix</literal> class.
1056 </para>
1057 </listitem>
1058 <listitem>
1059 <para>
1060 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1061 Furthermore, the <literal>Control.Monad.ST</literal> and <literal>Control.Monad.ST.Lazy</literal>
1062 modules provide the instances of the <literal>MonadFix</literal> class for Haskell's internal
1063 state monad (strict and lazy, respectively).
1064 </para>
1065 </listitem>
1066 <listitem>
1067 <para>
1068 Like <literal>let</literal> and <literal>where</literal> bindings, name shadowing is not allowed within
1069 an <literal>mdo</literal>-expression or a <literal>rec</literal>-block; that is, all the names bound in
1070 a single <literal>rec</literal> must be distinct. (GHC will complain if this is not the case.)
1071 </para>
1072 </listitem>
1073 </itemizedlist>
1074 </para>
1075 </sect3>
1076
1077
1078 </sect2>
1079
1080
1081 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1082
1083 <sect2 id="parallel-list-comprehensions">
1084 <title>Parallel List Comprehensions</title>
1085 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1086 </indexterm>
1087 <indexterm><primary>parallel list comprehensions</primary>
1088 </indexterm>
1089
1090 <para>Parallel list comprehensions are a natural extension to list
1091 comprehensions. List comprehensions can be thought of as a nice
1092 syntax for writing maps and filters. Parallel comprehensions
1093 extend this to include the zipWith family.</para>
1094
1095 <para>A parallel list comprehension has multiple independent
1096 branches of qualifier lists, each separated by a `|' symbol. For
1097 example, the following zips together two lists:</para>
1098
1099 <programlisting>
1100 [ (x, y) | x &lt;- xs | y &lt;- ys ]
1101 </programlisting>
1102
1103 <para>The behaviour of parallel list comprehensions follows that of
1104 zip, in that the resulting list will have the same length as the
1105 shortest branch.</para>
1106
1107 <para>We can define parallel list comprehensions by translation to
1108 regular comprehensions. Here's the basic idea:</para>
1109
1110 <para>Given a parallel comprehension of the form: </para>
1111
1112 <programlisting>
1113 [ e | p1 &lt;- e11, p2 &lt;- e12, ...
1114 | q1 &lt;- e21, q2 &lt;- e22, ...
1115 ...
1116 ]
1117 </programlisting>
1118
1119 <para>This will be translated to: </para>
1120
1121 <programlisting>
1122 [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
1123 [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
1124 ...
1125 ]
1126 </programlisting>
1127
1128 <para>where `zipN' is the appropriate zip for the given number of
1129 branches.</para>
1130
1131 </sect2>
1132
1133 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1134
1135 <sect2 id="generalised-list-comprehensions">
1136 <title>Generalised (SQL-Like) List Comprehensions</title>
1137 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1138 </indexterm>
1139 <indexterm><primary>extended list comprehensions</primary>
1140 </indexterm>
1141 <indexterm><primary>group</primary></indexterm>
1142 <indexterm><primary>sql</primary></indexterm>
1143
1144
1145 <para>Generalised list comprehensions are a further enhancement to the
1146 list comprehension syntactic sugar to allow operations such as sorting
1147 and grouping which are familiar from SQL. They are fully described in the
1148 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1149 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1150 except that the syntax we use differs slightly from the paper.</para>
1151 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1152 <para>Here is an example:
1153 <programlisting>
1154 employees = [ ("Simon", "MS", 80)
1155 , ("Erik", "MS", 100)
1156 , ("Phil", "Ed", 40)
1157 , ("Gordon", "Ed", 45)
1158 , ("Paul", "Yale", 60)]
1159
1160 output = [ (the dept, sum salary)
1161 | (name, dept, salary) &lt;- employees
1162 , then group by dept using groupWith
1163 , then sortWith by (sum salary)
1164 , then take 5 ]
1165 </programlisting>
1166 In this example, the list <literal>output</literal> would take on
1167 the value:
1168
1169 <programlisting>
1170 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1171 </programlisting>
1172 </para>
1173 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1174 (The functions <literal>sortWith</literal> and <literal>groupWith</literal> are not keywords; they are ordinary
1175 functions that are exported by <literal>GHC.Exts</literal>.)</para>
1176
1177 <para>There are five new forms of comprehension qualifier,
1178 all introduced by the (existing) keyword <literal>then</literal>:
1179 <itemizedlist>
1180 <listitem>
1181
1182 <programlisting>
1183 then f
1184 </programlisting>
1185
1186 This statement requires that <literal>f</literal> have the type <literal>
1187 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1188 motivating example, as this form is used to apply <literal>take 5</literal>.
1189
1190 </listitem>
1191
1192
1193 <listitem>
1194 <para>
1195 <programlisting>
1196 then f by e
1197 </programlisting>
1198
1199 This form is similar to the previous one, but allows you to create a function
1200 which will be passed as the first argument to f. As a consequence f must have
1201 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1202 from the type, this function lets f &quot;project out&quot; some information
1203 from the elements of the list it is transforming.</para>
1204
1205 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1206 is supplied with a function that lets it find out the <literal>sum salary</literal>
1207 for any item in the list comprehension it transforms.</para>
1208
1209 </listitem>
1210
1211
1212 <listitem>
1213
1214 <programlisting>
1215 then group by e using f
1216 </programlisting>
1217
1218 <para>This is the most general of the grouping-type statements. In this form,
1219 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1220 As with the <literal>then f by e</literal> case above, the first argument
1221 is a function supplied to f by the compiler which lets it compute e on every
1222 element of the list being transformed. However, unlike the non-grouping case,
1223 f additionally partitions the list into a number of sublists: this means that
1224 at every point after this statement, binders occurring before it in the comprehension
1225 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1226 this, let's look at an example:</para>
1227
1228 <programlisting>
1229 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1230 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1231 groupRuns f = groupBy (\x y -> f x == f y)
1232
1233 output = [ (the x, y)
1234 | x &lt;- ([1..3] ++ [1..2])
1235 , y &lt;- [4..6]
1236 , then group by x using groupRuns ]
1237 </programlisting>
1238
1239 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1240
1241 <programlisting>
1242 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1243 </programlisting>
1244
1245 <para>Note that we have used the <literal>the</literal> function to change the type
1246 of x from a list to its original numeric type. The variable y, in contrast, is left
1247 unchanged from the list form introduced by the grouping.</para>
1248
1249 </listitem>
1250
1251 <listitem>
1252
1253 <programlisting>
1254 then group using f
1255 </programlisting>
1256
1257 <para>With this form of the group statement, f is required to simply have the type
1258 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1259 comprehension so far directly. An example of this form is as follows:</para>
1260
1261 <programlisting>
1262 output = [ x
1263 | y &lt;- [1..5]
1264 , x &lt;- "hello"
1265 , then group using inits]
1266 </programlisting>
1267
1268 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1269
1270 <programlisting>
1271 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1272 </programlisting>
1273
1274 </listitem>
1275 </itemizedlist>
1276 </para>
1277 </sect2>
1278
1279 <!-- ===================== MONAD COMPREHENSIONS ===================== -->
1280
1281 <sect2 id="monad-comprehensions">
1282 <title>Monad comprehensions</title>
1283 <indexterm><primary>monad comprehensions</primary></indexterm>
1284
1285 <para>
1286 Monad comprehensions generalise the list comprehension notation,
1287 including parallel comprehensions
1288 (<xref linkend="parallel-list-comprehensions"/>) and
1289 transform comprehensions (<xref linkend="generalised-list-comprehensions"/>)
1290 to work for any monad.
1291 </para>
1292
1293 <para>Monad comprehensions support:</para>
1294
1295 <itemizedlist>
1296 <listitem>
1297 <para>
1298 Bindings:
1299 </para>
1300
1301 <programlisting>
1302 [ x + y | x &lt;- Just 1, y &lt;- Just 2 ]
1303 </programlisting>
1304
1305 <para>
1306 Bindings are translated with the <literal>(&gt;&gt;=)</literal> and
1307 <literal>return</literal> functions to the usual do-notation:
1308 </para>
1309
1310 <programlisting>
1311 do x &lt;- Just 1
1312 y &lt;- Just 2
1313 return (x+y)
1314 </programlisting>
1315
1316 </listitem>
1317 <listitem>
1318 <para>
1319 Guards:
1320 </para>
1321
1322 <programlisting>
1323 [ x | x &lt;- [1..10], x &lt;= 5 ]
1324 </programlisting>
1325
1326 <para>
1327 Guards are translated with the <literal>guard</literal> function,
1328 which requires a <literal>MonadPlus</literal> instance:
1329 </para>
1330
1331 <programlisting>
1332 do x &lt;- [1..10]
1333 guard (x &lt;= 5)
1334 return x
1335 </programlisting>
1336
1337 </listitem>
1338 <listitem>
1339 <para>
1340 Transform statements (as with <literal>-XTransformListComp</literal>):
1341 </para>
1342
1343 <programlisting>
1344 [ x+y | x &lt;- [1..10], y &lt;- [1..x], then take 2 ]
1345 </programlisting>
1346
1347 <para>
1348 This translates to:
1349 </para>
1350
1351 <programlisting>
1352 do (x,y) &lt;- take 2 (do x &lt;- [1..10]
1353 y &lt;- [1..x]
1354 return (x,y))
1355 return (x+y)
1356 </programlisting>
1357
1358 </listitem>
1359 <listitem>
1360 <para>
1361 Group statements (as with <literal>-XTransformListComp</literal>):
1362 </para>
1363
1364 <programlisting>
1365 [ x | x &lt;- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
1366 [ x | x &lt;- [1,1,2,2,3], then group using myGroup ]
1367 </programlisting>
1368
1369 </listitem>
1370 <listitem>
1371 <para>
1372 Parallel statements (as with <literal>-XParallelListComp</literal>):
1373 </para>
1374
1375 <programlisting>
1376 [ (x+y) | x &lt;- [1..10]
1377 | y &lt;- [11..20]
1378 ]
1379 </programlisting>
1380
1381 <para>
1382 Parallel statements are translated using the
1383 <literal>mzip</literal> function, which requires a
1384 <literal>MonadZip</literal> instance defined in
1385 <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
1386 </para>
1387
1388 <programlisting>
1389 do (x,y) &lt;- mzip (do x &lt;- [1..10]
1390 return x)
1391 (do y &lt;- [11..20]
1392 return y)
1393 return (x+y)
1394 </programlisting>
1395
1396 </listitem>
1397 </itemizedlist>
1398
1399 <para>
1400 All these features are enabled by default if the
1401 <literal>MonadComprehensions</literal> extension is enabled. The types
1402 and more detailed examples on how to use comprehensions are explained
1403 in the previous chapters <xref
1404 linkend="generalised-list-comprehensions"/> and <xref
1405 linkend="parallel-list-comprehensions"/>. In general you just have
1406 to replace the type <literal>[a]</literal> with the type
1407 <literal>Monad m => m a</literal> for monad comprehensions.
1408 </para>
1409
1410 <para>
1411 Note: Even though most of these examples are using the list monad,
1412 monad comprehensions work for any monad.
1413 The <literal>base</literal> package offers all necessary instances for
1414 lists, which make <literal>MonadComprehensions</literal> backward
1415 compatible to built-in, transform and parallel list comprehensions.
1416 </para>
1417 <para> More formally, the desugaring is as follows. We write <literal>D[ e | Q]</literal>
1418 to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
1419 <programlisting>
1420 Expressions: e
1421 Declarations: d
1422 Lists of qualifiers: Q,R,S
1423
1424 -- Basic forms
1425 D[ e | ] = return e
1426 D[ e | p &lt;- e, Q ] = e &gt;&gt;= \p -&gt; D[ e | Q ]
1427 D[ e | e, Q ] = guard e &gt;&gt; \p -&gt; D[ e | Q ]
1428 D[ e | let d, Q ] = let d in D[ e | Q ]
1429
1430 -- Parallel comprehensions (iterate for multiple parallel branches)
1431 D[ e | (Q | R), S ] = mzip D[ Qv | Q ] D[ Rv | R ] &gt;&gt;= \(Qv,Rv) -&gt; D[ e | S ]
1432
1433 -- Transform comprehensions
1434 D[ e | Q then f, R ] = f D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1435
1436 D[ e | Q then f by b, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1437
1438 D[ e | Q then group using f, R ] = f D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1439 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1440 Qv -&gt; D[ e | R ]
1441
1442 D[ e | Q then group by b using f, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1443 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1444 Qv -&gt; D[ e | R ]
1445
1446 where Qv is the tuple of variables bound by Q (and used subsequently)
1447 selQvi is a selector mapping Qv to the ith component of Qv
1448
1449 Operator Standard binding Expected type
1450 --------------------------------------------------------------------
1451 return GHC.Base t1 -&gt; m t2
1452 (&gt;&gt;=) GHC.Base m1 t1 -&gt; (t2 -&gt; m2 t3) -&gt; m3 t3
1453 (&gt;&gt;) GHC.Base m1 t1 -&gt; m2 t2 -&gt; m3 t3
1454 guard Control.Monad t1 -&gt; m t2
1455 fmap GHC.Base forall a b. (a-&gt;b) -&gt; n a -&gt; n b
1456 mzip Control.Monad.Zip forall a b. m a -&gt; m b -&gt; m (a,b)
1457 </programlisting>
1458 The comprehension should typecheck when its desugaring would typecheck.
1459 </para>
1460 <para>
1461 Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
1462 Without rebindable
1463 syntax, the operators from the "standard binding" module are used; with
1464 rebindable syntax, the operators are looked up in the current lexical scope.
1465 For example, parallel comprehensions will be typechecked and desugared
1466 using whatever "<literal>mzip</literal>" is in scope.
1467 </para>
1468 <para>
1469 The rebindable operators must have the "Expected type" given in the
1470 table above. These types are surprisingly general. For example, you can
1471 use a bind operator with the type
1472 <programlisting>
1473 (>>=) :: T x y a -> (a -> T y z b) -> T x z b
1474 </programlisting>
1475 In the case of transform comprehensions, notice that the groups are
1476 parameterised over some arbitrary type <literal>n</literal> (provided it
1477 has an <literal>fmap</literal>, as well as
1478 the comprehension being over an arbitrary monad.
1479 </para>
1480 </sect2>
1481
1482 <!-- ===================== REBINDABLE SYNTAX =================== -->
1483
1484 <sect2 id="rebindable-syntax">
1485 <title>Rebindable syntax and the implicit Prelude import</title>
1486
1487 <para><indexterm><primary>-XNoImplicitPrelude
1488 option</primary></indexterm> GHC normally imports
1489 <filename>Prelude.hi</filename> files for you. If you'd
1490 rather it didn't, then give it a
1491 <option>-XNoImplicitPrelude</option> option. The idea is
1492 that you can then import a Prelude of your own. (But don't
1493 call it <literal>Prelude</literal>; the Haskell module
1494 namespace is flat, and you must not conflict with any
1495 Prelude module.)</para>
1496
1497 <para>Suppose you are importing a Prelude of your own
1498 in order to define your own numeric class
1499 hierarchy. It completely defeats that purpose if the
1500 literal "1" means "<literal>Prelude.fromInteger
1501 1</literal>", which is what the Haskell Report specifies.
1502 So the <option>-XRebindableSyntax</option>
1503 flag causes
1504 the following pieces of built-in syntax to refer to
1505 <emphasis>whatever is in scope</emphasis>, not the Prelude
1506 versions:
1507 <itemizedlist>
1508 <listitem>
1509 <para>An integer literal <literal>368</literal> means
1510 "<literal>fromInteger (368::Integer)</literal>", rather than
1511 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1512 </para> </listitem>
1513
1514 <listitem><para>Fractional literals are handed in just the same way,
1515 except that the translation is
1516 <literal>fromRational (3.68::Rational)</literal>.
1517 </para> </listitem>
1518
1519 <listitem><para>The equality test in an overloaded numeric pattern
1520 uses whatever <literal>(==)</literal> is in scope.
1521 </para> </listitem>
1522
1523 <listitem><para>The subtraction operation, and the
1524 greater-than-or-equal test, in <literal>n+k</literal> patterns
1525 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1526 </para></listitem>
1527
1528 <listitem>
1529 <para>Negation (e.g. "<literal>- (f x)</literal>")
1530 means "<literal>negate (f x)</literal>", both in numeric
1531 patterns, and expressions.
1532 </para></listitem>
1533
1534 <listitem>
1535 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1536 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1537 </para></listitem>
1538
1539 <listitem>
1540 <para>"Do" notation is translated using whatever
1541 functions <literal>(>>=)</literal>,
1542 <literal>(>>)</literal>, and <literal>fail</literal>,
1543 are in scope (not the Prelude
1544 versions). List comprehensions, mdo (<xref linkend="recursive-do-notation"/>), and parallel array
1545 comprehensions, are unaffected. </para></listitem>
1546
1547 <listitem>
1548 <para>Arrow
1549 notation (see <xref linkend="arrow-notation"/>)
1550 uses whatever <literal>arr</literal>,
1551 <literal>(>>>)</literal>, <literal>first</literal>,
1552 <literal>app</literal>, <literal>(|||)</literal> and
1553 <literal>loop</literal> functions are in scope. But unlike the
1554 other constructs, the types of these functions must match the
1555 Prelude types very closely. Details are in flux; if you want
1556 to use this, ask!
1557 </para></listitem>
1558 </itemizedlist>
1559 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1560 </para>
1561 <para>
1562 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1563 even if that is a little unexpected. For example, the
1564 static semantics of the literal <literal>368</literal>
1565 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1566 <literal>fromInteger</literal> to have any of the types:
1567 <programlisting>
1568 fromInteger :: Integer -> Integer
1569 fromInteger :: forall a. Foo a => Integer -> a
1570 fromInteger :: Num a => a -> Integer
1571 fromInteger :: Integer -> Bool -> Bool
1572 </programlisting>
1573 </para>
1574
1575 <para>Be warned: this is an experimental facility, with
1576 fewer checks than usual. Use <literal>-dcore-lint</literal>
1577 to typecheck the desugared program. If Core Lint is happy
1578 you should be all right.</para>
1579
1580 </sect2>
1581
1582 <sect2 id="postfix-operators">
1583 <title>Postfix operators</title>
1584
1585 <para>
1586 The <option>-XPostfixOperators</option> flag enables a small
1587 extension to the syntax of left operator sections, which allows you to
1588 define postfix operators. The extension is this: the left section
1589 <programlisting>
1590 (e !)
1591 </programlisting>
1592 is equivalent (from the point of view of both type checking and execution) to the expression
1593 <programlisting>
1594 ((!) e)
1595 </programlisting>
1596 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1597 The strict Haskell 98 interpretation is that the section is equivalent to
1598 <programlisting>
1599 (\y -> (!) e y)
1600 </programlisting>
1601 That is, the operator must be a function of two arguments. GHC allows it to
1602 take only one argument, and that in turn allows you to write the function
1603 postfix.
1604 </para>
1605 <para>The extension does not extend to the left-hand side of function
1606 definitions; you must define such a function in prefix form.</para>
1607
1608 </sect2>
1609
1610 <sect2 id="tuple-sections">
1611 <title>Tuple sections</title>
1612
1613 <para>
1614 The <option>-XTupleSections</option> flag enables Python-style partially applied
1615 tuple constructors. For example, the following program
1616 <programlisting>
1617 (, True)
1618 </programlisting>
1619 is considered to be an alternative notation for the more unwieldy alternative
1620 <programlisting>
1621 \x -> (x, True)
1622 </programlisting>
1623 You can omit any combination of arguments to the tuple, as in the following
1624 <programlisting>
1625 (, "I", , , "Love", , 1337)
1626 </programlisting>
1627 which translates to
1628 <programlisting>
1629 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1630 </programlisting>
1631 </para>
1632
1633 <para>
1634 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1635 will also be available for them, like so
1636 <programlisting>
1637 (# , True #)
1638 </programlisting>
1639 Because there is no unboxed unit tuple, the following expression
1640 <programlisting>
1641 (# #)
1642 </programlisting>
1643 continues to stand for the unboxed singleton tuple data constructor.
1644 </para>
1645
1646 </sect2>
1647
1648 <sect2 id="lambda-case">
1649 <title>Lambda-case</title>
1650 <para>
1651 The <option>-XLambdaCase</option> flag enables expressions of the form
1652 <programlisting>
1653 \case { p1 -> e1; ...; pN -> eN }
1654 </programlisting>
1655 which is equivalent to
1656 <programlisting>
1657 \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }
1658 </programlisting>
1659 Note that <literal>\case</literal> starts a layout, so you can write
1660 <programlisting>
1661 \case
1662 p1 -> e1
1663 ...
1664 pN -> eN
1665 </programlisting>
1666 </para>
1667 </sect2>
1668
1669 <sect2 id="empty-case">
1670 <title>Empty case alternatives</title>
1671 <para>
1672 The <option>-XEmptyCase</option> flag enables
1673 case expressions, or lambda-case expressions, that have no alternatives,
1674 thus:
1675 <programlisting>
1676 case e of { } -- No alternatives
1677 or
1678 \case { } -- -XLambdaCase is also required
1679 </programlisting>
1680 This can be useful when you know that the expression being scrutinised
1681 has no non-bottom values. For example:
1682 <programlisting>
1683 data Void
1684 f :: Void -> Int
1685 f x = case x of { }
1686 </programlisting>
1687 With dependently-typed features it is more useful
1688 (see <ulink url="http://hackage.haskell.org/trac/ghc/ticket/2431">Trac</ulink>).
1689 For example, consider these two candidate definitions of <literal>absurd</literal>:
1690 <programlisting>
1691 data a :==: b where
1692 Refl :: a :==: a
1693
1694 absurd :: True :~: False -> a
1695 absurd x = error "absurd" -- (A)
1696 absurd x = case x of {} -- (B)
1697 </programlisting>
1698 We much prefer (B). Why? Because GHC can figure out that <literal>(True :~: False)</literal>
1699 is an empty type. So (B) has no partiality and GHC should be able to compile with
1700 <option>-fwarn-incomplete-patterns</option>. (Though the pattern match checking is not
1701 yet clever enough to do that.
1702 On the other hand (A) looks dangerous, and GHC doesn't check to make
1703 sure that, in fact, the function can never get called.
1704 </para>
1705 </sect2>
1706
1707 <sect2 id="multi-way-if">
1708 <title>Multi-way if-expressions</title>
1709 <para>
1710 With <option>-XMultiWayIf</option> flag GHC accepts conditional expressions
1711 with multiple branches:
1712 <programlisting>
1713 if | guard1 -> expr1
1714 | ...
1715 | guardN -> exprN
1716 </programlisting>
1717 which is roughly equivalent to
1718 <programlisting>
1719 case () of
1720 _ | guard1 -> expr1
1721 ...
1722 _ | guardN -> exprN
1723 </programlisting>
1724 except that multi-way if-expressions do not alter the layout.
1725 </para>
1726 </sect2>
1727
1728 <sect2 id="disambiguate-fields">
1729 <title>Record field disambiguation</title>
1730 <para>
1731 In record construction and record pattern matching
1732 it is entirely unambiguous which field is referred to, even if there are two different
1733 data types in scope with a common field name. For example:
1734 <programlisting>
1735 module M where
1736 data S = MkS { x :: Int, y :: Bool }
1737
1738 module Foo where
1739 import M
1740
1741 data T = MkT { x :: Int }
1742
1743 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1744 ok2 n = MkT { x = n+1 } -- Unambiguous
1745
1746 bad1 k = k { x = 3 } -- Ambiguous
1747 bad2 k = x k -- Ambiguous
1748 </programlisting>
1749 Even though there are two <literal>x</literal>'s in scope,
1750 it is clear that the <literal>x</literal> in the pattern in the
1751 definition of <literal>ok1</literal> can only mean the field
1752 <literal>x</literal> from type <literal>S</literal>. Similarly for
1753 the function <literal>ok2</literal>. However, in the record update
1754 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1755 it is not clear which of the two types is intended.
1756 </para>
1757 <para>
1758 Haskell 98 regards all four as ambiguous, but with the
1759 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1760 the former two. The rules are precisely the same as those for instance
1761 declarations in Haskell 98, where the method names on the left-hand side
1762 of the method bindings in an instance declaration refer unambiguously
1763 to the method of that class (provided they are in scope at all), even
1764 if there are other variables in scope with the same name.
1765 This reduces the clutter of qualified names when you import two
1766 records from different modules that use the same field name.
1767 </para>
1768 <para>
1769 Some details:
1770 <itemizedlist>
1771 <listitem><para>
1772 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For example:
1773 <programlisting>
1774 module Foo where
1775 import M
1776 x=True
1777 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1778 </programlisting>
1779 </para></listitem>
1780
1781 <listitem><para>
1782 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualified</emphasis>
1783 field names even if the corresponding selector is only in scope <emphasis>qualified</emphasis>
1784 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1785 <programlisting>
1786 module Foo where
1787 import qualified M -- Note qualified
1788
1789 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1790 </programlisting>
1791 Since the constructor <literal>MkS</literal> is only in scope qualified, you must
1792 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1793 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1794 is not. (In effect, it is qualified by the constructor.)
1795 </para></listitem>
1796 </itemizedlist>
1797 </para>
1798
1799 </sect2>
1800
1801 <!-- ===================== Record puns =================== -->
1802
1803 <sect2 id="record-puns">
1804 <title>Record puns
1805 </title>
1806
1807 <para>
1808 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1809 </para>
1810
1811 <para>
1812 When using records, it is common to write a pattern that binds a
1813 variable with the same name as a record field, such as:
1814
1815 <programlisting>
1816 data C = C {a :: Int}
1817 f (C {a = a}) = a
1818 </programlisting>
1819 </para>
1820
1821 <para>
1822 Record punning permits the variable name to be elided, so one can simply
1823 write
1824
1825 <programlisting>
1826 f (C {a}) = a
1827 </programlisting>
1828
1829 to mean the same pattern as above. That is, in a record pattern, the
1830 pattern <literal>a</literal> expands into the pattern <literal>a =
1831 a</literal> for the same name <literal>a</literal>.
1832 </para>
1833
1834 <para>
1835 Note that:
1836 <itemizedlist>
1837 <listitem><para>
1838 Record punning can also be used in an expression, writing, for example,
1839 <programlisting>
1840 let a = 1 in C {a}
1841 </programlisting>
1842 instead of
1843 <programlisting>
1844 let a = 1 in C {a = a}
1845 </programlisting>
1846 The expansion is purely syntactic, so the expanded right-hand side
1847 expression refers to the nearest enclosing variable that is spelled the
1848 same as the field name.
1849 </para></listitem>
1850
1851 <listitem><para>
1852 Puns and other patterns can be mixed in the same record:
1853 <programlisting>
1854 data C = C {a :: Int, b :: Int}
1855 f (C {a, b = 4}) = a
1856 </programlisting>
1857 </para></listitem>
1858
1859 <listitem><para>
1860 Puns can be used wherever record patterns occur (e.g. in
1861 <literal>let</literal> bindings or at the top-level).
1862 </para></listitem>
1863
1864 <listitem><para>
1865 A pun on a qualified field name is expanded by stripping off the module qualifier.
1866 For example:
1867 <programlisting>
1868 f (C {M.a}) = a
1869 </programlisting>
1870 means
1871 <programlisting>
1872 f (M.C {M.a = a}) = a
1873 </programlisting>
1874 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1875 is only in scope in qualified form.)
1876 </para></listitem>
1877 </itemizedlist>
1878 </para>
1879
1880
1881 </sect2>
1882
1883 <!-- ===================== Record wildcards =================== -->
1884
1885 <sect2 id="record-wildcards">
1886 <title>Record wildcards
1887 </title>
1888
1889 <para>
1890 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1891 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1892 </para>
1893
1894 <para>
1895 For records with many fields, it can be tiresome to write out each field
1896 individually in a record pattern, as in
1897 <programlisting>
1898 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1899 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1900 </programlisting>
1901 </para>
1902
1903 <para>
1904 Record wildcard syntax permits a "<literal>..</literal>" in a record
1905 pattern, where each elided field <literal>f</literal> is replaced by the
1906 pattern <literal>f = f</literal>. For example, the above pattern can be
1907 written as
1908 <programlisting>
1909 f (C {a = 1, ..}) = b + c + d
1910 </programlisting>
1911 </para>
1912
1913 <para>
1914 More details:
1915 <itemizedlist>
1916 <listitem><para>
1917 Wildcards can be mixed with other patterns, including puns
1918 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1919 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1920 wherever record patterns occur, including in <literal>let</literal>
1921 bindings and at the top-level. For example, the top-level binding
1922 <programlisting>
1923 C {a = 1, ..} = e
1924 </programlisting>
1925 defines <literal>b</literal>, <literal>c</literal>, and
1926 <literal>d</literal>.
1927 </para></listitem>
1928
1929 <listitem><para>
1930 Record wildcards can also be used in expressions, writing, for example,
1931 <programlisting>
1932 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1933 </programlisting>
1934 in place of
1935 <programlisting>
1936 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1937 </programlisting>
1938 The expansion is purely syntactic, so the record wildcard
1939 expression refers to the nearest enclosing variables that are spelled
1940 the same as the omitted field names.
1941 </para></listitem>
1942
1943 <listitem><para>
1944 The "<literal>..</literal>" expands to the missing
1945 <emphasis>in-scope</emphasis> record fields.
1946 Specifically the expansion of "<literal>C {..}</literal>" includes
1947 <literal>f</literal> if and only if:
1948 <itemizedlist>
1949 <listitem><para>
1950 <literal>f</literal> is a record field of constructor <literal>C</literal>.
1951 </para></listitem>
1952 <listitem><para>
1953 The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
1954 </para></listitem>
1955 <listitem><para>
1956 In the case of expressions (but not patterns),
1957 the variable <literal>f</literal> is in scope unqualified,
1958 apart from the binding of the record selector itself.
1959 </para></listitem>
1960 </itemizedlist>
1961 For example
1962 <programlisting>
1963 module M where
1964 data R = R { a,b,c :: Int }
1965 module X where
1966 import M( R(a,c) )
1967 f b = R { .. }
1968 </programlisting>
1969 The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
1970 omitting <literal>b</literal> since the record field is not in scope,
1971 and omitting <literal>c</literal> since the variable <literal>c</literal>
1972 is not in scope (apart from the binding of the
1973 record selector <literal>c</literal>, of course).
1974 </para></listitem>
1975 </itemizedlist>
1976 </para>
1977
1978 </sect2>
1979
1980 <!-- ===================== Local fixity declarations =================== -->
1981
1982 <sect2 id="local-fixity-declarations">
1983 <title>Local Fixity Declarations
1984 </title>
1985
1986 <para>A careful reading of the Haskell 98 Report reveals that fixity
1987 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1988 <literal>infixr</literal>) are permitted to appear inside local bindings
1989 such those introduced by <literal>let</literal> and
1990 <literal>where</literal>. However, the Haskell Report does not specify
1991 the semantics of such bindings very precisely.
1992 </para>
1993
1994 <para>In GHC, a fixity declaration may accompany a local binding:
1995 <programlisting>
1996 let f = ...
1997 infixr 3 `f`
1998 in
1999 ...
2000 </programlisting>
2001 and the fixity declaration applies wherever the binding is in scope.
2002 For example, in a <literal>let</literal>, it applies in the right-hand
2003 sides of other <literal>let</literal>-bindings and the body of the
2004 <literal>let</literal>C. Or, in recursive <literal>do</literal>
2005 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
2006 declarations of a <literal>let</literal> statement scope over other
2007 statements in the group, just as the bound name does.
2008 </para>
2009
2010 <para>
2011 Moreover, a local fixity declaration *must* accompany a local binding of
2012 that name: it is not possible to revise the fixity of name bound
2013 elsewhere, as in
2014 <programlisting>
2015 let infixr 9 $ in ...
2016 </programlisting>
2017
2018 Because local fixity declarations are technically Haskell 98, no flag is
2019 necessary to enable them.
2020 </para>
2021 </sect2>
2022
2023 <sect2 id="package-imports">
2024 <title>Package-qualified imports</title>
2025
2026 <para>With the <option>-XPackageImports</option> flag, GHC allows
2027 import declarations to be qualified by the package name that the
2028 module is intended to be imported from. For example:</para>
2029
2030 <programlisting>
2031 import "network" Network.Socket
2032 </programlisting>
2033
2034 <para>would import the module <literal>Network.Socket</literal> from
2035 the package <literal>network</literal> (any version). This may
2036 be used to disambiguate an import when the same module is
2037 available from multiple packages, or is present in both the
2038 current package being built and an external package.</para>
2039
2040 <para>The special package name <literal>this</literal> can be used to
2041 refer to the current package being built.</para>
2042
2043 <para>Note: you probably don't need to use this feature, it was
2044 added mainly so that we can build backwards-compatible versions of
2045 packages when APIs change. It can lead to fragile dependencies in
2046 the common case: modules occasionally move from one package to
2047 another, rendering any package-qualified imports broken.</para>
2048 </sect2>
2049
2050 <sect2 id="safe-imports-ext">
2051 <title>Safe imports</title>
2052
2053 <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
2054 and <option>-XUnsafe</option> language flags, GHC extends
2055 the import declaration syntax to take an optional <literal>safe</literal>
2056 keyword after the <literal>import</literal> keyword. This feature
2057 is part of the Safe Haskell GHC extension. For example:</para>
2058
2059 <programlisting>
2060 import safe qualified Network.Socket as NS
2061 </programlisting>
2062
2063 <para>would import the module <literal>Network.Socket</literal>
2064 with compilation only succeeding if Network.Socket can be
2065 safely imported. For a description of when a import is
2066 considered safe see <xref linkend="safe-haskell"/></para>
2067
2068 </sect2>
2069
2070 <sect2 id="syntax-stolen">
2071 <title>Summary of stolen syntax</title>
2072
2073 <para>Turning on an option that enables special syntax
2074 <emphasis>might</emphasis> cause working Haskell 98 code to fail
2075 to compile, perhaps because it uses a variable name which has
2076 become a reserved word. This section lists the syntax that is
2077 "stolen" by language extensions.
2078 We use
2079 notation and nonterminal names from the Haskell 98 lexical syntax
2080 (see the Haskell 98 Report).
2081 We only list syntax changes here that might affect
2082 existing working programs (i.e. "stolen" syntax). Many of these
2083 extensions will also enable new context-free syntax, but in all
2084 cases programs written to use the new syntax would not be
2085 compilable without the option enabled.</para>
2086
2087 <para>There are two classes of special
2088 syntax:
2089
2090 <itemizedlist>
2091 <listitem>
2092 <para>New reserved words and symbols: character sequences
2093 which are no longer available for use as identifiers in the
2094 program.</para>
2095 </listitem>
2096 <listitem>
2097 <para>Other special syntax: sequences of characters that have
2098 a different meaning when this particular option is turned
2099 on.</para>
2100 </listitem>
2101 </itemizedlist>
2102
2103 The following syntax is stolen:
2104
2105 <variablelist>
2106 <varlistentry>
2107 <term>
2108 <literal>forall</literal>
2109 <indexterm><primary><literal>forall</literal></primary></indexterm>
2110 </term>
2111 <listitem><para>
2112 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
2113 <option>-XScopedTypeVariables</option>,
2114 <option>-XLiberalTypeSynonyms</option>,
2115 <option>-XRankNTypes</option>,
2116 <option>-XExistentialQuantification</option>
2117 </para></listitem>
2118 </varlistentry>
2119
2120 <varlistentry>
2121 <term>
2122 <literal>mdo</literal>
2123 <indexterm><primary><literal>mdo</literal></primary></indexterm>
2124 </term>
2125 <listitem><para>
2126 Stolen by: <option>-XRecursiveDo</option>
2127 </para></listitem>
2128 </varlistentry>
2129
2130 <varlistentry>
2131 <term>
2132 <literal>foreign</literal>
2133 <indexterm><primary><literal>foreign</literal></primary></indexterm>
2134 </term>
2135 <listitem><para>
2136 Stolen by: <option>-XForeignFunctionInterface</option>
2137 </para></listitem>
2138 </varlistentry>
2139
2140 <varlistentry>
2141 <term>
2142 <literal>rec</literal>,
2143 <literal>proc</literal>, <literal>-&lt;</literal>,
2144 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
2145 <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
2146 <literal>|)</literal> brackets
2147 <indexterm><primary><literal>proc</literal></primary></indexterm>
2148 </term>
2149 <listitem><para>
2150 Stolen by: <option>-XArrows</option>
2151 </para></listitem>
2152 </varlistentry>
2153
2154 <varlistentry>
2155 <term>
2156 <literal>?<replaceable>varid</replaceable></literal>,
2157 <literal>%<replaceable>varid</replaceable></literal>
2158 <indexterm><primary>implicit parameters</primary></indexterm>
2159 </term>
2160 <listitem><para>
2161 Stolen by: <option>-XImplicitParams</option>
2162 </para></listitem>
2163 </varlistentry>
2164
2165 <varlistentry>
2166 <term>
2167 <literal>[|</literal>,
2168 <literal>[e|</literal>, <literal>[p|</literal>,
2169 <literal>[d|</literal>, <literal>[t|</literal>,
2170 <literal>$(</literal>,
2171 <literal>$<replaceable>varid</replaceable></literal>
2172 <indexterm><primary>Template Haskell</primary></indexterm>
2173 </term>
2174 <listitem><para>
2175 Stolen by: <option>-XTemplateHaskell</option>
2176 </para></listitem>
2177 </varlistentry>
2178
2179 <varlistentry>
2180 <term>
2181 <literal>[:<replaceable>varid</replaceable>|</literal>
2182 <indexterm><primary>quasi-quotation</primary></indexterm>
2183 </term>
2184 <listitem><para>
2185 Stolen by: <option>-XQuasiQuotes</option>
2186 </para></listitem>
2187 </varlistentry>
2188
2189 <varlistentry>
2190 <term>
2191 <replaceable>varid</replaceable>{<literal>&num;</literal>},
2192 <replaceable>char</replaceable><literal>&num;</literal>,
2193 <replaceable>string</replaceable><literal>&num;</literal>,
2194 <replaceable>integer</replaceable><literal>&num;</literal>,
2195 <replaceable>float</replaceable><literal>&num;</literal>,
2196 <replaceable>float</replaceable><literal>&num;&num;</literal>,
2197 <literal>(&num;</literal>, <literal>&num;)</literal>
2198 </term>
2199 <listitem><para>
2200 Stolen by: <option>-XMagicHash</option>
2201 </para></listitem>
2202 </varlistentry>
2203 </variablelist>
2204 </para>
2205 </sect2>
2206 </sect1>
2207
2208
2209 <!-- TYPE SYSTEM EXTENSIONS -->
2210 <sect1 id="data-type-extensions">
2211 <title>Extensions to data types and type synonyms</title>
2212
2213 <sect2 id="nullary-types">
2214 <title>Data types with no constructors</title>
2215
2216 <para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
2217 GHC lets you declare a data type with no constructors. For example:</para>
2218
2219 <programlisting>
2220 data S -- S :: *
2221 data T a -- T :: * -> *
2222 </programlisting>
2223
2224 <para>Syntactically, the declaration lacks the "= constrs" part. The
2225 type can be parameterised over types of any kind, but if the kind is
2226 not <literal>*</literal> then an explicit kind annotation must be used
2227 (see <xref linkend="kinding"/>).</para>
2228
2229 <para>Such data types have only one value, namely bottom.
2230 Nevertheless, they can be useful when defining "phantom types".</para>
2231 </sect2>
2232
2233 <sect2 id="datatype-contexts">
2234 <title>Data type contexts</title>
2235
2236 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2237
2238 <programlisting>
2239 data Eq a => Set a = NilSet | ConsSet a (Set a)
2240 </programlisting>
2241
2242 <para>give constructors with types:</para>
2243
2244 <programlisting>
2245 NilSet :: Set a
2246 ConsSet :: Eq a => a -> Set a -> Set a
2247 </programlisting>
2248
2249 <para>This is widely considered a misfeature, and is going to be removed from
2250 the language. In GHC, it is controlled by the deprecated extension
2251 <literal>DatatypeContexts</literal>.</para>
2252 </sect2>
2253
2254 <sect2 id="infix-tycons">
2255 <title>Infix type constructors, classes, and type variables</title>
2256
2257 <para>
2258 GHC allows type constructors, classes, and type variables to be operators, and
2259 to be written infix, very much like expressions. More specifically:
2260 <itemizedlist>
2261 <listitem><para>
2262 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
2263 The lexical syntax is the same as that for data constructors.
2264 </para></listitem>
2265 <listitem><para>
2266 Data type and type-synonym declarations can be written infix, parenthesised
2267 if you want further arguments. E.g.
2268 <screen>
2269 data a :*: b = Foo a b
2270 type a :+: b = Either a b
2271 class a :=: b where ...
2272
2273 data (a :**: b) x = Baz a b x
2274 type (a :++: b) y = Either (a,b) y
2275 </screen>
2276 </para></listitem>
2277 <listitem><para>
2278 Types, and class constraints, can be written infix. For example
2279 <screen>
2280 x :: Int :*: Bool
2281 f :: (a :=: b) => a -> b
2282 </screen>
2283 </para></listitem>
2284 <listitem><para>
2285 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
2286 The lexical syntax is the same as that for variable operators, excluding "(.)",
2287 "(!)", and "(*)". In a binding position, the operator must be
2288 parenthesised. For example:
2289 <programlisting>
2290 type T (+) = Int + Int
2291 f :: T Either
2292 f = Left 3
2293
2294 liftA2 :: Arrow (~>)
2295 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
2296 liftA2 = ...
2297 </programlisting>
2298 </para></listitem>
2299 <listitem><para>
2300 Back-quotes work
2301 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
2302 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
2303 </para></listitem>
2304 <listitem><para>
2305 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
2306 one cannot distinguish between the two in a fixity declaration; a fixity declaration
2307 sets the fixity for a data constructor and the corresponding type constructor. For example:
2308 <screen>
2309 infixl 7 T, :*:
2310 </screen>
2311 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
2312 and similarly for <literal>:*:</literal>.
2313 <literal>Int `a` Bool</literal>.
2314 </para></listitem>
2315 <listitem><para>
2316 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
2317 </para></listitem>
2318
2319 </itemizedlist>
2320 </para>
2321 </sect2>
2322
2323 <sect2 id="type-synonyms">
2324 <title>Liberalised type synonyms</title>
2325
2326 <para>
2327 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
2328 on individual synonym declarations.
2329 With the <option>-XLiberalTypeSynonyms</option> extension,
2330 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2331 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
2332
2333 <itemizedlist>
2334 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2335 in a type synonym, thus:
2336 <programlisting>
2337 type Discard a = forall b. Show b => a -> b -> (a, String)
2338
2339 f :: Discard a
2340 f x y = (x, show y)
2341
2342 g :: Discard Int -> (Int,String) -- A rank-2 type
2343 g f = f 3 True
2344 </programlisting>
2345 </para>
2346 </listitem>
2347
2348 <listitem><para>
2349 If you also use <option>-XUnboxedTuples</option>,
2350 you can write an unboxed tuple in a type synonym:
2351 <programlisting>
2352 type Pr = (# Int, Int #)
2353
2354 h :: Int -> Pr
2355 h x = (# x, x #)
2356 </programlisting>
2357 </para></listitem>
2358
2359 <listitem><para>
2360 You can apply a type synonym to a forall type:
2361 <programlisting>
2362 type Foo a = a -> a -> Bool
2363
2364 f :: Foo (forall b. b->b)
2365 </programlisting>
2366 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2367 <programlisting>
2368 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2369 </programlisting>
2370 </para></listitem>
2371
2372 <listitem><para>
2373 You can apply a type synonym to a partially applied type synonym:
2374 <programlisting>
2375 type Generic i o = forall x. i x -> o x
2376 type Id x = x
2377
2378 foo :: Generic Id []
2379 </programlisting>
2380 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2381 <programlisting>
2382 foo :: forall x. x -> [x]
2383 </programlisting>
2384 </para></listitem>
2385
2386 </itemizedlist>
2387 </para>
2388
2389 <para>
2390 GHC currently does kind checking before expanding synonyms (though even that
2391 could be changed.)
2392 </para>
2393 <para>
2394 After expanding type synonyms, GHC does validity checking on types, looking for
2395 the following mal-formedness which isn't detected simply by kind checking:
2396 <itemizedlist>
2397 <listitem><para>
2398 Type constructor applied to a type involving for-alls.
2399 </para></listitem>
2400 <listitem><para>
2401 Unboxed tuple on left of an arrow.
2402 </para></listitem>
2403 <listitem><para>
2404 Partially-applied type synonym.
2405 </para></listitem>
2406 </itemizedlist>
2407 So, for example,
2408 this will be rejected:
2409 <programlisting>
2410 type Pr = (# Int, Int #)
2411
2412 h :: Pr -> Int
2413 h x = ...
2414 </programlisting>
2415 because GHC does not allow unboxed tuples on the left of a function arrow.
2416 </para>
2417 </sect2>
2418
2419
2420 <sect2 id="existential-quantification">
2421 <title>Existentially quantified data constructors
2422 </title>
2423
2424 <para>
2425 The idea of using existential quantification in data type declarations
2426 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2427 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2428 London, 1991). It was later formalised by Laufer and Odersky
2429 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2430 TOPLAS, 16(5), pp1411-1430, 1994).
2431 It's been in Lennart
2432 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2433 proved very useful. Here's the idea. Consider the declaration:
2434 </para>
2435
2436 <para>
2437
2438 <programlisting>
2439 data Foo = forall a. MkFoo a (a -> Bool)
2440 | Nil
2441 </programlisting>
2442
2443 </para>
2444
2445 <para>
2446 The data type <literal>Foo</literal> has two constructors with types:
2447 </para>
2448
2449 <para>
2450
2451 <programlisting>
2452 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2453 Nil :: Foo
2454 </programlisting>
2455
2456 </para>
2457
2458 <para>
2459 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2460 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2461 For example, the following expression is fine:
2462 </para>
2463
2464 <para>
2465
2466 <programlisting>
2467 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2468 </programlisting>
2469
2470 </para>
2471
2472 <para>
2473 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2474 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2475 isUpper</function> packages a character with a compatible function. These
2476 two things are each of type <literal>Foo</literal> and can be put in a list.
2477 </para>
2478
2479 <para>
2480 What can we do with a value of type <literal>Foo</literal>?. In particular,
2481 what happens when we pattern-match on <function>MkFoo</function>?
2482 </para>
2483
2484 <para>
2485
2486 <programlisting>
2487 f (MkFoo val fn) = ???
2488 </programlisting>
2489
2490 </para>
2491
2492 <para>
2493 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2494 are compatible, the only (useful) thing we can do with them is to
2495 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2496 </para>
2497
2498 <para>
2499
2500 <programlisting>
2501 f :: Foo -> Bool
2502 f (MkFoo val fn) = fn val
2503 </programlisting>
2504
2505 </para>
2506
2507 <para>
2508 What this allows us to do is to package heterogeneous values
2509 together with a bunch of functions that manipulate them, and then treat
2510 that collection of packages in a uniform manner. You can express
2511 quite a bit of object-oriented-like programming this way.
2512 </para>
2513
2514 <sect3 id="existential">
2515 <title>Why existential?
2516 </title>
2517
2518 <para>
2519 What has this to do with <emphasis>existential</emphasis> quantification?
2520 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2521 </para>
2522
2523 <para>
2524
2525 <programlisting>
2526 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2527 </programlisting>
2528
2529 </para>
2530
2531 <para>
2532 But Haskell programmers can safely think of the ordinary
2533 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2534 adding a new existential quantification construct.
2535 </para>
2536
2537 </sect3>
2538
2539 <sect3 id="existential-with-context">
2540 <title>Existentials and type classes</title>
2541
2542 <para>
2543 An easy extension is to allow
2544 arbitrary contexts before the constructor. For example:
2545 </para>
2546
2547 <para>
2548
2549 <programlisting>
2550 data Baz = forall a. Eq a => Baz1 a a
2551 | forall b. Show b => Baz2 b (b -> b)
2552 </programlisting>
2553
2554 </para>
2555
2556 <para>
2557 The two constructors have the types you'd expect:
2558 </para>
2559
2560 <para>
2561
2562 <programlisting>
2563 Baz1 :: forall a. Eq a => a -> a -> Baz
2564 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2565 </programlisting>
2566
2567 </para>
2568
2569 <para>
2570 But when pattern matching on <function>Baz1</function> the matched values can be compared
2571 for equality, and when pattern matching on <function>Baz2</function> the first matched
2572 value can be converted to a string (as well as applying the function to it).
2573 So this program is legal:
2574 </para>
2575
2576 <para>
2577
2578 <programlisting>
2579 f :: Baz -> String
2580 f (Baz1 p q) | p == q = "Yes"
2581 | otherwise = "No"
2582 f (Baz2 v fn) = show (fn v)
2583 </programlisting>
2584
2585 </para>
2586
2587 <para>
2588 Operationally, in a dictionary-passing implementation, the
2589 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2590 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2591 extract it on pattern matching.
2592 </para>
2593
2594 </sect3>
2595
2596 <sect3 id="existential-records">
2597 <title>Record Constructors</title>
2598
2599 <para>
2600 GHC allows existentials to be used with records syntax as well. For example:
2601
2602 <programlisting>
2603 data Counter a = forall self. NewCounter
2604 { _this :: self
2605 , _inc :: self -> self
2606 , _display :: self -> IO ()
2607 , tag :: a
2608 }
2609 </programlisting>
2610 Here <literal>tag</literal> is a public field, with a well-typed selector
2611 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2612 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2613 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2614 compile-time error. In other words, <emphasis>GHC defines a record selector function
2615 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2616 (This example used an underscore in the fields for which record selectors
2617 will not be defined, but that is only programming style; GHC ignores them.)
2618 </para>
2619
2620 <para>
2621 To make use of these hidden fields, we need to create some helper functions:
2622
2623 <programlisting>
2624 inc :: Counter a -> Counter a
2625 inc (NewCounter x i d t) = NewCounter
2626 { _this = i x, _inc = i, _display = d, tag = t }
2627
2628 display :: Counter a -> IO ()
2629 display NewCounter{ _this = x, _display = d } = d x
2630 </programlisting>
2631
2632 Now we can define counters with different underlying implementations:
2633
2634 <programlisting>
2635 counterA :: Counter String
2636 counterA = NewCounter
2637 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2638
2639 counterB :: Counter String
2640 counterB = NewCounter
2641 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2642
2643 main = do
2644 display (inc counterA) -- prints "1"
2645 display (inc (inc counterB)) -- prints "##"
2646 </programlisting>
2647
2648 Record update syntax is supported for existentials (and GADTs):
2649 <programlisting>
2650 setTag :: Counter a -> a -> Counter a
2651 setTag obj t = obj{ tag = t }
2652 </programlisting>
2653 The rule for record update is this: <emphasis>
2654 the types of the updated fields may
2655 mention only the universally-quantified type variables
2656 of the data constructor. For GADTs, the field may mention only types
2657 that appear as a simple type-variable argument in the constructor's result
2658 type</emphasis>. For example:
2659 <programlisting>
2660 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2661 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2662 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2663 -- existentially quantified)
2664
2665 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2666 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2667 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2668 -- type-variable argument in G1's result type)
2669 </programlisting>
2670 </para>
2671
2672 </sect3>
2673
2674
2675 <sect3>
2676 <title>Restrictions</title>
2677
2678 <para>
2679 There are several restrictions on the ways in which existentially-quantified
2680 constructors can be use.
2681 </para>
2682
2683 <para>
2684
2685 <itemizedlist>
2686 <listitem>
2687
2688 <para>
2689 When pattern matching, each pattern match introduces a new,
2690 distinct, type for each existential type variable. These types cannot
2691 be unified with any other type, nor can they escape from the scope of
2692 the pattern match. For example, these fragments are incorrect:
2693
2694
2695 <programlisting>
2696 f1 (MkFoo a f) = a
2697 </programlisting>
2698
2699
2700 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2701 is the result of <function>f1</function>. One way to see why this is wrong is to
2702 ask what type <function>f1</function> has:
2703
2704
2705 <programlisting>
2706 f1 :: Foo -> a -- Weird!
2707 </programlisting>
2708
2709
2710 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2711 this:
2712
2713
2714 <programlisting>
2715 f1 :: forall a. Foo -> a -- Wrong!
2716 </programlisting>
2717
2718
2719 The original program is just plain wrong. Here's another sort of error
2720
2721
2722 <programlisting>
2723 f2 (Baz1 a b) (Baz1 p q) = a==q
2724 </programlisting>
2725
2726
2727 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2728 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2729 from the two <function>Baz1</function> constructors.
2730
2731
2732 </para>
2733 </listitem>
2734 <listitem>
2735
2736 <para>
2737 You can't pattern-match on an existentially quantified
2738 constructor in a <literal>let</literal> or <literal>where</literal> group of
2739 bindings. So this is illegal:
2740
2741
2742 <programlisting>
2743 f3 x = a==b where { Baz1 a b = x }
2744 </programlisting>
2745
2746 Instead, use a <literal>case</literal> expression:
2747
2748 <programlisting>
2749 f3 x = case x of Baz1 a b -> a==b
2750 </programlisting>
2751
2752 In general, you can only pattern-match
2753 on an existentially-quantified constructor in a <literal>case</literal> expression or
2754 in the patterns of a function definition.
2755
2756 The reason for this restriction is really an implementation one.
2757 Type-checking binding groups is already a nightmare without
2758 existentials complicating the picture. Also an existential pattern
2759 binding at the top level of a module doesn't make sense, because it's
2760 not clear how to prevent the existentially-quantified type "escaping".
2761 So for now, there's a simple-to-state restriction. We'll see how
2762 annoying it is.
2763
2764 </para>
2765 </listitem>
2766 <listitem>
2767
2768 <para>
2769 You can't use existential quantification for <literal>newtype</literal>
2770 declarations. So this is illegal:
2771
2772
2773 <programlisting>
2774 newtype T = forall a. Ord a => MkT a
2775 </programlisting>
2776
2777
2778 Reason: a value of type <literal>T</literal> must be represented as a
2779 pair of a dictionary for <literal>Ord t</literal> and a value of type
2780 <literal>t</literal>. That contradicts the idea that
2781 <literal>newtype</literal> should have no concrete representation.
2782 You can get just the same efficiency and effect by using
2783 <literal>data</literal> instead of <literal>newtype</literal>. If
2784 there is no overloading involved, then there is more of a case for
2785 allowing an existentially-quantified <literal>newtype</literal>,
2786 because the <literal>data</literal> version does carry an
2787 implementation cost, but single-field existentially quantified
2788 constructors aren't much use. So the simple restriction (no
2789 existential stuff on <literal>newtype</literal>) stands, unless there
2790 are convincing reasons to change it.
2791
2792
2793 </para>
2794 </listitem>
2795 <listitem>
2796
2797 <para>
2798 You can't use <literal>deriving</literal> to define instances of a
2799 data type with existentially quantified data constructors.
2800
2801 Reason: in most cases it would not make sense. For example:;
2802
2803 <programlisting>
2804 data T = forall a. MkT [a] deriving( Eq )
2805 </programlisting>
2806
2807 To derive <literal>Eq</literal> in the standard way we would need to have equality
2808 between the single component of two <function>MkT</function> constructors:
2809
2810 <programlisting>
2811 instance Eq T where
2812 (MkT a) == (MkT b) = ???
2813 </programlisting>
2814
2815 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2816 It's just about possible to imagine examples in which the derived instance
2817 would make sense, but it seems altogether simpler simply to prohibit such
2818 declarations. Define your own instances!
2819 </para>
2820 </listitem>
2821
2822 </itemizedlist>
2823
2824 </para>
2825
2826 </sect3>
2827 </sect2>
2828
2829 <!-- ====================== Generalised algebraic data types ======================= -->
2830
2831 <sect2 id="gadt-style">
2832 <title>Declaring data types with explicit constructor signatures</title>
2833
2834 <para>When the <literal>GADTSyntax</literal> extension is enabled,
2835 GHC allows you to declare an algebraic data type by
2836 giving the type signatures of constructors explicitly. For example:
2837 <programlisting>
2838 data Maybe a where
2839 Nothing :: Maybe a
2840 Just :: a -> Maybe a
2841 </programlisting>
2842 The form is called a "GADT-style declaration"
2843 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2844 can only be declared using this form.</para>
2845 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2846 For example, these two declarations are equivalent:
2847 <programlisting>
2848 data Foo = forall a. MkFoo a (a -> Bool)
2849 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2850 </programlisting>
2851 </para>
2852 <para>Any data type that can be declared in standard Haskell-98 syntax
2853 can also be declared using GADT-style syntax.
2854 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2855 they treat class constraints on the data constructors differently.
2856 Specifically, if the constructor is given a type-class context, that
2857 context is made available by pattern matching. For example:
2858 <programlisting>
2859 data Set a where
2860 MkSet :: Eq a => [a] -> Set a
2861
2862 makeSet :: Eq a => [a] -> Set a
2863 makeSet xs = MkSet (nub xs)
2864
2865 insert :: a -> Set a -> Set a
2866 insert a (MkSet as) | a `elem` as = MkSet as
2867 | otherwise = MkSet (a:as)
2868 </programlisting>
2869 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2870 gives rise to a <literal>(Eq a)</literal>
2871 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2872 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2873 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2874 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2875 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2876 In the example, the equality dictionary is used to satisfy the equality constraint
2877 generated by the call to <literal>elem</literal>, so that the type of
2878 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2879 </para>
2880 <para>
2881 For example, one possible application is to reify dictionaries:
2882 <programlisting>
2883 data NumInst a where
2884 MkNumInst :: Num a => NumInst a
2885
2886 intInst :: NumInst Int
2887 intInst = MkNumInst
2888
2889 plus :: NumInst a -> a -> a -> a
2890 plus MkNumInst p q = p + q
2891 </programlisting>
2892 Here, a value of type <literal>NumInst a</literal> is equivalent
2893 to an explicit <literal>(Num a)</literal> dictionary.
2894 </para>
2895 <para>
2896 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2897 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2898 like this:
2899 <programlisting>
2900 data NumInst a
2901 = Num a => MkNumInst (NumInst a)
2902 </programlisting>
2903 Notice that, unlike the situation when declaring an existential, there is
2904 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2905 data type's universally quantified type variable <literal>a</literal>.
2906 A constructor may have both universal and existential type variables: for example,
2907 the following two declarations are equivalent:
2908 <programlisting>
2909 data T1 a
2910 = forall b. (Num a, Eq b) => MkT1 a b
2911 data T2 a where
2912 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2913 </programlisting>
2914 </para>
2915 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2916 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2917 In Haskell 98 the definition
2918 <programlisting>
2919 data Eq a => Set' a = MkSet' [a]
2920 </programlisting>
2921 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2922 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2923 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2924 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2925 GHC's behaviour is much more useful, as well as much more intuitive.
2926 </para>
2927
2928 <para>
2929 The rest of this section gives further details about GADT-style data
2930 type declarations.
2931
2932 <itemizedlist>
2933 <listitem><para>
2934 The result type of each data constructor must begin with the type constructor being defined.
2935 If the result type of all constructors
2936 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2937 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2938 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2939 </para></listitem>
2940
2941 <listitem><para>
2942 As with other type signatures, you can give a single signature for several data constructors.
2943 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2944 <programlisting>
2945 data T a where
2946 T1,T2 :: a -> T a
2947 T3 :: T a
2948 </programlisting>
2949 </para></listitem>
2950
2951 <listitem><para>
2952 The type signature of
2953 each constructor is independent, and is implicitly universally quantified as usual.
2954 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2955 have no scope, and different constructors may have different universally-quantified type variables:
2956 <programlisting>
2957 data T a where -- The 'a' has no scope
2958 T1,T2 :: b -> T b -- Means forall b. b -> T b
2959 T3 :: T a -- Means forall a. T a
2960 </programlisting>
2961 </para></listitem>
2962
2963 <listitem><para>
2964 A constructor signature may mention type class constraints, which can differ for
2965 different constructors. For example, this is fine:
2966 <programlisting>
2967 data T a where
2968 T1 :: Eq b => b -> b -> T b
2969 T2 :: (Show c, Ix c) => c -> [c] -> T c
2970 </programlisting>
2971 When pattern matching, these constraints are made available to discharge constraints
2972 in the body of the match. For example:
2973 <programlisting>
2974 f :: T a -> String
2975 f (T1 x y) | x==y = "yes"
2976 | otherwise = "no"
2977 f (T2 a b) = show a
2978 </programlisting>
2979 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2980 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2981 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2982 </para></listitem>
2983
2984 <listitem><para>
2985 Unlike a Haskell-98-style
2986 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2987 have no scope. Indeed, one can write a kind signature instead:
2988 <programlisting>
2989 data Set :: * -> * where ...
2990 </programlisting>
2991 or even a mixture of the two:
2992 <programlisting>
2993 data Bar a :: (* -> *) -> * where ...
2994 </programlisting>
2995 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2996 like this:
2997 <programlisting>
2998 data Bar a (b :: * -> *) where ...
2999 </programlisting>
3000 </para></listitem>
3001
3002
3003 <listitem><para>
3004 You can use strictness annotations, in the obvious places
3005 in the constructor type:
3006 <programlisting>
3007 data Term a where
3008 Lit :: !Int -> Term Int
3009 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3010 Pair :: Term a -> Term b -> Term (a,b)
3011 </programlisting>
3012 </para></listitem>
3013
3014 <listitem><para>
3015 You can use a <literal>deriving</literal> clause on a GADT-style data type
3016 declaration. For example, these two declarations are equivalent
3017 <programlisting>
3018 data Maybe1 a where {
3019 Nothing1 :: Maybe1 a ;
3020 Just1 :: a -> Maybe1 a
3021 } deriving( Eq, Ord )
3022
3023 data Maybe2 a = Nothing2 | Just2 a
3024 deriving( Eq, Ord )
3025 </programlisting>
3026 </para></listitem>
3027
3028 <listitem><para>
3029 The type signature may have quantified type variables that do not appear
3030 in the result type:
3031 <programlisting>
3032 data Foo where
3033 MkFoo :: a -> (a->Bool) -> Foo
3034 Nil :: Foo
3035 </programlisting>
3036 Here the type variable <literal>a</literal> does not appear in the result type
3037 of either constructor.
3038 Although it is universally quantified in the type of the constructor, such
3039 a type variable is often called "existential".
3040 Indeed, the above declaration declares precisely the same type as
3041 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
3042 </para><para>
3043 The type may contain a class context too, of course:
3044 <programlisting>
3045 data Showable where
3046 MkShowable :: Show a => a -> Showable
3047 </programlisting>
3048 </para></listitem>
3049
3050 <listitem><para>
3051 You can use record syntax on a GADT-style data type declaration:
3052
3053 <programlisting>
3054 data Person where
3055 Adult :: { name :: String, children :: [Person] } -> Person
3056 Child :: Show a => { name :: !String, funny :: a } -> Person
3057 </programlisting>
3058 As usual, for every constructor that has a field <literal>f</literal>, the type of
3059 field <literal>f</literal> must be the same (modulo alpha conversion).
3060 The <literal>Child</literal> constructor above shows that the signature
3061 may have a context, existentially-quantified variables, and strictness annotations,
3062 just as in the non-record case. (NB: the "type" that follows the double-colon
3063 is not really a type, because of the record syntax and strictness annotations.
3064 A "type" of this form can appear only in a constructor signature.)
3065 </para></listitem>
3066
3067 <listitem><para>
3068 Record updates are allowed with GADT-style declarations,
3069 only fields that have the following property: the type of the field
3070 mentions no existential type variables.
3071 </para></listitem>
3072
3073 <listitem><para>
3074 As in the case of existentials declared using the Haskell-98-like record syntax
3075 (<xref linkend="existential-records"/>),
3076 record-selector functions are generated only for those fields that have well-typed
3077 selectors.
3078 Here is the example of that section, in GADT-style syntax:
3079 <programlisting>
3080 data Counter a where
3081 NewCounter { _this :: self
3082 , _inc :: self -> self
3083 , _display :: self -> IO ()
3084 , tag :: a
3085 }
3086 :: Counter a
3087 </programlisting>
3088 As before, only one selector function is generated here, that for <literal>tag</literal>.
3089 Nevertheless, you can still use all the field names in pattern matching and record construction.
3090 </para></listitem>
3091
3092 <listitem><para>
3093 In a GADT-style data type declaration there is no obvious way to specify that a data constructor
3094 should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
3095 (Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
3096 So GHC implements the following design: a data constructor declared in a GADT-style data type
3097 declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
3098 (b) it has two arguments, (c) it has a programmer-supplied fixity declaration. For example
3099 <programlisting>
3100 infix 6 (:--:)
3101 data T a where
3102 (:--:) :: Int -> Bool -> T Int
3103 </programlisting>
3104 </para></listitem>
3105 </itemizedlist></para>
3106 </sect2>
3107
3108 <sect2 id="gadt">
3109 <title>Generalised Algebraic Data Types (GADTs)</title>
3110
3111 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
3112 by allowing constructors to have richer return types. Here is an example:
3113 <programlisting>
3114 data Term a where
3115 Lit :: Int -> Term Int
3116 Succ :: Term Int -> Term Int
3117 IsZero :: Term Int -> Term Bool
3118 If :: Term Bool -> Term a -> Term a -> Term a
3119 Pair :: Term a -> Term b -> Term (a,b)
3120 </programlisting>
3121 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3122 case with ordinary data types. This generality allows us to
3123 write a well-typed <literal>eval</literal> function
3124 for these <literal>Terms</literal>:
3125 <programlisting>
3126 eval :: Term a -> a
3127 eval (Lit i) = i
3128 eval (Succ t) = 1 + eval t
3129 eval (IsZero t) = eval t == 0
3130 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3131 eval (Pair e1 e2) = (eval e1, eval e2)
3132 </programlisting>
3133 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
3134 For example, in the right hand side of the equation
3135 <programlisting>
3136 eval :: Term a -> a
3137 eval (Lit i) = ...
3138 </programlisting>
3139 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
3140 A precise specification of the type rules is beyond what this user manual aspires to,
3141 but the design closely follows that described in
3142 the paper <ulink
3143 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
3144 unification-based type inference for GADTs</ulink>,
3145 (ICFP 2006).
3146 The general principle is this: <emphasis>type refinement is only carried out
3147 based on user-supplied type annotations</emphasis>.
3148 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
3149 and lots of obscure error messages will
3150 occur. However, the refinement is quite general. For example, if we had:
3151 <programlisting>
3152 eval :: Term a -> a -> a
3153 eval (Lit i) j = i+j
3154 </programlisting>
3155 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3156 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
3157 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3158 </para>
3159 <para>
3160 These and many other examples are given in papers by Hongwei Xi, and
3161 Tim Sheard. There is a longer introduction
3162 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3163 and Ralf Hinze's
3164 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
3165 may use different notation to that implemented in GHC.
3166 </para>
3167 <para>
3168 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
3169 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
3170 <itemizedlist>
3171 <listitem><para>
3172 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
3173 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
3174 The result type of each constructor must begin with the type constructor being defined,
3175 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
3176 For example, in the <literal>Term</literal> data
3177 type above, the type of each constructor must end with <literal>Term ty</literal>, but
3178 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
3179 constructor).
3180 </para></listitem>
3181
3182 <listitem><para>
3183 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
3184 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
3185 whose result type is not just <literal>T a b</literal>.
3186 </para></listitem>
3187
3188 <listitem><para>
3189 You cannot use a <literal>deriving</literal> clause for a GADT; only for
3190 an ordinary data type.
3191 </para></listitem>
3192
3193 <listitem><para>
3194 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
3195 For example:
3196 <programlisting>
3197 data Term a where
3198 Lit { val :: Int } :: Term Int
3199 Succ { num :: Term Int } :: Term Int
3200 Pred { num :: Term Int } :: Term Int
3201 IsZero { arg :: Term Int } :: Term Bool
3202 Pair { arg1 :: Term a
3203 , arg2 :: Term b
3204 } :: Term (a,b)
3205 If { cnd :: Term Bool
3206 , tru :: Term a
3207 , fls :: Term a
3208 } :: Term a
3209 </programlisting>
3210 However, for GADTs there is the following additional constraint:
3211 every constructor that has a field <literal>f</literal> must have
3212 the same result type (modulo alpha conversion)
3213 Hence, in the above example, we cannot merge the <literal>num</literal>
3214 and <literal>arg</literal> fields above into a
3215 single name. Although their field types are both <literal>Term Int</literal>,
3216 their selector functions actually have different types:
3217
3218 <programlisting>
3219 num :: Term Int -> Term Int
3220 arg :: Term Bool -> Term Int
3221 </programlisting>
3222 </para></listitem>
3223
3224 <listitem><para>
3225 When pattern-matching against data constructors drawn from a GADT,
3226 for example in a <literal>case</literal> expression, the following rules apply:
3227 <itemizedlist>
3228 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
3229 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
3230 <listitem><para>The type of any free variable mentioned in any of
3231 the <literal>case</literal> alternatives must be rigid.</para></listitem>
3232 </itemizedlist>
3233 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
3234 way to ensure that a variable a rigid type is to give it a type signature.
3235 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
3236 Simple unification-based type inference for GADTs
3237 </ulink>. The criteria implemented by GHC are given in the Appendix.
3238
3239 </para></listitem>
3240
3241 </itemizedlist>
3242 </para>
3243
3244 </sect2>
3245 </sect1>
3246
3247 <!-- ====================== End of Generalised algebraic data types ======================= -->
3248
3249 <sect1 id="deriving">
3250 <title>Extensions to the "deriving" mechanism</title>
3251
3252 <sect2 id="deriving-inferred">
3253 <title>Inferred context for deriving clauses</title>
3254
3255 <para>
3256 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
3257 legal. For example:
3258 <programlisting>
3259 data T0 f a = MkT0 a deriving( Eq )
3260 data T1 f a = MkT1 (f a) deriving( Eq )
3261 data T2 f a = MkT2 (f (f a)) deriving( Eq )
3262 </programlisting>
3263 The natural generated <literal>Eq</literal> code would result in these instance declarations:
3264 <programlisting>
3265 instance Eq a => Eq (T0 f a) where ...
3266 instance Eq (f a) => Eq (T1 f a) where ...
3267 instance Eq (f (f a)) => Eq (T2 f a) where ...
3268 </programlisting>
3269 The first of these is obviously fine. The second is still fine, although less obviously.
3270 The third is not Haskell 98, and risks losing termination of instances.
3271 </para>
3272 <para>
3273 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
3274 each constraint in the inferred instance context must consist only of type variables,
3275 with no repetitions.
3276 </para>
3277 <para>
3278 This rule is applied regardless of flags. If you want a more exotic context, you can write
3279 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
3280 </para>
3281 </sect2>
3282
3283 <sect2 id="stand-alone-deriving">
3284 <title>Stand-alone deriving declarations</title>
3285
3286 <para>
3287 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
3288 <programlisting>
3289 data Foo a = Bar a | Baz String
3290
3291 deriving instance Eq a => Eq (Foo a)
3292 </programlisting>
3293 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
3294 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
3295 Note the following points:
3296 <itemizedlist>
3297 <listitem><para>
3298 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
3299 exactly as you would in an ordinary instance declaration.
3300 (In contrast, in a <literal>deriving</literal> clause
3301 attached to a data type declaration, the context is inferred.)
3302 </para></listitem>
3303
3304 <listitem><para>
3305 A <literal>deriving instance</literal> declaration
3306 must obey the same rules concerning form and termination as ordinary instance declarations,
3307 controlled by the same flags; see <xref linkend="instance-decls"/>.
3308 </para></listitem>
3309
3310 <listitem><para>
3311 Unlike a <literal>deriving</literal>
3312 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
3313 than the data type (assuming you also use
3314 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
3315 for example
3316 <programlisting>
3317 data Foo a = Bar a | Baz String
3318
3319 deriving instance Eq a => Eq (Foo [a])
3320 deriving instance Eq a => Eq (Foo (Maybe a))
3321 </programlisting>
3322 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
3323 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
3324 </para></listitem>
3325
3326 <listitem><para>
3327 Unlike a <literal>deriving</literal>
3328 declaration attached to a <literal>data</literal> declaration,
3329 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
3330 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
3331 your problem. (GHC will show you the offending code if it has a type error.)
3332 The merit of this is that you can derive instances for GADTs and other exotic
3333 data types, providing only that the boilerplate code does indeed typecheck. For example:
3334 <programlisting>
3335 data T a where
3336 T1 :: T Int
3337 T2 :: T Bool
3338
3339 deriving instance Show (T a)
3340 </programlisting>
3341 In this example, you cannot say <literal>... deriving( Show )</literal> on the
3342 data type declaration for <literal>T</literal>,
3343 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
3344 the instance declaration using stand-alone deriving.
3345 </para>
3346 </listitem>
3347
3348 <listitem>
3349 <para>The stand-alone syntax is generalised for newtypes in exactly the same
3350 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3351 For example:
3352 <programlisting>
3353 newtype Foo a = MkFoo (State Int a)
3354
3355 deriving instance MonadState Int Foo
3356 </programlisting>
3357 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3358 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3359 </para></listitem>
3360 </itemizedlist></para>
3361
3362 </sect2>
3363
3364
3365 <sect2 id="deriving-typeable">
3366 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
3367
3368 <para>
3369 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3370 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3371 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3372 classes <literal>Eq</literal>, <literal>Ord</literal>,
3373 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3374 </para>
3375 <para>
3376 GHC extends this list with several more classes that may be automatically derived:
3377 <itemizedlist>
3378 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
3379 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
3380 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
3381 </para>
3382 <para>Since GHC 7.8.1, <literal>Typeable</literal> is kind-polymorphic (see
3383 <xref linkend="kind-polymorphism"/>) and can be derived for any datatype and
3384 type class. Instances for datatypes can be derived by attaching a
3385 <literal>deriving Typeable</literal> clause to the datatype declaration, or by
3386 using standalone deriving (see <xref linkend="stand-alone-deriving"/>).
3387 Instances for type classes can only be derived using standalone deriving.
3388 See also <xref linkend="auto-derive-typeable"/>.
3389 </para>
3390 <para>
3391 Also since GHC 7.8.1, handwritten (ie. not derived) instances of
3392 <literal>Typeable</literal> are forbidden, and will be ignored with a warning.
3393 </para>
3394 </listitem>
3395
3396 <listitem><para> With <option>-XDeriveGeneric</option>, you can derive
3397 instances of the classes <literal>Generic</literal> and
3398 <literal>Generic1</literal>, defined in <literal>GHC.Generics</literal>.
3399 You can use these to define generic functions,
3400 as described in <xref linkend="generic-programming"/>.
3401 </para></listitem>
3402
3403 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3404 the class <literal>Functor</literal>,
3405 defined in <literal>GHC.Base</literal>.
3406 </para></listitem>
3407
3408 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3409 the class <literal>Foldable</literal>,
3410 defined in <literal>Data.Foldable</literal>.
3411 </para></listitem>
3412
3413 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3414 the class <literal>Traversable</literal>,
3415 defined in <literal>Data.Traversable</literal>.
3416 </para></listitem>
3417 </itemizedlist>
3418 In each case the appropriate class must be in scope before it
3419 can be mentioned in the <literal>deriving</literal> clause.
3420 </para>
3421 </sect2>
3422
3423 <sect2 id="auto-derive-typeable">
3424 <title>Automatically deriving <literal>Typeable</literal> instances</title>
3425
3426 <para>
3427 The flag <option>-XAutoDeriveTypeable</option> triggers the generation
3428 of derived <literal>Typeable</literal> instances for every datatype and type
3429 class declaration in the module it is used.
3430 </para>
3431
3432 </sect2>
3433
3434 <sect2 id="newtype-deriving">
3435 <title>Generalised derived instances for newtypes</title>
3436
3437 <para>
3438 When you define an abstract type using <literal>newtype</literal>, you may want
3439 the new type to inherit some instances from its representation. In
3440 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3441 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3442 other classes you have to write an explicit instance declaration. For
3443 example, if you define
3444
3445 <programlisting>
3446 newtype Dollars = Dollars Int
3447 </programlisting>
3448
3449 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3450 explicitly define an instance of <literal>Num</literal>:
3451
3452 <programlisting>
3453 instance Num Dollars where
3454 Dollars a + Dollars b = Dollars (a+b)
3455 ...
3456 </programlisting>
3457 All the instance does is apply and remove the <literal>newtype</literal>
3458 constructor. It is particularly galling that, since the constructor
3459 doesn't appear at run-time, this instance declaration defines a
3460 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3461 dictionary, only slower!
3462 </para>
3463
3464
3465 <sect3> <title> Generalising the deriving clause </title>
3466 <para>
3467 GHC now permits such instances to be derived instead,
3468 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3469 so one can write
3470 <programlisting>
3471 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3472 </programlisting>
3473
3474 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3475 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3476 derives an instance declaration of the form
3477
3478 <programlisting>
3479 instance Num Int => Num Dollars
3480 </programlisting>
3481
3482 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3483 </para>
3484 <para>
3485
3486 We can also derive instances of constructor classes in a similar
3487 way. For example, suppose we have implemented state and failure monad
3488 transformers, such that
3489
3490 <programlisting>
3491 instance Monad m => Monad (State s m)
3492 instance Monad m => Monad (Failure m)
3493 </programlisting>
3494 In Haskell 98, we can define a parsing monad by
3495 <programlisting>
3496 type Parser tok m a = State [tok] (Failure m) a
3497 </programlisting>
3498
3499 which is automatically a monad thanks to the instance declarations
3500 above. With the extension, we can make the parser type abstract,
3501 without needing to write an instance of class <literal>Monad</literal>, via
3502
3503 <programlisting>
3504 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3505 deriving Monad
3506 </programlisting>
3507 In this case the derived instance declaration is of the form
3508 <programlisting>
3509 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3510 </programlisting>
3511
3512 Notice that, since <literal>Monad</literal> is a constructor class, the
3513 instance is a <emphasis>partial application</emphasis> of the new type, not the
3514 entire left hand side. We can imagine that the type declaration is
3515 "eta-converted" to generate the context of the instance
3516 declaration.
3517 </para>
3518 <para>
3519
3520 We can even derive instances of multi-parameter classes, provided the
3521 newtype is the last class parameter. In this case, a ``partial
3522 application'' of the class appears in the <literal>deriving</literal>
3523 clause. For example, given the class
3524
3525 <programlisting>
3526 class StateMonad s m | m -> s where ...
3527 instance Monad m => StateMonad s (State s m) where ...
3528 </programlisting>
3529 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3530 <programlisting>
3531 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3532 deriving (Monad, StateMonad [tok])
3533 </programlisting>
3534
3535 The derived instance is obtained by completing the application of the
3536 class to the new type:
3537
3538 <programlisting>
3539 instance StateMonad [tok] (State [tok] (Failure m)) =>
3540 StateMonad [tok] (Parser tok m)
3541 </programlisting>
3542 </para>
3543 <para>
3544
3545 As a result of this extension, all derived instances in newtype
3546 declarations are treated uniformly (and implemented just by reusing
3547 the dictionary for the representation type), <emphasis>except</emphasis>
3548 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3549 the newtype and its representation.
3550 </para>
3551 </sect3>
3552
3553 <sect3> <title> A more precise specification </title>
3554 <para>
3555 Derived instance declarations are constructed as follows. Consider the
3556 declaration (after expansion of any type synonyms)
3557
3558 <programlisting>
3559 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3560 </programlisting>
3561
3562 where
3563 <itemizedlist>
3564 <listitem><para>
3565 The <literal>ci</literal> are partial applications of
3566 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3567 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3568 </para></listitem>
3569 <listitem><para>
3570 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3571 </para></listitem>
3572 <listitem><para>
3573 The type <literal>t</literal> is an arbitrary type.
3574 </para></listitem>
3575 <listitem><para>
3576 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3577 nor in the <literal>ci</literal>, and
3578 </para></listitem>
3579 <listitem><para>
3580 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3581 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3582 should not "look through" the type or its constructor. You can still
3583 derive these classes for a newtype, but it happens in the usual way, not
3584 via this new mechanism.
3585 </para></listitem>
3586 </itemizedlist>
3587 Then, for each <literal>ci</literal>, the derived instance
3588 declaration is:
3589 <programlisting>
3590 instance ci t => ci (T v1...vk)
3591 </programlisting>
3592 As an example which does <emphasis>not</emphasis> work, consider
3593 <programlisting>
3594 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3595 </programlisting>
3596 Here we cannot derive the instance
3597 <programlisting>
3598 instance Monad (State s m) => Monad (NonMonad m)
3599 </programlisting>
3600
3601 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3602 and so cannot be "eta-converted" away. It is a good thing that this
3603 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3604 not, in fact, a monad --- for the same reason. Try defining
3605 <literal>>>=</literal> with the correct type: you won't be able to.
3606 </para>
3607 <para>
3608
3609 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3610 important, since we can only derive instances for the last one. If the
3611 <literal>StateMonad</literal> class above were instead defined as
3612
3613 <programlisting>
3614 class StateMonad m s | m -> s where ...
3615 </programlisting>
3616
3617 then we would not have been able to derive an instance for the
3618 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3619 classes usually have one "main" parameter for which deriving new
3620 instances is most interesting.
3621 </para>
3622 <para>Lastly, all of this applies only for classes other than
3623 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3624 and <literal>Data</literal>, for which the built-in derivation applies (section
3625 4.3.3. of the Haskell Report).
3626 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3627 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3628 the standard method is used or the one described here.)
3629 </para>
3630 </sect3>
3631 </sect2>
3632 </sect1>
3633
3634
3635 <!-- TYPE SYSTEM EXTENSIONS -->
3636 <sect1 id="type-class-extensions">
3637 <title>Class and instances declarations</title>
3638
3639 <sect2 id="multi-param-type-classes">
3640 <title>Class declarations</title>
3641
3642 <para>
3643 This section, and the next one, documents GHC's type-class extensions.
3644 There's lots of background in the paper <ulink
3645 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3646 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3647 Jones, Erik Meijer).
3648 </para>
3649
3650 <sect3>
3651 <title>Multi-parameter type classes</title>
3652 <para>
3653 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3654 For example:
3655
3656
3657 <programlisting>
3658 class Collection c a where
3659 union :: c a -> c a -> c a
3660 ...etc.
3661 </programlisting>
3662
3663 </para>
3664 </sect3>
3665
3666 <sect3 id="superclass-rules">
3667 <title>The superclasses of a class declaration</title>
3668
3669 <para>
3670 In Haskell 98 the context of a class declaration (which introduces superclasses)
3671 must be simple; that is, each predicate must consist of a class applied to
3672 type variables. The flag <option>-XFlexibleContexts</option>
3673 (<xref linkend="flexible-contexts"/>)
3674 lifts this restriction,
3675 so that the only restriction on the context in a class declaration is
3676 that the class hierarchy must be acyclic. So these class declarations are OK:
3677
3678
3679 <programlisting>
3680 class Functor (m k) => FiniteMap m k where
3681 ...
3682
3683 class (Monad m, Monad (t m)) => Transform t m where
3684 lift :: m a -> (t m) a
3685 </programlisting>
3686
3687
3688 </para>
3689 <para>
3690 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3691 of "acyclic" involves only the superclass relationships. For example,
3692 this is OK:
3693
3694
3695 <programlisting>
3696 class C a where {
3697 op :: D b => a -> b -> b
3698 }
3699
3700 class C a => D a where { ... }
3701 </programlisting>
3702
3703
3704 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3705 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3706 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3707 </para>
3708 <para>
3709 With the extension that adds a <link linkend="constraint-kind">kind of constraints</link>,
3710 you can write more exotic superclass definitions. The superclass cycle check is even more
3711 liberal in these case. For example, this is OK:
3712
3713 <programlisting>
3714 class A cls c where
3715 meth :: cls c => c -> c
3716
3717 class A B c => B c where
3718 </programlisting>
3719
3720 A superclass context for a class <literal>C</literal> is allowed if, after expanding
3721 type synonyms to their right-hand-sides, and uses of classes (other than <literal>C</literal>)
3722 to their superclasses, <literal>C</literal> does not occur syntactically in the context.
3723 </para>
3724 </sect3>
3725
3726
3727
3728
3729 <sect3 id="class-method-types">
3730 <title>Class method types</title>
3731
3732 <para>
3733 Haskell 98 prohibits class method types to mention constraints on the
3734 class type variable, thus:
3735 <programlisting>
3736 class Seq s a where
3737 fromList :: [a] -> s a
3738 elem :: Eq a => a -> s a -> Bool
3739 </programlisting>
3740 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3741 contains the constraint <literal>Eq a</literal>, constrains only the
3742 class type variable (in this case <literal>a</literal>).
3743 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3744 </para>
3745
3746
3747 </sect3>
3748
3749
3750 <sect3 id="class-default-signatures">
3751 <title>Default method signatures</title>
3752
3753 <para>
3754 Haskell 98 allows you to define a default implementation when declaring a class:
3755 <programlisting>
3756 class Enum a where
3757 enum :: [a]
3758 enum = []
3759 </programlisting>
3760 The type of the <literal>enum</literal> method is <literal>[a]</literal>, and
3761 this is also the type of the default method. You can lift this restriction
3762 and give another type to the default method using the flag
3763 <option>-XDefaultSignatures</option>. For instance, if you have written a
3764 generic implementation of enumeration in a class <literal>GEnum</literal>
3765 with method <literal>genum</literal> in terms of <literal>GHC.Generics</literal>,
3766 you can specify a default method that uses that generic implementation:
3767 <programlisting>
3768 class Enum a where
3769 enum :: [a]
3770 default enum :: (Generic a, GEnum (Rep a)) => [a]
3771 enum = map to genum
3772 </programlisting>
3773 We reuse the keyword <literal>default</literal> to signal that a signature
3774 applies to the default method only; when defining instances of the
3775 <literal>Enum</literal> class, the original type <literal>[a]</literal> of
3776 <literal>enum</literal> still applies. When giving an empty instance, however,
3777 the default implementation <literal>map to genum</literal> is filled-in,
3778 and type-checked with the type
3779 <literal>(Generic a, GEnum (Rep a)) => [a]</literal>.
3780 </para>
3781
3782 <para>
3783 We use default signatures to simplify generic programming in GHC
3784 (<xref linkend="generic-programming"/>).
3785 </para>
3786
3787
3788 </sect3>
3789 </sect2>
3790
3791 <sect2 id="functional-dependencies">
3792 <title>Functional dependencies
3793 </title>
3794
3795 <para> Functional dependencies are implemented as described by Mark Jones
3796 in &ldquo;<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>&rdquo;, Mark P. Jones,
3797 In Proceedings of the 9th European Symposium on Programming,
3798 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3799 .
3800 </para>
3801 <para>
3802 Functional dependencies are introduced by a vertical bar in the syntax of a
3803 class declaration; e.g.
3804 <programlisting>
3805 class (Monad m) => MonadState s m | m -> s where ...
3806
3807 class Foo a b c | a b -> c where ...
3808 </programlisting>
3809 There should be more documentation, but there isn't (yet). Yell if you need it.
3810 </para>
3811
3812 <sect3><title>Rules for functional dependencies </title>
3813 <para>
3814 In a class declaration, all of the class type variables must be reachable (in the sense
3815 mentioned in <xref linkend="flexible-contexts"/>)
3816 from the free variables of each method type.
3817 For example:
3818
3819 <programlisting>
3820 class Coll s a where
3821 empty :: s
3822 insert :: s -> a -> s
3823 </programlisting>
3824
3825 is not OK, because the type of <literal>empty</literal> doesn't mention
3826 <literal>a</literal>. Functional dependencies can make the type variable
3827 reachable:
3828 <programlisting>
3829 class Coll s a | s -> a where
3830 empty :: s
3831 insert :: s -> a -> s
3832 </programlisting>
3833
3834 Alternatively <literal>Coll</literal> might be rewritten
3835
3836 <programlisting>
3837 class Coll s a where
3838 empty :: s a
3839 insert :: s a -> a -> s a
3840 </programlisting>
3841
3842
3843 which makes the connection between the type of a collection of
3844 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3845 Occasionally this really doesn't work, in which case you can split the
3846 class like this:
3847
3848
3849 <programlisting>
3850 class CollE s where
3851 empty :: s
3852
3853 class CollE s => Coll s a where
3854 insert :: s -> a -> s
3855 </programlisting>
3856 </para>
3857 </sect3>
3858
3859
3860 <sect3>
3861 <title>Background on functional dependencies</title>
3862
3863 <para>The following description of the motivation and use of functional dependencies is taken
3864 from the Hugs user manual, reproduced here (with minor changes) by kind
3865 permission of Mark Jones.
3866 </para>
3867 <para>
3868 Consider the following class, intended as part of a
3869 library for collection types:
3870 <programlisting>
3871 class Collects e ce where
3872 empty :: ce
3873 insert :: e -> ce -> ce
3874 member :: e -> ce -> Bool
3875 </programlisting>
3876 The type variable e used here represents the element type, while ce is the type
3877 of the container itself. Within this framework, we might want to define
3878 instances of this class for lists or characteristic functions (both of which
3879 can be used to represent collections of any equality type), bit sets (which can
3880 be used to represent collections of characters), or hash tables (which can be
3881 used to represent any collection whose elements have a hash function). Omitting
3882 standard implementation details, this would lead to the following declarations:
3883 <programlisting>
3884 instance Eq e => Collects e [e] where ...
3885 instance Eq e => Collects e (e -> Bool) where ...
3886 instance Collects Char BitSet where ...
3887 instance (Hashable e, Collects a ce)
3888 => Collects e (Array Int ce) where ...
3889 </programlisting>
3890 All this looks quite promising; we have a class and a range of interesting
3891 implementations. Unfortunately, there are some serious problems with the class
3892 declaration. First, the empty function has an ambiguous type:
3893 <programlisting>
3894 empty :: Collects e ce => ce
3895 </programlisting>
3896 By "ambiguous" we mean that there is a type variable e that appears on the left
3897 of the <literal>=&gt;</literal> symbol, but not on the right. The problem with
3898 this is that, according to the theoretical foundations of Haskell overloading,
3899 we cannot guarantee a well-defined semantics for any term with an ambiguous
3900 type.
3901 </para>
3902 <para>
3903 We can sidestep this specific problem by removing the empty member from the
3904 class declaration. However, although the remaining members, insert and member,
3905 do not have ambiguous types, we still run into problems when we try to use
3906 them. For example, consider the following two functions:
3907 <programlisting>
3908 f x y = insert x . insert y
3909 g = f True 'a'
3910 </programlisting>
3911 for which GHC infers the following types:
3912 <programlisting>
3913 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3914 g :: (Collects Bool c, Collects Char c) => c -> c
3915 </programlisting>
3916 Notice that the type for f allows the two parameters x and y to be assigned
3917 different types, even though it attempts to insert each of the two values, one
3918 after the other, into the same collection. If we're trying to model collections
3919 that contain only one type of value, then this is clearly an inaccurate
3920 type. Worse still, the definition for g is accepted, without causing a type
3921 error. As a result, the error in this code will not be flagged at the point
3922 where it appears. Instead, it will show up only when we try to use g, which
3923 might even be in a different module.
3924 </para>
3925
3926 <sect4><title>An attempt to use constructor classes</title>
3927
3928 <para>
3929 Faced with the problems described above, some Haskell programmers might be
3930 tempted to use something like the following version of the class declaration:
3931 <programlisting>
3932 class Collects e c where
3933 empty :: c e
3934 insert :: e -> c e -> c e
3935 member :: e -> c e -> Bool
3936 </programlisting>
3937 The key difference here is that we abstract over the type constructor c that is
3938 used to form the collection type c e, and not over that collection type itself,
3939 represented by ce in the original class declaration. This avoids the immediate
3940 problems that we mentioned above: empty has type <literal>Collects e c => c
3941 e</literal>, which is not ambiguous.
3942 </para>
3943 <para>
3944 The function f from the previous section has a more accurate type:
3945 <programlisting>
3946 f :: (Collects e c) => e -> e -> c e -> c e
3947 </programlisting>
3948 The function g from the previous section is now rejected with a type error as
3949 we would hope because the type of f does not allow the two arguments to have
3950 different types.
3951 This, then, is an example of a multiple parameter class that does actually work
3952 quite well in practice, without ambiguity problems.
3953 There is, however, a catch. This version of the Collects class is nowhere near
3954 as general as the original class seemed to be: only one of the four instances
3955 for <literal>Collects</literal>
3956 given above can be used with this version of Collects because only one of
3957 them---the instance for lists---has a collection type that can be written in
3958 the form c e, for some type constructor c, and element type e.
3959 </para>
3960 </sect4>
3961
3962 <sect4><title>Adding functional dependencies</title>
3963
3964 <para>
3965 To get a more useful version of the Collects class, Hugs provides a mechanism
3966 that allows programmers to specify dependencies between the parameters of a
3967 multiple parameter class (For readers with an interest in theoretical
3968 foundations and previous work: The use of dependency information can be seen
3969 both as a generalization of the proposal for `parametric type classes' that was
3970 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3971 later framework for "improvement" of qualified types. The
3972 underlying ideas are also discussed in a more theoretical and abstract setting
3973 in a manuscript [implparam], where they are identified as one point in a
3974 general design space for systems of implicit parameterization.).
3975
3976 To start with an abstract example, consider a declaration such as:
3977 <programlisting>
3978 class C a b where ...
3979 </programlisting>
3980 which tells us simply that C can be thought of as a binary relation on types
3981 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3982 included in the definition of classes to add information about dependencies
3983 between parameters, as in the following examples:
3984 <programlisting>
3985 class D a b | a -> b where ...
3986 class E a b | a -> b, b -> a where ...
3987 </programlisting>
3988 The notation <literal>a -&gt; b</literal> used here between the | and where
3989 symbols --- not to be
3990 confused with a function type --- indicates that the a parameter uniquely
3991 determines the b parameter, and might be read as "a determines b." Thus D is
3992 not just a relation, but actually a (partial) function. Similarly, from the two
3993 dependencies that are included in the definition of E, we can see that E
3994 represents a (partial) one-one mapping between types.
3995 </para>
3996 <para>
3997 More generally, dependencies take the form <literal>x1 ... xn -&gt; y1 ... ym</literal>,
3998 where x1, ..., xn, and y1, ..., yn are type variables with n&gt;0 and
3999 m&gt;=0, meaning that the y parameters are uniquely determined by the x
4000 parameters. Spaces can be used as separators if more than one variable appears
4001 on any single side of a dependency, as in <literal>t -&gt; a b</literal>. Note that a class may be
4002 annotated with multiple dependencies using commas as separators, as in the
4003 definition of E above. Some dependencies that we can write in this notation are
4004 redundant, and will be rejected because they don't serve any useful
4005 purpose, and may instead indicate an error in the program. Examples of
4006 dependencies like this include <literal>a -&gt; a </literal>,
4007 <literal>a -&gt; a a </literal>,
4008 <literal>a -&gt; </literal>, etc. There can also be
4009 some redundancy if multiple dependencies are given, as in
4010 <literal>a-&gt;b</literal>,
4011 <literal>b-&gt;c </literal>, <literal>a-&gt;c </literal>, and
4012 in which some subset implies the remaining dependencies. Examples like this are
4013 not treated as errors. Note that dependencies appear only in class
4014 declarations, and not in any other part of the language. In particular, the
4015 syntax for instance declarations, class constraints, and types is completely
4016 unchanged.
4017 </para>
4018 <para>
4019 By including dependencies in a class declaration, we provide a mechanism for
4020 the programmer to specify each multiple parameter class more precisely. The
4021 compiler, on the other hand, is responsible for ensuring that the set of
4022 instances that are in scope at any given point in the program is consistent
4023 with any declared dependencies. For example, the following pair of instance
4024 declarations cannot appear together in the same scope because they violate the
4025 dependency for D, even though either one on its own would be acceptable:
4026 <programlisting>
4027 instance D Bool Int where ...
4028 instance D Bool Char where ...
4029 </programlisting>
4030 Note also that the following declaration is not allowed, even by itself:
4031 <programlisting>
4032 instance D [a] b where ...
4033 </programlisting>
4034 The problem here is that this instance would allow one particular choice of [a]
4035 to be associated with more than one choice for b, which contradicts the
4036 dependency specified in the definition of D. More generally, this means that,
4037 in any instance of the form:
4038 <programlisting>
4039 instance D t s where ...
4040 </programlisting>
4041 for some particular types t and s, the only variables that can appear in s are
4042 the ones that appear in t, and hence, if the type t is known, then s will be
4043 uniquely determined.
4044 </para>
4045 <para>
4046 The benefit of including dependency information is that it allows us to define
4047 more general multiple parameter classes, without ambiguity problems, and with
4048 the benefit of more accurate types. To illustrate this, we return to the
4049 collection class example, and annotate the original definition of <literal>Collects</literal>
4050 with a simple dependency:
4051 <programlisting>
4052 class Collects e ce | ce -> e where
4053 empty :: ce
4054 insert :: e -> ce -> ce
4055 member :: e -> ce -> Bool
4056 </programlisting>
4057 The dependency <literal>ce -&gt; e</literal> here specifies that the type e of elements is uniquely
4058 determined by the type of the collection ce. Note that both parameters of
4059 Collects are of kind *; there are no constructor classes here. Note too that
4060 all of the instances of Collects that we gave earlier can be used
4061 together with this new definition.
4062 </para>
4063 <para>
4064 What about the ambiguity problems that we encountered with the original
4065 definition? The empty function still has type Collects e ce => ce, but it is no
4066 longer necessary to regard that as an ambiguous type: Although the variable e
4067 does not appear on the right of the => symbol, the dependency for class
4068 Collects tells us that it is uniquely determined by ce, which does appear on
4069 the right of the => symbol. Hence the context in which empty is used can still
4070 give enough information to determine types for both ce and e, without
4071 ambiguity. More generally, we need only regard a type as ambiguous if it
4072 contains a variable on the left of the => that is not uniquely determined
4073 (either directly or indirectly) by the variables on the right.
4074 </para>
4075 <para>
4076 Dependencies also help to produce more accurate types for user defined
4077 functions, and hence to provide earlier detection of errors, and less cluttered
4078 types for programmers to work with. Recall the previous definition for a
4079 function f:
4080 <programlisting>
4081 f x y = insert x y = insert x . insert y
4082 </programlisting>
4083 for which we originally obtained a type:
4084 <programlisting>
4085 f :: (Collects a c, Collects b c) => a -> b -> c -> c
4086 </programlisting>
4087 Given the dependency information that we have for Collects, however, we can
4088 deduce that a and b must be equal because they both appear as the second
4089 parameter in a Collects constraint with the same first parameter c. Hence we
4090 can infer a shorter and more accurate type for f:
4091 <programlisting>
4092 f :: (Collects a c) => a -> a -> c -> c
4093 </programlisting>
4094 In a similar way, the earlier definition of g will now be flagged as a type error.
4095 </para>
4096 <para>
4097 Although we have given only a few examples here, it should be clear that the
4098 addition of dependency information can help to make multiple parameter classes
4099 more useful in practice, avoiding ambiguity problems, and allowing more general
4100 sets of instance declarations.
4101 </para>
4102 </sect4>
4103 </sect3>
4104 </sect2>
4105