More release note touchups.
[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 Note that when unboxed tuples are enabled,
229 <literal>(#</literal> is a single lexeme, so for example when using
230 operators like <literal>#</literal> and <literal>#-</literal> you need
231 to write <literal>( # )</literal> and <literal>( #- )</literal> rather than
232 <literal>(#)</literal> and <literal>(#-)</literal>.
233 </para>
234
235 <para>
236 Unboxed tuples are used for functions that need to return multiple
237 values, but they avoid the heap allocation normally associated with
238 using fully-fledged tuples. When an unboxed tuple is returned, the
239 components are put directly into registers or on the stack; the
240 unboxed tuple itself does not have a composite representation. Many
241 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
242 tuples.
243 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
244 tuples to avoid unnecessary allocation during sequences of operations.
245 </para>
246
247 <para>
248 There are some restrictions on the use of unboxed tuples:
249 <itemizedlist>
250
251 <listitem>
252 <para>
253 Values of unboxed tuple types are subject to the same restrictions as
254 other unboxed types; i.e. they may not be stored in polymorphic data
255 structures or passed to polymorphic functions.
256 </para>
257 </listitem>
258
259 <listitem>
260 <para>
261 The typical use of unboxed tuples is simply to return multiple values,
262 binding those multiple results with a <literal>case</literal> expression, thus:
263 <programlisting>
264 f x y = (# x+1, y-1 #)
265 g x = case f x x of { (# a, b #) -&#62; a + b }
266 </programlisting>
267 You can have an unboxed tuple in a pattern binding, thus
268 <programlisting>
269 f x = let (# p,q #) = h x in ..body..
270 </programlisting>
271 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
272 the resulting binding is lazy like any other Haskell pattern binding. The
273 above example desugars like this:
274 <programlisting>
275 f x = let t = case h x of { (# p,q #) -> (p,q) }
276 p = fst t
277 q = snd t
278 in ..body..
279 </programlisting>
280 Indeed, the bindings can even be recursive.
281 </para>
282 </listitem>
283 </itemizedlist>
284
285 </para>
286
287 </sect2>
288 </sect1>
289
290
291 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
292
293 <sect1 id="syntax-extns">
294 <title>Syntactic extensions</title>
295
296 <sect2 id="unicode-syntax">
297 <title>Unicode syntax</title>
298 <para>The language
299 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
300 enables Unicode characters to be used to stand for certain ASCII
301 character sequences. The following alternatives are provided:</para>
302
303 <informaltable>
304 <tgroup cols="2" align="left" colsep="1" rowsep="1">
305 <thead>
306 <row>
307 <entry>ASCII</entry>
308 <entry>Unicode alternative</entry>
309 <entry>Code point</entry>
310 <entry>Name</entry>
311 </row>
312 </thead>
313
314 <!--
315 to find the DocBook entities for these characters, find
316 the Unicode code point (e.g. 0x2237), and grep for it in
317 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
318 your system. Some of these Unicode code points don't have
319 equivalent DocBook entities.
320 -->
321
322 <tbody>
323 <row>
324 <entry><literal>::</literal></entry>
325 <entry>::</entry> <!-- no special char, apparently -->
326 <entry>0x2237</entry>
327 <entry>PROPORTION</entry>
328 </row>
329 </tbody>
330 <tbody>
331 <row>
332 <entry><literal>=&gt;</literal></entry>
333 <entry>&rArr;</entry>
334 <entry>0x21D2</entry>
335 <entry>RIGHTWARDS DOUBLE ARROW</entry>
336 </row>
337 </tbody>
338 <tbody>
339 <row>
340 <entry><literal>forall</literal></entry>
341 <entry>&forall;</entry>
342 <entry>0x2200</entry>
343 <entry>FOR ALL</entry>
344 </row>
345 </tbody>
346 <tbody>
347 <row>
348 <entry><literal>-&gt;</literal></entry>
349 <entry>&rarr;</entry>
350 <entry>0x2192</entry>
351 <entry>RIGHTWARDS ARROW</entry>
352 </row>
353 </tbody>
354 <tbody>
355 <row>
356 <entry><literal>&lt;-</literal></entry>
357 <entry>&larr;</entry>
358 <entry>0x2190</entry>
359 <entry>LEFTWARDS ARROW</entry>
360 </row>
361 </tbody>
362
363 <tbody>
364 <row>
365 <entry>-&lt;</entry>
366 <entry>&larrtl;</entry>
367 <entry>0x2919</entry>
368 <entry>LEFTWARDS ARROW-TAIL</entry>
369 </row>
370 </tbody>
371
372 <tbody>
373 <row>
374 <entry>&gt;-</entry>
375 <entry>&rarrtl;</entry>
376 <entry>0x291A</entry>
377 <entry>RIGHTWARDS ARROW-TAIL</entry>
378 </row>
379 </tbody>
380
381 <tbody>
382 <row>
383 <entry>-&lt;&lt;</entry>
384 <entry></entry>
385 <entry>0x291B</entry>
386 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
387 </row>
388 </tbody>
389
390 <tbody>
391 <row>
392 <entry>&gt;&gt;-</entry>
393 <entry></entry>
394 <entry>0x291C</entry>
395 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
396 </row>
397 </tbody>
398
399 <tbody>
400 <row>
401 <entry>*</entry>
402 <entry>&starf;</entry>
403 <entry>0x2605</entry>
404 <entry>BLACK STAR</entry>
405 </row>
406 </tbody>
407
408 </tgroup>
409 </informaltable>
410 </sect2>
411
412 <sect2 id="magic-hash">
413 <title>The magic hash</title>
414 <para>The language extension <option>-XMagicHash</option> allows "&num;" as a
415 postfix modifier to identifiers. Thus, "x&num;" is a valid variable, and "T&num;" is
416 a valid type constructor or data constructor.</para>
417
418 <para>The hash sign does not change semantics at all. We tend to use variable
419 names ending in "&num;" for unboxed values or types (e.g. <literal>Int&num;</literal>),
420 but there is no requirement to do so; they are just plain ordinary variables.
421 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
422 For example, to bring <literal>Int&num;</literal> into scope you must
423 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
424 the <option>-XMagicHash</option> extension
425 then allows you to <emphasis>refer</emphasis> to the <literal>Int&num;</literal>
426 that is now in scope. Note that with this option, the meaning of <literal>x&num;y = 0</literal>
427 is changed: it defines a function <literal>x&num;</literal> taking a single argument <literal>y</literal>;
428 to define the operator <literal>&num;</literal>, put a space: <literal>x &num; y = 0</literal>.
429
430 </para>
431 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
432 <itemizedlist>
433 <listitem><para> <literal>'x'&num;</literal> has type <literal>Char&num;</literal></para> </listitem>
434 <listitem><para> <literal>&quot;foo&quot;&num;</literal> has type <literal>Addr&num;</literal></para> </listitem>
435 <listitem><para> <literal>3&num;</literal> has type <literal>Int&num;</literal>. In general,
436 any Haskell integer lexeme followed by a <literal>&num;</literal> is an <literal>Int&num;</literal> literal, e.g.
437 <literal>-0x3A&num;</literal> as well as <literal>32&num;</literal>.</para></listitem>
438 <listitem><para> <literal>3&num;&num;</literal> has type <literal>Word&num;</literal>. In general,
439 any non-negative Haskell integer lexeme followed by <literal>&num;&num;</literal>
440 is a <literal>Word&num;</literal>. </para> </listitem>
441 <listitem><para> <literal>3.2&num;</literal> has type <literal>Float&num;</literal>.</para> </listitem>
442 <listitem><para> <literal>3.2&num;&num;</literal> has type <literal>Double&num;</literal></para> </listitem>
443 </itemizedlist>
444 </para>
445 </sect2>
446
447 <sect2 id="negative-literals">
448 <title>Negative literals</title>
449 <para>
450 The literal <literal>-123</literal> is, according to
451 Haskell98 and Haskell 2010, desugared as
452 <literal>negate (fromInteger 123)</literal>.
453 The language extension <option>-XNegativeLiterals</option>
454 means that it is instead desugared as
455 <literal>fromInteger (-123)</literal>.
456 </para>
457
458 <para>
459 This can make a difference when the positive and negative range of
460 a numeric data type don't match up. For example,
461 in 8-bit arithmetic -128 is representable, but +128 is not.
462 So <literal>negate (fromInteger 128)</literal> will elicit an
463 unexpected integer-literal-overflow message.
464 </para>
465 </sect2>
466
467 <sect2 id="num-decimals">
468 <title>Fractional looking integer literals</title>
469 <para>
470 Haskell 2010 and Haskell 98 define floating literals with
471 the syntax <literal>1.2e6</literal>. These literals have the
472 type <literal>Fractional a => a</literal>.
473 </para>
474
475 <para>
476 The language extension <option>-XNumDecimals</option> allows
477 you to also use the floating literal syntax for instances of
478 <literal>Integral</literal>, and have values like
479 <literal>(1.2e6 :: Num a => a)</literal>
480 </para>
481 </sect2>
482
483
484 <!-- ====================== HIERARCHICAL MODULES ======================= -->
485
486
487 <sect2 id="hierarchical-modules">
488 <title>Hierarchical Modules</title>
489
490 <para>GHC supports a small extension to the syntax of module
491 names: a module name is allowed to contain a dot
492 <literal>&lsquo;.&rsquo;</literal>. This is also known as the
493 &ldquo;hierarchical module namespace&rdquo; extension, because
494 it extends the normally flat Haskell module namespace into a
495 more flexible hierarchy of modules.</para>
496
497 <para>This extension has very little impact on the language
498 itself; modules names are <emphasis>always</emphasis> fully
499 qualified, so you can just think of the fully qualified module
500 name as <quote>the module name</quote>. In particular, this
501 means that the full module name must be given after the
502 <literal>module</literal> keyword at the beginning of the
503 module; for example, the module <literal>A.B.C</literal> must
504 begin</para>
505
506 <programlisting>module A.B.C</programlisting>
507
508
509 <para>It is a common strategy to use the <literal>as</literal>
510 keyword to save some typing when using qualified names with
511 hierarchical modules. For example:</para>
512
513 <programlisting>
514 import qualified Control.Monad.ST.Strict as ST
515 </programlisting>
516
517 <para>For details on how GHC searches for source and interface
518 files in the presence of hierarchical modules, see <xref
519 linkend="search-path"/>.</para>
520
521 <para>GHC comes with a large collection of libraries arranged
522 hierarchically; see the accompanying <ulink
523 url="../libraries/index.html">library
524 documentation</ulink>. More libraries to install are available
525 from <ulink
526 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
527 </sect2>
528
529 <!-- ====================== PATTERN GUARDS ======================= -->
530
531 <sect2 id="pattern-guards">
532 <title>Pattern guards</title>
533
534 <para>
535 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
536 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.)
537 </para>
538
539 <para>
540 Suppose we have an abstract data type of finite maps, with a
541 lookup operation:
542
543 <programlisting>
544 lookup :: FiniteMap -> Int -> Maybe Int
545 </programlisting>
546
547 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
548 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
549 </para>
550
551 <programlisting>
552 clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
553 | otherwise = var1 + var2
554 where
555 m1 = lookup env var1
556 m2 = lookup env var2
557 ok1 = maybeToBool m1
558 ok2 = maybeToBool m2
559 val1 = expectJust m1
560 val2 = expectJust m2
561 </programlisting>
562
563 <para>
564 The auxiliary functions are
565 </para>
566
567 <programlisting>
568 maybeToBool :: Maybe a -&gt; Bool
569 maybeToBool (Just x) = True
570 maybeToBool Nothing = False
571
572 expectJust :: Maybe a -&gt; a
573 expectJust (Just x) = x
574 expectJust Nothing = error "Unexpected Nothing"
575 </programlisting>
576
577 <para>
578 What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
579 ok2</literal> checks that both lookups succeed, using
580 <function>maybeToBool</function> to convert the <function>Maybe</function>
581 types to booleans. The (lazily evaluated) <function>expectJust</function>
582 calls extract the values from the results of the lookups, and binds the
583 returned values to <varname>val1</varname> and <varname>val2</varname>
584 respectively. If either lookup fails, then clunky takes the
585 <literal>otherwise</literal> case and returns the sum of its arguments.
586 </para>
587
588 <para>
589 This is certainly legal Haskell, but it is a tremendously verbose and
590 un-obvious way to achieve the desired effect. Arguably, a more direct way
591 to write clunky would be to use case expressions:
592 </para>
593
594 <programlisting>
595 clunky env var1 var2 = case lookup env var1 of
596 Nothing -&gt; fail
597 Just val1 -&gt; case lookup env var2 of
598 Nothing -&gt; fail
599 Just val2 -&gt; val1 + val2
600 where
601 fail = var1 + var2
602 </programlisting>
603
604 <para>
605 This is a bit shorter, but hardly better. Of course, we can rewrite any set
606 of pattern-matching, guarded equations as case expressions; that is
607 precisely what the compiler does when compiling equations! The reason that
608 Haskell provides guarded equations is because they allow us to write down
609 the cases we want to consider, one at a time, independently of each other.
610 This structure is hidden in the case version. Two of the right-hand sides
611 are really the same (<function>fail</function>), and the whole expression
612 tends to become more and more indented.
613 </para>
614
615 <para>
616 Here is how I would write clunky:
617 </para>
618
619 <programlisting>
620 clunky env var1 var2
621 | Just val1 &lt;- lookup env var1
622 , Just val2 &lt;- lookup env var2
623 = val1 + val2
624 ...other equations for clunky...
625 </programlisting>
626
627 <para>
628 The semantics should be clear enough. The qualifiers are matched in order.
629 For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
630 right hand side is evaluated and matched against the pattern on the left.
631 If the match fails then the whole guard fails and the next equation is
632 tried. If it succeeds, then the appropriate binding takes place, and the
633 next qualifier is matched, in the augmented environment. Unlike list
634 comprehensions, however, the type of the expression to the right of the
635 <literal>&lt;-</literal> is the same as the type of the pattern to its
636 left. The bindings introduced by pattern guards scope over all the
637 remaining guard qualifiers, and over the right hand side of the equation.
638 </para>
639
640 <para>
641 Just as with list comprehensions, boolean expressions can be freely mixed
642 with among the pattern guards. For example:
643 </para>
644
645 <programlisting>
646 f x | [y] &lt;- x
647 , y > 3
648 , Just z &lt;- h y
649 = ...
650 </programlisting>
651
652 <para>
653 Haskell's current guards therefore emerge as a special case, in which the
654 qualifier list has just one element, a boolean expression.
655 </para>
656 </sect2>
657
658 <!-- ===================== View patterns =================== -->
659
660 <sect2 id="view-patterns">
661 <title>View patterns
662 </title>
663
664 <para>
665 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
666 More information and examples of view patterns can be found on the
667 <ulink url="http://ghc.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
668 page</ulink>.
669 </para>
670
671 <para>
672 View patterns are somewhat like pattern guards that can be nested inside
673 of other patterns. They are a convenient way of pattern-matching
674 against values of abstract types. For example, in a programming language
675 implementation, we might represent the syntax of the types of the
676 language as follows:
677
678 <programlisting>
679 type Typ
680
681 data TypView = Unit
682 | Arrow Typ Typ
683
684 view :: Typ -> TypView
685
686 -- additional operations for constructing Typ's ...
687 </programlisting>
688
689 The representation of Typ is held abstract, permitting implementations
690 to use a fancy representation (e.g., hash-consing to manage sharing).
691
692 Without view patterns, using this signature a little inconvenient:
693 <programlisting>
694 size :: Typ -> Integer
695 size t = case view t of
696 Unit -> 1
697 Arrow t1 t2 -> size t1 + size t2
698 </programlisting>
699
700 It is necessary to iterate the case, rather than using an equational
701 function definition. And the situation is even worse when the matching
702 against <literal>t</literal> is buried deep inside another pattern.
703 </para>
704
705 <para>
706 View patterns permit calling the view function inside the pattern and
707 matching against the result:
708 <programlisting>
709 size (view -> Unit) = 1
710 size (view -> Arrow t1 t2) = size t1 + size t2
711 </programlisting>
712
713 That is, we add a new form of pattern, written
714 <replaceable>expression</replaceable> <literal>-></literal>
715 <replaceable>pattern</replaceable> that means "apply the expression to
716 whatever we're trying to match against, and then match the result of
717 that application against the pattern". The expression can be any Haskell
718 expression of function type, and view patterns can be used wherever
719 patterns are used.
720 </para>
721
722 <para>
723 The semantics of a pattern <literal>(</literal>
724 <replaceable>exp</replaceable> <literal>-></literal>
725 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
726
727 <itemizedlist>
728
729 <listitem> Scoping:
730
731 <para>The variables bound by the view pattern are the variables bound by
732 <replaceable>pat</replaceable>.
733 </para>
734
735 <para>
736 Any variables in <replaceable>exp</replaceable> are bound occurrences,
737 but variables bound "to the left" in a pattern are in scope. This
738 feature permits, for example, one argument to a function to be used in
739 the view of another argument. For example, the function
740 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
741 written using view patterns as follows:
742
743 <programlisting>
744 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
745 ...other equations for clunky...
746 </programlisting>
747 </para>
748
749 <para>
750 More precisely, the scoping rules are:
751 <itemizedlist>
752 <listitem>
753 <para>
754 In a single pattern, variables bound by patterns to the left of a view
755 pattern expression are in scope. For example:
756 <programlisting>
757 example :: Maybe ((String -> Integer,Integer), String) -> Bool
758 example Just ((f,_), f -> 4) = True
759 </programlisting>
760
761 Additionally, in function definitions, variables bound by matching earlier curried
762 arguments may be used in view pattern expressions in later arguments:
763 <programlisting>
764 example :: (String -> Integer) -> String -> Bool
765 example f (f -> 4) = True
766 </programlisting>
767 That is, the scoping is the same as it would be if the curried arguments
768 were collected into a tuple.
769 </para>
770 </listitem>
771
772 <listitem>
773 <para>
774 In mutually recursive bindings, such as <literal>let</literal>,
775 <literal>where</literal>, or the top level, view patterns in one
776 declaration may not mention variables bound by other declarations. That
777 is, each declaration must be self-contained. For example, the following
778 program is not allowed:
779 <programlisting>
780 let {(x -> y) = e1 ;
781 (y -> x) = e2 } in x
782 </programlisting>
783
784 (For some amplification on this design choice see
785 <ulink url="http://ghc.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
786
787 </para>
788 </listitem>
789 </itemizedlist>
790
791 </para>
792 </listitem>
793
794 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
795 <replaceable>T1</replaceable> <literal>-></literal>
796 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
797 a <replaceable>T2</replaceable>, then the whole view pattern matches a
798 <replaceable>T1</replaceable>.
799 </para></listitem>
800
801 <listitem><para> Matching: To the equations in Section 3.17.3 of the
802 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
803 Report</ulink>, add the following:
804 <programlisting>
805 case v of { (e -> p) -> e1 ; _ -> e2 }
806 =
807 case (e v) of { p -> e1 ; _ -> e2 }
808 </programlisting>
809 That is, to match a variable <replaceable>v</replaceable> against a pattern
810 <literal>(</literal> <replaceable>exp</replaceable>
811 <literal>-></literal> <replaceable>pat</replaceable>
812 <literal>)</literal>, evaluate <literal>(</literal>
813 <replaceable>exp</replaceable> <replaceable> v</replaceable>
814 <literal>)</literal> and match the result against
815 <replaceable>pat</replaceable>.
816 </para></listitem>
817
818 <listitem><para> Efficiency: When the same view function is applied in
819 multiple branches of a function definition or a case expression (e.g.,
820 in <literal>size</literal> above), GHC makes an attempt to collect these
821 applications into a single nested case expression, so that the view
822 function is only applied once. Pattern compilation in GHC follows the
823 matrix algorithm described in Chapter 4 of <ulink
824 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
825 Implementation of Functional Programming Languages</ulink>. When the
826 top rows of the first column of a matrix are all view patterns with the
827 "same" expression, these patterns are transformed into a single nested
828 case. This includes, for example, adjacent view patterns that line up
829 in a tuple, as in
830 <programlisting>
831 f ((view -> A, p1), p2) = e1
832 f ((view -> B, p3), p4) = e2
833 </programlisting>
834 </para>
835
836 <para> The current notion of when two view pattern expressions are "the
837 same" is very restricted: it is not even full syntactic equality.
838 However, it does include variables, literals, applications, and tuples;
839 e.g., two instances of <literal>view ("hi", "there")</literal> will be
840 collected. However, the current implementation does not compare up to
841 alpha-equivalence, so two instances of <literal>(x, view x ->
842 y)</literal> will not be coalesced.
843 </para>
844
845 </listitem>
846
847 </itemizedlist>
848 </para>
849
850 </sect2>
851
852 <!-- ===================== n+k patterns =================== -->
853
854 <sect2 id="n-k-patterns">
855 <title>n+k patterns</title>
856 <indexterm><primary><option>-XNPlusKPatterns</option></primary></indexterm>
857
858 <para>
859 <literal>n+k</literal> pattern support is disabled by default. To enable
860 it, you can use the <option>-XNPlusKPatterns</option> flag.
861 </para>
862
863 </sect2>
864
865 <!-- ===================== Traditional record syntax =================== -->
866
867 <sect2 id="traditional-record-syntax">
868 <title>Traditional record syntax</title>
869 <indexterm><primary><option>-XNoTraditionalRecordSyntax</option></primary></indexterm>
870
871 <para>
872 Traditional record syntax, such as <literal>C {f = x}</literal>, is enabled by default.
873 To disable it, you can use the <option>-XNoTraditionalRecordSyntax</option> flag.
874 </para>
875
876 </sect2>
877
878 <!-- ===================== Recursive do-notation =================== -->
879
880 <sect2 id="recursive-do-notation">
881 <title>The recursive do-notation
882 </title>
883
884 <para>
885 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
886 that is, the variables bound in a do-expression are visible only in the textually following
887 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
888 group.
889 </para>
890
891 <para>
892 It turns out that such recursive bindings do indeed make sense for a variety of monads, but
893 not all. In particular, recursion in this sense requires a fixed-point operator for the underlying
894 monad, captured by the <literal>mfix</literal> method of the <literal>MonadFix</literal> class, defined in <literal>Control.Monad.Fix</literal> as follows:
895 <programlisting>
896 class Monad m => MonadFix m where
897 mfix :: (a -> m a) -> m a
898 </programlisting>
899 Haskell's
900 <literal>Maybe</literal>, <literal>[]</literal> (list), <literal>ST</literal> (both strict and lazy versions),
901 <literal>IO</literal>, and many other monads have <literal>MonadFix</literal> instances. On the negative
902 side, the continuation monad, with the signature <literal>(a -> r) -> r</literal>, does not.
903 </para>
904
905 <para>
906 For monads that do belong to the <literal>MonadFix</literal> class, GHC provides
907 an extended version of the do-notation that allows recursive bindings.
908 The <option>-XRecursiveDo</option> (language pragma: <literal>RecursiveDo</literal>)
909 provides the necessary syntactic support, introducing the keywords <literal>mdo</literal> and
910 <literal>rec</literal> for higher and lower levels of the notation respectively. Unlike
911 bindings in a <literal>do</literal> expression, those introduced by <literal>mdo</literal> and <literal>rec</literal>
912 are recursively defined, much like in an ordinary let-expression. Due to the new
913 keyword <literal>mdo</literal>, we also call this notation the <emphasis>mdo-notation</emphasis>.
914 </para>
915
916 <para>
917 Here is a simple (albeit contrived) example:
918 <programlisting>
919 {-# LANGUAGE RecursiveDo #-}
920 justOnes = mdo { xs &lt;- Just (1:xs)
921 ; return (map negate xs) }
922 </programlisting>
923 or equivalently
924 <programlisting>
925 {-# LANGUAGE RecursiveDo #-}
926 justOnes = do { rec { xs &lt;- Just (1:xs) }
927 ; return (map negate xs) }
928 </programlisting>
929 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
930 </para>
931
932 <para>
933 GHC's implementation the mdo-notation closely follows the original translation as described in the paper
934 <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for Haskell</ulink>, which
935 in turn is based on the work <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion
936 in Monadic Computations</ulink>. Furthermore, GHC extends the syntax described in the former paper
937 with a lower level syntax flagged by the <literal>rec</literal> keyword, as we describe next.
938 </para>
939
940 <sect3>
941 <title>Recursive binding groups</title>
942
943 <para>
944 The flag <option>-XRecursiveDo</option> also introduces a new keyword <literal>rec</literal>, which wraps a
945 mutually-recursive group of monadic statements inside a <literal>do</literal> expression, producing a single statement.
946 Similar to a <literal>let</literal> statement inside a <literal>do</literal>, variables bound in
947 the <literal>rec</literal> are visible throughout the <literal>rec</literal> group, and below it. For example, compare
948 <programlisting>
949 do { a &lt;- getChar do { a &lt;- getChar
950 ; let { r1 = f a r2 ; rec { r1 &lt;- f a r2
951 ; ; r2 = g r1 } ; ; r2 &lt;- g r1 }
952 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
953 </programlisting>
954 In both cases, <literal>r1</literal> and <literal>r2</literal> are available both throughout
955 the <literal>let</literal> or <literal>rec</literal> block, and in the statements that follow it.
956 The difference is that <literal>let</literal> is non-monadic, while <literal>rec</literal> is monadic.
957 (In Haskell <literal>let</literal> is really <literal>letrec</literal>, of course.)
958 </para>
959
960 <para>
961 The semantics of <literal>rec</literal> is fairly straightforward. Whenever GHC finds a <literal>rec</literal>
962 group, it will compute its set of bound variables, and will introduce an appropriate call
963 to the underlying monadic value-recursion operator <literal>mfix</literal>, belonging to the
964 <literal>MonadFix</literal> class. Here is an example:
965 <programlisting>
966 rec { b &lt;- f a c ===> (b,c) &lt;- mfix (\ ~(b,c) -> do { b &lt;- f a c
967 ; c &lt;- f b a } ; c &lt;- f b a
968 ; return (b,c) })
969 </programlisting>
970 As usual, the meta-variables <literal>b</literal>, <literal>c</literal> etc., can be arbitrary patterns.
971 In general, the statement <literal>rec <replaceable>ss</replaceable></literal> is desugared to the statement
972 <programlisting>
973 <replaceable>vs</replaceable> &lt;- mfix (\ ~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
974 </programlisting>
975 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
976 </para>
977
978 <para>
979 Note in particular that the translation for a <literal>rec</literal> block only involves wrapping a call
980 to <literal>mfix</literal>: it performs no other analysis on the bindings. The latter is the task
981 for the <literal>mdo</literal> notation, which is described next.
982 </para>
983 </sect3>
984
985 <sect3>
986 <title>The <literal>mdo</literal> notation</title>
987
988 <para>
989 A <literal>rec</literal>-block tells the compiler where precisely the recursive knot should be tied. It turns out that
990 the placement of the recursive knots can be rather delicate: in particular, we would like the knots to be wrapped
991 around as minimal groups as possible. This process is known as <emphasis>segmentation</emphasis>, and is described
992 in detail in Secton 3.2 of <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for
993 Haskell</ulink>. Segmentation improves polymorphism and reduces the size of the recursive knot. Most importantly, it avoids
994 unnecessary interference caused by a fundamental issue with the so-called <emphasis>right-shrinking</emphasis>
995 axiom for monadic recursion. In brief, most monads of interest (IO, strict state, etc.) do <emphasis>not</emphasis>
996 have recursion operators that satisfy this axiom, and thus not performing segmentation can cause unnecessary
997 interference, changing the termination behavior of the resulting translation.
998 (Details can be found in Sections 3.1 and 7.2.2 of
999 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.)
1000 </para>
1001
1002 <para>
1003 The <literal>mdo</literal> notation removes the burden of placing
1004 explicit <literal>rec</literal> blocks in the code. Unlike an
1005 ordinary <literal>do</literal> expression, in which variables bound by
1006 statements are only in scope for later statements, variables bound in
1007 an <literal>mdo</literal> expression are in scope for all statements
1008 of the expression. The compiler then automatically identifies minimal
1009 mutually recursively dependent segments of statements, treating them as
1010 if the user had wrapped a <literal>rec</literal> qualifier around them.
1011 </para>
1012
1013 <para>
1014 The definition is syntactic:
1015 </para>
1016 <itemizedlist>
1017 <listitem>
1018 <para>
1019 A generator <replaceable>g</replaceable>
1020 <emphasis>depends</emphasis> on a textually following generator
1021 <replaceable>g'</replaceable>, if
1022 </para>
1023 <itemizedlist>
1024 <listitem>
1025 <para>
1026 <replaceable>g'</replaceable> defines a variable that
1027 is used by <replaceable>g</replaceable>, or
1028 </para>
1029 </listitem>
1030 <listitem>
1031 <para>
1032 <replaceable>g'</replaceable> textually appears between
1033 <replaceable>g</replaceable> and
1034 <replaceable>g''</replaceable>, where <replaceable>g</replaceable>
1035 depends on <replaceable>g''</replaceable>.
1036 </para>
1037 </listitem>
1038 </itemizedlist>
1039 </listitem>
1040 <listitem>
1041 <para>
1042 A <emphasis>segment</emphasis> of a given
1043 <literal>mdo</literal>-expression is a minimal sequence of generators
1044 such that no generator of the sequence depends on an outside
1045 generator. As a special case, although it is not a generator,
1046 the final expression in an <literal>mdo</literal>-expression is
1047 considered to form a segment by itself.
1048 </para>
1049 </listitem>
1050 </itemizedlist>
1051 <para>
1052 Segments in this sense are
1053 related to <emphasis>strongly-connected components</emphasis> analysis,
1054 with the exception that bindings in a segment cannot be reordered and
1055 must be contiguous.
1056 </para>
1057
1058 <para>
1059 Here is an example <literal>mdo</literal>-expression, and its translation to <literal>rec</literal> blocks:
1060 <programlisting>
1061 mdo { a &lt;- getChar ===> do { a &lt;- getChar
1062 ; b &lt;- f a c ; rec { b &lt;- f a c
1063 ; c &lt;- f b a ; ; c &lt;- f b a }
1064 ; z &lt;- h a b ; z &lt;- h a b
1065 ; d &lt;- g d e ; rec { d &lt;- g d e
1066 ; e &lt;- g a z ; ; e &lt;- g a z }
1067 ; putChar c } ; putChar c }
1068 </programlisting>
1069 Note that a given <literal>mdo</literal> expression can cause the creation of multiple <literal>rec</literal> blocks.
1070 If there are no recursive dependencies, <literal>mdo</literal> will introduce no <literal>rec</literal> blocks. In this
1071 latter case an <literal>mdo</literal> expression is precisely the same as a <literal>do</literal> expression, as one
1072 would expect.
1073 </para>
1074
1075 <para>
1076 In summary, given an <literal>mdo</literal> expression, GHC first performs segmentation, introducing
1077 <literal>rec</literal> blocks to wrap over minimal recursive groups. Then, each resulting
1078 <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal> as described
1079 in the previous section. The original <literal>mdo</literal>-expression typechecks exactly when the desugared
1080 version would do so.
1081 </para>
1082
1083 <para>
1084 Here are some other important points in using the recursive-do notation:
1085
1086 <itemizedlist>
1087 <listitem>
1088 <para>
1089 It is enabled with the flag <literal>-XRecursiveDo</literal>, or the <literal>LANGUAGE RecursiveDo</literal>
1090 pragma. (The same flag enables both <literal>mdo</literal>-notation, and the use of <literal>rec</literal>
1091 blocks inside <literal>do</literal> expressions.)
1092 </para>
1093 </listitem>
1094 <listitem>
1095 <para>
1096 <literal>rec</literal> blocks can also be used inside <literal>mdo</literal>-expressions, which will be
1097 treated as a single statement. However, it is good style to either use <literal>mdo</literal> or
1098 <literal>rec</literal> blocks in a single expression.
1099 </para>
1100 </listitem>
1101 <listitem>
1102 <para>
1103 If recursive bindings are required for a monad, then that monad must be declared an instance of
1104 the <literal>MonadFix</literal> class.
1105 </para>
1106 </listitem>
1107 <listitem>
1108 <para>
1109 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1110 Furthermore, the <literal>Control.Monad.ST</literal> and <literal>Control.Monad.ST.Lazy</literal>
1111 modules provide the instances of the <literal>MonadFix</literal> class for Haskell's internal
1112 state monad (strict and lazy, respectively).
1113 </para>
1114 </listitem>
1115 <listitem>
1116 <para>
1117 Like <literal>let</literal> and <literal>where</literal> bindings, name shadowing is not allowed within
1118 an <literal>mdo</literal>-expression or a <literal>rec</literal>-block; that is, all the names bound in
1119 a single <literal>rec</literal> must be distinct. (GHC will complain if this is not the case.)
1120 </para>
1121 </listitem>
1122 </itemizedlist>
1123 </para>
1124 </sect3>
1125
1126
1127 </sect2>
1128
1129
1130 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1131
1132 <sect2 id="parallel-list-comprehensions">
1133 <title>Parallel List Comprehensions</title>
1134 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1135 </indexterm>
1136 <indexterm><primary>parallel list comprehensions</primary>
1137 </indexterm>
1138
1139 <para>Parallel list comprehensions are a natural extension to list
1140 comprehensions. List comprehensions can be thought of as a nice
1141 syntax for writing maps and filters. Parallel comprehensions
1142 extend this to include the zipWith family.</para>
1143
1144 <para>A parallel list comprehension has multiple independent
1145 branches of qualifier lists, each separated by a `|' symbol. For
1146 example, the following zips together two lists:</para>
1147
1148 <programlisting>
1149 [ (x, y) | x &lt;- xs | y &lt;- ys ]
1150 </programlisting>
1151
1152 <para>The behaviour of parallel list comprehensions follows that of
1153 zip, in that the resulting list will have the same length as the
1154 shortest branch.</para>
1155
1156 <para>We can define parallel list comprehensions by translation to
1157 regular comprehensions. Here's the basic idea:</para>
1158
1159 <para>Given a parallel comprehension of the form: </para>
1160
1161 <programlisting>
1162 [ e | p1 &lt;- e11, p2 &lt;- e12, ...
1163 | q1 &lt;- e21, q2 &lt;- e22, ...
1164 ...
1165 ]
1166 </programlisting>
1167
1168 <para>This will be translated to: </para>
1169
1170 <programlisting>
1171 [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
1172 [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
1173 ...
1174 ]
1175 </programlisting>
1176
1177 <para>where `zipN' is the appropriate zip for the given number of
1178 branches.</para>
1179
1180 </sect2>
1181
1182 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1183
1184 <sect2 id="generalised-list-comprehensions">
1185 <title>Generalised (SQL-Like) List Comprehensions</title>
1186 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1187 </indexterm>
1188 <indexterm><primary>extended list comprehensions</primary>
1189 </indexterm>
1190 <indexterm><primary>group</primary></indexterm>
1191 <indexterm><primary>sql</primary></indexterm>
1192
1193
1194 <para>Generalised list comprehensions are a further enhancement to the
1195 list comprehension syntactic sugar to allow operations such as sorting
1196 and grouping which are familiar from SQL. They are fully described in the
1197 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1198 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1199 except that the syntax we use differs slightly from the paper.</para>
1200 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1201 <para>Here is an example:
1202 <programlisting>
1203 employees = [ ("Simon", "MS", 80)
1204 , ("Erik", "MS", 100)
1205 , ("Phil", "Ed", 40)
1206 , ("Gordon", "Ed", 45)
1207 , ("Paul", "Yale", 60)]
1208
1209 output = [ (the dept, sum salary)
1210 | (name, dept, salary) &lt;- employees
1211 , then group by dept using groupWith
1212 , then sortWith by (sum salary)
1213 , then take 5 ]
1214 </programlisting>
1215 In this example, the list <literal>output</literal> would take on
1216 the value:
1217
1218 <programlisting>
1219 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1220 </programlisting>
1221 </para>
1222 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1223 (The functions <literal>sortWith</literal> and <literal>groupWith</literal> are not keywords; they are ordinary
1224 functions that are exported by <literal>GHC.Exts</literal>.)</para>
1225
1226 <para>There are five new forms of comprehension qualifier,
1227 all introduced by the (existing) keyword <literal>then</literal>:
1228 <itemizedlist>
1229 <listitem>
1230
1231 <programlisting>
1232 then f
1233 </programlisting>
1234
1235 This statement requires that <literal>f</literal> have the type <literal>
1236 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1237 motivating example, as this form is used to apply <literal>take 5</literal>.
1238
1239 </listitem>
1240
1241
1242 <listitem>
1243 <para>
1244 <programlisting>
1245 then f by e
1246 </programlisting>
1247
1248 This form is similar to the previous one, but allows you to create a function
1249 which will be passed as the first argument to f. As a consequence f must have
1250 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1251 from the type, this function lets f &quot;project out&quot; some information
1252 from the elements of the list it is transforming.</para>
1253
1254 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1255 is supplied with a function that lets it find out the <literal>sum salary</literal>
1256 for any item in the list comprehension it transforms.</para>
1257
1258 </listitem>
1259
1260
1261 <listitem>
1262
1263 <programlisting>
1264 then group by e using f
1265 </programlisting>
1266
1267 <para>This is the most general of the grouping-type statements. In this form,
1268 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1269 As with the <literal>then f by e</literal> case above, the first argument
1270 is a function supplied to f by the compiler which lets it compute e on every
1271 element of the list being transformed. However, unlike the non-grouping case,
1272 f additionally partitions the list into a number of sublists: this means that
1273 at every point after this statement, binders occurring before it in the comprehension
1274 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1275 this, let's look at an example:</para>
1276
1277 <programlisting>
1278 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1279 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1280 groupRuns f = groupBy (\x y -> f x == f y)
1281
1282 output = [ (the x, y)
1283 | x &lt;- ([1..3] ++ [1..2])
1284 , y &lt;- [4..6]
1285 , then group by x using groupRuns ]
1286 </programlisting>
1287
1288 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1289
1290 <programlisting>
1291 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1292 </programlisting>
1293
1294 <para>Note that we have used the <literal>the</literal> function to change the type
1295 of x from a list to its original numeric type. The variable y, in contrast, is left
1296 unchanged from the list form introduced by the grouping.</para>
1297
1298 </listitem>
1299
1300 <listitem>
1301
1302 <programlisting>
1303 then group using f
1304 </programlisting>
1305
1306 <para>With this form of the group statement, f is required to simply have the type
1307 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1308 comprehension so far directly. An example of this form is as follows:</para>
1309
1310 <programlisting>
1311 output = [ x
1312 | y &lt;- [1..5]
1313 , x &lt;- "hello"
1314 , then group using inits]
1315 </programlisting>
1316
1317 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1318
1319 <programlisting>
1320 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1321 </programlisting>
1322
1323 </listitem>
1324 </itemizedlist>
1325 </para>
1326 </sect2>
1327
1328 <!-- ===================== MONAD COMPREHENSIONS ===================== -->
1329
1330 <sect2 id="monad-comprehensions">
1331 <title>Monad comprehensions</title>
1332 <indexterm><primary>monad comprehensions</primary></indexterm>
1333
1334 <para>
1335 Monad comprehensions generalise the list comprehension notation,
1336 including parallel comprehensions
1337 (<xref linkend="parallel-list-comprehensions"/>) and
1338 transform comprehensions (<xref linkend="generalised-list-comprehensions"/>)
1339 to work for any monad.
1340 </para>
1341
1342 <para>Monad comprehensions support:</para>
1343
1344 <itemizedlist>
1345 <listitem>
1346 <para>
1347 Bindings:
1348 </para>
1349
1350 <programlisting>
1351 [ x + y | x &lt;- Just 1, y &lt;- Just 2 ]
1352 </programlisting>
1353
1354 <para>
1355 Bindings are translated with the <literal>(&gt;&gt;=)</literal> and
1356 <literal>return</literal> functions to the usual do-notation:
1357 </para>
1358
1359 <programlisting>
1360 do x &lt;- Just 1
1361 y &lt;- Just 2
1362 return (x+y)
1363 </programlisting>
1364
1365 </listitem>
1366 <listitem>
1367 <para>
1368 Guards:
1369 </para>
1370
1371 <programlisting>
1372 [ x | x &lt;- [1..10], x &lt;= 5 ]
1373 </programlisting>
1374
1375 <para>
1376 Guards are translated with the <literal>guard</literal> function,
1377 which requires a <literal>MonadPlus</literal> instance:
1378 </para>
1379
1380 <programlisting>
1381 do x &lt;- [1..10]
1382 guard (x &lt;= 5)
1383 return x
1384 </programlisting>
1385
1386 </listitem>
1387 <listitem>
1388 <para>
1389 Transform statements (as with <literal>-XTransformListComp</literal>):
1390 </para>
1391
1392 <programlisting>
1393 [ x+y | x &lt;- [1..10], y &lt;- [1..x], then take 2 ]
1394 </programlisting>
1395
1396 <para>
1397 This translates to:
1398 </para>
1399
1400 <programlisting>
1401 do (x,y) &lt;- take 2 (do x &lt;- [1..10]
1402 y &lt;- [1..x]
1403 return (x,y))
1404 return (x+y)
1405 </programlisting>
1406
1407 </listitem>
1408 <listitem>
1409 <para>
1410 Group statements (as with <literal>-XTransformListComp</literal>):
1411 </para>
1412
1413 <programlisting>
1414 [ x | x &lt;- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
1415 [ x | x &lt;- [1,1,2,2,3], then group using myGroup ]
1416 </programlisting>
1417
1418 </listitem>
1419 <listitem>
1420 <para>
1421 Parallel statements (as with <literal>-XParallelListComp</literal>):
1422 </para>
1423
1424 <programlisting>
1425 [ (x+y) | x &lt;- [1..10]
1426 | y &lt;- [11..20]
1427 ]
1428 </programlisting>
1429
1430 <para>
1431 Parallel statements are translated using the
1432 <literal>mzip</literal> function, which requires a
1433 <literal>MonadZip</literal> instance defined in
1434 <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
1435 </para>
1436
1437 <programlisting>
1438 do (x,y) &lt;- mzip (do x &lt;- [1..10]
1439 return x)
1440 (do y &lt;- [11..20]
1441 return y)
1442 return (x+y)
1443 </programlisting>
1444
1445 </listitem>
1446 </itemizedlist>
1447
1448 <para>
1449 All these features are enabled by default if the
1450 <literal>MonadComprehensions</literal> extension is enabled. The types
1451 and more detailed examples on how to use comprehensions are explained
1452 in the previous chapters <xref
1453 linkend="generalised-list-comprehensions"/> and <xref
1454 linkend="parallel-list-comprehensions"/>. In general you just have
1455 to replace the type <literal>[a]</literal> with the type
1456 <literal>Monad m => m a</literal> for monad comprehensions.
1457 </para>
1458
1459 <para>
1460 Note: Even though most of these examples are using the list monad,
1461 monad comprehensions work for any monad.
1462 The <literal>base</literal> package offers all necessary instances for
1463 lists, which make <literal>MonadComprehensions</literal> backward
1464 compatible to built-in, transform and parallel list comprehensions.
1465 </para>
1466 <para> More formally, the desugaring is as follows. We write <literal>D[ e | Q]</literal>
1467 to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
1468 <programlisting>
1469 Expressions: e
1470 Declarations: d
1471 Lists of qualifiers: Q,R,S
1472
1473 -- Basic forms
1474 D[ e | ] = return e
1475 D[ e | p &lt;- e, Q ] = e &gt;&gt;= \p -&gt; D[ e | Q ]
1476 D[ e | e, Q ] = guard e &gt;&gt; \p -&gt; D[ e | Q ]
1477 D[ e | let d, Q ] = let d in D[ e | Q ]
1478
1479 -- Parallel comprehensions (iterate for multiple parallel branches)
1480 D[ e | (Q | R), S ] = mzip D[ Qv | Q ] D[ Rv | R ] &gt;&gt;= \(Qv,Rv) -&gt; D[ e | S ]
1481
1482 -- Transform comprehensions
1483 D[ e | Q then f, R ] = f D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1484
1485 D[ e | Q then f by b, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1486
1487 D[ e | Q then group using f, R ] = f D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1488 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1489 Qv -&gt; D[ e | R ]
1490
1491 D[ e | Q then group by b using f, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1492 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1493 Qv -&gt; D[ e | R ]
1494
1495 where Qv is the tuple of variables bound by Q (and used subsequently)
1496 selQvi is a selector mapping Qv to the ith component of Qv
1497
1498 Operator Standard binding Expected type
1499 --------------------------------------------------------------------
1500 return GHC.Base t1 -&gt; m t2
1501 (&gt;&gt;=) GHC.Base m1 t1 -&gt; (t2 -&gt; m2 t3) -&gt; m3 t3
1502 (&gt;&gt;) GHC.Base m1 t1 -&gt; m2 t2 -&gt; m3 t3
1503 guard Control.Monad t1 -&gt; m t2
1504 fmap GHC.Base forall a b. (a-&gt;b) -&gt; n a -&gt; n b
1505 mzip Control.Monad.Zip forall a b. m a -&gt; m b -&gt; m (a,b)
1506 </programlisting>
1507 The comprehension should typecheck when its desugaring would typecheck.
1508 </para>
1509 <para>
1510 Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
1511 Without rebindable
1512 syntax, the operators from the "standard binding" module are used; with
1513 rebindable syntax, the operators are looked up in the current lexical scope.
1514 For example, parallel comprehensions will be typechecked and desugared
1515 using whatever "<literal>mzip</literal>" is in scope.
1516 </para>
1517 <para>
1518 The rebindable operators must have the "Expected type" given in the
1519 table above. These types are surprisingly general. For example, you can
1520 use a bind operator with the type
1521 <programlisting>
1522 (>>=) :: T x y a -> (a -> T y z b) -> T x z b
1523 </programlisting>
1524 In the case of transform comprehensions, notice that the groups are
1525 parameterised over some arbitrary type <literal>n</literal> (provided it
1526 has an <literal>fmap</literal>, as well as
1527 the comprehension being over an arbitrary monad.
1528 </para>
1529 </sect2>
1530
1531 <!-- ===================== REBINDABLE SYNTAX =================== -->
1532
1533 <sect2 id="rebindable-syntax">
1534 <title>Rebindable syntax and the implicit Prelude import</title>
1535
1536 <para><indexterm><primary>-XNoImplicitPrelude
1537 option</primary></indexterm> GHC normally imports
1538 <filename>Prelude.hi</filename> files for you. If you'd
1539 rather it didn't, then give it a
1540 <option>-XNoImplicitPrelude</option> option. The idea is
1541 that you can then import a Prelude of your own. (But don't
1542 call it <literal>Prelude</literal>; the Haskell module
1543 namespace is flat, and you must not conflict with any
1544 Prelude module.)</para>
1545
1546 <para>Suppose you are importing a Prelude of your own
1547 in order to define your own numeric class
1548 hierarchy. It completely defeats that purpose if the
1549 literal "1" means "<literal>Prelude.fromInteger
1550 1</literal>", which is what the Haskell Report specifies.
1551 So the <option>-XRebindableSyntax</option>
1552 flag causes
1553 the following pieces of built-in syntax to refer to
1554 <emphasis>whatever is in scope</emphasis>, not the Prelude
1555 versions:
1556 <itemizedlist>
1557 <listitem>
1558 <para>An integer literal <literal>368</literal> means
1559 "<literal>fromInteger (368::Integer)</literal>", rather than
1560 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1561 </para> </listitem>
1562
1563 <listitem><para>Fractional literals are handed in just the same way,
1564 except that the translation is
1565 <literal>fromRational (3.68::Rational)</literal>.
1566 </para> </listitem>
1567
1568 <listitem><para>The equality test in an overloaded numeric pattern
1569 uses whatever <literal>(==)</literal> is in scope.
1570 </para> </listitem>
1571
1572 <listitem><para>The subtraction operation, and the
1573 greater-than-or-equal test, in <literal>n+k</literal> patterns
1574 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1575 </para></listitem>
1576
1577 <listitem>
1578 <para>Negation (e.g. "<literal>- (f x)</literal>")
1579 means "<literal>negate (f x)</literal>", both in numeric
1580 patterns, and expressions.
1581 </para></listitem>
1582
1583 <listitem>
1584 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1585 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1586 </para></listitem>
1587
1588 <listitem>
1589 <para>"Do" notation is translated using whatever
1590 functions <literal>(>>=)</literal>,
1591 <literal>(>>)</literal>, and <literal>fail</literal>,
1592 are in scope (not the Prelude
1593 versions). List comprehensions, mdo (<xref linkend="recursive-do-notation"/>), and parallel array
1594 comprehensions, are unaffected. </para></listitem>
1595
1596 <listitem>
1597 <para>Arrow
1598 notation (see <xref linkend="arrow-notation"/>)
1599 uses whatever <literal>arr</literal>,
1600 <literal>(>>>)</literal>, <literal>first</literal>,
1601 <literal>app</literal>, <literal>(|||)</literal> and
1602 <literal>loop</literal> functions are in scope. But unlike the
1603 other constructs, the types of these functions must match the
1604 Prelude types very closely. Details are in flux; if you want
1605 to use this, ask!
1606 </para></listitem>
1607 </itemizedlist>
1608 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1609 </para>
1610 <para>
1611 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1612 even if that is a little unexpected. For example, the
1613 static semantics of the literal <literal>368</literal>
1614 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1615 <literal>fromInteger</literal> to have any of the types:
1616 <programlisting>
1617 fromInteger :: Integer -> Integer
1618 fromInteger :: forall a. Foo a => Integer -> a
1619 fromInteger :: Num a => a -> Integer
1620 fromInteger :: Integer -> Bool -> Bool
1621 </programlisting>
1622 </para>
1623
1624 <para>Be warned: this is an experimental facility, with
1625 fewer checks than usual. Use <literal>-dcore-lint</literal>
1626 to typecheck the desugared program. If Core Lint is happy
1627 you should be all right.</para>
1628
1629 </sect2>
1630
1631 <sect2 id="postfix-operators">
1632 <title>Postfix operators</title>
1633
1634 <para>
1635 The <option>-XPostfixOperators</option> flag enables a small
1636 extension to the syntax of left operator sections, which allows you to
1637 define postfix operators. The extension is this: the left section
1638 <programlisting>
1639 (e !)
1640 </programlisting>
1641 is equivalent (from the point of view of both type checking and execution) to the expression
1642 <programlisting>
1643 ((!) e)
1644 </programlisting>
1645 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1646 The strict Haskell 98 interpretation is that the section is equivalent to
1647 <programlisting>
1648 (\y -> (!) e y)
1649 </programlisting>
1650 That is, the operator must be a function of two arguments. GHC allows it to
1651 take only one argument, and that in turn allows you to write the function
1652 postfix.
1653 </para>
1654 <para>The extension does not extend to the left-hand side of function
1655 definitions; you must define such a function in prefix form.</para>
1656
1657 </sect2>
1658
1659 <sect2 id="tuple-sections">
1660 <title>Tuple sections</title>
1661
1662 <para>
1663 The <option>-XTupleSections</option> flag enables Python-style partially applied
1664 tuple constructors. For example, the following program
1665 <programlisting>
1666 (, True)
1667 </programlisting>
1668 is considered to be an alternative notation for the more unwieldy alternative
1669 <programlisting>
1670 \x -> (x, True)
1671 </programlisting>
1672 You can omit any combination of arguments to the tuple, as in the following
1673 <programlisting>
1674 (, "I", , , "Love", , 1337)
1675 </programlisting>
1676 which translates to
1677 <programlisting>
1678 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1679 </programlisting>
1680 </para>
1681
1682 <para>
1683 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1684 will also be available for them, like so
1685 <programlisting>
1686 (# , True #)
1687 </programlisting>
1688 Because there is no unboxed unit tuple, the following expression
1689 <programlisting>
1690 (# #)
1691 </programlisting>
1692 continues to stand for the unboxed singleton tuple data constructor.
1693 </para>
1694
1695 </sect2>
1696
1697 <sect2 id="lambda-case">
1698 <title>Lambda-case</title>
1699 <para>
1700 The <option>-XLambdaCase</option> flag enables expressions of the form
1701 <programlisting>
1702 \case { p1 -> e1; ...; pN -> eN }
1703 </programlisting>
1704 which is equivalent to
1705 <programlisting>
1706 \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }
1707 </programlisting>
1708 Note that <literal>\case</literal> starts a layout, so you can write
1709 <programlisting>
1710 \case
1711 p1 -> e1
1712 ...
1713 pN -> eN
1714 </programlisting>
1715 </para>
1716 </sect2>
1717
1718 <sect2 id="empty-case">
1719 <title>Empty case alternatives</title>
1720 <para>
1721 The <option>-XEmptyCase</option> flag enables
1722 case expressions, or lambda-case expressions, that have no alternatives,
1723 thus:
1724 <programlisting>
1725 case e of { } -- No alternatives
1726 or
1727 \case { } -- -XLambdaCase is also required
1728 </programlisting>
1729 This can be useful when you know that the expression being scrutinised
1730 has no non-bottom values. For example:
1731 <programlisting>
1732 data Void
1733 f :: Void -> Int
1734 f x = case x of { }
1735 </programlisting>
1736 With dependently-typed features it is more useful
1737 (see <ulink url="http://ghc.haskell.org/trac/ghc/ticket/2431">Trac</ulink>).
1738 For example, consider these two candidate definitions of <literal>absurd</literal>:
1739 <programlisting>
1740 data a :==: b where
1741 Refl :: a :==: a
1742
1743 absurd :: True :~: False -> a
1744 absurd x = error "absurd" -- (A)
1745 absurd x = case x of {} -- (B)
1746 </programlisting>
1747 We much prefer (B). Why? Because GHC can figure out that <literal>(True :~: False)</literal>
1748 is an empty type. So (B) has no partiality and GHC should be able to compile with
1749 <option>-fwarn-incomplete-patterns</option>. (Though the pattern match checking is not
1750 yet clever enough to do that.)
1751 On the other hand (A) looks dangerous, and GHC doesn't check to make
1752 sure that, in fact, the function can never get called.
1753 </para>
1754 </sect2>
1755
1756 <sect2 id="multi-way-if">
1757 <title>Multi-way if-expressions</title>
1758 <para>
1759 With <option>-XMultiWayIf</option> flag GHC accepts conditional expressions
1760 with multiple branches:
1761 <programlisting>
1762 if | guard1 -> expr1
1763 | ...
1764 | guardN -> exprN
1765 </programlisting>
1766 which is roughly equivalent to
1767 <programlisting>
1768 case () of
1769 _ | guard1 -> expr1
1770 ...
1771 _ | guardN -> exprN
1772 </programlisting>
1773 </para>
1774
1775 <para>Multi-way if expressions introduce a new layout context. So the
1776 example above is equivalent to:
1777 <programlisting>
1778 if { | guard1 -> expr1
1779 ; | ...
1780 ; | guardN -> exprN
1781 }
1782 </programlisting>
1783 The following behaves as expected:
1784 <programlisting>
1785 if | guard1 -> if | guard2 -> expr2
1786 | guard3 -> expr3
1787 | guard4 -> expr4
1788 </programlisting>
1789 because layout translates it as
1790 <programlisting>
1791 if { | guard1 -> if { | guard2 -> expr2
1792 ; | guard3 -> expr3
1793 }
1794 ; | guard4 -> expr4
1795 }
1796 </programlisting>
1797 Layout with multi-way if works in the same way as other layout
1798 contexts, except that the semi-colons between guards in a multi-way if
1799 are optional. So it is not necessary to line up all the guards at the
1800 same column; this is consistent with the way guards work in function
1801 definitions and case expressions.
1802 </para>
1803 </sect2>
1804
1805 <sect2 id="disambiguate-fields">
1806 <title>Record field disambiguation</title>
1807 <para>
1808 In record construction and record pattern matching
1809 it is entirely unambiguous which field is referred to, even if there are two different
1810 data types in scope with a common field name. For example:
1811 <programlisting>
1812 module M where
1813 data S = MkS { x :: Int, y :: Bool }
1814
1815 module Foo where
1816 import M
1817
1818 data T = MkT { x :: Int }
1819
1820 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1821 ok2 n = MkT { x = n+1 } -- Unambiguous
1822
1823 bad1 k = k { x = 3 } -- Ambiguous
1824 bad2 k = x k -- Ambiguous
1825 </programlisting>
1826 Even though there are two <literal>x</literal>'s in scope,
1827 it is clear that the <literal>x</literal> in the pattern in the
1828 definition of <literal>ok1</literal> can only mean the field
1829 <literal>x</literal> from type <literal>S</literal>. Similarly for
1830 the function <literal>ok2</literal>. However, in the record update
1831 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1832 it is not clear which of the two types is intended.
1833 </para>
1834 <para>
1835 Haskell 98 regards all four as ambiguous, but with the
1836 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1837 the former two. The rules are precisely the same as those for instance
1838 declarations in Haskell 98, where the method names on the left-hand side
1839 of the method bindings in an instance declaration refer unambiguously
1840 to the method of that class (provided they are in scope at all), even
1841 if there are other variables in scope with the same name.
1842 This reduces the clutter of qualified names when you import two
1843 records from different modules that use the same field name.
1844 </para>
1845 <para>
1846 Some details:
1847 <itemizedlist>
1848 <listitem><para>
1849 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For example:
1850 <programlisting>
1851 module Foo where
1852 import M
1853 x=True
1854 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1855 </programlisting>
1856 </para></listitem>
1857
1858 <listitem><para>
1859 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualified</emphasis>
1860 field names even if the corresponding selector is only in scope <emphasis>qualified</emphasis>
1861 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1862 <programlisting>
1863 module Foo where
1864 import qualified M -- Note qualified
1865
1866 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1867 </programlisting>
1868 Since the constructor <literal>MkS</literal> is only in scope qualified, you must
1869 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1870 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1871 is not. (In effect, it is qualified by the constructor.)
1872 </para></listitem>
1873 </itemizedlist>
1874 </para>
1875
1876 </sect2>
1877
1878 <!-- ===================== Record puns =================== -->
1879
1880 <sect2 id="record-puns">
1881 <title>Record puns
1882 </title>
1883
1884 <para>
1885 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1886 </para>
1887
1888 <para>
1889 When using records, it is common to write a pattern that binds a
1890 variable with the same name as a record field, such as:
1891
1892 <programlisting>
1893 data C = C {a :: Int}
1894 f (C {a = a}) = a
1895 </programlisting>
1896 </para>
1897
1898 <para>
1899 Record punning permits the variable name to be elided, so one can simply
1900 write
1901
1902 <programlisting>
1903 f (C {a}) = a
1904 </programlisting>
1905
1906 to mean the same pattern as above. That is, in a record pattern, the
1907 pattern <literal>a</literal> expands into the pattern <literal>a =
1908 a</literal> for the same name <literal>a</literal>.
1909 </para>
1910
1911 <para>
1912 Note that:
1913 <itemizedlist>
1914 <listitem><para>
1915 Record punning can also be used in an expression, writing, for example,
1916 <programlisting>
1917 let a = 1 in C {a}
1918 </programlisting>
1919 instead of
1920 <programlisting>
1921 let a = 1 in C {a = a}
1922 </programlisting>
1923 The expansion is purely syntactic, so the expanded right-hand side
1924 expression refers to the nearest enclosing variable that is spelled the
1925 same as the field name.
1926 </para></listitem>
1927
1928 <listitem><para>
1929 Puns and other patterns can be mixed in the same record:
1930 <programlisting>
1931 data C = C {a :: Int, b :: Int}
1932 f (C {a, b = 4}) = a
1933 </programlisting>
1934 </para></listitem>
1935
1936 <listitem><para>
1937 Puns can be used wherever record patterns occur (e.g. in
1938 <literal>let</literal> bindings or at the top-level).
1939 </para></listitem>
1940
1941 <listitem><para>
1942 A pun on a qualified field name is expanded by stripping off the module qualifier.
1943 For example:
1944 <programlisting>
1945 f (C {M.a}) = a
1946 </programlisting>
1947 means
1948 <programlisting>
1949 f (M.C {M.a = a}) = a
1950 </programlisting>
1951 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1952 is only in scope in qualified form.)
1953 </para></listitem>
1954 </itemizedlist>
1955 </para>
1956
1957
1958 </sect2>
1959
1960 <!-- ===================== Record wildcards =================== -->
1961
1962 <sect2 id="record-wildcards">
1963 <title>Record wildcards
1964 </title>
1965
1966 <para>
1967 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1968 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1969 </para>
1970
1971 <para>
1972 For records with many fields, it can be tiresome to write out each field
1973 individually in a record pattern, as in
1974 <programlisting>
1975 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1976 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1977 </programlisting>
1978 </para>
1979
1980 <para>
1981 Record wildcard syntax permits a "<literal>..</literal>" in a record
1982 pattern, where each elided field <literal>f</literal> is replaced by the
1983 pattern <literal>f = f</literal>. For example, the above pattern can be
1984 written as
1985 <programlisting>
1986 f (C {a = 1, ..}) = b + c + d
1987 </programlisting>
1988 </para>
1989
1990 <para>
1991 More details:
1992 <itemizedlist>
1993 <listitem><para>
1994 Wildcards can be mixed with other patterns, including puns
1995 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1996 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1997 wherever record patterns occur, including in <literal>let</literal>
1998 bindings and at the top-level. For example, the top-level binding
1999 <programlisting>
2000 C {a = 1, ..} = e
2001 </programlisting>
2002 defines <literal>b</literal>, <literal>c</literal>, and
2003 <literal>d</literal>.
2004 </para></listitem>
2005
2006 <listitem><para>
2007 Record wildcards can also be used in expressions, writing, for example,
2008 <programlisting>
2009 let {a = 1; b = 2; c = 3; d = 4} in C {..}
2010 </programlisting>
2011 in place of
2012 <programlisting>
2013 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
2014 </programlisting>
2015 The expansion is purely syntactic, so the record wildcard
2016 expression refers to the nearest enclosing variables that are spelled
2017 the same as the omitted field names.
2018 </para></listitem>
2019
2020 <listitem><para>
2021 The "<literal>..</literal>" expands to the missing
2022 <emphasis>in-scope</emphasis> record fields.
2023 Specifically the expansion of "<literal>C {..}</literal>" includes
2024 <literal>f</literal> if and only if:
2025 <itemizedlist>
2026 <listitem><para>
2027 <literal>f</literal> is a record field of constructor <literal>C</literal>.
2028 </para></listitem>
2029 <listitem><para>
2030 The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
2031 </para></listitem>
2032 <listitem><para>
2033 In the case of expressions (but not patterns),
2034 the variable <literal>f</literal> is in scope unqualified,
2035 apart from the binding of the record selector itself.
2036 </para></listitem>
2037 </itemizedlist>
2038 For example
2039 <programlisting>
2040 module M where
2041 data R = R { a,b,c :: Int }
2042 module X where
2043 import M( R(a,c) )
2044 f b = R { .. }
2045 </programlisting>
2046 The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
2047 omitting <literal>b</literal> since the record field is not in scope,
2048 and omitting <literal>c</literal> since the variable <literal>c</literal>
2049 is not in scope (apart from the binding of the
2050 record selector <literal>c</literal>, of course).
2051 </para></listitem>
2052 </itemizedlist>
2053 </para>
2054
2055 </sect2>
2056
2057 <!-- ===================== Local fixity declarations =================== -->
2058
2059 <sect2 id="local-fixity-declarations">
2060 <title>Local Fixity Declarations
2061 </title>
2062
2063 <para>A careful reading of the Haskell 98 Report reveals that fixity
2064 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
2065 <literal>infixr</literal>) are permitted to appear inside local bindings
2066 such those introduced by <literal>let</literal> and
2067 <literal>where</literal>. However, the Haskell Report does not specify
2068 the semantics of such bindings very precisely.
2069 </para>
2070
2071 <para>In GHC, a fixity declaration may accompany a local binding:
2072 <programlisting>
2073 let f = ...
2074 infixr 3 `f`
2075 in
2076 ...
2077 </programlisting>
2078 and the fixity declaration applies wherever the binding is in scope.
2079 For example, in a <literal>let</literal>, it applies in the right-hand
2080 sides of other <literal>let</literal>-bindings and the body of the
2081 <literal>let</literal>C. Or, in recursive <literal>do</literal>
2082 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
2083 declarations of a <literal>let</literal> statement scope over other
2084 statements in the group, just as the bound name does.
2085 </para>
2086
2087 <para>
2088 Moreover, a local fixity declaration *must* accompany a local binding of
2089 that name: it is not possible to revise the fixity of name bound
2090 elsewhere, as in
2091 <programlisting>
2092 let infixr 9 $ in ...
2093 </programlisting>
2094
2095 Because local fixity declarations are technically Haskell 98, no flag is
2096 necessary to enable them.
2097 </para>
2098 </sect2>
2099
2100 <sect2 id="package-imports">
2101 <title>Package-qualified imports</title>
2102
2103 <para>With the <option>-XPackageImports</option> flag, GHC allows
2104 import declarations to be qualified by the package name that the
2105 module is intended to be imported from. For example:</para>
2106
2107 <programlisting>
2108 import "network" Network.Socket
2109 </programlisting>
2110
2111 <para>would import the module <literal>Network.Socket</literal> from
2112 the package <literal>network</literal> (any version). This may
2113 be used to disambiguate an import when the same module is
2114 available from multiple packages, or is present in both the
2115 current package being built and an external package.</para>
2116
2117 <para>The special package name <literal>this</literal> can be used to
2118 refer to the current package being built.</para>
2119
2120 <para>Note: you probably don't need to use this feature, it was
2121 added mainly so that we can build backwards-compatible versions of
2122 packages when APIs change. It can lead to fragile dependencies in
2123 the common case: modules occasionally move from one package to
2124 another, rendering any package-qualified imports broken.</para>
2125 </sect2>
2126
2127 <sect2 id="safe-imports-ext">
2128 <title>Safe imports</title>
2129
2130 <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
2131 and <option>-XUnsafe</option> language flags, GHC extends
2132 the import declaration syntax to take an optional <literal>safe</literal>
2133 keyword after the <literal>import</literal> keyword. This feature
2134 is part of the Safe Haskell GHC extension. For example:</para>
2135
2136 <programlisting>
2137 import safe qualified Network.Socket as NS
2138 </programlisting>
2139
2140 <para>would import the module <literal>Network.Socket</literal>
2141 with compilation only succeeding if Network.Socket can be
2142 safely imported. For a description of when a import is
2143 considered safe see <xref linkend="safe-haskell"/></para>
2144
2145 </sect2>
2146
2147 <sect2 id="explicit-namespaces">
2148 <title>Explicit namespaces in import/export</title>
2149
2150 <para> In an import or export list, such as
2151 <programlisting>
2152 module M( f, (++) ) where ...
2153 import N( f, (++) )
2154 ...
2155 </programlisting>
2156 the entities <literal>f</literal> and <literal>(++)</literal> are <emphasis>values</emphasis>.
2157 However, with type operators (<xref linkend="type-operators"/>) it becomes possible
2158 to declare <literal>(++)</literal> as a <emphasis>type constructor</emphasis>. In that
2159 case, how would you export or import it?
2160 </para>
2161 <para>
2162 The <option>-XExplicitNamespaces</option> extension allows you to prefix the name of
2163 a type constructor in an import or export list with "<literal>type</literal>" to
2164 disambiguate this case, thus:
2165 <programlisting>
2166 module M( f, type (++) ) where ...
2167 import N( f, type (++) )
2168 ...
2169 module N( f, type (++) ) where
2170 data family a ++ b = L a | R b
2171 </programlisting>
2172 The extension <option>-XExplicitNamespaces</option>
2173 is implied by <option>-XTypeOperators</option> and (for some reason) by <option>-XTypeFamilies</option>.
2174 </para>
2175 </sect2>
2176
2177 <sect2 id="syntax-stolen">
2178 <title>Summary of stolen syntax</title>
2179
2180 <para>Turning on an option that enables special syntax
2181 <emphasis>might</emphasis> cause working Haskell 98 code to fail
2182 to compile, perhaps because it uses a variable name which has
2183 become a reserved word. This section lists the syntax that is
2184 "stolen" by language extensions.
2185 We use
2186 notation and nonterminal names from the Haskell 98 lexical syntax
2187 (see the Haskell 98 Report).
2188 We only list syntax changes here that might affect
2189 existing working programs (i.e. "stolen" syntax). Many of these
2190 extensions will also enable new context-free syntax, but in all
2191 cases programs written to use the new syntax would not be
2192 compilable without the option enabled.</para>
2193
2194 <para>There are two classes of special
2195 syntax:
2196
2197 <itemizedlist>
2198 <listitem>
2199 <para>New reserved words and symbols: character sequences
2200 which are no longer available for use as identifiers in the
2201 program.</para>
2202 </listitem>
2203 <listitem>
2204 <para>Other special syntax: sequences of characters that have
2205 a different meaning when this particular option is turned
2206 on.</para>
2207 </listitem>
2208 </itemizedlist>
2209
2210 The following syntax is stolen:
2211
2212 <variablelist>
2213 <varlistentry>
2214 <term>
2215 <literal>forall</literal>
2216 <indexterm><primary><literal>forall</literal></primary></indexterm>
2217 </term>
2218 <listitem><para>
2219 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
2220 <option>-XScopedTypeVariables</option>,
2221 <option>-XLiberalTypeSynonyms</option>,
2222 <option>-XRankNTypes</option>,
2223 <option>-XExistentialQuantification</option>
2224 </para></listitem>
2225 </varlistentry>
2226
2227 <varlistentry>
2228 <term>
2229 <literal>mdo</literal>
2230 <indexterm><primary><literal>mdo</literal></primary></indexterm>
2231 </term>
2232 <listitem><para>
2233 Stolen by: <option>-XRecursiveDo</option>
2234 </para></listitem>
2235 </varlistentry>
2236
2237 <varlistentry>
2238 <term>
2239 <literal>foreign</literal>
2240 <indexterm><primary><literal>foreign</literal></primary></indexterm>
2241 </term>
2242 <listitem><para>
2243 Stolen by: <option>-XForeignFunctionInterface</option>
2244 </para></listitem>
2245 </varlistentry>
2246
2247 <varlistentry>
2248 <term>
2249 <literal>rec</literal>,
2250 <literal>proc</literal>, <literal>-&lt;</literal>,
2251 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
2252 <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
2253 <literal>|)</literal> brackets
2254 <indexterm><primary><literal>proc</literal></primary></indexterm>
2255 </term>
2256 <listitem><para>
2257 Stolen by: <option>-XArrows</option>
2258 </para></listitem>
2259 </varlistentry>
2260
2261 <varlistentry>
2262 <term>
2263 <literal>?<replaceable>varid</replaceable></literal>
2264 <indexterm><primary>implicit parameters</primary></indexterm>
2265 </term>
2266 <listitem><para>
2267 Stolen by: <option>-XImplicitParams</option>
2268 </para></listitem>
2269 </varlistentry>
2270
2271 <varlistentry>
2272 <term>
2273 <literal>[|</literal>,
2274 <literal>[e|</literal>, <literal>[p|</literal>,
2275 <literal>[d|</literal>, <literal>[t|</literal>,
2276 <literal>$(</literal>,
2277 <literal>$$(</literal>,
2278 <literal>[||</literal>,
2279 <literal>[e||</literal>,
2280 <literal>$<replaceable>varid</replaceable></literal>,
2281 <literal>$$<replaceable>varid</replaceable></literal>
2282 <indexterm><primary>Template Haskell</primary></indexterm>
2283 </term>
2284 <listitem><para>
2285 Stolen by: <option>-XTemplateHaskell</option>
2286 </para></listitem>
2287 </varlistentry>
2288
2289 <varlistentry>
2290 <term>
2291 <literal>[<replaceable>varid</replaceable>|</literal>
2292 <indexterm><primary>quasi-quotation</primary></indexterm>
2293 </term>
2294 <listitem><para>
2295 Stolen by: <option>-XQuasiQuotes</option>
2296 </para></listitem>
2297 </varlistentry>
2298
2299 <varlistentry>
2300 <term>
2301 <replaceable>varid</replaceable>{<literal>&num;</literal>},
2302 <replaceable>char</replaceable><literal>&num;</literal>,
2303 <replaceable>string</replaceable><literal>&num;</literal>,
2304 <replaceable>integer</replaceable><literal>&num;</literal>,
2305 <replaceable>float</replaceable><literal>&num;</literal>,
2306 <replaceable>float</replaceable><literal>&num;&num;</literal>
2307 </term>
2308 <listitem><para>
2309 Stolen by: <option>-XMagicHash</option>
2310 </para></listitem>
2311 </varlistentry>
2312
2313 <varlistentry>
2314 <term>
2315 <literal>(&num;</literal>, <literal>&num;)</literal>
2316 </term>
2317 <listitem><para>
2318 Stolen by: <option>-XUnboxedTuples</option>
2319 </para></listitem>
2320 </varlistentry>
2321
2322 <varlistentry>
2323 <term>
2324 <replaceable>varid</replaceable><literal>!</literal><replaceable>varid</replaceable>
2325 </term>
2326 <listitem><para>
2327 Stolen by: <option>-XBangPatterns</option>
2328 </para></listitem>
2329 </varlistentry>
2330 </variablelist>
2331 </para>
2332 </sect2>
2333 </sect1>
2334
2335
2336 <!-- TYPE SYSTEM EXTENSIONS -->
2337 <sect1 id="data-type-extensions">
2338 <title>Extensions to data types and type synonyms</title>
2339
2340 <sect2 id="nullary-types">
2341 <title>Data types with no constructors</title>
2342
2343 <para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
2344 GHC lets you declare a data type with no constructors. For example:</para>
2345
2346 <programlisting>
2347 data S -- S :: *
2348 data T a -- T :: * -> *
2349 </programlisting>
2350
2351 <para>Syntactically, the declaration lacks the "= constrs" part. The
2352 type can be parameterised over types of any kind, but if the kind is
2353 not <literal>*</literal> then an explicit kind annotation must be used
2354 (see <xref linkend="kinding"/>).</para>
2355
2356 <para>Such data types have only one value, namely bottom.
2357 Nevertheless, they can be useful when defining "phantom types".</para>
2358 </sect2>
2359
2360 <sect2 id="datatype-contexts">
2361 <title>Data type contexts</title>
2362
2363 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2364
2365 <programlisting>
2366 data Eq a => Set a = NilSet | ConsSet a (Set a)
2367 </programlisting>
2368
2369 <para>give constructors with types:</para>
2370
2371 <programlisting>
2372 NilSet :: Set a
2373 ConsSet :: Eq a => a -> Set a -> Set a
2374 </programlisting>
2375
2376 <para>This is widely considered a misfeature, and is going to be removed from
2377 the language. In GHC, it is controlled by the deprecated extension
2378 <literal>DatatypeContexts</literal>.</para>
2379 </sect2>
2380
2381 <sect2 id="infix-tycons">
2382 <title>Infix type constructors, classes, and type variables</title>
2383
2384 <para>
2385 GHC allows type constructors, classes, and type variables to be operators, and
2386 to be written infix, very much like expressions. More specifically:
2387 <itemizedlist>
2388 <listitem><para>
2389 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
2390 The lexical syntax is the same as that for data constructors.
2391 </para></listitem>
2392 <listitem><para>
2393 Data type and type-synonym declarations can be written infix, parenthesised
2394 if you want further arguments. E.g.
2395 <screen>
2396 data a :*: b = Foo a b
2397 type a :+: b = Either a b
2398 class a :=: b where ...
2399
2400 data (a :**: b) x = Baz a b x
2401 type (a :++: b) y = Either (a,b) y
2402 </screen>
2403 </para></listitem>
2404 <listitem><para>
2405 Types, and class constraints, can be written infix. For example
2406 <screen>
2407 x :: Int :*: Bool
2408 f :: (a :=: b) => a -> b
2409 </screen>
2410 </para></listitem>
2411 <listitem><para>
2412 Back-quotes work
2413 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
2414 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
2415 </para></listitem>
2416 <listitem><para>
2417 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
2418 one cannot distinguish between the two in a fixity declaration; a fixity declaration
2419 sets the fixity for a data constructor and the corresponding type constructor. For example:
2420 <screen>
2421 infixl 7 T, :*:
2422 </screen>
2423 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
2424 and similarly for <literal>:*:</literal>.
2425 <literal>Int `a` Bool</literal>.
2426 </para></listitem>
2427 <listitem><para>
2428 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
2429 </para></listitem>
2430
2431 </itemizedlist>
2432 </para>
2433 </sect2>
2434
2435 <sect2 id="type-operators">
2436 <title>Type operators</title>
2437 <para>
2438 In types, an operator symbol like <literal>(+)</literal> is normally treated as a type
2439 <emphasis>variable</emphasis>, just like <literal>a</literal>. Thus in Haskell 98 you can say
2440 <programlisting>
2441 type T (+) = ((+), (+))
2442 -- Just like: type T a = (a,a)
2443
2444 f :: T Int -> Int
2445 f (x,y)= x
2446 </programlisting>
2447 As you can see, using operators in this way is not very useful, and Haskell 98 does not even
2448 allow you to write them infix.
2449 </para>
2450 <para>
2451 The language <option>-XTypeOperators</option> changes this behaviour:
2452 <itemizedlist>
2453 <listitem><para>
2454 Operator symbols become type <emphasis>constructors</emphasis> rather than
2455 type <emphasis>variables</emphasis>.
2456 </para></listitem>
2457 <listitem><para>
2458 Operator symbols in types can be written infix, both in definitions and uses.
2459 for example:
2460 <programlisting>
2461 data a + b = Plus a b
2462 type Foo = Int + Bool
2463 </programlisting>
2464 </para></listitem>
2465 <listitem><para>
2466 There is now some potential ambiguity in import and export lists; for example
2467 if you write <literal>import M( (+) )</literal> do you mean the
2468 <emphasis>function</emphasis> <literal>(+)</literal> or the
2469 <emphasis>type constructor</emphasis> <literal>(+)</literal>?
2470 The default is the former, but with <option>-XExplicitNamespaces</option> (which is implied
2471 by <option>-XExplicitTypeOperators</option>) GHC allows you to specify the latter
2472 by preceding it with the keyword <literal>type</literal>, thus:
2473 <programlisting>
2474 import M( type (+) )
2475 </programlisting>
2476 See <xref linkend="explicit-namespaces"/>.
2477 </para></listitem>
2478 <listitem><para>
2479 The fixity of a type operator may be set using the usual fixity declarations
2480 but, as in <xref linkend="infix-tycons"/>, the function and type constructor share
2481 a single fixity.
2482 </para></listitem>
2483 </itemizedlist>
2484 </para>
2485 </sect2>
2486
2487 <sect2 id="type-synonyms">
2488 <title>Liberalised type synonyms</title>
2489
2490 <para>
2491 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
2492 on individual synonym declarations.
2493 With the <option>-XLiberalTypeSynonyms</option> extension,
2494 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2495 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
2496
2497 <itemizedlist>
2498 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2499 in a type synonym, thus:
2500 <programlisting>
2501 type Discard a = forall b. Show b => a -> b -> (a, String)
2502
2503 f :: Discard a
2504 f x y = (x, show y)
2505
2506 g :: Discard Int -> (Int,String) -- A rank-2 type
2507 g f = f 3 True
2508 </programlisting>
2509 </para>
2510 </listitem>
2511
2512 <listitem><para>
2513 If you also use <option>-XUnboxedTuples</option>,
2514 you can write an unboxed tuple in a type synonym:
2515 <programlisting>
2516 type Pr = (# Int, Int #)
2517
2518 h :: Int -> Pr
2519 h x = (# x, x #)
2520 </programlisting>
2521 </para></listitem>
2522
2523 <listitem><para>
2524 You can apply a type synonym to a forall type:
2525 <programlisting>
2526 type Foo a = a -> a -> Bool
2527
2528 f :: Foo (forall b. b->b)
2529 </programlisting>
2530 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2531 <programlisting>
2532 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2533 </programlisting>
2534 </para></listitem>
2535
2536 <listitem><para>
2537 You can apply a type synonym to a partially applied type synonym:
2538 <programlisting>
2539 type Generic i o = forall x. i x -> o x
2540 type Id x = x
2541
2542 foo :: Generic Id []
2543 </programlisting>
2544 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2545 <programlisting>
2546 foo :: forall x. x -> [x]
2547 </programlisting>
2548 </para></listitem>
2549
2550 </itemizedlist>
2551 </para>
2552
2553 <para>
2554 GHC currently does kind checking before expanding synonyms (though even that
2555 could be changed.)
2556 </para>
2557 <para>
2558 After expanding type synonyms, GHC does validity checking on types, looking for
2559 the following mal-formedness which isn't detected simply by kind checking:
2560 <itemizedlist>
2561 <listitem><para>
2562 Type constructor applied to a type involving for-alls (if <literal>XImpredicativeTypes</literal>
2563 is off)
2564 </para></listitem>
2565 <listitem><para>
2566 Partially-applied type synonym.
2567 </para></listitem>
2568 </itemizedlist>
2569 So, for example, this will be rejected:
2570 <programlisting>
2571 type Pr = forall a. a
2572
2573 h :: [Pr]
2574 h = ...
2575 </programlisting>
2576 because GHC does not allow type constructors applied to for-all types.
2577 </para>
2578 </sect2>
2579
2580
2581 <sect2 id="existential-quantification">
2582 <title>Existentially quantified data constructors
2583 </title>
2584
2585 <para>
2586 The idea of using existential quantification in data type declarations
2587 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2588 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2589 London, 1991). It was later formalised by Laufer and Odersky
2590 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2591 TOPLAS, 16(5), pp1411-1430, 1994).
2592 It's been in Lennart
2593 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2594 proved very useful. Here's the idea. Consider the declaration:
2595 </para>
2596
2597 <para>
2598
2599 <programlisting>
2600 data Foo = forall a. MkFoo a (a -> Bool)
2601 | Nil
2602 </programlisting>
2603
2604 </para>
2605
2606 <para>
2607 The data type <literal>Foo</literal> has two constructors with types:
2608 </para>
2609
2610 <para>
2611
2612 <programlisting>
2613 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2614 Nil :: Foo
2615 </programlisting>
2616
2617 </para>
2618
2619 <para>
2620 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2621 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2622 For example, the following expression is fine:
2623 </para>
2624
2625 <para>
2626
2627 <programlisting>
2628 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2629 </programlisting>
2630
2631 </para>
2632
2633 <para>
2634 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2635 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2636 isUpper</function> packages a character with a compatible function. These
2637 two things are each of type <literal>Foo</literal> and can be put in a list.
2638 </para>
2639
2640 <para>
2641 What can we do with a value of type <literal>Foo</literal>?. In particular,
2642 what happens when we pattern-match on <function>MkFoo</function>?
2643 </para>
2644
2645 <para>
2646
2647 <programlisting>
2648 f (MkFoo val fn) = ???
2649 </programlisting>
2650
2651 </para>
2652
2653 <para>
2654 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2655 are compatible, the only (useful) thing we can do with them is to
2656 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2657 </para>
2658
2659 <para>
2660
2661 <programlisting>
2662 f :: Foo -> Bool
2663 f (MkFoo val fn) = fn val
2664 </programlisting>
2665
2666 </para>
2667
2668 <para>
2669 What this allows us to do is to package heterogeneous values
2670 together with a bunch of functions that manipulate them, and then treat
2671 that collection of packages in a uniform manner. You can express
2672 quite a bit of object-oriented-like programming this way.
2673 </para>
2674
2675 <sect3 id="existential">
2676 <title>Why existential?
2677 </title>
2678
2679 <para>
2680 What has this to do with <emphasis>existential</emphasis> quantification?
2681 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2682 </para>
2683
2684 <para>
2685
2686 <programlisting>
2687 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2688 </programlisting>
2689
2690 </para>
2691
2692 <para>
2693 But Haskell programmers can safely think of the ordinary
2694 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2695 adding a new existential quantification construct.
2696 </para>
2697
2698 </sect3>
2699
2700 <sect3 id="existential-with-context">
2701 <title>Existentials and type classes</title>
2702
2703 <para>
2704 An easy extension is to allow
2705 arbitrary contexts before the constructor. For example:
2706 </para>
2707
2708 <para>
2709
2710 <programlisting>
2711 data Baz = forall a. Eq a => Baz1 a a
2712 | forall b. Show b => Baz2 b (b -> b)
2713 </programlisting>
2714
2715 </para>
2716
2717 <para>
2718 The two constructors have the types you'd expect:
2719 </para>
2720
2721 <para>
2722
2723 <programlisting>
2724 Baz1 :: forall a. Eq a => a -> a -> Baz
2725 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2726 </programlisting>
2727
2728 </para>
2729
2730 <para>
2731 But when pattern matching on <function>Baz1</function> the matched values can be compared
2732 for equality, and when pattern matching on <function>Baz2</function> the first matched
2733 value can be converted to a string (as well as applying the function to it).
2734 So this program is legal:
2735 </para>
2736
2737 <para>
2738
2739 <programlisting>
2740 f :: Baz -> String
2741 f (Baz1 p q) | p == q = "Yes"
2742 | otherwise = "No"
2743 f (Baz2 v fn) = show (fn v)
2744 </programlisting>
2745
2746 </para>
2747
2748 <para>
2749 Operationally, in a dictionary-passing implementation, the
2750 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2751 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2752 extract it on pattern matching.
2753 </para>
2754
2755 </sect3>
2756
2757 <sect3 id="existential-records">
2758 <title>Record Constructors</title>
2759
2760 <para>
2761 GHC allows existentials to be used with records syntax as well. For example:
2762
2763 <programlisting>
2764 data Counter a = forall self. NewCounter
2765 { _this :: self
2766 , _inc :: self -> self
2767 , _display :: self -> IO ()
2768 , tag :: a
2769 }
2770 </programlisting>
2771 Here <literal>tag</literal> is a public field, with a well-typed selector
2772 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2773 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2774 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2775 compile-time error. In other words, <emphasis>GHC defines a record selector function
2776 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2777 (This example used an underscore in the fields for which record selectors
2778 will not be defined, but that is only programming style; GHC ignores them.)
2779 </para>
2780
2781 <para>
2782 To make use of these hidden fields, we need to create some helper functions:
2783
2784 <programlisting>
2785 inc :: Counter a -> Counter a
2786 inc (NewCounter x i d t) = NewCounter
2787 { _this = i x, _inc = i, _display = d, tag = t }
2788
2789 display :: Counter a -> IO ()
2790 display NewCounter{ _this = x, _display = d } = d x
2791 </programlisting>
2792
2793 Now we can define counters with different underlying implementations:
2794
2795 <programlisting>
2796 counterA :: Counter String
2797 counterA = NewCounter
2798 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2799
2800 counterB :: Counter String
2801 counterB = NewCounter
2802 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2803
2804 main = do
2805 display (inc counterA) -- prints "1"
2806 display (inc (inc counterB)) -- prints "##"
2807 </programlisting>
2808
2809 Record update syntax is supported for existentials (and GADTs):
2810 <programlisting>
2811 setTag :: Counter a -> a -> Counter a
2812 setTag obj t = obj{ tag = t }
2813 </programlisting>
2814 The rule for record update is this: <emphasis>
2815 the types of the updated fields may
2816 mention only the universally-quantified type variables
2817 of the data constructor. For GADTs, the field may mention only types
2818 that appear as a simple type-variable argument in the constructor's result
2819 type</emphasis>. For example:
2820 <programlisting>
2821 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2822 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2823 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2824 -- existentially quantified)
2825
2826 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2827 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2828 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2829 -- type-variable argument in G1's result type)
2830 </programlisting>
2831 </para>
2832
2833 </sect3>
2834
2835
2836 <sect3>
2837 <title>Restrictions</title>
2838
2839 <para>
2840 There are several restrictions on the ways in which existentially-quantified
2841 constructors can be use.
2842 </para>
2843
2844 <para>
2845
2846 <itemizedlist>
2847 <listitem>
2848
2849 <para>
2850 When pattern matching, each pattern match introduces a new,
2851 distinct, type for each existential type variable. These types cannot
2852 be unified with any other type, nor can they escape from the scope of
2853 the pattern match. For example, these fragments are incorrect:
2854
2855
2856 <programlisting>
2857 f1 (MkFoo a f) = a
2858 </programlisting>
2859
2860
2861 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2862 is the result of <function>f1</function>. One way to see why this is wrong is to
2863 ask what type <function>f1</function> has:
2864
2865
2866 <programlisting>
2867 f1 :: Foo -> a -- Weird!
2868 </programlisting>
2869
2870
2871 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2872 this:
2873
2874
2875 <programlisting>
2876 f1 :: forall a. Foo -> a -- Wrong!
2877 </programlisting>
2878
2879
2880 The original program is just plain wrong. Here's another sort of error
2881
2882
2883 <programlisting>
2884 f2 (Baz1 a b) (Baz1 p q) = a==q
2885 </programlisting>
2886
2887
2888 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2889 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2890 from the two <function>Baz1</function> constructors.
2891
2892
2893 </para>
2894 </listitem>
2895 <listitem>
2896
2897 <para>
2898 You can't pattern-match on an existentially quantified
2899 constructor in a <literal>let</literal> or <literal>where</literal> group of
2900 bindings. So this is illegal:
2901
2902
2903 <programlisting>
2904 f3 x = a==b where { Baz1 a b = x }
2905 </programlisting>
2906
2907 Instead, use a <literal>case</literal> expression:
2908
2909 <programlisting>
2910 f3 x = case x of Baz1 a b -> a==b
2911 </programlisting>
2912
2913 In general, you can only pattern-match
2914 on an existentially-quantified constructor in a <literal>case</literal> expression or
2915 in the patterns of a function definition.
2916
2917 The reason for this restriction is really an implementation one.
2918 Type-checking binding groups is already a nightmare without
2919 existentials complicating the picture. Also an existential pattern
2920 binding at the top level of a module doesn't make sense, because it's
2921 not clear how to prevent the existentially-quantified type "escaping".
2922 So for now, there's a simple-to-state restriction. We'll see how
2923 annoying it is.
2924
2925 </para>
2926 </listitem>
2927 <listitem>
2928
2929 <para>
2930 You can't use existential quantification for <literal>newtype</literal>
2931 declarations. So this is illegal:
2932
2933
2934 <programlisting>
2935 newtype T = forall a. Ord a => MkT a
2936 </programlisting>
2937
2938
2939 Reason: a value of type <literal>T</literal> must be represented as a
2940 pair of a dictionary for <literal>Ord t</literal> and a value of type
2941 <literal>t</literal>. That contradicts the idea that
2942 <literal>newtype</literal> should have no concrete representation.
2943 You can get just the same efficiency and effect by using
2944 <literal>data</literal> instead of <literal>newtype</literal>. If
2945 there is no overloading involved, then there is more of a case for
2946 allowing an existentially-quantified <literal>newtype</literal>,
2947 because the <literal>data</literal> version does carry an
2948 implementation cost, but single-field existentially quantified
2949 constructors aren't much use. So the simple restriction (no
2950 existential stuff on <literal>newtype</literal>) stands, unless there
2951 are convincing reasons to change it.
2952
2953
2954 </para>
2955 </listitem>
2956 <listitem>
2957
2958 <para>
2959 You can't use <literal>deriving</literal> to define instances of a
2960 data type with existentially quantified data constructors.
2961
2962 Reason: in most cases it would not make sense. For example:;
2963
2964 <programlisting>
2965 data T = forall a. MkT [a] deriving( Eq )
2966 </programlisting>
2967
2968 To derive <literal>Eq</literal> in the standard way we would need to have equality
2969 between the single component of two <function>MkT</function> constructors:
2970
2971 <programlisting>
2972 instance Eq T where
2973 (MkT a) == (MkT b) = ???
2974 </programlisting>
2975
2976 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2977 It's just about possible to imagine examples in which the derived instance
2978 would make sense, but it seems altogether simpler simply to prohibit such
2979 declarations. Define your own instances!
2980 </para>
2981 </listitem>
2982
2983 </itemizedlist>
2984
2985 </para>
2986
2987 </sect3>
2988 </sect2>
2989
2990 <!-- ====================== Generalised algebraic data types ======================= -->
2991
2992 <sect2 id="gadt-style">
2993 <title>Declaring data types with explicit constructor signatures</title>
2994
2995 <para>When the <literal>GADTSyntax</literal> extension is enabled,
2996 GHC allows you to declare an algebraic data type by
2997 giving the type signatures of constructors explicitly. For example:
2998 <programlisting>
2999 data Maybe a where
3000 Nothing :: Maybe a
3001 Just :: a -> Maybe a
3002 </programlisting>
3003 The form is called a "GADT-style declaration"
3004 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
3005 can only be declared using this form.</para>
3006 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
3007 For example, these two declarations are equivalent:
3008 <programlisting>
3009 data Foo = forall a. MkFoo a (a -> Bool)
3010 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
3011 </programlisting>
3012 </para>
3013 <para>Any data type that can be declared in standard Haskell-98 syntax
3014 can also be declared using GADT-style syntax.
3015 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
3016 they treat class constraints on the data constructors differently.
3017 Specifically, if the constructor is given a type-class context, that
3018 context is made available by pattern matching. For example:
3019 <programlisting>
3020 data Set a where
3021 MkSet :: Eq a => [a] -> Set a
3022
3023 makeSet :: Eq a => [a] -> Set a
3024 makeSet xs = MkSet (nub xs)
3025
3026 insert :: a -> Set a -> Set a
3027 insert a (MkSet as) | a `elem` as = MkSet as
3028 | otherwise = MkSet (a:as)
3029 </programlisting>
3030 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
3031 gives rise to a <literal>(Eq a)</literal>
3032 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
3033 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
3034 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
3035 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
3036 when pattern-matching that dictionary becomes available for the right-hand side of the match.
3037 In the example, the equality dictionary is used to satisfy the equality constraint
3038 generated by the call to <literal>elem</literal>, so that the type of
3039 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
3040 </para>
3041 <para>
3042 For example, one possible application is to reify dictionaries:
3043 <programlisting>
3044 data NumInst a where
3045 MkNumInst :: Num a => NumInst a
3046
3047 intInst :: NumInst Int
3048 intInst = MkNumInst
3049
3050 plus :: NumInst a -> a -> a -> a
3051 plus MkNumInst p q = p + q
3052 </programlisting>
3053 Here, a value of type <literal>NumInst a</literal> is equivalent
3054 to an explicit <literal>(Num a)</literal> dictionary.
3055 </para>
3056 <para>
3057 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
3058 For example, the <literal>NumInst</literal> data type above could equivalently be declared
3059 like this:
3060 <programlisting>
3061 data NumInst a
3062 = Num a => MkNumInst (NumInst a)
3063 </programlisting>
3064 Notice that, unlike the situation when declaring an existential, there is
3065 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
3066 data type's universally quantified type variable <literal>a</literal>.
3067 A constructor may have both universal and existential type variables: for example,
3068 the following two declarations are equivalent:
3069 <programlisting>
3070 data T1 a
3071 = forall b. (Num a, Eq b) => MkT1 a b
3072 data T2 a where
3073 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
3074 </programlisting>
3075 </para>
3076 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
3077 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
3078 In Haskell 98 the definition
3079 <programlisting>
3080 data Eq a => Set' a = MkSet' [a]
3081 </programlisting>
3082 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
3083 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
3084 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
3085 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
3086 GHC's behaviour is much more useful, as well as much more intuitive.
3087 </para>
3088
3089 <para>
3090 The rest of this section gives further details about GADT-style data
3091 type declarations.
3092
3093 <itemizedlist>
3094 <listitem><para>
3095 The result type of each data constructor must begin with the type constructor being defined.
3096 If the result type of all constructors
3097 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
3098 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
3099 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
3100 </para></listitem>
3101
3102 <listitem><para>
3103 As with other type signatures, you can give a single signature for several data constructors.
3104 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
3105 <programlisting>
3106 data T a where
3107 T1,T2 :: a -> T a
3108 T3 :: T a
3109 </programlisting>
3110 </para></listitem>
3111
3112 <listitem><para>
3113 The type signature of
3114 each constructor is independent, and is implicitly universally quantified as usual.
3115 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
3116 have no scope, and different constructors may have different universally-quantified type variables:
3117 <programlisting>
3118 data T a where -- The 'a' has no scope
3119 T1,T2 :: b -> T b -- Means forall b. b -> T b
3120 T3 :: T a -- Means forall a. T a
3121 </programlisting>
3122 </para></listitem>
3123
3124 <listitem><para>
3125 A constructor signature may mention type class constraints, which can differ for
3126 different constructors. For example, this is fine:
3127 <programlisting>
3128 data T a where
3129 T1 :: Eq b => b -> b -> T b
3130 T2 :: (Show c, Ix c) => c -> [c] -> T c
3131 </programlisting>
3132 When pattern matching, these constraints are made available to discharge constraints
3133 in the body of the match. For example:
3134 <programlisting>
3135 f :: T a -> String
3136 f (T1 x y) | x==y = "yes"
3137 | otherwise = "no"
3138 f (T2 a b) = show a
3139 </programlisting>
3140 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
3141 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
3142 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
3143 </para></listitem>
3144
3145 <listitem><para>
3146 Unlike a Haskell-98-style
3147 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
3148 have no scope. Indeed, one can write a kind signature instead:
3149 <programlisting>
3150 data Set :: * -> * where ...
3151 </programlisting>
3152 or even a mixture of the two:
3153 <programlisting>
3154 data Bar a :: (* -> *) -> * where ...
3155 </programlisting>
3156 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3157 like this:
3158 <programlisting>
3159 data Bar a (b :: * -> *) where ...
3160 </programlisting>
3161 </para></listitem>
3162
3163
3164 <listitem><para>
3165 You can use strictness annotations, in the obvious places
3166 in the constructor type:
3167 <programlisting>
3168 data Term a where
3169 Lit :: !Int -> Term Int
3170 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3171 Pair :: Term a -> Term b -> Term (a,b)
3172 </programlisting>
3173 </para></listitem>
3174
3175 <listitem><para>
3176 You can use a <literal>deriving</literal> clause on a GADT-style data type
3177 declaration. For example, these two declarations are equivalent
3178 <programlisting>
3179 data Maybe1 a where {
3180 Nothing1 :: Maybe1 a ;
3181 Just1 :: a -> Maybe1 a
3182 } deriving( Eq, Ord )
3183
3184 data Maybe2 a = Nothing2 | Just2 a
3185 deriving( Eq, Ord )
3186 </programlisting>
3187 </para></listitem>
3188
3189 <listitem><para>
3190 The type signature may have quantified type variables that do not appear
3191 in the result type:
3192 <programlisting>
3193 data Foo where
3194 MkFoo :: a -> (a->Bool) -> Foo
3195 Nil :: Foo
3196 </programlisting>
3197 Here the type variable <literal>a</literal> does not appear in the result type
3198 of either constructor.
3199 Although it is universally quantified in the type of the constructor, such
3200 a type variable is often called "existential".
3201 Indeed, the above declaration declares precisely the same type as
3202 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
3203 </para><para>
3204 The type may contain a class context too, of course:
3205 <programlisting>
3206 data Showable where
3207 MkShowable :: Show a => a -> Showable
3208 </programlisting>
3209 </para></listitem>
3210
3211 <listitem><para>
3212 You can use record syntax on a GADT-style data type declaration:
3213
3214 <programlisting>
3215 data Person where
3216 Adult :: { name :: String, children :: [Person] } -> Person
3217 Child :: Show a => { name :: !String, funny :: a } -> Person
3218 </programlisting>
3219 As usual, for every constructor that has a field <literal>f</literal>, the type of
3220 field <literal>f</literal> must be the same (modulo alpha conversion).
3221 The <literal>Child</literal> constructor above shows that the signature
3222 may have a context, existentially-quantified variables, and strictness annotations,
3223 just as in the non-record case. (NB: the "type" that follows the double-colon
3224 is not really a type, because of the record syntax and strictness annotations.
3225 A "type" of this form can appear only in a constructor signature.)
3226 </para></listitem>
3227
3228 <listitem><para>
3229 Record updates are allowed with GADT-style declarations,
3230 only fields that have the following property: the type of the field
3231 mentions no existential type variables.
3232 </para></listitem>
3233
3234 <listitem><para>
3235 As in the case of existentials declared using the Haskell-98-like record syntax
3236 (<xref linkend="existential-records"/>),
3237 record-selector functions are generated only for those fields that have well-typed
3238 selectors.
3239 Here is the example of that section, in GADT-style syntax:
3240 <programlisting>
3241 data Counter a where
3242 NewCounter :: { _this :: self
3243 , _inc :: self -> self
3244 , _display :: self -> IO ()
3245 , tag :: a
3246 } -> Counter a
3247 </programlisting>
3248 As before, only one selector function is generated here, that for <literal>tag</literal>.
3249 Nevertheless, you can still use all the field names in pattern matching and record construction.
3250 </para></listitem>
3251
3252 <listitem><para>
3253 In a GADT-style data type declaration there is no obvious way to specify that a data constructor
3254 should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
3255 (Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
3256 So GHC implements the following design: a data constructor declared in a GADT-style data type
3257 declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
3258 (b) it has two arguments, (c) it has a programmer-supplied fixity declaration. For example
3259 <programlisting>
3260 infix 6 (:--:)
3261 data T a where
3262 (:--:) :: Int -> Bool -> T Int
3263 </programlisting>
3264 </para></listitem>
3265 </itemizedlist></para>
3266 </sect2>
3267
3268 <sect2 id="gadt">
3269 <title>Generalised Algebraic Data Types (GADTs)</title>
3270
3271 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
3272 by allowing constructors to have richer return types. Here is an example:
3273 <programlisting>
3274 data Term a where
3275 Lit :: Int -> Term Int
3276 Succ :: Term Int -> Term Int
3277 IsZero :: Term Int -> Term Bool
3278 If :: Term Bool -> Term a -> Term a -> Term a
3279 Pair :: Term a -> Term b -> Term (a,b)
3280 </programlisting>
3281 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3282 case with ordinary data types. This generality allows us to
3283 write a well-typed <literal>eval</literal> function
3284 for these <literal>Terms</literal>:
3285 <programlisting>
3286 eval :: Term a -> a
3287 eval (Lit i) = i
3288 eval (Succ t) = 1 + eval t
3289 eval (IsZero t) = eval t == 0
3290 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3291 eval (Pair e1 e2) = (eval e1, eval e2)
3292 </programlisting>
3293 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
3294 For example, in the right hand side of the equation
3295 <programlisting>
3296 eval :: Term a -> a
3297 eval (Lit i) = ...
3298 </programlisting>
3299 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
3300 A precise specification of the type rules is beyond what this user manual aspires to,
3301 but the design closely follows that described in
3302 the paper <ulink
3303 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
3304 unification-based type inference for GADTs</ulink>,
3305 (ICFP 2006).
3306 The general principle is this: <emphasis>type refinement is only carried out
3307 based on user-supplied type annotations</emphasis>.
3308 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
3309 and lots of obscure error messages will
3310 occur. However, the refinement is quite general. For example, if we had:
3311 <programlisting>
3312 eval :: Term a -> a -> a
3313 eval (Lit i) j = i+j
3314 </programlisting>
3315 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3316 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
3317 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3318 </para>
3319 <para>
3320 These and many other examples are given in papers by Hongwei Xi, and
3321 Tim Sheard. There is a longer introduction
3322 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3323 and Ralf Hinze's
3324 <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
3325 may use different notation to that implemented in GHC.
3326 </para>
3327 <para>
3328 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
3329 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
3330 <itemizedlist>
3331 <listitem><para>
3332 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
3333 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
3334 The result type of each constructor must begin with the type constructor being defined,
3335 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
3336 For example, in the <literal>Term</literal> data
3337 type above, the type of each constructor must end with <literal>Term ty</literal>, but
3338 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
3339 constructor).
3340 </para></listitem>
3341
3342 <listitem><para>
3343 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
3344 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
3345 whose result type is not just <literal>T a b</literal>.
3346 </para></listitem>
3347
3348 <listitem><para>
3349 You cannot use a <literal>deriving</literal> clause for a GADT; only for
3350 an ordinary data type.
3351 </para></listitem>
3352
3353 <listitem><para>
3354 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
3355 For example:
3356 <programlisting>
3357 data Term a where
3358 Lit :: { val :: Int } -> Term Int
3359 Succ :: { num :: Term Int } -> Term Int
3360 Pred :: { num :: Term Int } -> Term Int
3361 IsZero :: { arg :: Term Int } -> Term Bool
3362 Pair :: { arg1 :: Term a
3363 , arg2 :: Term b
3364 } -> Term (a,b)
3365 If :: { cnd :: Term Bool
3366 , tru :: Term a
3367 , fls :: Term a
3368 } -> Term a
3369 </programlisting>
3370 However, for GADTs there is the following additional constraint:
3371 every constructor that has a field <literal>f</literal> must have
3372 the same result type (modulo alpha conversion)
3373 Hence, in the above example, we cannot merge the <literal>num</literal>
3374 and <literal>arg</literal> fields above into a
3375 single name. Although their field types are both <literal>Term Int</literal>,
3376 their selector functions actually have different types:
3377
3378 <programlisting>
3379 num :: Term Int -> Term Int
3380 arg :: Term Bool -> Term Int
3381 </programlisting>
3382 </para></listitem>
3383
3384 <listitem><para>
3385 When pattern-matching against data constructors drawn from a GADT,
3386 for example in a <literal>case</literal> expression, the following rules apply:
3387 <itemizedlist>
3388 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
3389 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
3390 <listitem><para>The type of any free variable mentioned in any of
3391 the <literal>case</literal> alternatives must be rigid.</para></listitem>
3392 </itemizedlist>
3393 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
3394 way to ensure that a variable a rigid type is to give it a type signature.
3395 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
3396 Simple unification-based type inference for GADTs
3397 </ulink>. The criteria implemented by GHC are given in the Appendix.
3398
3399 </para></listitem>
3400
3401 </itemizedlist>
3402 </para>
3403
3404 </sect2>
3405 </sect1>
3406
3407 <!-- ====================== End of Generalised algebraic data types ======================= -->
3408
3409 <sect1 id="deriving">
3410 <title>Extensions to the "deriving" mechanism</title>
3411
3412 <sect2 id="deriving-inferred">
3413 <title>Inferred context for deriving clauses</title>
3414
3415 <para>
3416 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
3417 legal. For example:
3418 <programlisting>
3419 data T0 f a = MkT0 a deriving( Eq )
3420 data T1 f a = MkT1 (f a) deriving( Eq )
3421 data T2 f a = MkT2 (f (f a)) deriving( Eq )
3422 </programlisting>
3423 The natural generated <literal>Eq</literal> code would result in these instance declarations:
3424 <programlisting>
3425 instance Eq a => Eq (T0 f a) where ...
3426 instance Eq (f a) => Eq (T1 f a) where ...
3427 instance Eq (f (f a)) => Eq (T2 f a) where ...
3428 </programlisting>
3429 The first of these is obviously fine. The second is still fine, although less obviously.
3430 The third is not Haskell 98, and risks losing termination of instances.
3431 </para>
3432 <para>
3433 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
3434 each constraint in the inferred instance context must consist only of type variables,
3435 with no repetitions.
3436 </para>
3437 <para>
3438 This rule is applied regardless of flags. If you want a more exotic context, you can write
3439 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
3440 </para>
3441 </sect2>
3442
3443 <sect2 id="stand-alone-deriving">
3444 <title>Stand-alone deriving declarations</title>
3445
3446 <para>
3447 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
3448 <programlisting>
3449 data Foo a = Bar a | Baz String
3450
3451 deriving instance Eq a => Eq (Foo a)
3452 </programlisting>
3453 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
3454 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
3455 Note the following points:
3456 <itemizedlist>
3457 <listitem><para>
3458 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
3459 exactly as you would in an ordinary instance declaration.
3460 (In contrast, in a <literal>deriving</literal> clause
3461 attached to a data type declaration, the context is inferred.)
3462 </para></listitem>
3463
3464 <listitem><para>
3465 A <literal>deriving instance</literal> declaration
3466 must obey the same rules concerning form and termination as ordinary instance declarations,
3467 controlled by the same flags; see <xref linkend="instance-decls"/>.
3468 </para></listitem>
3469
3470 <listitem><para>
3471 Unlike a <literal>deriving</literal>
3472 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
3473 than the data type (assuming you also use
3474 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
3475 for example
3476 <programlisting>
3477 data Foo a = Bar a | Baz String
3478
3479 deriving instance Eq a => Eq (Foo [a])
3480 deriving instance Eq a => Eq (Foo (Maybe a))
3481 </programlisting>
3482 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
3483 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
3484 </para></listitem>
3485
3486 <listitem><para>
3487 Unlike a <literal>deriving</literal>
3488 declaration attached to a <literal>data</literal> declaration,
3489 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
3490 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
3491 your problem. (GHC will show you the offending code if it has a type error.)
3492 The merit of this is that you can derive instances for GADTs and other exotic
3493 data types, providing only that the boilerplate code does indeed typecheck. For example:
3494 <programlisting>
3495 data T a where
3496 T1 :: T Int
3497 T2 :: T Bool
3498
3499 deriving instance Show (T a)
3500 </programlisting>
3501 In this example, you cannot say <literal>... deriving( Show )</literal> on the
3502 data type declaration for <literal>T</literal>,
3503 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
3504 the instance declaration using stand-alone deriving.
3505 </para>
3506 </listitem>
3507
3508 <listitem>
3509 <para>The stand-alone syntax is generalised for newtypes in exactly the same
3510 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3511 For example:
3512 <programlisting>
3513 newtype Foo a = MkFoo (State Int a)
3514
3515 deriving instance MonadState Int Foo
3516 </programlisting>
3517 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3518 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3519 </para></listitem>
3520 </itemizedlist></para>
3521
3522 </sect2>
3523
3524
3525 <sect2 id="deriving-typeable">
3526 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
3527
3528 <para>
3529 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3530 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3531 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3532 classes <literal>Eq</literal>, <literal>Ord</literal>,
3533 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3534 </para>
3535 <para>
3536 GHC extends this list with several more classes that may be automatically derived:
3537 <itemizedlist>
3538 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
3539 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
3540 modules <literal>Data.Typeable</literal> and <literal>Data.Data</literal> respectively.
3541 </para>
3542 <para>Since GHC 7.8.1, <literal>Typeable</literal> is kind-polymorphic (see
3543 <xref linkend="kind-polymorphism"/>) and can be derived for any datatype and
3544 type class. Instances for datatypes can be derived by attaching a
3545 <literal>deriving Typeable</literal> clause to the datatype declaration, or by
3546 using standalone deriving (see <xref linkend="stand-alone-deriving"/>).
3547 Instances for type classes can only be derived using standalone deriving.
3548 For data families, <literal>Typeable</literal> should only be derived for the
3549 uninstantiated family type; each instance will then automatically have a
3550 <literal>Typeable</literal> instance too.
3551 See also <xref linkend="auto-derive-typeable"/>.
3552 </para>
3553 <para>
3554 Also since GHC 7.8.1, handwritten (ie. not derived) instances of
3555 <literal>Typeable</literal> are forbidden, and will result in an error.
3556 </para>
3557 </listitem>
3558
3559 <listitem><para> With <option>-XDeriveGeneric</option>, you can derive
3560 instances of the classes <literal>Generic</literal> and
3561 <literal>Generic1</literal>, defined in <literal>GHC.Generics</literal>.
3562 You can use these to define generic functions,
3563 as described in <xref linkend="generic-programming"/>.
3564 </para></listitem>
3565
3566 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3567 the class <literal>Functor</literal>,
3568 defined in <literal>GHC.Base</literal>.
3569 </para></listitem>
3570
3571 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3572 the class <literal>Foldable</literal>,
3573 defined in <literal>Data.Foldable</literal>.
3574 </para></listitem>
3575
3576 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3577 the class <literal>Traversable</literal>,
3578 defined in <literal>Data.Traversable</literal>.
3579 </para></listitem>
3580 </itemizedlist>
3581 In each case the appropriate class must be in scope before it
3582 can be mentioned in the <literal>deriving</literal> clause.
3583 </para>
3584 </sect2>
3585
3586 <sect2 id="auto-derive-typeable">
3587 <title>Automatically deriving <literal>Typeable</literal> instances</title>
3588
3589 <para>
3590 The flag <option>-XAutoDeriveTypeable</option> triggers the generation
3591 of derived <literal>Typeable</literal> instances for every datatype and type
3592 class declaration in the module it is used. It will also generate
3593 <literal>Typeable</literal> instances for any promoted data constructors
3594 (<xref linkend="promotion"/>). This flag implies
3595 <option>-XDeriveDataTypeable</option> (<xref linkend="deriving-typeable"/>).
3596 </para>
3597
3598 </sect2>
3599
3600 <sect2 id="newtype-deriving">
3601 <title>Generalised derived instances for newtypes</title>
3602
3603 <para>
3604 When you define an abstract type using <literal>newtype</literal>, you may want
3605 the new type to inherit some instances from its representation. In
3606 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3607 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3608 other classes you have to write an explicit instance declaration. For
3609 example, if you define
3610
3611 <programlisting>
3612 newtype Dollars = Dollars Int
3613 </programlisting>
3614
3615 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3616 explicitly define an instance of <literal>Num</literal>:
3617
3618 <programlisting>
3619 instance Num Dollars where
3620 Dollars a + Dollars b = Dollars (a+b)
3621 ...
3622 </programlisting>
3623 All the instance does is apply and remove the <literal>newtype</literal>
3624 constructor. It is particularly galling that, since the constructor
3625 doesn't appear at run-time, this instance declaration defines a
3626 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3627 dictionary, only slower!
3628 </para>
3629
3630
3631 <sect3 id="generalized-newtype-deriving"> <title> Generalising the deriving clause </title>
3632 <para>
3633 GHC now permits such instances to be derived instead,
3634 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3635 so one can write
3636 <programlisting>
3637 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3638 </programlisting>
3639
3640 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3641 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3642 derives an instance declaration of the form
3643
3644 <programlisting>
3645 instance Num Int => Num Dollars
3646 </programlisting>
3647
3648 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3649 </para>
3650 <para>
3651
3652 We can also derive instances of constructor classes in a similar
3653 way. For example, suppose we have implemented state and failure monad
3654 transformers, such that
3655
3656 <programlisting>
3657 instance Monad m => Monad (State s m)
3658 instance Monad m => Monad (Failure m)
3659 </programlisting>
3660 In Haskell 98, we can define a parsing monad by
3661 <programlisting>
3662 type Parser tok m a = State [tok] (Failure m) a
3663 </programlisting>
3664
3665 which is automatically a monad thanks to the instance declarations
3666 above. With the extension, we can make the parser type abstract,
3667 without needing to write an instance of class <literal>Monad</literal>, via
3668
3669 <programlisting>
3670 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3671 deriving Monad
3672 </programlisting>
3673 In this case the derived instance declaration is of the form
3674 <programlisting>
3675 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3676 </programlisting>
3677
3678 Notice that, since <literal>Monad</literal> is a constructor class, the
3679 instance is a <emphasis>partial application</emphasis> of the new type, not the
3680 entire left hand side. We can imagine that the type declaration is
3681 "eta-converted" to generate the context of the instance
3682 declaration.
3683 </para>
3684 <para>
3685
3686 We can even derive instances of multi-parameter classes, provided the
3687 newtype is the last class parameter. In this case, a ``partial
3688 application'' of the class appears in the <literal>deriving</literal>
3689 clause. For example, given the class
3690
3691 <programlisting>
3692 class StateMonad s m | m -> s where ...
3693 instance Monad m => StateMonad s (State s m) where ...
3694 </programlisting>
3695 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3696 <programlisting>
3697 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3698 deriving (Monad, StateMonad [tok])
3699 </programlisting>
3700
3701 The derived instance is obtained by completing the application of the
3702 class to the new type:
3703
3704 <programlisting>
3705 instance StateMonad [tok] (State [tok] (Failure m)) =>
3706 StateMonad [tok] (Parser tok m)
3707 </programlisting>
3708 </para>
3709 <para>
3710
3711 As a result of this extension, all derived instances in newtype
3712 declarations are treated uniformly (and implemented just by reusing
3713 the dictionary for the representation type), <emphasis>except</emphasis>
3714 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3715 the newtype and its representation.
3716 </para>
3717 </sect3>
3718
3719 <sect3> <title> A more precise specification </title>
3720 <para>
3721 Derived instance declarations are constructed as follows. Consider the
3722 declaration (after expansion of any type synonyms)
3723
3724 <programlisting>
3725 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3726 </programlisting>
3727
3728 where
3729 <itemizedlist>
3730 <listitem><para>
3731 The <literal>ci</literal> are partial applications of
3732 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3733 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3734 </para></listitem>
3735 <listitem><para>
3736 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3737 </para></listitem>
3738 <listitem><para>
3739 The type <literal>t</literal> is an arbitrary type.
3740 </para></listitem>
3741 <listitem><para>
3742 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3743 nor in the <literal>ci</literal>, and
3744 </para></listitem>
3745 <listitem><para>
3746 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3747 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3748 should not "look through" the type or its constructor. You can still
3749 derive these classes for a newtype, but it happens in the usual way, not
3750 via this new mechanism.
3751 </para></listitem>
3752 <listitem><para>
3753 It is safe to coerce each of the methods of <literal>ci</literal>. That is,
3754 the missing last argument to each of the <literal>ci</literal> is not used
3755 at a nominal role in any of the <literal>ci</literal>'s methods.
3756 (See <xref linkend="roles"/>.)</para></listitem>
3757 </itemizedlist>
3758 Then, for each <literal>ci</literal>, the derived instance
3759 declaration is:
3760 <programlisting>
3761 instance ci t => ci (T v1...vk)
3762 </programlisting>
3763 As an example which does <emphasis>not</emphasis> work, consider
3764 <programlisting>
3765 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3766 </programlisting>
3767 Here we cannot derive the instance
3768 <programlisting>
3769 instance Monad (State s m) => Monad (NonMonad m)
3770 </programlisting>
3771
3772 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3773 and so cannot be "eta-converted" away. It is a good thing that this
3774 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3775 not, in fact, a monad --- for the same reason. Try defining
3776 <literal>>>=</literal> with the correct type: you won't be able to.
3777 </para>
3778 <para>
3779
3780 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3781 important, since we can only derive instances for the last one. If the
3782 <literal>StateMonad</literal> class above were instead defined as
3783
3784 <programlisting>
3785 class StateMonad m s | m -> s where ...
3786 </programlisting>
3787
3788 then we would not have been able to derive an instance for the
3789 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3790 classes usually have one "main" parameter for which deriving new
3791 instances is most interesting.
3792 </para>
3793 <para>Lastly, all of this applies only for classes other than
3794 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3795 and <literal>Data</literal>, for which the built-in derivation applies (section
3796 4.3.3. of the Haskell Report).
3797 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3798 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3799 the standard method is used or the one described here.)
3800 </para>
3801 </sect3>
3802 </sect2>
3803 </sect1>
3804
3805
3806 <!-- TYPE SYSTEM EXTENSIONS -->
3807 <sect1 id="type-class-extensions">
3808 <title>Class and instances declarations</title>
3809
3810 <sect2 id="multi-param-type-classes">
3811 <title>Class declarations</title>
3812
3813 <para>
3814 This section, and the next one, documents GHC's type-class extensions.
3815 There's lots of background in the paper <ulink
3816 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3817 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3818 Jones, Erik Meijer).
3819 </para>
3820
3821 <sect3>
3822 <title>Multi-parameter type classes</title>
3823 <para>
3824 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3825 For example:
3826
3827
3828 <programlisting>
3829 class Collection c a where
3830 union :: c a -> c a -> c a
3831 ...etc.
3832 </programlisting>
3833
3834 </para>
3835 </sect3>
3836
3837 <sect3 id="superclass-rules">
3838 <title>The superclasses of a class declaration</title>
3839
3840 <para>
3841 In Haskell 98 the context of a class declaration (which introduces superclasses)
3842 must be simple; that is, each predicate must consist of a class applied to
3843 type variables. The flag <option>-XFlexibleContexts</option>
3844 (<xref linkend="flexible-contexts"/>)
3845 lifts this restriction,
3846 so that the only restriction on the context in a class declaration is
3847 that the class hierarchy must be acyclic. So these class declarations are OK:
3848
3849
3850 <programlisting>
3851 class Functor (m k) => FiniteMap m k where
3852 ...
3853
3854 class (Monad m, Monad (t m)) => Transform t m where
3855 lift :: m a -> (t m) a
3856 </programlisting>
3857
3858
3859 </para>
3860 <para>
3861 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3862 of "acyclic" involves only the superclass relationships. For example,
3863 this is OK:
3864
3865
3866 <programlisting>
3867 class C a where {
3868 op :: D b => a -> b -> b
3869 }
3870
3871 class C a => D a where { ... }
3872 </programlisting>
3873
3874
3875 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3876 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3877 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3878 </para>
3879 <para>
3880 With the extension that adds a <link linkend="constraint-kind">kind of constraints</link>,
3881 you can write more exotic superclass definitions. The superclass cycle check is even more
3882 liberal in these case. For example, this is OK:
3883
3884 <programlisting>
3885 class A cls c where
3886 meth :: cls c => c -> c
3887
3888 class A B c => B c where
3889 </programlisting>
3890
3891 A superclass context for a class <literal>C</literal> is allowed if, after expanding
3892 type synonyms to their right-hand-sides, and uses of classes (other than <literal>C</literal>)
3893 to their superclasses, <literal>C</literal> does not occur syntactically in the context.
3894 </para>
3895 </sect3>
3896
3897
3898
3899
3900 <sect3 id="class-method-types">
3901 <title>Class method types</title>
3902
3903 <para>
3904 Haskell 98 prohibits class method types to mention constraints on the
3905 class type variable, thus:
3906 <programlisting>
3907 class Seq s a where
3908 fromList :: [a] -> s a
3909 elem :: Eq a => a -> s a -> Bool
3910 </programlisting>
3911 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3912 contains the constraint <literal>Eq a</literal>, constrains only the
3913 class type variable (in this case <literal>a</literal>).
3914 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3915 </para>
3916
3917
3918 </sect3>
3919
3920
3921 <sect3 id="class-default-signatures">
3922 <title>Default method signatures</title>
3923
3924 <para>
3925 Haskell 98 allows you to define a default implementation when declaring a class:
3926 <programlisting>
3927 class Enum a where
3928 enum :: [a]
3929 enum = []
3930 </programlisting>
3931 The type of the <literal>enum</literal> method is <literal>[a]</literal>, and
3932 this is also the type of the default method. You can lift this restriction
3933 and give another type to the default method using the flag
3934 <option>-XDefaultSignatures</option>. For instance, if you have written a
3935 generic implementation of enumeration in a class <literal>GEnum</literal>
3936 with method <literal>genum</literal> in terms of <literal>GHC.Generics</literal>,
3937 you can specify a default method that uses that generic implementation:
3938 <programlisting>
3939 class Enum a where
3940 enum :: [a]
3941 default enum :: (Generic a, GEnum (Rep a)) => [a]
3942 enum = map to genum
3943 </programlisting>
3944 We reuse the keyword <literal>default</literal> to signal that a signature
3945 applies to the default method only; when defining instances of the
3946 <literal>Enum</literal> class, the original type <literal>[a]</literal> of
3947 <literal>enum</literal> still applies. When giving an empty instance, however,
3948 the default implementation <literal>map to genum</literal> is filled-in,
3949 and type-checked with the type
3950 <literal>(Generic a, GEnum (Rep a)) => [a]</literal>.
3951 </para>
3952
3953 <para>
3954 We use default signatures to simplify generic programming in GHC
3955 (<xref linkend="generic-programming"/>).
3956 </para>
3957
3958
3959 </sect3>
3960
3961 <sect3 id="nullary-type-classes">
3962 <title>Nullary type classes</title>
3963 Nullary (no parameter) type classes are enabled with <option>-XNullaryTypeClasses</option>.
3964 Since there are no available parameters, there can be at most one instance
3965 of a nullary class. A nullary type class might be used to document some assumption
3966 in a type signature (such as reliance on the Riemann hypothesis) or add some
3967 globally configurable settings in a program. For example,
3968
3969 <programlisting>
3970 class RiemannHypothesis where
3971 assumeRH :: a -> a
3972
3973 -- Deterministic version of the Miller test
3974 -- correctness depends on the generalized Riemann hypothesis
3975 isPrime :: RiemannHypothesis => Integer -> Bool
3976 isPrime n = assumeRH (...)
3977 </programlisting>
3978
3979 The type signature of <literal>isPrime</literal> informs users that its correctness
3980 depends on an unproven conjecture. If the function is used, the user has
3981 to acknowledge the dependence with:
3982
3983 <programlisting>
3984 instance RiemannHypothesis where
3985 assumeRH = id
3986 </programlisting>
3987
3988 </sect3>
3989 </sect2>
3990
3991 <sect2 id="functional-dependencies">
3992 <title>Functional dependencies
3993 </title>
3994
3995 <para> Functional dependencies are implemented as described by Mark Jones
3996 in &ldquo;<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>&rdquo;, Mark P. Jones,
3997 In Proceedings of the 9th European Symposium on Programming,
3998 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3999 .
4000 </para>
4001 <para>
4002 Functional dependencies are introduced by a vertical bar in the syntax of a
4003 class declaration; e.g.
4004 <programlisting>
4005 class (Monad m) => MonadState s m | m -> s where ...
4006
4007 class Foo a b c | a b -> c where ...
4008 </programlisting>
4009 There should be more documentation, but there isn't (yet). Yell if you need it.
4010 </para>
4011
4012 <sect3><title>Rules for functional dependencies </title>
4013 <para>
4014 In a class declaration, all of the class type variables must be reachable (in the sense
4015 mentioned in <xref linkend="flexible-contexts"/>)
4016 from the free variables of each method type.
4017 For example:
4018
4019 <programlisting>
4020 class Coll s a where
4021 empty :: s
4022 insert :: s -> a -> s
4023 </programlisting>
4024
4025 is not OK, because the type of <literal>empty</literal> doesn't mention
4026 <literal>a</literal>. Functional dependencies can make the type variable
4027 reachable:
4028 <programlisting>
4029 class Coll s a | s -> a where
4030 empty :: s
4031 insert :: s -> a -> s
4032 </programlisting>
4033
4034 Alternatively <literal>Coll</literal> might be rewritten
4035
4036 <programlisting>
4037 class Coll s a where
4038 empty :: s a
4039 insert :: s a -> a -> s a
4040 </programlisting>
4041
4042
4043 which makes the connection between the type of a collection of
4044 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
4045 Occasionally this really doesn't work, in which case you can split the
4046 class like this:
4047
4048
4049 <programlisting>
4050 class CollE s where
4051 empty :: s
4052
4053 class CollE s => Coll s a where
4054 insert :: s -> a -> s
4055 </programlisting>
4056 </para>
4057 </sect3>
4058
4059
4060 <sect3>
4061 <title>Background on functional dependencies</title>
4062
4063 <para>The following description of the motivation and use of functional dependencies is taken
4064 from the Hugs user manual, reproduced here (with minor changes) by kind
4065 permission of Mark Jones.
4066 </para>
4067 <para>
4068 Consider the following class, intended as part of a
4069 library for collection types:
4070 <programlisting>
4071 class Collects e ce where
4072 empty :: ce
4073 insert :: e -> ce -> ce
4074 member :: e -> ce -> Bool
4075 </programlisting>
4076 The type variable e used here represents the element type, while ce is the type
4077 of the container itself. Within this framework, we might want to define
4078 instances of this class for lists or characteristic functions (both of which
4079 can be used to represent collections of any equality type), bit sets (which can
4080 be used to represent collections of characters), or hash tables (which can be
4081 used to represent any collection whose elements have a hash function). Omitting
4082 standard implementation details, this would lead to the following declarations:
4083 <programlisting>
4084 instance Eq e => Collects e [e] where ...
4085 instance Eq e => Collects e (e -> Bool) where ...
4086 instance Collects Char BitSet where ...
4087 instance (Hashable e, Collects a ce)
4088 => Collects e (Array Int ce) where ...
4089 </programlisting>
4090 All this looks quite promising; we have a class and a range of interesting
4091 implementations. Unfortunately, there are some serious problems with the class
4092 declaration. First, the empty function has an ambiguous type:
4093 <programlisting>
4094 empty :: Collects e ce => ce
4095 </programlisting>