User manual section to document the principles of kind inference
[ghc.git] / docs / users_guide / glasgow_exts.xml
1 <?xml version="1.0" encoding="iso-8859-1"?>
2 <para>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They can all be enabled or disabled by command line flags
7 or language pragmas. By default GHC understands the most recent Haskell
8 version it supports, plus a handful of extensions.
9 </para>
10
11 <para>
12 Some of the Glasgow extensions serve to give you access to the
13 underlying facilities with which we implement Haskell. Thus, you can
14 get at the Raw Iron, if you are willing to write some non-portable
15 code at a more primitive level. You need not be &ldquo;stuck&rdquo;
16 on performance because of the implementation costs of Haskell's
17 &ldquo;high-level&rdquo; features&mdash;you can always code
18 &ldquo;under&rdquo; them. In an extreme case, you can write all your
19 time-critical code in C, and then just glue it together with Haskell!
20 </para>
21
22 <para>
23 Before you get too carried away working at the lowest level (e.g.,
24 sloshing <literal>MutableByteArray&num;</literal>s around your
25 program), you may wish to check if there are libraries that provide a
26 &ldquo;Haskellised veneer&rdquo; over the features you want. The
27 separate <ulink url="../libraries/index.html">libraries
28 documentation</ulink> describes all the libraries that come with GHC.
29 </para>
30
31 <!-- LANGUAGE OPTIONS -->
32 <sect1 id="options-language">
33 <title>Language options</title>
34
35 <indexterm><primary>language</primary><secondary>option</secondary>
36 </indexterm>
37 <indexterm><primary>options</primary><secondary>language</secondary>
38 </indexterm>
39 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
40 </indexterm>
41
42 <para>The language option flags control what variation of the language are
43 permitted.</para>
44
45 <para>Language options can be controlled in two ways:
46 <itemizedlist>
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
50 <listitem><para>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
53 </listitem>
54 </itemizedlist></para>
55
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 &what_glasgow_exts_does;
60 Enabling these options is the <emphasis>only</emphasis>
61 effect of <option>-fglasgow-exts</option>.
62 We are trying to move away from this portmanteau flag,
63 and towards enabling features individually.</para>
64
65 </sect1>
66
67 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
68 <sect1 id="primitives">
69 <title>Unboxed types and primitive operations</title>
70
71 <para>GHC is built on a raft of primitive data types and operations;
72 "primitive" in the sense that they cannot be defined in Haskell itself.
73 While you really can use this stuff to write fast code,
74 we generally find it a lot less painful, and more satisfying in the
75 long run, to use higher-level language features and libraries. With
76 any luck, the code you write will be optimised to the efficient
77 unboxed version in any case. And if it isn't, we'd like to know
78 about it.</para>
79
80 <para>All these primitive data types and operations are exported by the
81 library <literal>GHC.Prim</literal>, for which there is
82 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
83 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
84 </para>
85
86 <para>
87 If you want to mention any of the primitive data types or operations in your
88 program, you must first import <literal>GHC.Prim</literal> to bring them
89 into scope. Many of them have names ending in "&num;", and to mention such
90 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
91 </para>
92
93 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
94 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
95 we briefly summarise here. </para>
96
97 <sect2 id="glasgow-unboxed">
98 <title>Unboxed types</title>
99
100 <para>
101 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
102 </para>
103
104 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
105 that values of that type are represented by a pointer to a heap
106 object. The representation of a Haskell <literal>Int</literal>, for
107 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
108 type, however, is represented by the value itself, no pointers or heap
109 allocation are involved.
110 </para>
111
112 <para>
113 Unboxed types correspond to the &ldquo;raw machine&rdquo; types you
114 would use in C: <literal>Int&num;</literal> (long int),
115 <literal>Double&num;</literal> (double), <literal>Addr&num;</literal>
116 (void *), etc. The <emphasis>primitive operations</emphasis>
117 (PrimOps) on these types are what you might expect; e.g.,
118 <literal>(+&num;)</literal> is addition on
119 <literal>Int&num;</literal>s, and is the machine-addition that we all
120 know and love&mdash;usually one instruction.
121 </para>
122
123 <para>
124 Primitive (unboxed) types cannot be defined in Haskell, and are
125 therefore built into the language and compiler. Primitive types are
126 always unlifted; that is, a value of a primitive type cannot be
127 bottom. We use the convention (but it is only a convention)
128 that primitive types, values, and
129 operations have a <literal>&num;</literal> suffix (see <xref linkend="magic-hash"/>).
130 For some primitive types we have special syntax for literals, also
131 described in the <link linkend="magic-hash">same section</link>.
132 </para>
133
134 <para>
135 Primitive values are often represented by a simple bit-pattern, such
136 as <literal>Int&num;</literal>, <literal>Float&num;</literal>,
137 <literal>Double&num;</literal>. But this is not necessarily the case:
138 a primitive value might be represented by a pointer to a
139 heap-allocated object. Examples include
140 <literal>Array&num;</literal>, the type of primitive arrays. A
141 primitive array is heap-allocated because it is too big a value to fit
142 in a register, and would be too expensive to copy around; in a sense,
143 it is accidental that it is represented by a pointer. If a pointer
144 represents a primitive value, then it really does point to that value:
145 no unevaluated thunks, no indirections&hellip;nothing can be at the
146 other end of the pointer than the primitive value.
147 A numerically-intensive program using unboxed types can
148 go a <emphasis>lot</emphasis> faster than its &ldquo;standard&rdquo;
149 counterpart&mdash;we saw a threefold speedup on one example.
150 </para>
151
152 <para>
153 There are some restrictions on the use of primitive types:
154 <itemizedlist>
155 <listitem><para>The main restriction
156 is that you can't pass a primitive value to a polymorphic
157 function or store one in a polymorphic data type. This rules out
158 things like <literal>[Int&num;]</literal> (i.e. lists of primitive
159 integers). The reason for this restriction is that polymorphic
160 arguments and constructor fields are assumed to be pointers: if an
161 unboxed integer is stored in one of these, the garbage collector would
162 attempt to follow it, leading to unpredictable space leaks. Or a
163 <function>seq</function> operation on the polymorphic component may
164 attempt to dereference the pointer, with disastrous results. Even
165 worse, the unboxed value might be larger than a pointer
166 (<literal>Double&num;</literal> for instance).
167 </para>
168 </listitem>
169 <listitem><para> You cannot define a newtype whose representation type
170 (the argument type of the data constructor) is an unboxed type. Thus,
171 this is illegal:
172 <programlisting>
173 newtype A = MkA Int#
174 </programlisting>
175 </para></listitem>
176 <listitem><para> You cannot bind a variable with an unboxed type
177 in a <emphasis>top-level</emphasis> binding.
178 </para></listitem>
179 <listitem><para> You cannot bind a variable with an unboxed type
180 in a <emphasis>recursive</emphasis> binding.
181 </para></listitem>
182 <listitem><para> You may bind unboxed variables in a (non-recursive,
183 non-top-level) pattern binding, but you must make any such pattern-match
184 strict. For example, rather than:
185 <programlisting>
186 data Foo = Foo Int Int#
187
188 f x = let (Foo a b, w) = ..rhs.. in ..body..
189 </programlisting>
190 you must write:
191 <programlisting>
192 data Foo = Foo Int Int#
193
194 f x = let !(Foo a b, w) = ..rhs.. in ..body..
195 </programlisting>
196 since <literal>b</literal> has type <literal>Int#</literal>.
197 </para>
198 </listitem>
199 </itemizedlist>
200 </para>
201
202 </sect2>
203
204 <sect2 id="unboxed-tuples">
205 <title>Unboxed tuples</title>
206
207 <para>
208 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>;
209 they are a syntactic extension enabled by the language flag <option>-XUnboxedTuples</option>. An
210 unboxed tuple looks like this:
211 </para>
212
213 <para>
214
215 <programlisting>
216 (# e_1, ..., e_n #)
217 </programlisting>
218
219 </para>
220
221 <para>
222 where <literal>e&lowbar;1..e&lowbar;n</literal> are expressions of any
223 type (primitive or non-primitive). The type of an unboxed tuple looks
224 the same.
225 </para>
226
227 <para>
228 Note that when unboxed tuples are enabled,
229 <literal>(#</literal> is a single lexeme, so for example when using
230 operators like <literal>#</literal> and <literal>#-</literal> you need
231 to write <literal>( # )</literal> and <literal>( #- )</literal> rather than
232 <literal>(#)</literal> and <literal>(#-)</literal>.
233 </para>
234
235 <para>
236 Unboxed tuples are used for functions that need to return multiple
237 values, but they avoid the heap allocation normally associated with
238 using fully-fledged tuples. When an unboxed tuple is returned, the
239 components are put directly into registers or on the stack; the
240 unboxed tuple itself does not have a composite representation. Many
241 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
242 tuples.
243 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
244 tuples to avoid unnecessary allocation during sequences of operations.
245 </para>
246
247 <para>
248 There are some restrictions on the use of unboxed tuples:
249 <itemizedlist>
250
251 <listitem>
252 <para>
253 Values of unboxed tuple types are subject to the same restrictions as
254 other unboxed types; i.e. they may not be stored in polymorphic data
255 structures or passed to polymorphic functions.
256 </para>
257 </listitem>
258
259 <listitem>
260 <para>
261 The typical use of unboxed tuples is simply to return multiple values,
262 binding those multiple results with a <literal>case</literal> expression, thus:
263 <programlisting>
264 f x y = (# x+1, y-1 #)
265 g x = case f x x of { (# a, b #) -&#62; a + b }
266 </programlisting>
267 You can have an unboxed tuple in a pattern binding, thus
268 <programlisting>
269 f x = let (# p,q #) = h x in ..body..
270 </programlisting>
271 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
272 the resulting binding is lazy like any other Haskell pattern binding. The
273 above example desugars like this:
274 <programlisting>
275 f x = let t = case h x of { (# p,q #) -> (p,q) }
276 p = fst t
277 q = snd t
278 in ..body..
279 </programlisting>
280 Indeed, the bindings can even be recursive.
281 </para>
282 </listitem>
283 </itemizedlist>
284
285 </para>
286
287 </sect2>
288 </sect1>
289
290
291 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
292
293 <sect1 id="syntax-extns">
294 <title>Syntactic extensions</title>
295
296 <sect2 id="unicode-syntax">
297 <title>Unicode syntax</title>
298 <para>The language
299 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
300 enables Unicode characters to be used to stand for certain ASCII
301 character sequences. The following alternatives are provided:</para>
302
303 <informaltable>
304 <tgroup cols="2" align="left" colsep="1" rowsep="1">
305 <thead>
306 <row>
307 <entry>ASCII</entry>
308 <entry>Unicode alternative</entry>
309 <entry>Code point</entry>
310 <entry>Name</entry>
311 </row>
312 </thead>
313
314 <!--
315 to find the DocBook entities for these characters, find
316 the Unicode code point (e.g. 0x2237), and grep for it in
317 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
318 your system. Some of these Unicode code points don't have
319 equivalent DocBook entities.
320 -->
321
322 <tbody>
323 <row>
324 <entry><literal>::</literal></entry>
325 <entry>::</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 <sect2 id="binary-literals">
484 <title>Binary integer literals</title>
485 <para>
486 Haskell 2010 and Haskell 98 allows for integer literals to
487 be given in decimal, octal (prefixed by
488 <literal>0o</literal> or <literal>0O</literal>), or
489 hexadecimal notation (prefixed by <literal>0x</literal> or
490 <literal>0X</literal>).
491 </para>
492
493 <para>
494 The language extension <option>-XBinaryLiterals</option>
495 adds support for expressing integer literals in binary
496 notation with the prefix <literal>0b</literal> or
497 <literal>0B</literal>. For instance, the binary integer
498 literal <literal>0b11001001</literal> will be desugared into
499 <literal>fromInteger 201</literal> when
500 <option>-XBinaryLiterals</option> is enabled.
501 </para>
502 </sect2>
503
504 <!-- ====================== HIERARCHICAL MODULES ======================= -->
505
506
507 <sect2 id="hierarchical-modules">
508 <title>Hierarchical Modules</title>
509
510 <para>GHC supports a small extension to the syntax of module
511 names: a module name is allowed to contain a dot
512 <literal>&lsquo;.&rsquo;</literal>. This is also known as the
513 &ldquo;hierarchical module namespace&rdquo; extension, because
514 it extends the normally flat Haskell module namespace into a
515 more flexible hierarchy of modules.</para>
516
517 <para>This extension has very little impact on the language
518 itself; modules names are <emphasis>always</emphasis> fully
519 qualified, so you can just think of the fully qualified module
520 name as <quote>the module name</quote>. In particular, this
521 means that the full module name must be given after the
522 <literal>module</literal> keyword at the beginning of the
523 module; for example, the module <literal>A.B.C</literal> must
524 begin</para>
525
526 <programlisting>module A.B.C</programlisting>
527
528
529 <para>It is a common strategy to use the <literal>as</literal>
530 keyword to save some typing when using qualified names with
531 hierarchical modules. For example:</para>
532
533 <programlisting>
534 import qualified Control.Monad.ST.Strict as ST
535 </programlisting>
536
537 <para>For details on how GHC searches for source and interface
538 files in the presence of hierarchical modules, see <xref
539 linkend="search-path"/>.</para>
540
541 <para>GHC comes with a large collection of libraries arranged
542 hierarchically; see the accompanying <ulink
543 url="../libraries/index.html">library
544 documentation</ulink>. More libraries to install are available
545 from <ulink
546 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
547 </sect2>
548
549 <!-- ====================== PATTERN GUARDS ======================= -->
550
551 <sect2 id="pattern-guards">
552 <title>Pattern guards</title>
553
554 <para>
555 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
556 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
557 </para>
558
559 <para>
560 Suppose we have an abstract data type of finite maps, with a
561 lookup operation:
562
563 <programlisting>
564 lookup :: FiniteMap -> Int -> Maybe Int
565 </programlisting>
566
567 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
568 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
569 </para>
570
571 <programlisting>
572 clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
573 | otherwise = var1 + var2
574 where
575 m1 = lookup env var1
576 m2 = lookup env var2
577 ok1 = maybeToBool m1
578 ok2 = maybeToBool m2
579 val1 = expectJust m1
580 val2 = expectJust m2
581 </programlisting>
582
583 <para>
584 The auxiliary functions are
585 </para>
586
587 <programlisting>
588 maybeToBool :: Maybe a -&gt; Bool
589 maybeToBool (Just x) = True
590 maybeToBool Nothing = False
591
592 expectJust :: Maybe a -&gt; a
593 expectJust (Just x) = x
594 expectJust Nothing = error "Unexpected Nothing"
595 </programlisting>
596
597 <para>
598 What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
599 ok2</literal> checks that both lookups succeed, using
600 <function>maybeToBool</function> to convert the <function>Maybe</function>
601 types to booleans. The (lazily evaluated) <function>expectJust</function>
602 calls extract the values from the results of the lookups, and binds the
603 returned values to <varname>val1</varname> and <varname>val2</varname>
604 respectively. If either lookup fails, then clunky takes the
605 <literal>otherwise</literal> case and returns the sum of its arguments.
606 </para>
607
608 <para>
609 This is certainly legal Haskell, but it is a tremendously verbose and
610 un-obvious way to achieve the desired effect. Arguably, a more direct way
611 to write clunky would be to use case expressions:
612 </para>
613
614 <programlisting>
615 clunky env var1 var2 = case lookup env var1 of
616 Nothing -&gt; fail
617 Just val1 -&gt; case lookup env var2 of
618 Nothing -&gt; fail
619 Just val2 -&gt; val1 + val2
620 where
621 fail = var1 + var2
622 </programlisting>
623
624 <para>
625 This is a bit shorter, but hardly better. Of course, we can rewrite any set
626 of pattern-matching, guarded equations as case expressions; that is
627 precisely what the compiler does when compiling equations! The reason that
628 Haskell provides guarded equations is because they allow us to write down
629 the cases we want to consider, one at a time, independently of each other.
630 This structure is hidden in the case version. Two of the right-hand sides
631 are really the same (<function>fail</function>), and the whole expression
632 tends to become more and more indented.
633 </para>
634
635 <para>
636 Here is how I would write clunky:
637 </para>
638
639 <programlisting>
640 clunky env var1 var2
641 | Just val1 &lt;- lookup env var1
642 , Just val2 &lt;- lookup env var2
643 = val1 + val2
644 ...other equations for clunky...
645 </programlisting>
646
647 <para>
648 The semantics should be clear enough. The qualifiers are matched in order.
649 For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
650 right hand side is evaluated and matched against the pattern on the left.
651 If the match fails then the whole guard fails and the next equation is
652 tried. If it succeeds, then the appropriate binding takes place, and the
653 next qualifier is matched, in the augmented environment. Unlike list
654 comprehensions, however, the type of the expression to the right of the
655 <literal>&lt;-</literal> is the same as the type of the pattern to its
656 left. The bindings introduced by pattern guards scope over all the
657 remaining guard qualifiers, and over the right hand side of the equation.
658 </para>
659
660 <para>
661 Just as with list comprehensions, boolean expressions can be freely mixed
662 with among the pattern guards. For example:
663 </para>
664
665 <programlisting>
666 f x | [y] &lt;- x
667 , y > 3
668 , Just z &lt;- h y
669 = ...
670 </programlisting>
671
672 <para>
673 Haskell's current guards therefore emerge as a special case, in which the
674 qualifier list has just one element, a boolean expression.
675 </para>
676 </sect2>
677
678 <!-- ===================== View patterns =================== -->
679
680 <sect2 id="view-patterns">
681 <title>View patterns
682 </title>
683
684 <para>
685 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
686 More information and examples of view patterns can be found on the
687 <ulink url="http://ghc.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
688 page</ulink>.
689 </para>
690
691 <para>
692 View patterns are somewhat like pattern guards that can be nested inside
693 of other patterns. They are a convenient way of pattern-matching
694 against values of abstract types. For example, in a programming language
695 implementation, we might represent the syntax of the types of the
696 language as follows:
697
698 <programlisting>
699 type Typ
700
701 data TypView = Unit
702 | Arrow Typ Typ
703
704 view :: Typ -> TypView
705
706 -- additional operations for constructing Typ's ...
707 </programlisting>
708
709 The representation of Typ is held abstract, permitting implementations
710 to use a fancy representation (e.g., hash-consing to manage sharing).
711
712 Without view patterns, using this signature a little inconvenient:
713 <programlisting>
714 size :: Typ -> Integer
715 size t = case view t of
716 Unit -> 1
717 Arrow t1 t2 -> size t1 + size t2
718 </programlisting>
719
720 It is necessary to iterate the case, rather than using an equational
721 function definition. And the situation is even worse when the matching
722 against <literal>t</literal> is buried deep inside another pattern.
723 </para>
724
725 <para>
726 View patterns permit calling the view function inside the pattern and
727 matching against the result:
728 <programlisting>
729 size (view -> Unit) = 1
730 size (view -> Arrow t1 t2) = size t1 + size t2
731 </programlisting>
732
733 That is, we add a new form of pattern, written
734 <replaceable>expression</replaceable> <literal>-></literal>
735 <replaceable>pattern</replaceable> that means "apply the expression to
736 whatever we're trying to match against, and then match the result of
737 that application against the pattern". The expression can be any Haskell
738 expression of function type, and view patterns can be used wherever
739 patterns are used.
740 </para>
741
742 <para>
743 The semantics of a pattern <literal>(</literal>
744 <replaceable>exp</replaceable> <literal>-></literal>
745 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
746
747 <itemizedlist>
748
749 <listitem> Scoping:
750
751 <para>The variables bound by the view pattern are the variables bound by
752 <replaceable>pat</replaceable>.
753 </para>
754
755 <para>
756 Any variables in <replaceable>exp</replaceable> are bound occurrences,
757 but variables bound "to the left" in a pattern are in scope. This
758 feature permits, for example, one argument to a function to be used in
759 the view of another argument. For example, the function
760 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
761 written using view patterns as follows:
762
763 <programlisting>
764 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
765 ...other equations for clunky...
766 </programlisting>
767 </para>
768
769 <para>
770 More precisely, the scoping rules are:
771 <itemizedlist>
772 <listitem>
773 <para>
774 In a single pattern, variables bound by patterns to the left of a view
775 pattern expression are in scope. For example:
776 <programlisting>
777 example :: Maybe ((String -> Integer,Integer), String) -> Bool
778 example Just ((f,_), f -> 4) = True
779 </programlisting>
780
781 Additionally, in function definitions, variables bound by matching earlier curried
782 arguments may be used in view pattern expressions in later arguments:
783 <programlisting>
784 example :: (String -> Integer) -> String -> Bool
785 example f (f -> 4) = True
786 </programlisting>
787 That is, the scoping is the same as it would be if the curried arguments
788 were collected into a tuple.
789 </para>
790 </listitem>
791
792 <listitem>
793 <para>
794 In mutually recursive bindings, such as <literal>let</literal>,
795 <literal>where</literal>, or the top level, view patterns in one
796 declaration may not mention variables bound by other declarations. That
797 is, each declaration must be self-contained. For example, the following
798 program is not allowed:
799 <programlisting>
800 let {(x -> y) = e1 ;
801 (y -> x) = e2 } in x
802 </programlisting>
803
804 (For some amplification on this design choice see
805 <ulink url="http://ghc.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
806
807 </para>
808 </listitem>
809 </itemizedlist>
810
811 </para>
812 </listitem>
813
814 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
815 <replaceable>T1</replaceable> <literal>-></literal>
816 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
817 a <replaceable>T2</replaceable>, then the whole view pattern matches a
818 <replaceable>T1</replaceable>.
819 </para></listitem>
820
821 <listitem><para> Matching: To the equations in Section 3.17.3 of the
822 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
823 Report</ulink>, add the following:
824 <programlisting>
825 case v of { (e -> p) -> e1 ; _ -> e2 }
826 =
827 case (e v) of { p -> e1 ; _ -> e2 }
828 </programlisting>
829 That is, to match a variable <replaceable>v</replaceable> against a pattern
830 <literal>(</literal> <replaceable>exp</replaceable>
831 <literal>-></literal> <replaceable>pat</replaceable>
832 <literal>)</literal>, evaluate <literal>(</literal>
833 <replaceable>exp</replaceable> <replaceable> v</replaceable>
834 <literal>)</literal> and match the result against
835 <replaceable>pat</replaceable>.
836 </para></listitem>
837
838 <listitem><para> Efficiency: When the same view function is applied in
839 multiple branches of a function definition or a case expression (e.g.,
840 in <literal>size</literal> above), GHC makes an attempt to collect these
841 applications into a single nested case expression, so that the view
842 function is only applied once. Pattern compilation in GHC follows the
843 matrix algorithm described in Chapter 4 of <ulink
844 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
845 Implementation of Functional Programming Languages</ulink>. When the
846 top rows of the first column of a matrix are all view patterns with the
847 "same" expression, these patterns are transformed into a single nested
848 case. This includes, for example, adjacent view patterns that line up
849 in a tuple, as in
850 <programlisting>
851 f ((view -> A, p1), p2) = e1
852 f ((view -> B, p3), p4) = e2
853 </programlisting>
854 </para>
855
856 <para> The current notion of when two view pattern expressions are "the
857 same" is very restricted: it is not even full syntactic equality.
858 However, it does include variables, literals, applications, and tuples;
859 e.g., two instances of <literal>view ("hi", "there")</literal> will be
860 collected. However, the current implementation does not compare up to
861 alpha-equivalence, so two instances of <literal>(x, view x ->
862 y)</literal> will not be coalesced.
863 </para>
864
865 </listitem>
866
867 </itemizedlist>
868 </para>
869
870 </sect2>
871
872 <!-- ===================== Pattern synonyms =================== -->
873
874 <sect2 id="pattern-synonyms">
875 <title>Pattern synonyms
876 </title>
877
878 <para>
879 Pattern synonyms are enabled by the flag
880 <literal>-XPatternSynonyms</literal>, which is required for defining
881 them, but <emphasis>not</emphasis> for using them. More information
882 and examples of view patterns can be found on the <ulink
883 url="http://ghc.haskell.org/trac/ghc/wiki/PatternSynonyms">Wiki
884 page</ulink>.
885 </para>
886
887 <para>
888 Pattern synonyms enable giving names to parametrized pattern
889 schemes. They can also be thought of as abstract constructors that
890 don't have a bearing on data representation. For example, in a
891 programming language implementation, we might represent types of the
892 language as follows:
893 </para>
894
895 <programlisting>
896 data Type = App String [Type]
897 </programlisting>
898
899 <para>
900 Here are some examples of using said representation.
901 Consider a few types of the <literal>Type</literal> universe encoded
902 like this:
903 </para>
904
905 <programlisting>
906 App "->" [t1, t2] -- t1 -> t2
907 App "Int" [] -- Int
908 App "Maybe" [App "Int" []] -- Maybe Int
909 </programlisting>
910
911 <para>
912 This representation is very generic in that no types are given special
913 treatment. However, some functions might need to handle some known
914 types specially, for example the following two functions collect all
915 argument types of (nested) arrow types, and recognize the
916 <literal>Int</literal> type, respectively:
917 </para>
918
919 <programlisting>
920 collectArgs :: Type -> [Type]
921 collectArgs (App "->" [t1, t2]) = t1 : collectArgs t2
922 collectArgs _ = []
923
924 isInt :: Type -> Bool
925 isInt (App "Int" []) = True
926 isInt _ = False
927 </programlisting>
928
929 <para>
930 Matching on <literal>App</literal> directly is both hard to read and
931 error prone to write. And the situation is even worse when the
932 matching is nested:
933 </para>
934
935 <programlisting>
936 isIntEndo :: Type -> Bool
937 isIntEndo (App "->" [App "Int" [], App "Int" []]) = True
938 isIntEndo _ = False
939 </programlisting>
940
941 <para>
942 Pattern synonyms permit abstracting from the representation to expose
943 matchers that behave in a constructor-like manner with respect to
944 pattern matching. We can create pattern synonyms for the known types
945 we care about, without committing the representation to them (note
946 that these don't have to be defined in the same module as the
947 <literal>Type</literal> type):
948 </para>
949
950 <programlisting>
951 pattern Arrow t1 t2 = App "->" [t1, t2]
952 pattern Int = App "Int" []
953 pattern Maybe t = App "Maybe" [t]
954 </programlisting>
955
956 <para>
957 Which enables us to rewrite our functions in a much cleaner style:
958 </para>
959
960 <programlisting>
961 collectArgs :: Type -> [Type]
962 collectArgs (Arrow t1 t2) = t1 : collectArgs t2
963 collectArgs _ = []
964
965 isInt :: Type -> Bool
966 isInt Int = True
967 isInt _ = False
968
969 isIntEndo :: Type -> Bool
970 isIntEndo (Arrow Int Int) = True
971 isIntEndo _ = False
972 </programlisting>
973
974 <para>
975 Note that in this example, the pattern synonyms
976 <literal>Int</literal> and <literal>Arrow</literal> can also be used
977 as expressions (they are <emphasis>bidirectional</emphasis>). This
978 is not necessarily the case: <emphasis>unidirectional</emphasis>
979 pattern synonyms can also be declared with the following syntax:
980 </para>
981
982 <programlisting>
983 pattern Head x &lt;- x:xs
984 </programlisting>
985
986 <para>
987 In this case, <literal>Head</literal> <replaceable>x</replaceable>
988 cannot be used in expressions, only patterns, since it wouldn't
989 specify a value for the <replaceable>xs</replaceable> on the
990 right-hand side. We can give an explicit inversion of a pattern
991 synonym using the following syntax:
992 </para>
993
994 <programlisting>
995 pattern Head x &lt;- x:xs where
996 Head x = [x]
997 </programlisting>
998
999 <para>
1000 The syntax and semantics of pattern synonyms are elaborated in the
1001 following subsections.
1002 See the <ulink
1003 url="http://ghc.haskell.org/trac/ghc/wiki/PatternSynonyms">Wiki
1004 page</ulink> for more details.
1005 </para>
1006
1007 <sect3> <title>Syntax and scoping of pattern synonyms</title>
1008 <para>
1009 A pattern synonym declaration can be either unidirectional or
1010 bidirectional. The syntax for unidirectional pattern synonyms is:
1011 <programlisting>
1012 pattern Name args &lt;- pat
1013 </programlisting>
1014 and the syntax for bidirectional pattern synonyms is:
1015 <programlisting>
1016 pattern Name args = pat
1017 </programlisting> or
1018 <programlisting>
1019 pattern Name args &lt;- pat where
1020 Name args = expr
1021 </programlisting>
1022 Either prefix or infix syntax can be
1023 used.
1024 </para>
1025 <para>
1026 Pattern synonym declarations can only occur in the top level of a
1027 module. In particular, they are not allowed as local
1028 definitions.
1029 </para>
1030 <para>
1031 The variables in the left-hand side of the definition are bound by
1032 the pattern on the right-hand side. For implicitly bidirectional
1033 pattern synonyms, all the variables of the right-hand side must also
1034 occur on the left-hand side; also, wildcard patterns and view
1035 patterns are not allowed. For unidirectional and
1036 explicitly-bidirectional pattern synonyms, there is no restriction
1037 on the right-hand side pattern.
1038 </para>
1039
1040 <para>
1041 Pattern synonyms cannot be defined recursively.
1042 </para>
1043 </sect3>
1044
1045 <sect3 id="patsyn-impexp"> <title>Import and export of pattern synonyms</title>
1046
1047 <para>
1048 The name of the pattern synonym itself is in the same namespace as
1049 proper data constructors. In an export or import specification,
1050 you must prefix pattern
1051 names with the <literal>pattern</literal> keyword, e.g.:
1052 <programlisting>
1053 module Example (pattern Single) where
1054 pattern Single x = [x]
1055 </programlisting>
1056 Without the <literal>pattern</literal> prefix, <literal>Single</literal> would
1057 be interpreted as a type constructor in the export list.
1058 </para>
1059 <para>
1060 You may also use the <literal>pattern</literal> keyword in an import/export
1061 specification to import or export an ordinary data constructor. For example:
1062 <programlisting>
1063 import Data.Maybe( pattern Just )
1064 </programlisting>
1065 would bring into scope the data constructor <literal>Just</literal> from the
1066 <literal>Maybe</literal> type, without also bringing the type constructor
1067 <literal>Maybe</literal> into scope.
1068 </para>
1069 </sect3>
1070
1071 <sect3> <title>Typing of pattern synonyms</title>
1072
1073 <para>
1074 Given a pattern synonym definition of the form
1075 <programlisting>
1076 pattern P var1 var2 ... varN &lt;- pat
1077 </programlisting>
1078 it is assigned a <emphasis>pattern type</emphasis> of the form
1079 <programlisting>
1080 pattern P :: CProv => CReq => t1 -> t2 -> ... -> tN -> t
1081 </programlisting>
1082 where <replaceable>CProv</replaceable> and
1083 <replaceable>CReq</replaceable> are type contexts, and
1084 <replaceable>t1</replaceable>, <replaceable>t2</replaceable>, ...,
1085 <replaceable>tN</replaceable> and <replaceable>t</replaceable> are
1086 types.
1087 Notice the unusual form of the type, with two contexts <replaceable>CProv</replaceable> and <replaceable>CReq</replaceable>:
1088 <itemizedlist>
1089 <listitem><para><replaceable>CReq</replaceable> are the constraints <emphasis>required</emphasis> to match the pattern.</para></listitem>
1090 <listitem><para><replaceable>CProv</replaceable> are the constraints <emphasis>made available (provided)</emphasis>
1091 by a successful pattern match.</para></listitem>
1092 </itemizedlist>
1093 For example, consider
1094 <programlisting>
1095 data T a where
1096 MkT :: (Show b) => a -> b -> T a
1097
1098 f1 :: (Eq a, Num a) => MkT a -> String
1099 f1 (MkT 42 x) = show x
1100
1101 pattern ExNumPat :: (Show b) => (Num a, Eq a) => b -> T a
1102 pattern ExNumPat x = MkT 42 x
1103
1104 f2 :: (Eq a, Num a) => MkT a -> String
1105 f2 (ExNumPat x) = show x
1106 </programlisting>
1107 Here <literal>f1</literal> does not use pattern synonyms. To match against the
1108 numeric pattern <literal>42</literal> <emphasis>requires</emphasis> the caller to
1109 satisfy the constraints <literal>(Num a, Eq a)</literal>,
1110 so they appear in <literal>f1</literal>'s type. The call to <literal>show</literal> generates a <literal>(Show b)</literal>
1111 constraint, where <literal>b</literal> is an existentially type variable bound by the pattern match
1112 on <literal>MkT</literal>. But the same pattern match also <emphasis>provides</emphasis> the constraint
1113 <literal>(Show b)</literal> (see <literal>MkT</literal>'s type), and so all is well.
1114 </para>
1115 <para>
1116 Exactly the same reasoning applies to <literal>ExNumPat</literal>:
1117 matching against <literal>ExNumPat</literal> <emphasis>requires</emphasis>
1118 the constraints <literal>(Num a, Eq a)</literal>, and <emphasis>provides</emphasis>
1119 the constraint <literal>(Show b)</literal>.
1120 </para>
1121 <para>
1122 Note also the following points
1123 <itemizedlist>
1124 <listitem><para>
1125 In the common case where <replaceable>CReq</replaceable> is empty,
1126 <literal>()</literal>, it can be omitted altogether.
1127 </para> </listitem>
1128
1129 <listitem><para>
1130 You may specify an explicit <emphasis>pattern signature</emphasis>, as
1131 we did for <literal>ExNumPat</literal> above, to specify the type of a pattern,
1132 just as you can for a function. As usual, the type signature can be less polymorphic
1133 than the inferred type. For example
1134 <programlisting>
1135 -- Inferred type would be 'a -> [a]'
1136 pattern SinglePair :: (a, a) -> [(a, a)]
1137 pattern SinglePair x = [x]
1138 </programlisting>
1139 </para> </listitem>
1140
1141 <listitem><para>
1142 The GHCi <literal>:info</literal> command shows pattern types in this format.
1143 </para> </listitem>
1144
1145 <listitem><para>
1146 For a bidirectional pattern synonym, a use of the pattern synonym as an expression has the type
1147 <programlisting>
1148 (CProv, CReq) => t1 -> t2 -> ... -> tN -> t
1149 </programlisting>
1150 So in the previous example, when used in an expression, <literal>ExNumPat</literal> has type
1151 <programlisting>
1152 ExNumPat :: (Show b, Num a, Eq a) => b -> T t
1153 </programlisting>
1154 Notice that this is a tiny bit more restrictive than the expression <literal>MkT 42 x</literal>
1155 which would not require <literal>(Eq a)</literal>.
1156 </para> </listitem>
1157
1158 <listitem><para>
1159 Consider these two pattern synonyms:
1160 <programlisting>
1161 data S a where
1162 S1 :: Bool -> S Bool
1163
1164 pattern P1 b = Just b -- P1 :: Bool -> Maybe Bool
1165 pattern P2 b = S1 b -- P2 :: (b~Bool) => Bool -> S b
1166
1167 f :: Maybe a -> String
1168 f (P1 x) = "no no no" -- Type-incorrect
1169
1170 g :: S a -> String
1171 g (P2 b) = "yes yes yes" -- Fine
1172 </programlisting>
1173 Pattern <literal>P1</literal> can only match against a value of type <literal>Maybe Bool</literal>,
1174 so function <literal>f</literal> is rejected because the type signature is <literal>Maybe a</literal>.
1175 (To see this, imagine expanding the pattern synonym.)
1176 </para>
1177 <para>
1178 On the other hand, function <literal>g</literal> works fine, becuase matching against <literal>P2</literal>
1179 (which wraps the GADT <literal>S</literal>) provides the local equality <literal>(a~Bool)</literal>.
1180 If you were to give an explicit pattern signature <literal>P2 :: Bool -> S Bool</literal>, then <literal>P2</literal>
1181 would become less polymorphic, and would behave exactly like <literal>P1</literal> so that <literal>g</literal>
1182 would then be rejected.
1183 </para>
1184 <para>
1185 In short, if you want GADT-like behaviour for pattern synonyms,
1186 then (unlike unlike concrete data constructors like <literal>S1</literal>)
1187 you must write its type with explicit provided equalities.
1188 For a concrete data construoctr like <literal>S1</literal> you can write
1189 its type signature as eigher <literal>S1 :: Bool -> S Bool</literal> or
1190 <literal>S1 :: (b~Bool) => Bool -> S b</literal>; the two are equivalent.
1191 Not so for pattern synonyms: the two forms are different, in order to
1192 distinguish the two cases above. (See <ulink url="https://ghc.haskell.org/trac/ghc/ticket/9953">Trac #9953</ulink> for
1193 discussion of this choice.)
1194 </para></listitem>
1195 </itemizedlist>
1196 </para>
1197 </sect3>
1198
1199 <sect3><title>Matching of pattern synonyms</title>
1200
1201 <para>
1202 A pattern synonym occurrence in a pattern is evaluated by first
1203 matching against the pattern synonym itself, and then on the argument
1204 patterns. For example, in the following program, <literal>f</literal>
1205 and <literal>f'</literal> are equivalent:
1206 </para>
1207
1208 <programlisting>
1209 pattern Pair x y &lt;- [x, y]
1210
1211 f (Pair True True) = True
1212 f _ = False
1213
1214 f' [x, y] | True &lt;- x, True &lt;- y = True
1215 f' _ = False
1216 </programlisting>
1217
1218 <para>
1219 Note that the strictness of <literal>f</literal> differs from that
1220 of <literal>g</literal> defined below:
1221 <programlisting>
1222 g [True, True] = True
1223 g _ = False
1224
1225 *Main> f (False:undefined)
1226 *** Exception: Prelude.undefined
1227 *Main> g (False:undefined)
1228 False
1229 </programlisting>
1230 </para>
1231 </sect3>
1232
1233 </sect2>
1234
1235 <!-- ===================== n+k patterns =================== -->
1236
1237 <sect2 id="n-k-patterns">
1238 <title>n+k patterns</title>
1239 <indexterm><primary><option>-XNPlusKPatterns</option></primary></indexterm>
1240
1241 <para>
1242 <literal>n+k</literal> pattern support is disabled by default. To enable
1243 it, you can use the <option>-XNPlusKPatterns</option> flag.
1244 </para>
1245
1246 </sect2>
1247
1248 <!-- ===================== Traditional record syntax =================== -->
1249
1250 <sect2 id="traditional-record-syntax">
1251 <title>Traditional record syntax</title>
1252 <indexterm><primary><option>-XNoTraditionalRecordSyntax</option></primary></indexterm>
1253
1254 <para>
1255 Traditional record syntax, such as <literal>C {f = x}</literal>, is enabled by default.
1256 To disable it, you can use the <option>-XNoTraditionalRecordSyntax</option> flag.
1257 </para>
1258
1259 </sect2>
1260
1261 <!-- ===================== Recursive do-notation =================== -->
1262
1263 <sect2 id="recursive-do-notation">
1264 <title>The recursive do-notation
1265 </title>
1266
1267 <para>
1268 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
1269 that is, the variables bound in a do-expression are visible only in the textually following
1270 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
1271 group.
1272 </para>
1273
1274 <para>
1275 It turns out that such recursive bindings do indeed make sense for a variety of monads, but
1276 not all. In particular, recursion in this sense requires a fixed-point operator for the underlying
1277 monad, captured by the <literal>mfix</literal> method of the <literal>MonadFix</literal> class, defined in <literal>Control.Monad.Fix</literal> as follows:
1278 <programlisting>
1279 class Monad m => MonadFix m where
1280 mfix :: (a -> m a) -> m a
1281 </programlisting>
1282 Haskell's
1283 <literal>Maybe</literal>, <literal>[]</literal> (list), <literal>ST</literal> (both strict and lazy versions),
1284 <literal>IO</literal>, and many other monads have <literal>MonadFix</literal> instances. On the negative
1285 side, the continuation monad, with the signature <literal>(a -> r) -> r</literal>, does not.
1286 </para>
1287
1288 <para>
1289 For monads that do belong to the <literal>MonadFix</literal> class, GHC provides
1290 an extended version of the do-notation that allows recursive bindings.
1291 The <option>-XRecursiveDo</option> (language pragma: <literal>RecursiveDo</literal>)
1292 provides the necessary syntactic support, introducing the keywords <literal>mdo</literal> and
1293 <literal>rec</literal> for higher and lower levels of the notation respectively. Unlike
1294 bindings in a <literal>do</literal> expression, those introduced by <literal>mdo</literal> and <literal>rec</literal>
1295 are recursively defined, much like in an ordinary let-expression. Due to the new
1296 keyword <literal>mdo</literal>, we also call this notation the <emphasis>mdo-notation</emphasis>.
1297 </para>
1298
1299 <para>
1300 Here is a simple (albeit contrived) example:
1301 <programlisting>
1302 {-# LANGUAGE RecursiveDo #-}
1303 justOnes = mdo { xs &lt;- Just (1:xs)
1304 ; return (map negate xs) }
1305 </programlisting>
1306 or equivalently
1307 <programlisting>
1308 {-# LANGUAGE RecursiveDo #-}
1309 justOnes = do { rec { xs &lt;- Just (1:xs) }
1310 ; return (map negate xs) }
1311 </programlisting>
1312 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
1313 </para>
1314
1315 <para>
1316 GHC's implementation the mdo-notation closely follows the original translation as described in the paper
1317 <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for Haskell</ulink>, which
1318 in turn is based on the work <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion
1319 in Monadic Computations</ulink>. Furthermore, GHC extends the syntax described in the former paper
1320 with a lower level syntax flagged by the <literal>rec</literal> keyword, as we describe next.
1321 </para>
1322
1323 <sect3>
1324 <title>Recursive binding groups</title>
1325
1326 <para>
1327 The flag <option>-XRecursiveDo</option> also introduces a new keyword <literal>rec</literal>, which wraps a
1328 mutually-recursive group of monadic statements inside a <literal>do</literal> expression, producing a single statement.
1329 Similar to a <literal>let</literal> statement inside a <literal>do</literal>, variables bound in
1330 the <literal>rec</literal> are visible throughout the <literal>rec</literal> group, and below it. For example, compare
1331 <programlisting>
1332 do { a &lt;- getChar do { a &lt;- getChar
1333 ; let { r1 = f a r2 ; rec { r1 &lt;- f a r2
1334 ; ; r2 = g r1 } ; ; r2 &lt;- g r1 }
1335 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
1336 </programlisting>
1337 In both cases, <literal>r1</literal> and <literal>r2</literal> are available both throughout
1338 the <literal>let</literal> or <literal>rec</literal> block, and in the statements that follow it.
1339 The difference is that <literal>let</literal> is non-monadic, while <literal>rec</literal> is monadic.
1340 (In Haskell <literal>let</literal> is really <literal>letrec</literal>, of course.)
1341 </para>
1342
1343 <para>
1344 The semantics of <literal>rec</literal> is fairly straightforward. Whenever GHC finds a <literal>rec</literal>
1345 group, it will compute its set of bound variables, and will introduce an appropriate call
1346 to the underlying monadic value-recursion operator <literal>mfix</literal>, belonging to the
1347 <literal>MonadFix</literal> class. Here is an example:
1348 <programlisting>
1349 rec { b &lt;- f a c ===> (b,c) &lt;- mfix (\ ~(b,c) -> do { b &lt;- f a c
1350 ; c &lt;- f b a } ; c &lt;- f b a
1351 ; return (b,c) })
1352 </programlisting>
1353 As usual, the meta-variables <literal>b</literal>, <literal>c</literal> etc., can be arbitrary patterns.
1354 In general, the statement <literal>rec <replaceable>ss</replaceable></literal> is desugared to the statement
1355 <programlisting>
1356 <replaceable>vs</replaceable> &lt;- mfix (\ ~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
1357 </programlisting>
1358 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
1359 </para>
1360
1361 <para>
1362 Note in particular that the translation for a <literal>rec</literal> block only involves wrapping a call
1363 to <literal>mfix</literal>: it performs no other analysis on the bindings. The latter is the task
1364 for the <literal>mdo</literal> notation, which is described next.
1365 </para>
1366 </sect3>
1367
1368 <sect3>
1369 <title>The <literal>mdo</literal> notation</title>
1370
1371 <para>
1372 A <literal>rec</literal>-block tells the compiler where precisely the recursive knot should be tied. It turns out that
1373 the placement of the recursive knots can be rather delicate: in particular, we would like the knots to be wrapped
1374 around as minimal groups as possible. This process is known as <emphasis>segmentation</emphasis>, and is described
1375 in detail in Secton 3.2 of <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for
1376 Haskell</ulink>. Segmentation improves polymorphism and reduces the size of the recursive knot. Most importantly, it avoids
1377 unnecessary interference caused by a fundamental issue with the so-called <emphasis>right-shrinking</emphasis>
1378 axiom for monadic recursion. In brief, most monads of interest (IO, strict state, etc.) do <emphasis>not</emphasis>
1379 have recursion operators that satisfy this axiom, and thus not performing segmentation can cause unnecessary
1380 interference, changing the termination behavior of the resulting translation.
1381 (Details can be found in Sections 3.1 and 7.2.2 of
1382 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.)
1383 </para>
1384
1385 <para>
1386 The <literal>mdo</literal> notation removes the burden of placing
1387 explicit <literal>rec</literal> blocks in the code. Unlike an
1388 ordinary <literal>do</literal> expression, in which variables bound by
1389 statements are only in scope for later statements, variables bound in
1390 an <literal>mdo</literal> expression are in scope for all statements
1391 of the expression. The compiler then automatically identifies minimal
1392 mutually recursively dependent segments of statements, treating them as
1393 if the user had wrapped a <literal>rec</literal> qualifier around them.
1394 </para>
1395
1396 <para>
1397 The definition is syntactic:
1398 </para>
1399 <itemizedlist>
1400 <listitem>
1401 <para>
1402 A generator <replaceable>g</replaceable>
1403 <emphasis>depends</emphasis> on a textually following generator
1404 <replaceable>g'</replaceable>, if
1405 </para>
1406 <itemizedlist>
1407 <listitem>
1408 <para>
1409 <replaceable>g'</replaceable> defines a variable that
1410 is used by <replaceable>g</replaceable>, or
1411 </para>
1412 </listitem>
1413 <listitem>
1414 <para>
1415 <replaceable>g'</replaceable> textually appears between
1416 <replaceable>g</replaceable> and
1417 <replaceable>g''</replaceable>, where <replaceable>g</replaceable>
1418 depends on <replaceable>g''</replaceable>.
1419 </para>
1420 </listitem>
1421 </itemizedlist>
1422 </listitem>
1423 <listitem>
1424 <para>
1425 A <emphasis>segment</emphasis> of a given
1426 <literal>mdo</literal>-expression is a minimal sequence of generators
1427 such that no generator of the sequence depends on an outside
1428 generator. As a special case, although it is not a generator,
1429 the final expression in an <literal>mdo</literal>-expression is
1430 considered to form a segment by itself.
1431 </para>
1432 </listitem>
1433 </itemizedlist>
1434 <para>
1435 Segments in this sense are
1436 related to <emphasis>strongly-connected components</emphasis> analysis,
1437 with the exception that bindings in a segment cannot be reordered and
1438 must be contiguous.
1439 </para>
1440
1441 <para>
1442 Here is an example <literal>mdo</literal>-expression, and its translation to <literal>rec</literal> blocks:
1443 <programlisting>
1444 mdo { a &lt;- getChar ===> do { a &lt;- getChar
1445 ; b &lt;- f a c ; rec { b &lt;- f a c
1446 ; c &lt;- f b a ; ; c &lt;- f b a }
1447 ; z &lt;- h a b ; z &lt;- h a b
1448 ; d &lt;- g d e ; rec { d &lt;- g d e
1449 ; e &lt;- g a z ; ; e &lt;- g a z }
1450 ; putChar c } ; putChar c }
1451 </programlisting>
1452 Note that a given <literal>mdo</literal> expression can cause the creation of multiple <literal>rec</literal> blocks.
1453 If there are no recursive dependencies, <literal>mdo</literal> will introduce no <literal>rec</literal> blocks. In this
1454 latter case an <literal>mdo</literal> expression is precisely the same as a <literal>do</literal> expression, as one
1455 would expect.
1456 </para>
1457
1458 <para>
1459 In summary, given an <literal>mdo</literal> expression, GHC first performs segmentation, introducing
1460 <literal>rec</literal> blocks to wrap over minimal recursive groups. Then, each resulting
1461 <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal> as described
1462 in the previous section. The original <literal>mdo</literal>-expression typechecks exactly when the desugared
1463 version would do so.
1464 </para>
1465
1466 <para>
1467 Here are some other important points in using the recursive-do notation:
1468
1469 <itemizedlist>
1470 <listitem>
1471 <para>
1472 It is enabled with the flag <literal>-XRecursiveDo</literal>, or the <literal>LANGUAGE RecursiveDo</literal>
1473 pragma. (The same flag enables both <literal>mdo</literal>-notation, and the use of <literal>rec</literal>
1474 blocks inside <literal>do</literal> expressions.)
1475 </para>
1476 </listitem>
1477 <listitem>
1478 <para>
1479 <literal>rec</literal> blocks can also be used inside <literal>mdo</literal>-expressions, which will be
1480 treated as a single statement. However, it is good style to either use <literal>mdo</literal> or
1481 <literal>rec</literal> blocks in a single expression.
1482 </para>
1483 </listitem>
1484 <listitem>
1485 <para>
1486 If recursive bindings are required for a monad, then that monad must be declared an instance of
1487 the <literal>MonadFix</literal> class.
1488 </para>
1489 </listitem>
1490 <listitem>
1491 <para>
1492 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1493 Furthermore, the <literal>Control.Monad.ST</literal> and <literal>Control.Monad.ST.Lazy</literal>
1494 modules provide the instances of the <literal>MonadFix</literal> class for Haskell's internal
1495 state monad (strict and lazy, respectively).
1496 </para>
1497 </listitem>
1498 <listitem>
1499 <para>
1500 Like <literal>let</literal> and <literal>where</literal> bindings, name shadowing is not allowed within
1501 an <literal>mdo</literal>-expression or a <literal>rec</literal>-block; that is, all the names bound in
1502 a single <literal>rec</literal> must be distinct. (GHC will complain if this is not the case.)
1503 </para>
1504 </listitem>
1505 </itemizedlist>
1506 </para>
1507 </sect3>
1508
1509
1510 </sect2>
1511
1512
1513 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1514
1515 <sect2 id="parallel-list-comprehensions">
1516 <title>Parallel List Comprehensions</title>
1517 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1518 </indexterm>
1519 <indexterm><primary>parallel list comprehensions</primary>
1520 </indexterm>
1521
1522 <para>Parallel list comprehensions are a natural extension to list
1523 comprehensions. List comprehensions can be thought of as a nice
1524 syntax for writing maps and filters. Parallel comprehensions
1525 extend this to include the zipWith family.</para>
1526
1527 <para>A parallel list comprehension has multiple independent
1528 branches of qualifier lists, each separated by a `|' symbol. For
1529 example, the following zips together two lists:</para>
1530
1531 <programlisting>
1532 [ (x, y) | x &lt;- xs | y &lt;- ys ]
1533 </programlisting>
1534
1535 <para>The behaviour of parallel list comprehensions follows that of
1536 zip, in that the resulting list will have the same length as the
1537 shortest branch.</para>
1538
1539 <para>We can define parallel list comprehensions by translation to
1540 regular comprehensions. Here's the basic idea:</para>
1541
1542 <para>Given a parallel comprehension of the form: </para>
1543
1544 <programlisting>
1545 [ e | p1 &lt;- e11, p2 &lt;- e12, ...
1546 | q1 &lt;- e21, q2 &lt;- e22, ...
1547 ...
1548 ]
1549 </programlisting>
1550
1551 <para>This will be translated to: </para>
1552
1553 <programlisting>
1554 [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
1555 [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
1556 ...
1557 ]
1558 </programlisting>
1559
1560 <para>where `zipN' is the appropriate zip for the given number of
1561 branches.</para>
1562
1563 </sect2>
1564
1565 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1566
1567 <sect2 id="generalised-list-comprehensions">
1568 <title>Generalised (SQL-Like) List Comprehensions</title>
1569 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1570 </indexterm>
1571 <indexterm><primary>extended list comprehensions</primary>
1572 </indexterm>
1573 <indexterm><primary>group</primary></indexterm>
1574 <indexterm><primary>sql</primary></indexterm>
1575
1576
1577 <para>Generalised list comprehensions are a further enhancement to the
1578 list comprehension syntactic sugar to allow operations such as sorting
1579 and grouping which are familiar from SQL. They are fully described in the
1580 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1581 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1582 except that the syntax we use differs slightly from the paper.</para>
1583 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1584 <para>Here is an example:
1585 <programlisting>
1586 employees = [ ("Simon", "MS", 80)
1587 , ("Erik", "MS", 100)
1588 , ("Phil", "Ed", 40)
1589 , ("Gordon", "Ed", 45)
1590 , ("Paul", "Yale", 60)]
1591
1592 output = [ (the dept, sum salary)
1593 | (name, dept, salary) &lt;- employees
1594 , then group by dept using groupWith
1595 , then sortWith by (sum salary)
1596 , then take 5 ]
1597 </programlisting>
1598 In this example, the list <literal>output</literal> would take on
1599 the value:
1600
1601 <programlisting>
1602 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1603 </programlisting>
1604 </para>
1605 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1606 (The functions <literal>sortWith</literal> and <literal>groupWith</literal> are not keywords; they are ordinary
1607 functions that are exported by <literal>GHC.Exts</literal>.)</para>
1608
1609 <para>There are five new forms of comprehension qualifier,
1610 all introduced by the (existing) keyword <literal>then</literal>:
1611 <itemizedlist>
1612 <listitem>
1613
1614 <programlisting>
1615 then f
1616 </programlisting>
1617
1618 This statement requires that <literal>f</literal> have the type <literal>
1619 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1620 motivating example, as this form is used to apply <literal>take 5</literal>.
1621
1622 </listitem>
1623
1624
1625 <listitem>
1626 <para>
1627 <programlisting>
1628 then f by e
1629 </programlisting>
1630
1631 This form is similar to the previous one, but allows you to create a function
1632 which will be passed as the first argument to f. As a consequence f must have
1633 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1634 from the type, this function lets f &quot;project out&quot; some information
1635 from the elements of the list it is transforming.</para>
1636
1637 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1638 is supplied with a function that lets it find out the <literal>sum salary</literal>
1639 for any item in the list comprehension it transforms.</para>
1640
1641 </listitem>
1642
1643
1644 <listitem>
1645
1646 <programlisting>
1647 then group by e using f
1648 </programlisting>
1649
1650 <para>This is the most general of the grouping-type statements. In this form,
1651 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1652 As with the <literal>then f by e</literal> case above, the first argument
1653 is a function supplied to f by the compiler which lets it compute e on every
1654 element of the list being transformed. However, unlike the non-grouping case,
1655 f additionally partitions the list into a number of sublists: this means that
1656 at every point after this statement, binders occurring before it in the comprehension
1657 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1658 this, let's look at an example:</para>
1659
1660 <programlisting>
1661 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1662 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1663 groupRuns f = groupBy (\x y -> f x == f y)
1664
1665 output = [ (the x, y)
1666 | x &lt;- ([1..3] ++ [1..2])
1667 , y &lt;- [4..6]
1668 , then group by x using groupRuns ]
1669 </programlisting>
1670
1671 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1672
1673 <programlisting>
1674 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1675 </programlisting>
1676
1677 <para>Note that we have used the <literal>the</literal> function to change the type
1678 of x from a list to its original numeric type. The variable y, in contrast, is left
1679 unchanged from the list form introduced by the grouping.</para>
1680
1681 </listitem>
1682
1683 <listitem>
1684
1685 <programlisting>
1686 then group using f
1687 </programlisting>
1688
1689 <para>With this form of the group statement, f is required to simply have the type
1690 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1691 comprehension so far directly. An example of this form is as follows:</para>
1692
1693 <programlisting>
1694 output = [ x
1695 | y &lt;- [1..5]
1696 , x &lt;- "hello"
1697 , then group using inits]
1698 </programlisting>
1699
1700 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1701
1702 <programlisting>
1703 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1704 </programlisting>
1705
1706 </listitem>
1707 </itemizedlist>
1708 </para>
1709 </sect2>
1710
1711 <!-- ===================== MONAD COMPREHENSIONS ===================== -->
1712
1713 <sect2 id="monad-comprehensions">
1714 <title>Monad comprehensions</title>
1715 <indexterm><primary>monad comprehensions</primary></indexterm>
1716
1717 <para>
1718 Monad comprehensions generalise the list comprehension notation,
1719 including parallel comprehensions
1720 (<xref linkend="parallel-list-comprehensions"/>) and
1721 transform comprehensions (<xref linkend="generalised-list-comprehensions"/>)
1722 to work for any monad.
1723 </para>
1724
1725 <para>Monad comprehensions support:</para>
1726
1727 <itemizedlist>
1728 <listitem>
1729 <para>
1730 Bindings:
1731 </para>
1732
1733 <programlisting>
1734 [ x + y | x &lt;- Just 1, y &lt;- Just 2 ]
1735 </programlisting>
1736
1737 <para>
1738 Bindings are translated with the <literal>(&gt;&gt;=)</literal> and
1739 <literal>return</literal> functions to the usual do-notation:
1740 </para>
1741
1742 <programlisting>
1743 do x &lt;- Just 1
1744 y &lt;- Just 2
1745 return (x+y)
1746 </programlisting>
1747
1748 </listitem>
1749 <listitem>
1750 <para>
1751 Guards:
1752 </para>
1753
1754 <programlisting>
1755 [ x | x &lt;- [1..10], x &lt;= 5 ]
1756 </programlisting>
1757
1758 <para>
1759 Guards are translated with the <literal>guard</literal> function,
1760 which requires a <literal>MonadPlus</literal> instance:
1761 </para>
1762
1763 <programlisting>
1764 do x &lt;- [1..10]
1765 guard (x &lt;= 5)
1766 return x
1767 </programlisting>
1768
1769 </listitem>
1770 <listitem>
1771 <para>
1772 Transform statements (as with <literal>-XTransformListComp</literal>):
1773 </para>
1774
1775 <programlisting>
1776 [ x+y | x &lt;- [1..10], y &lt;- [1..x], then take 2 ]
1777 </programlisting>
1778
1779 <para>
1780 This translates to:
1781 </para>
1782
1783 <programlisting>
1784 do (x,y) &lt;- take 2 (do x &lt;- [1..10]
1785 y &lt;- [1..x]
1786 return (x,y))
1787 return (x+y)
1788 </programlisting>
1789
1790 </listitem>
1791 <listitem>
1792 <para>
1793 Group statements (as with <literal>-XTransformListComp</literal>):
1794 </para>
1795
1796 <programlisting>
1797 [ x | x &lt;- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
1798 [ x | x &lt;- [1,1,2,2,3], then group using myGroup ]
1799 </programlisting>
1800
1801 </listitem>
1802 <listitem>
1803 <para>
1804 Parallel statements (as with <literal>-XParallelListComp</literal>):
1805 </para>
1806
1807 <programlisting>
1808 [ (x+y) | x &lt;- [1..10]
1809 | y &lt;- [11..20]
1810 ]
1811 </programlisting>
1812
1813 <para>
1814 Parallel statements are translated using the
1815 <literal>mzip</literal> function, which requires a
1816 <literal>MonadZip</literal> instance defined in
1817 <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
1818 </para>
1819
1820 <programlisting>
1821 do (x,y) &lt;- mzip (do x &lt;- [1..10]
1822 return x)
1823 (do y &lt;- [11..20]
1824 return y)
1825 return (x+y)
1826 </programlisting>
1827
1828 </listitem>
1829 </itemizedlist>
1830
1831 <para>
1832 All these features are enabled by default if the
1833 <literal>MonadComprehensions</literal> extension is enabled. The types
1834 and more detailed examples on how to use comprehensions are explained
1835 in the previous chapters <xref
1836 linkend="generalised-list-comprehensions"/> and <xref
1837 linkend="parallel-list-comprehensions"/>. In general you just have
1838 to replace the type <literal>[a]</literal> with the type
1839 <literal>Monad m => m a</literal> for monad comprehensions.
1840 </para>
1841
1842 <para>
1843 Note: Even though most of these examples are using the list monad,
1844 monad comprehensions work for any monad.
1845 The <literal>base</literal> package offers all necessary instances for
1846 lists, which make <literal>MonadComprehensions</literal> backward
1847 compatible to built-in, transform and parallel list comprehensions.
1848 </para>
1849 <para> More formally, the desugaring is as follows. We write <literal>D[ e | Q]</literal>
1850 to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
1851 <programlisting>
1852 Expressions: e
1853 Declarations: d
1854 Lists of qualifiers: Q,R,S
1855
1856 -- Basic forms
1857 D[ e | ] = return e
1858 D[ e | p &lt;- e, Q ] = e &gt;&gt;= \p -&gt; D[ e | Q ]
1859 D[ e | e, Q ] = guard e &gt;&gt; \p -&gt; D[ e | Q ]
1860 D[ e | let d, Q ] = let d in D[ e | Q ]
1861
1862 -- Parallel comprehensions (iterate for multiple parallel branches)
1863 D[ e | (Q | R), S ] = mzip D[ Qv | Q ] D[ Rv | R ] &gt;&gt;= \(Qv,Rv) -&gt; D[ e | S ]
1864
1865 -- Transform comprehensions
1866 D[ e | Q then f, R ] = f D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1867
1868 D[ e | Q then f by b, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1869
1870 D[ e | Q then group using f, R ] = f D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1871 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1872 Qv -&gt; D[ e | R ]
1873
1874 D[ e | Q then group by b using f, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1875 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1876 Qv -&gt; D[ e | R ]
1877
1878 where Qv is the tuple of variables bound by Q (and used subsequently)
1879 selQvi is a selector mapping Qv to the ith component of Qv
1880
1881 Operator Standard binding Expected type
1882 --------------------------------------------------------------------
1883 return GHC.Base t1 -&gt; m t2
1884 (&gt;&gt;=) GHC.Base m1 t1 -&gt; (t2 -&gt; m2 t3) -&gt; m3 t3
1885 (&gt;&gt;) GHC.Base m1 t1 -&gt; m2 t2 -&gt; m3 t3
1886 guard Control.Monad t1 -&gt; m t2
1887 fmap GHC.Base forall a b. (a-&gt;b) -&gt; n a -&gt; n b
1888 mzip Control.Monad.Zip forall a b. m a -&gt; m b -&gt; m (a,b)
1889 </programlisting>
1890 The comprehension should typecheck when its desugaring would typecheck.
1891 </para>
1892 <para>
1893 Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
1894 Without rebindable
1895 syntax, the operators from the "standard binding" module are used; with
1896 rebindable syntax, the operators are looked up in the current lexical scope.
1897 For example, parallel comprehensions will be typechecked and desugared
1898 using whatever "<literal>mzip</literal>" is in scope.
1899 </para>
1900 <para>
1901 The rebindable operators must have the "Expected type" given in the
1902 table above. These types are surprisingly general. For example, you can
1903 use a bind operator with the type
1904 <programlisting>
1905 (>>=) :: T x y a -> (a -> T y z b) -> T x z b
1906 </programlisting>
1907 In the case of transform comprehensions, notice that the groups are
1908 parameterised over some arbitrary type <literal>n</literal> (provided it
1909 has an <literal>fmap</literal>, as well as
1910 the comprehension being over an arbitrary monad.
1911 </para>
1912 </sect2>
1913
1914 <!-- ===================== REBINDABLE SYNTAX =================== -->
1915
1916 <sect2 id="rebindable-syntax">
1917 <title>Rebindable syntax and the implicit Prelude import</title>
1918
1919 <para><indexterm><primary>-XNoImplicitPrelude
1920 option</primary></indexterm> GHC normally imports
1921 <filename>Prelude.hi</filename> files for you. If you'd
1922 rather it didn't, then give it a
1923 <option>-XNoImplicitPrelude</option> option. The idea is
1924 that you can then import a Prelude of your own. (But don't
1925 call it <literal>Prelude</literal>; the Haskell module
1926 namespace is flat, and you must not conflict with any
1927 Prelude module.)</para>
1928
1929 <para>Suppose you are importing a Prelude of your own
1930 in order to define your own numeric class
1931 hierarchy. It completely defeats that purpose if the
1932 literal "1" means "<literal>Prelude.fromInteger
1933 1</literal>", which is what the Haskell Report specifies.
1934 So the <option>-XRebindableSyntax</option>
1935 flag causes
1936 the following pieces of built-in syntax to refer to
1937 <emphasis>whatever is in scope</emphasis>, not the Prelude
1938 versions:
1939 <itemizedlist>
1940 <listitem>
1941 <para>An integer literal <literal>368</literal> means
1942 "<literal>fromInteger (368::Integer)</literal>", rather than
1943 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1944 </para> </listitem>
1945
1946 <listitem><para>Fractional literals are handed in just the same way,
1947 except that the translation is
1948 <literal>fromRational (3.68::Rational)</literal>.
1949 </para> </listitem>
1950
1951 <listitem><para>The equality test in an overloaded numeric pattern
1952 uses whatever <literal>(==)</literal> is in scope.
1953 </para> </listitem>
1954
1955 <listitem><para>The subtraction operation, and the
1956 greater-than-or-equal test, in <literal>n+k</literal> patterns
1957 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1958 </para></listitem>
1959
1960 <listitem>
1961 <para>Negation (e.g. "<literal>- (f x)</literal>")
1962 means "<literal>negate (f x)</literal>", both in numeric
1963 patterns, and expressions.
1964 </para></listitem>
1965
1966 <listitem>
1967 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1968 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1969 </para></listitem>
1970
1971 <listitem>
1972 <para>"Do" notation is translated using whatever
1973 functions <literal>(>>=)</literal>,
1974 <literal>(>>)</literal>, and <literal>fail</literal>,
1975 are in scope (not the Prelude
1976 versions). List comprehensions, <literal>mdo</literal>
1977 (<xref linkend="recursive-do-notation"/>), and parallel array
1978 comprehensions, are unaffected. </para></listitem>
1979
1980 <listitem>
1981 <para>Arrow
1982 notation (see <xref linkend="arrow-notation"/>)
1983 uses whatever <literal>arr</literal>,
1984 <literal>(>>>)</literal>, <literal>first</literal>,
1985 <literal>app</literal>, <literal>(|||)</literal> and
1986 <literal>loop</literal> functions are in scope. But unlike the
1987 other constructs, the types of these functions must match the
1988 Prelude types very closely. Details are in flux; if you want
1989 to use this, ask!
1990 </para></listitem>
1991 </itemizedlist>
1992 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1993 </para>
1994 <para>
1995 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1996 even if that is a little unexpected. For example, the
1997 static semantics of the literal <literal>368</literal>
1998 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1999 <literal>fromInteger</literal> to have any of the types:
2000 <programlisting>
2001 fromInteger :: Integer -> Integer
2002 fromInteger :: forall a. Foo a => Integer -> a
2003 fromInteger :: Num a => a -> Integer
2004 fromInteger :: Integer -> Bool -> Bool
2005 </programlisting>
2006 </para>
2007
2008 <para>Be warned: this is an experimental facility, with
2009 fewer checks than usual. Use <literal>-dcore-lint</literal>
2010 to typecheck the desugared program. If Core Lint is happy
2011 you should be all right.</para>
2012
2013 </sect2>
2014
2015 <sect2 id="postfix-operators">
2016 <title>Postfix operators</title>
2017
2018 <para>
2019 The <option>-XPostfixOperators</option> flag enables a small
2020 extension to the syntax of left operator sections, which allows you to
2021 define postfix operators. The extension is this: the left section
2022 <programlisting>
2023 (e !)
2024 </programlisting>
2025 is equivalent (from the point of view of both type checking and execution) to the expression
2026 <programlisting>
2027 ((!) e)
2028 </programlisting>
2029 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
2030 The strict Haskell 98 interpretation is that the section is equivalent to
2031 <programlisting>
2032 (\y -> (!) e y)
2033 </programlisting>
2034 That is, the operator must be a function of two arguments. GHC allows it to
2035 take only one argument, and that in turn allows you to write the function
2036 postfix.
2037 </para>
2038 <para>The extension does not extend to the left-hand side of function
2039 definitions; you must define such a function in prefix form.</para>
2040
2041 </sect2>
2042
2043 <sect2 id="tuple-sections">
2044 <title>Tuple sections</title>
2045
2046 <para>
2047 The <option>-XTupleSections</option> flag enables Python-style partially applied
2048 tuple constructors. For example, the following program
2049 <programlisting>
2050 (, True)
2051 </programlisting>
2052 is considered to be an alternative notation for the more unwieldy alternative
2053 <programlisting>
2054 \x -> (x, True)
2055 </programlisting>
2056 You can omit any combination of arguments to the tuple, as in the following
2057 <programlisting>
2058 (, "I", , , "Love", , 1337)
2059 </programlisting>
2060 which translates to
2061 <programlisting>
2062 \a b c d -> (a, "I", b, c, "Love", d, 1337)
2063 </programlisting>
2064 </para>
2065
2066 <para>
2067 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
2068 will also be available for them, like so
2069 <programlisting>
2070 (# , True #)
2071 </programlisting>
2072 Because there is no unboxed unit tuple, the following expression
2073 <programlisting>
2074 (# #)
2075 </programlisting>
2076 continues to stand for the unboxed singleton tuple data constructor.
2077 </para>
2078
2079 </sect2>
2080
2081 <sect2 id="lambda-case">
2082 <title>Lambda-case</title>
2083 <para>
2084 The <option>-XLambdaCase</option> flag enables expressions of the form
2085 <programlisting>
2086 \case { p1 -> e1; ...; pN -> eN }
2087 </programlisting>
2088 which is equivalent to
2089 <programlisting>
2090 \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }
2091 </programlisting>
2092 Note that <literal>\case</literal> starts a layout, so you can write
2093 <programlisting>
2094 \case
2095 p1 -> e1
2096 ...
2097 pN -> eN
2098 </programlisting>
2099 </para>
2100 </sect2>
2101
2102 <sect2 id="empty-case">
2103 <title>Empty case alternatives</title>
2104 <para>
2105 The <option>-XEmptyCase</option> flag enables
2106 case expressions, or lambda-case expressions, that have no alternatives,
2107 thus:
2108 <programlisting>
2109 case e of { } -- No alternatives
2110 or
2111 \case { } -- -XLambdaCase is also required
2112 </programlisting>
2113 This can be useful when you know that the expression being scrutinised
2114 has no non-bottom values. For example:
2115 <programlisting>
2116 data Void
2117 f :: Void -> Int
2118 f x = case x of { }
2119 </programlisting>
2120 With dependently-typed features it is more useful
2121 (see <ulink url="http://ghc.haskell.org/trac/ghc/ticket/2431">Trac</ulink>).
2122 For example, consider these two candidate definitions of <literal>absurd</literal>:
2123 <programlisting>
2124 data a :==: b where
2125 Refl :: a :==: a
2126
2127 absurd :: True :~: False -> a
2128 absurd x = error "absurd" -- (A)
2129 absurd x = case x of {} -- (B)
2130 </programlisting>
2131 We much prefer (B). Why? Because GHC can figure out that <literal>(True :~: False)</literal>
2132 is an empty type. So (B) has no partiality and GHC should be able to compile with
2133 <option>-fwarn-incomplete-patterns</option>. (Though the pattern match checking is not
2134 yet clever enough to do that.)
2135 On the other hand (A) looks dangerous, and GHC doesn't check to make
2136 sure that, in fact, the function can never get called.
2137 </para>
2138 </sect2>
2139
2140 <sect2 id="multi-way-if">
2141 <title>Multi-way if-expressions</title>
2142 <para>
2143 With <option>-XMultiWayIf</option> flag GHC accepts conditional expressions
2144 with multiple branches:
2145 <programlisting>
2146 if | guard1 -> expr1
2147 | ...
2148 | guardN -> exprN
2149 </programlisting>
2150 which is roughly equivalent to
2151 <programlisting>
2152 case () of
2153 _ | guard1 -> expr1
2154 ...
2155 _ | guardN -> exprN
2156 </programlisting>
2157 </para>
2158
2159 <para>Multi-way if expressions introduce a new layout context. So the
2160 example above is equivalent to:
2161 <programlisting>
2162 if { | guard1 -> expr1
2163 ; | ...
2164 ; | guardN -> exprN
2165 }
2166 </programlisting>
2167 The following behaves as expected:
2168 <programlisting>
2169 if | guard1 -> if | guard2 -> expr2
2170 | guard3 -> expr3
2171 | guard4 -> expr4
2172 </programlisting>
2173 because layout translates it as
2174 <programlisting>
2175 if { | guard1 -> if { | guard2 -> expr2
2176 ; | guard3 -> expr3
2177 }
2178 ; | guard4 -> expr4
2179 }
2180 </programlisting>
2181 Layout with multi-way if works in the same way as other layout
2182 contexts, except that the semi-colons between guards in a multi-way if
2183 are optional. So it is not necessary to line up all the guards at the
2184 same column; this is consistent with the way guards work in function
2185 definitions and case expressions.
2186 </para>
2187 </sect2>
2188
2189 <sect2 id="disambiguate-fields">
2190 <title>Record field disambiguation</title>
2191 <para>
2192 In record construction and record pattern matching
2193 it is entirely unambiguous which field is referred to, even if there are two different
2194 data types in scope with a common field name. For example:
2195 <programlisting>
2196 module M where
2197 data S = MkS { x :: Int, y :: Bool }
2198
2199 module Foo where
2200 import M
2201
2202 data T = MkT { x :: Int }
2203
2204 ok1 (MkS { x = n }) = n+1 -- Unambiguous
2205 ok2 n = MkT { x = n+1 } -- Unambiguous
2206
2207 bad1 k = k { x = 3 } -- Ambiguous
2208 bad2 k = x k -- Ambiguous
2209 </programlisting>
2210 Even though there are two <literal>x</literal>'s in scope,
2211 it is clear that the <literal>x</literal> in the pattern in the
2212 definition of <literal>ok1</literal> can only mean the field
2213 <literal>x</literal> from type <literal>S</literal>. Similarly for
2214 the function <literal>ok2</literal>. However, in the record update
2215 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
2216 it is not clear which of the two types is intended.
2217 </para>
2218 <para>
2219 Haskell 98 regards all four as ambiguous, but with the
2220 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
2221 the former two. The rules are precisely the same as those for instance
2222 declarations in Haskell 98, where the method names on the left-hand side
2223 of the method bindings in an instance declaration refer unambiguously
2224 to the method of that class (provided they are in scope at all), even
2225 if there are other variables in scope with the same name.
2226 This reduces the clutter of qualified names when you import two
2227 records from different modules that use the same field name.
2228 </para>
2229 <para>
2230 Some details:
2231 <itemizedlist>
2232 <listitem><para>
2233 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For example:
2234 <programlisting>
2235 module Foo where
2236 import M
2237 x=True
2238 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
2239 </programlisting>
2240 </para></listitem>
2241
2242 <listitem><para>
2243 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualified</emphasis>
2244 field names even if the corresponding selector is only in scope <emphasis>qualified</emphasis>
2245 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
2246 <programlisting>
2247 module Foo where
2248 import qualified M -- Note qualified
2249
2250 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
2251 </programlisting>
2252 Since the constructor <literal>MkS</literal> is only in scope qualified, you must
2253 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
2254 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
2255 is not. (In effect, it is qualified by the constructor.)
2256 </para></listitem>
2257 </itemizedlist>
2258 </para>
2259
2260 </sect2>
2261
2262 <!-- ===================== Record puns =================== -->
2263
2264 <sect2 id="record-puns">
2265 <title>Record puns
2266 </title>
2267
2268 <para>
2269 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
2270 </para>
2271
2272 <para>
2273 When using records, it is common to write a pattern that binds a
2274 variable with the same name as a record field, such as:
2275
2276 <programlisting>
2277 data C = C {a :: Int}
2278 f (C {a = a}) = a
2279 </programlisting>
2280 </para>
2281
2282 <para>
2283 Record punning permits the variable name to be elided, so one can simply
2284 write
2285
2286 <programlisting>
2287 f (C {a}) = a
2288 </programlisting>
2289
2290 to mean the same pattern as above. That is, in a record pattern, the
2291 pattern <literal>a</literal> expands into the pattern <literal>a =
2292 a</literal> for the same name <literal>a</literal>.
2293 </para>
2294
2295 <para>
2296 Note that:
2297 <itemizedlist>
2298 <listitem><para>
2299 Record punning can also be used in an expression, writing, for example,
2300 <programlisting>
2301 let a = 1 in C {a}
2302 </programlisting>
2303 instead of
2304 <programlisting>
2305 let a = 1 in C {a = a}
2306 </programlisting>
2307 The expansion is purely syntactic, so the expanded right-hand side
2308 expression refers to the nearest enclosing variable that is spelled the
2309 same as the field name.
2310 </para></listitem>
2311
2312 <listitem><para>
2313 Puns and other patterns can be mixed in the same record:
2314 <programlisting>
2315 data C = C {a :: Int, b :: Int}
2316 f (C {a, b = 4}) = a
2317 </programlisting>
2318 </para></listitem>
2319
2320 <listitem><para>
2321 Puns can be used wherever record patterns occur (e.g. in
2322 <literal>let</literal> bindings or at the top-level).
2323 </para></listitem>
2324
2325 <listitem><para>
2326 A pun on a qualified field name is expanded by stripping off the module qualifier.
2327 For example:
2328 <programlisting>
2329 f (C {M.a}) = a
2330 </programlisting>
2331 means
2332 <programlisting>
2333 f (M.C {M.a = a}) = a
2334 </programlisting>
2335 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
2336 is only in scope in qualified form.)
2337 </para></listitem>
2338 </itemizedlist>
2339 </para>
2340
2341
2342 </sect2>
2343
2344 <!-- ===================== Record wildcards =================== -->
2345
2346 <sect2 id="record-wildcards">
2347 <title>Record wildcards
2348 </title>
2349
2350 <para>
2351 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
2352 This flag implies <literal>-XDisambiguateRecordFields</literal>.
2353 </para>
2354
2355 <para>
2356 For records with many fields, it can be tiresome to write out each field
2357 individually in a record pattern, as in
2358 <programlisting>
2359 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
2360 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
2361 </programlisting>
2362 </para>
2363
2364 <para>
2365 Record wildcard syntax permits a "<literal>..</literal>" in a record
2366 pattern, where each elided field <literal>f</literal> is replaced by the
2367 pattern <literal>f = f</literal>. For example, the above pattern can be
2368 written as
2369 <programlisting>
2370 f (C {a = 1, ..}) = b + c + d
2371 </programlisting>
2372 </para>
2373
2374 <para>
2375 More details:
2376 <itemizedlist>
2377 <listitem><para>
2378 Record wildcards in patterns can be mixed with other patterns, including puns
2379 (<xref linkend="record-puns"/>); for example, in a pattern <literal>(C {a
2380 = 1, b, ..})</literal>. Additionally, record wildcards can be used
2381 wherever record patterns occur, including in <literal>let</literal>
2382 bindings and at the top-level. For example, the top-level binding
2383 <programlisting>
2384 C {a = 1, ..} = e
2385 </programlisting>
2386 defines <literal>b</literal>, <literal>c</literal>, and
2387 <literal>d</literal>.
2388 </para></listitem>
2389
2390 <listitem><para>
2391 Record wildcards can also be used in an expression, when constructing a record. For example,
2392 <programlisting>
2393 let {a = 1; b = 2; c = 3; d = 4} in C {..}
2394 </programlisting>
2395 in place of
2396 <programlisting>
2397 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
2398 </programlisting>
2399 The expansion is purely syntactic, so the record wildcard
2400 expression refers to the nearest enclosing variables that are spelled
2401 the same as the omitted field names.
2402 </para></listitem>
2403
2404 <listitem><para>
2405 Record wildcards may <emphasis>not</emphasis> be used in record <emphasis>updates</emphasis>. For example this
2406 is illegal:
2407 <programlisting>
2408 f r = r { x = 3, .. }
2409 </programlisting>
2410 </para></listitem>
2411
2412 <listitem><para>
2413 For both pattern and expression wildcards, the "<literal>..</literal>" expands to the missing
2414 <emphasis>in-scope</emphasis> record fields.
2415 Specifically the expansion of "<literal>C {..}</literal>" includes
2416 <literal>f</literal> if and only if:
2417 <itemizedlist>
2418 <listitem><para>
2419 <literal>f</literal> is a record field of constructor <literal>C</literal>.
2420 </para></listitem>
2421 <listitem><para>
2422 The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
2423 </para></listitem>
2424 <listitem><para>
2425 In the case of expressions (but not patterns),
2426 the variable <literal>f</literal> is in scope unqualified,
2427 apart from the binding of the record selector itself.
2428 </para></listitem>
2429 </itemizedlist>
2430 These rules restrict record wildcards to the situations in which the user
2431 could have written the expanded version.
2432 For example
2433 <programlisting>
2434 module M where
2435 data R = R { a,b,c :: Int }
2436 module X where
2437 import M( R(a,c) )
2438 f b = R { .. }
2439 </programlisting>
2440 The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
2441 omitting <literal>b</literal> since the record field is not in scope,
2442 and omitting <literal>c</literal> since the variable <literal>c</literal>
2443 is not in scope (apart from the binding of the
2444 record selector <literal>c</literal>, of course).
2445 </para></listitem>
2446
2447 <listitem><para>
2448 Record wildcards cannot be used (a) in a record update construct, and (b) for data
2449 constructors that are not declared with record fields. For example:
2450 <programlisting>
2451 f x = x { v=True, .. } -- Illegal (a)
2452
2453 data T = MkT Int Bool
2454 g = MkT { .. } -- Illegal (b)
2455 h (MkT { .. }) = True -- Illegal (b)
2456 </programlisting>
2457 </para></listitem>
2458 </itemizedlist>
2459 </para>
2460
2461 </sect2>
2462
2463 <!-- ===================== Local fixity declarations =================== -->
2464
2465 <sect2 id="local-fixity-declarations">
2466 <title>Local Fixity Declarations
2467 </title>
2468
2469 <para>A careful reading of the Haskell 98 Report reveals that fixity
2470 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
2471 <literal>infixr</literal>) are permitted to appear inside local bindings
2472 such those introduced by <literal>let</literal> and
2473 <literal>where</literal>. However, the Haskell Report does not specify
2474 the semantics of such bindings very precisely.
2475 </para>
2476
2477 <para>In GHC, a fixity declaration may accompany a local binding:
2478 <programlisting>
2479 let f = ...
2480 infixr 3 `f`
2481 in
2482 ...
2483 </programlisting>
2484 and the fixity declaration applies wherever the binding is in scope.
2485 For example, in a <literal>let</literal>, it applies in the right-hand
2486 sides of other <literal>let</literal>-bindings and the body of the
2487 <literal>let</literal>C. Or, in recursive <literal>do</literal>
2488 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
2489 declarations of a <literal>let</literal> statement scope over other
2490 statements in the group, just as the bound name does.
2491 </para>
2492
2493 <para>
2494 Moreover, a local fixity declaration *must* accompany a local binding of
2495 that name: it is not possible to revise the fixity of name bound
2496 elsewhere, as in
2497 <programlisting>
2498 let infixr 9 $ in ...
2499 </programlisting>
2500
2501 Because local fixity declarations are technically Haskell 98, no flag is
2502 necessary to enable them.
2503 </para>
2504 </sect2>
2505
2506 <sect2 id="package-imports">
2507 <title>Import and export extensions</title>
2508
2509 <sect3>
2510 <title>Hiding things the imported module doesn't export</title>
2511
2512 <para>
2513 Technically in Haskell 2010 this is illegal:
2514 <programlisting>
2515 module A( f ) where
2516 f = True
2517
2518 module B where
2519 import A hiding( g ) -- A does not export g
2520 g = f
2521 </programlisting>
2522 The <literal>import A hiding( g )</literal> in module <literal>B</literal>
2523 is technically an error (<ulink url="http://www.haskell.org/onlinereport/haskell2010/haskellch5.html#x11-1020005.3.1">Haskell Report, 5.3.1</ulink>)
2524 because <literal>A</literal> does not export <literal>g</literal>.
2525 However GHC allows it, in the interests of supporting backward compatibility; for example, a newer version of
2526 <literal>A</literal> might export <literal>g</literal>, and you want <literal>B</literal> to work
2527 in either case.
2528 </para>
2529 <para>
2530 The warning <literal>-fwarn-dodgy-imports</literal>, which is off by default but included with <literal>-W</literal>,
2531 warns if you hide something that the imported module does not export.
2532 </para>
2533 </sect3>
2534
2535 <sect3>
2536 <title id="package-qualified-imports">Package-qualified imports</title>
2537
2538 <para>With the <option>-XPackageImports</option> flag, GHC allows
2539 import declarations to be qualified by the package name that the
2540 module is intended to be imported from. For example:</para>
2541
2542 <programlisting>
2543 import "network" Network.Socket
2544 </programlisting>
2545
2546 <para>would import the module <literal>Network.Socket</literal> from
2547 the package <literal>network</literal> (any version). This may
2548 be used to disambiguate an import when the same module is
2549 available from multiple packages, or is present in both the
2550 current package being built and an external package.</para>
2551
2552 <para>The special package name <literal>this</literal> can be used to
2553 refer to the current package being built.</para>
2554
2555 <para>Note: you probably don't need to use this feature, it was
2556 added mainly so that we can build backwards-compatible versions of
2557 packages when APIs change. It can lead to fragile dependencies in
2558 the common case: modules occasionally move from one package to
2559 another, rendering any package-qualified imports broken.
2560 See also <xref linkend="package-thinning-and-renaming" /> for
2561 an alternative way of disambiguating between module names.</para>
2562 </sect3>
2563
2564 <sect3 id="safe-imports-ext">
2565 <title>Safe imports</title>
2566
2567 <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
2568 and <option>-XUnsafe</option> language flags, GHC extends
2569 the import declaration syntax to take an optional <literal>safe</literal>
2570 keyword after the <literal>import</literal> keyword. This feature
2571 is part of the Safe Haskell GHC extension. For example:</para>
2572
2573 <programlisting>
2574 import safe qualified Network.Socket as NS
2575 </programlisting>
2576
2577 <para>would import the module <literal>Network.Socket</literal>
2578 with compilation only succeeding if Network.Socket can be
2579 safely imported. For a description of when a import is
2580 considered safe see <xref linkend="safe-haskell"/></para>
2581
2582 </sect3>
2583
2584 <sect3 id="explicit-namespaces">
2585 <title>Explicit namespaces in import/export</title>
2586
2587 <para> In an import or export list, such as
2588 <programlisting>
2589 module M( f, (++) ) where ...
2590 import N( f, (++) )
2591 ...
2592 </programlisting>
2593 the entities <literal>f</literal> and <literal>(++)</literal> are <emphasis>values</emphasis>.
2594 However, with type operators (<xref linkend="type-operators"/>) it becomes possible
2595 to declare <literal>(++)</literal> as a <emphasis>type constructor</emphasis>. In that
2596 case, how would you export or import it?
2597 </para>
2598 <para>
2599 The <option>-XExplicitNamespaces</option> extension allows you to prefix the name of
2600 a type constructor in an import or export list with "<literal>type</literal>" to
2601 disambiguate this case, thus:
2602 <programlisting>
2603 module M( f, type (++) ) where ...
2604 import N( f, type (++) )
2605 ...
2606 module N( f, type (++) ) where
2607 data family a ++ b = L a | R b
2608 </programlisting>
2609 The extension <option>-XExplicitNamespaces</option>
2610 is implied by <option>-XTypeOperators</option> and (for some reason) by <option>-XTypeFamilies</option>.
2611 </para>
2612 <para>
2613 In addition, with <option>-XPatternSynonyms</option> you can prefix the name of
2614 a data constructor in an import or export list with the keyword <literal>pattern</literal>,
2615 to allow the import or export of a data constructor without its parent type constructor
2616 (see <xref linkend="patsyn-impexp"/>).
2617 </para>
2618 </sect3>
2619
2620 </sect2>
2621
2622 <sect2 id="syntax-stolen">
2623 <title>Summary of stolen syntax</title>
2624
2625 <para>Turning on an option that enables special syntax
2626 <emphasis>might</emphasis> cause working Haskell 98 code to fail
2627 to compile, perhaps because it uses a variable name which has
2628 become a reserved word. This section lists the syntax that is
2629 "stolen" by language extensions.
2630 We use
2631 notation and nonterminal names from the Haskell 98 lexical syntax
2632 (see the Haskell 98 Report).
2633 We only list syntax changes here that might affect
2634 existing working programs (i.e. "stolen" syntax). Many of these
2635 extensions will also enable new context-free syntax, but in all
2636 cases programs written to use the new syntax would not be
2637 compilable without the option enabled.</para>
2638
2639 <para>There are two classes of special
2640 syntax:
2641
2642 <itemizedlist>
2643 <listitem>
2644 <para>New reserved words and symbols: character sequences
2645 which are no longer available for use as identifiers in the
2646 program.</para>
2647 </listitem>
2648 <listitem>
2649 <para>Other special syntax: sequences of characters that have
2650 a different meaning when this particular option is turned
2651 on.</para>
2652 </listitem>
2653 </itemizedlist>
2654
2655 The following syntax is stolen:
2656
2657 <variablelist>
2658 <varlistentry>
2659 <term>
2660 <literal>forall</literal>
2661 <indexterm><primary><literal>forall</literal></primary></indexterm>
2662 </term>
2663 <listitem><para>
2664 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
2665 <option>-XScopedTypeVariables</option>,
2666 <option>-XLiberalTypeSynonyms</option>,
2667 <option>-XRankNTypes</option>,
2668 <option>-XExistentialQuantification</option>
2669 </para></listitem>
2670 </varlistentry>
2671
2672 <varlistentry>
2673 <term>
2674 <literal>mdo</literal>
2675 <indexterm><primary><literal>mdo</literal></primary></indexterm>
2676 </term>
2677 <listitem><para>
2678 Stolen by: <option>-XRecursiveDo</option>
2679 </para></listitem>
2680 </varlistentry>
2681
2682 <varlistentry>
2683 <term>
2684 <literal>foreign</literal>
2685 <indexterm><primary><literal>foreign</literal></primary></indexterm>
2686 </term>
2687 <listitem><para>
2688 Stolen by: <option>-XForeignFunctionInterface</option>
2689 </para></listitem>
2690 </varlistentry>
2691
2692 <varlistentry>
2693 <term>
2694 <literal>rec</literal>,
2695 <literal>proc</literal>, <literal>-&lt;</literal>,
2696 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
2697 <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
2698 <literal>|)</literal> brackets
2699 <indexterm><primary><literal>proc</literal></primary></indexterm>
2700 </term>
2701 <listitem><para>
2702 Stolen by: <option>-XArrows</option>
2703 </para></listitem>
2704 </varlistentry>
2705
2706 <varlistentry>
2707 <term>
2708 <literal>?<replaceable>varid</replaceable></literal>
2709 <indexterm><primary>implicit parameters</primary></indexterm>
2710 </term>
2711 <listitem><para>
2712 Stolen by: <option>-XImplicitParams</option>
2713 </para></listitem>
2714 </varlistentry>
2715
2716 <varlistentry>
2717 <term>
2718 <literal>[|</literal>,
2719 <literal>[e|</literal>, <literal>[p|</literal>,
2720 <literal>[d|</literal>, <literal>[t|</literal>,
2721 <literal>$(</literal>,
2722 <literal>$$(</literal>,
2723 <literal>[||</literal>,
2724 <literal>[e||</literal>,
2725 <literal>$<replaceable>varid</replaceable></literal>,
2726 <literal>$$<replaceable>varid</replaceable></literal>
2727 <indexterm><primary>Template Haskell</primary></indexterm>
2728 </term>
2729 <listitem><para>
2730 Stolen by: <option>-XTemplateHaskell</option>
2731 </para></listitem>
2732 </varlistentry>
2733
2734 <varlistentry>
2735 <term>
2736 <literal>[<replaceable>varid</replaceable>|</literal>
2737 <indexterm><primary>quasi-quotation</primary></indexterm>
2738 </term>
2739 <listitem><para>
2740 Stolen by: <option>-XQuasiQuotes</option>
2741 </para></listitem>
2742 </varlistentry>
2743
2744 <varlistentry>
2745 <term>
2746 <replaceable>varid</replaceable>{<literal>&num;</literal>},
2747 <replaceable>char</replaceable><literal>&num;</literal>,
2748 <replaceable>string</replaceable><literal>&num;</literal>,
2749 <replaceable>integer</replaceable><literal>&num;</literal>,
2750 <replaceable>float</replaceable><literal>&num;</literal>,
2751 <replaceable>float</replaceable><literal>&num;&num;</literal>
2752 </term>
2753 <listitem><para>
2754 Stolen by: <option>-XMagicHash</option>
2755 </para></listitem>
2756 </varlistentry>
2757
2758 <varlistentry>
2759 <term>
2760 <literal>(&num;</literal>, <literal>&num;)</literal>
2761 </term>
2762 <listitem><para>
2763 Stolen by: <option>-XUnboxedTuples</option>
2764 </para></listitem>
2765 </varlistentry>
2766
2767 <varlistentry>
2768 <term>
2769 <replaceable>varid</replaceable><literal>!</literal><replaceable>varid</replaceable>
2770 </term>
2771 <listitem><para>
2772 Stolen by: <option>-XBangPatterns</option>
2773 </para></listitem>
2774 </varlistentry>
2775
2776 <varlistentry>
2777 <term>
2778 <literal>pattern</literal>
2779 </term>
2780 <listitem><para>
2781 Stolen by: <option>-XPatternSynonyms</option>
2782 </para></listitem>
2783 </varlistentry>
2784 </variablelist>
2785 </para>
2786 </sect2>
2787 </sect1>
2788
2789
2790 <!-- TYPE SYSTEM EXTENSIONS -->
2791 <sect1 id="data-type-extensions">
2792 <title>Extensions to data types and type synonyms</title>
2793
2794 <sect2 id="nullary-types">
2795 <title>Data types with no constructors</title>
2796
2797 <para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
2798 GHC lets you declare a data type with no constructors. For example:</para>
2799
2800 <programlisting>
2801 data S -- S :: *
2802 data T a -- T :: * -> *
2803 </programlisting>
2804
2805 <para>Syntactically, the declaration lacks the "= constrs" part. The
2806 type can be parameterised over types of any kind, but if the kind is
2807 not <literal>*</literal> then an explicit kind annotation must be used
2808 (see <xref linkend="kinding"/>).</para>
2809
2810 <para>Such data types have only one value, namely bottom.
2811 Nevertheless, they can be useful when defining "phantom types".</para>
2812 </sect2>
2813
2814 <sect2 id="datatype-contexts">
2815 <title>Data type contexts</title>
2816
2817 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2818
2819 <programlisting>
2820 data Eq a => Set a = NilSet | ConsSet a (Set a)
2821 </programlisting>
2822
2823 <para>give constructors with types:</para>
2824
2825 <programlisting>
2826 NilSet :: Set a
2827 ConsSet :: Eq a => a -> Set a -> Set a
2828 </programlisting>
2829
2830 <para>This is widely considered a misfeature, and is going to be removed from
2831 the language. In GHC, it is controlled by the deprecated extension
2832 <literal>DatatypeContexts</literal>.</para>
2833 </sect2>
2834
2835 <sect2 id="infix-tycons">
2836 <title>Infix type constructors, classes, and type variables</title>
2837
2838 <para>
2839 GHC allows type constructors, classes, and type variables to be operators, and
2840 to be written infix, very much like expressions. More specifically:
2841 <itemizedlist>
2842 <listitem><para>
2843 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
2844 The lexical syntax is the same as that for data constructors.
2845 </para></listitem>
2846 <listitem><para>
2847 Data type and type-synonym declarations can be written infix, parenthesised
2848 if you want further arguments. E.g.
2849 <screen>
2850 data a :*: b = Foo a b
2851 type a :+: b = Either a b
2852 class a :=: b where ...
2853
2854 data (a :**: b) x = Baz a b x
2855 type (a :++: b) y = Either (a,b) y
2856 </screen>
2857 </para></listitem>
2858 <listitem><para>
2859 Types, and class constraints, can be written infix. For example
2860 <screen>
2861 x :: Int :*: Bool
2862 f :: (a :=: b) => a -> b
2863 </screen>
2864 </para></listitem>
2865 <listitem><para>
2866 Back-quotes work
2867 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
2868 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
2869 </para></listitem>
2870 <listitem><para>
2871 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
2872 one cannot distinguish between the two in a fixity declaration; a fixity declaration
2873 sets the fixity for a data constructor and the corresponding type constructor. For example:
2874 <screen>
2875 infixl 7 T, :*:
2876 </screen>
2877 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
2878 and similarly for <literal>:*:</literal>.
2879 <literal>Int `a` Bool</literal>.
2880 </para></listitem>
2881 <listitem><para>
2882 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
2883 </para></listitem>
2884
2885 </itemizedlist>
2886 </para>
2887 </sect2>
2888
2889 <sect2 id="type-operators">
2890 <title>Type operators</title>
2891 <para>
2892 In types, an operator symbol like <literal>(+)</literal> is normally treated as a type
2893 <emphasis>variable</emphasis>, just like <literal>a</literal>. Thus in Haskell 98 you can say
2894 <programlisting>
2895 type T (+) = ((+), (+))
2896 -- Just like: type T a = (a,a)
2897
2898 f :: T Int -> Int
2899 f (x,y)= x
2900 </programlisting>
2901 As you can see, using operators in this way is not very useful, and Haskell 98 does not even
2902 allow you to write them infix.
2903 </para>
2904 <para>
2905 The language <option>-XTypeOperators</option> changes this behaviour:
2906 <itemizedlist>
2907 <listitem><para>
2908 Operator symbols become type <emphasis>constructors</emphasis> rather than
2909 type <emphasis>variables</emphasis>.
2910 </para></listitem>
2911 <listitem><para>
2912 Operator symbols in types can be written infix, both in definitions and uses.
2913 for example:
2914 <programlisting>
2915 data a + b = Plus a b
2916 type Foo = Int + Bool
2917 </programlisting>
2918 </para></listitem>
2919 <listitem><para>
2920 There is now some potential ambiguity in import and export lists; for example
2921 if you write <literal>import M( (+) )</literal> do you mean the
2922 <emphasis>function</emphasis> <literal>(+)</literal> or the
2923 <emphasis>type constructor</emphasis> <literal>(+)</literal>?
2924 The default is the former, but with <option>-XExplicitNamespaces</option> (which is implied
2925 by <option>-XExplicitTypeOperators</option>) GHC allows you to specify the latter
2926 by preceding it with the keyword <literal>type</literal>, thus:
2927 <programlisting>
2928 import M( type (+) )
2929 </programlisting>
2930 See <xref linkend="explicit-namespaces"/>.
2931 </para></listitem>
2932 <listitem><para>
2933 The fixity of a type operator may be set using the usual fixity declarations
2934 but, as in <xref linkend="infix-tycons"/>, the function and type constructor share
2935 a single fixity.
2936 </para></listitem>
2937 </itemizedlist>
2938 </para>
2939 </sect2>
2940
2941 <sect2 id="type-synonyms">
2942 <title>Liberalised type synonyms</title>
2943
2944 <para>
2945 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
2946 on individual synonym declarations.
2947 With the <option>-XLiberalTypeSynonyms</option> extension,
2948 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2949 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
2950
2951 <itemizedlist>
2952 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2953 in a type synonym, thus:
2954 <programlisting>
2955 type Discard a = forall b. Show b => a -> b -> (a, String)
2956
2957 f :: Discard a
2958 f x y = (x, show y)
2959
2960 g :: Discard Int -> (Int,String) -- A rank-2 type
2961 g f = f 3 True
2962 </programlisting>
2963 </para>
2964 </listitem>
2965
2966 <listitem><para>
2967 If you also use <option>-XUnboxedTuples</option>,
2968 you can write an unboxed tuple in a type synonym:
2969 <programlisting>
2970 type Pr = (# Int, Int #)
2971
2972 h :: Int -> Pr
2973 h x = (# x, x #)
2974 </programlisting>
2975 </para></listitem>
2976
2977 <listitem><para>
2978 You can apply a type synonym to a forall type:
2979 <programlisting>
2980 type Foo a = a -> a -> Bool
2981
2982 f :: Foo (forall b. b->b)
2983 </programlisting>
2984 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2985 <programlisting>
2986 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2987 </programlisting>
2988 </para></listitem>
2989
2990 <listitem><para>
2991 You can apply a type synonym to a partially applied type synonym:
2992 <programlisting>
2993 type Generic i o = forall x. i x -> o x
2994 type Id x = x
2995
2996 foo :: Generic Id []
2997 </programlisting>
2998 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2999 <programlisting>
3000 foo :: forall x. x -> [x]
3001 </programlisting>
3002 </para></listitem>
3003
3004 </itemizedlist>
3005 </para>
3006
3007 <para>
3008 GHC currently does kind checking before expanding synonyms (though even that
3009 could be changed.)
3010 </para>
3011 <para>
3012 After expanding type synonyms, GHC does validity checking on types, looking for
3013 the following mal-formedness which isn't detected simply by kind checking:
3014 <itemizedlist>
3015 <listitem><para>
3016 Type constructor applied to a type involving for-alls (if <literal>XImpredicativeTypes</literal>
3017 is off)
3018 </para></listitem>
3019 <listitem><para>
3020 Partially-applied type synonym.
3021 </para></listitem>
3022 </itemizedlist>
3023 So, for example, this will be rejected:
3024 <programlisting>
3025 type Pr = forall a. a
3026
3027 h :: [Pr]
3028 h = ...
3029 </programlisting>
3030 because GHC does not allow type constructors applied to for-all types.
3031 </para>
3032 </sect2>
3033
3034
3035 <sect2 id="existential-quantification">
3036 <title>Existentially quantified data constructors
3037 </title>
3038
3039 <para>
3040 The idea of using existential quantification in data type declarations
3041 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
3042 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
3043 London, 1991). It was later formalised by Laufer and Odersky
3044 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
3045 TOPLAS, 16(5), pp1411-1430, 1994).
3046 It's been in Lennart
3047 Augustsson's <command>hbc</command> Haskell compiler for several years, and
3048 proved very useful. Here's the idea. Consider the declaration:
3049 </para>
3050
3051 <para>
3052
3053 <programlisting>
3054 data Foo = forall a. MkFoo a (a -> Bool)
3055 | Nil
3056 </programlisting>
3057
3058 </para>
3059
3060 <para>
3061 The data type <literal>Foo</literal> has two constructors with types:
3062 </para>
3063
3064 <para>
3065
3066 <programlisting>
3067 MkFoo :: forall a. a -> (a -> Bool) -> Foo
3068 Nil :: Foo
3069 </programlisting>
3070
3071 </para>
3072
3073 <para>
3074 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
3075 does not appear in the data type itself, which is plain <literal>Foo</literal>.
3076 For example, the following expression is fine:
3077 </para>
3078
3079 <para>
3080
3081 <programlisting>
3082 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
3083 </programlisting>
3084
3085 </para>
3086
3087 <para>
3088 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
3089 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
3090 isUpper</function> packages a character with a compatible function. These
3091 two things are each of type <literal>Foo</literal> and can be put in a list.
3092 </para>
3093
3094 <para>
3095 What can we do with a value of type <literal>Foo</literal>?. In particular,
3096 what happens when we pattern-match on <function>MkFoo</function>?
3097 </para>
3098
3099 <para>
3100
3101 <programlisting>
3102 f (MkFoo val fn) = ???
3103 </programlisting>
3104
3105 </para>
3106
3107 <para>
3108 Since all we know about <literal>val</literal> and <function>fn</function> is that they
3109 are compatible, the only (useful) thing we can do with them is to
3110 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
3111 </para>
3112
3113 <para>
3114
3115 <programlisting>
3116 f :: Foo -> Bool
3117 f (MkFoo val fn) = fn val
3118 </programlisting>
3119
3120 </para>
3121
3122 <para>
3123 What this allows us to do is to package heterogeneous values
3124 together with a bunch of functions that manipulate them, and then treat
3125 that collection of packages in a uniform manner. You can express
3126 quite a bit of object-oriented-like programming this way.
3127 </para>
3128
3129 <sect3 id="existential">
3130 <title>Why existential?
3131 </title>
3132
3133 <para>
3134 What has this to do with <emphasis>existential</emphasis> quantification?
3135 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
3136 </para>
3137
3138 <para>
3139
3140 <programlisting>
3141 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
3142 </programlisting>
3143
3144 </para>
3145
3146 <para>
3147 But Haskell programmers can safely think of the ordinary
3148 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
3149 adding a new existential quantification construct.
3150 </para>
3151
3152 </sect3>
3153
3154 <sect3 id="existential-with-context">
3155 <title>Existentials and type classes</title>
3156
3157 <para>
3158 An easy extension is to allow
3159 arbitrary contexts before the constructor. For example:
3160 </para>
3161
3162 <para>
3163
3164 <programlisting>
3165 data Baz = forall a. Eq a => Baz1 a a
3166 | forall b. Show b => Baz2 b (b -> b)
3167 </programlisting>
3168
3169 </para>
3170
3171 <para>
3172 The two constructors have the types you'd expect:
3173 </para>
3174
3175 <para>
3176
3177 <programlisting>
3178 Baz1 :: forall a. Eq a => a -> a -> Baz
3179 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
3180 </programlisting>
3181
3182 </para>
3183
3184 <para>
3185 But when pattern matching on <function>Baz1</function> the matched values can be compared
3186 for equality, and when pattern matching on <function>Baz2</function> the first matched
3187 value can be converted to a string (as well as applying the function to it).
3188 So this program is legal:
3189 </para>
3190
3191 <para>
3192
3193 <programlisting>
3194 f :: Baz -> String
3195 f (Baz1 p q) | p == q = "Yes"
3196 | otherwise = "No"
3197 f (Baz2 v fn) = show (fn v)
3198 </programlisting>
3199
3200 </para>
3201
3202 <para>
3203 Operationally, in a dictionary-passing implementation, the
3204 constructors <function>Baz1</function> and <function>Baz2</function> must store the
3205 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
3206 extract it on pattern matching.
3207 </para>
3208
3209 </sect3>
3210
3211 <sect3 id="existential-records">
3212 <title>Record Constructors</title>
3213
3214 <para>
3215 GHC allows existentials to be used with records syntax as well. For example:
3216
3217 <programlisting>
3218 data Counter a = forall self. NewCounter
3219 { _this :: self
3220 , _inc :: self -> self
3221 , _display :: self -> IO ()
3222 , tag :: a
3223 }
3224 </programlisting>
3225 Here <literal>tag</literal> is a public field, with a well-typed selector
3226 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
3227 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
3228 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
3229 compile-time error. In other words, <emphasis>GHC defines a record selector function
3230 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
3231 (This example used an underscore in the fields for which record selectors
3232 will not be defined, but that is only programming style; GHC ignores them.)
3233 </para>
3234
3235 <para>
3236 To make use of these hidden fields, we need to create some helper functions:
3237
3238 <programlisting>
3239 inc :: Counter a -> Counter a
3240 inc (NewCounter x i d t) = NewCounter
3241 { _this = i x, _inc = i, _display = d, tag = t }
3242
3243 display :: Counter a -> IO ()
3244 display NewCounter{ _this = x, _display = d } = d x
3245 </programlisting>
3246
3247 Now we can define counters with different underlying implementations:
3248
3249 <programlisting>
3250 counterA :: Counter String
3251 counterA = NewCounter
3252 { _this = 0, _inc = (1+), _display = print, tag = "A" }
3253
3254 counterB :: Counter String
3255 counterB = NewCounter
3256 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
3257
3258 main = do
3259 display (inc counterA) -- prints "1"
3260 display (inc (inc counterB)) -- prints "##"
3261 </programlisting>
3262
3263 Record update syntax is supported for existentials (and GADTs):
3264 <programlisting>
3265 setTag :: Counter a -> a -> Counter a
3266 setTag obj t = obj{ tag = t }
3267 </programlisting>
3268 The rule for record update is this: <emphasis>
3269 the types of the updated fields may
3270 mention only the universally-quantified type variables
3271 of the data constructor. For GADTs, the field may mention only types
3272 that appear as a simple type-variable argument in the constructor's result
3273 type</emphasis>. For example:
3274 <programlisting>
3275 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
3276 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
3277 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
3278 -- existentially quantified)
3279
3280 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
3281 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
3282 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
3283 -- type-variable argument in G1's result type)
3284 </programlisting>
3285 </para>
3286
3287 </sect3>
3288
3289
3290 <sect3>
3291 <title>Restrictions</title>
3292
3293 <para>
3294 There are several restrictions on the ways in which existentially-quantified
3295 constructors can be use.
3296 </para>
3297
3298 <para>
3299
3300 <itemizedlist>
3301 <listitem>
3302
3303 <para>
3304 When pattern matching, each pattern match introduces a new,
3305 distinct, type for each existential type variable. These types cannot
3306 be unified with any other type, nor can they escape from the scope of
3307 the pattern match. For example, these fragments are incorrect:
3308
3309
3310 <programlisting>
3311 f1 (MkFoo a f) = a
3312 </programlisting>
3313
3314
3315 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
3316 is the result of <function>f1</function>. One way to see why this is wrong is to
3317 ask what type <function>f1</function> has:
3318
3319
3320 <programlisting>
3321 f1 :: Foo -> a -- Weird!
3322 </programlisting>
3323
3324
3325 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
3326 this:
3327
3328
3329 <programlisting>
3330 f1 :: forall a. Foo -> a -- Wrong!
3331 </programlisting>
3332
3333
3334 The original program is just plain wrong. Here's another sort of error
3335
3336
3337 <programlisting>
3338 f2 (Baz1 a b) (Baz1 p q) = a==q
3339 </programlisting>
3340
3341
3342 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
3343 <literal>a==q</literal> is wrong because it equates the two distinct types arising
3344 from the two <function>Baz1</function> constructors.
3345
3346
3347 </para>
3348 </listitem>
3349 <listitem>
3350
3351 <para>
3352 You can't pattern-match on an existentially quantified
3353 constructor in a <literal>let</literal> or <literal>where</literal> group of
3354 bindings. So this is illegal:
3355
3356
3357 <programlisting>
3358 f3 x = a==b where { Baz1 a b = x }
3359 </programlisting>
3360
3361 Instead, use a <literal>case</literal> expression:
3362
3363 <programlisting>
3364 f3 x = case x of Baz1 a b -> a==b
3365 </programlisting>
3366
3367 In general, you can only pattern-match
3368 on an existentially-quantified constructor in a <literal>case</literal> expression or
3369 in the patterns of a function definition.
3370
3371 The reason for this restriction is really an implementation one.
3372 Type-checking binding groups is already a nightmare without
3373 existentials complicating the picture. Also an existential pattern
3374 binding at the top level of a module doesn't make sense, because it's
3375 not clear how to prevent the existentially-quantified type "escaping".
3376 So for now, there's a simple-to-state restriction. We'll see how
3377 annoying it is.
3378
3379 </para>
3380 </listitem>
3381 <listitem>
3382
3383 <para>
3384 You can't use existential quantification for <literal>newtype</literal>
3385 declarations. So this is illegal:
3386
3387
3388 <programlisting>
3389 newtype T = forall a. Ord a => MkT a
3390 </programlisting>
3391
3392
3393 Reason: a value of type <literal>T</literal> must be represented as a
3394 pair of a dictionary for <literal>Ord t</literal> and a value of type
3395 <literal>t</literal>. That contradicts the idea that
3396 <literal>newtype</literal> should have no concrete representation.
3397 You can get just the same efficiency and effect by using
3398 <literal>data</literal> instead of <literal>newtype</literal>. If
3399 there is no overloading involved, then there is more of a case for
3400 allowing an existentially-quantified <literal>newtype</literal>,
3401 because the <literal>data</literal> version does carry an
3402 implementation cost, but single-field existentially quantified
3403 constructors aren't much use. So the simple restriction (no
3404 existential stuff on <literal>newtype</literal>) stands, unless there
3405 are convincing reasons to change it.
3406
3407
3408 </para>
3409 </listitem>
3410 <listitem>
3411
3412 <para>
3413 You can't use <literal>deriving</literal> to define instances of a
3414 data type with existentially quantified data constructors.
3415
3416 Reason: in most cases it would not make sense. For example:;
3417
3418 <programlisting>
3419 data T = forall a. MkT [a] deriving( Eq )
3420 </programlisting>
3421
3422 To derive <literal>Eq</literal> in the standard way we would need to have equality
3423 between the single component of two <function>MkT</function> constructors:
3424
3425 <programlisting>
3426 instance Eq T where
3427 (MkT a) == (MkT b) = ???
3428 </programlisting>
3429
3430 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
3431 It's just about possible to imagine examples in which the derived instance
3432 would make sense, but it seems altogether simpler simply to prohibit such
3433 declarations. Define your own instances!
3434 </para>
3435 </listitem>
3436
3437 </itemizedlist>
3438
3439 </para>
3440
3441 </sect3>
3442 </sect2>
3443
3444 <!-- ====================== Generalised algebraic data types ======================= -->
3445
3446 <sect2 id="gadt-style">
3447 <title>Declaring data types with explicit constructor signatures</title>
3448
3449 <para>When the <literal>GADTSyntax</literal> extension is enabled,
3450 GHC allows you to declare an algebraic data type by
3451 giving the type signatures of constructors explicitly. For example:
3452 <programlisting>
3453 data Maybe a where
3454 Nothing :: Maybe a
3455 Just :: a -> Maybe a
3456 </programlisting>
3457 The form is called a "GADT-style declaration"
3458 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
3459 can only be declared using this form.</para>
3460 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
3461 For example, these two declarations are equivalent:
3462 <programlisting>
3463 data Foo = forall a. MkFoo a (a -> Bool)
3464 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
3465 </programlisting>
3466 </para>
3467 <para>Any data type that can be declared in standard Haskell-98 syntax
3468 can also be declared using GADT-style syntax.
3469 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
3470 they treat class constraints on the data constructors differently.
3471 Specifically, if the constructor is given a type-class context, that
3472 context is made available by pattern matching. For example:
3473 <programlisting>
3474 data Set a where
3475 MkSet :: Eq a => [a] -> Set a
3476
3477 makeSet :: Eq a => [a] -> Set a
3478 makeSet xs = MkSet (nub xs)
3479
3480 insert :: a -> Set a -> Set a
3481 insert a (MkSet as) | a `elem` as = MkSet as
3482 | otherwise = MkSet (a:as)
3483 </programlisting>
3484 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
3485 gives rise to a <literal>(Eq a)</literal>
3486 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
3487 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
3488 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
3489 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
3490 when pattern-matching that dictionary becomes available for the right-hand side of the match.
3491 In the example, the equality dictionary is used to satisfy the equality constraint
3492 generated by the call to <literal>elem</literal>, so that the type of
3493 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
3494 </para>
3495 <para>
3496 For example, one possible application is to reify dictionaries:
3497 <programlisting>
3498 data NumInst a where
3499 MkNumInst :: Num a => NumInst a
3500
3501 intInst :: NumInst Int
3502 intInst = MkNumInst
3503
3504 plus :: NumInst a -> a -> a -> a
3505 plus MkNumInst p q = p + q
3506 </programlisting>
3507 Here, a value of type <literal>NumInst a</literal> is equivalent
3508 to an explicit <literal>(Num a)</literal> dictionary.
3509 </para>
3510 <para>
3511 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
3512 For example, the <literal>NumInst</literal> data type above could equivalently be declared
3513 like this:
3514 <programlisting>
3515 data NumInst a
3516 = Num a => MkNumInst (NumInst a)
3517 </programlisting>
3518 Notice that, unlike the situation when declaring an existential, there is
3519 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
3520 data type's universally quantified type variable <literal>a</literal>.
3521 A constructor may have both universal and existential type variables: for example,
3522 the following two declarations are equivalent:
3523 <programlisting>
3524 data T1 a
3525 = forall b. (Num a, Eq b) => MkT1 a b
3526 data T2 a where
3527 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
3528 </programlisting>
3529 </para>
3530 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
3531 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
3532 In Haskell 98 the definition
3533 <programlisting>
3534 data Eq a => Set' a = MkSet' [a]
3535 </programlisting>
3536 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
3537 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
3538 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
3539 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
3540 GHC's behaviour is much more useful, as well as much more intuitive.
3541 </para>
3542
3543 <para>
3544 The rest of this section gives further details about GADT-style data
3545 type declarations.
3546
3547 <itemizedlist>
3548 <listitem><para>
3549 The result type of each data constructor must begin with the type constructor being defined.
3550 If the result type of all constructors
3551 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
3552 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
3553 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
3554 </para></listitem>
3555
3556 <listitem><para>
3557 As with other type signatures, you can give a single signature for several data constructors.
3558 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
3559 <programlisting>
3560 data T a where
3561 T1,T2 :: a -> T a
3562 T3 :: T a
3563 </programlisting>
3564 </para></listitem>
3565
3566 <listitem><para>
3567 The type signature of
3568 each constructor is independent, and is implicitly universally quantified as usual.
3569 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
3570 have no scope, and different constructors may have different universally-quantified type variables:
3571 <programlisting>
3572 data T a where -- The 'a' has no scope
3573 T1,T2 :: b -> T b -- Means forall b. b -> T b
3574 T3 :: T a -- Means forall a. T a
3575 </programlisting>
3576 </para></listitem>
3577
3578 <listitem><para>
3579 A constructor signature may mention type class constraints, which can differ for
3580 different constructors. For example, this is fine:
3581 <programlisting>
3582 data T a where
3583 T1 :: Eq b => b -> b -> T b
3584 T2 :: (Show c, Ix c) => c -> [c] -> T c
3585 </programlisting>
3586 When pattern matching, these constraints are made available to discharge constraints
3587 in the body of the match. For example:
3588 <programlisting>
3589 f :: T a -> String
3590 f (T1 x y) | x==y = "yes"
3591 | otherwise = "no"
3592 f (T2 a b) = show a
3593 </programlisting>
3594 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
3595 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
3596 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
3597 </para></listitem>
3598
3599 <listitem><para>
3600 Unlike a Haskell-98-style
3601 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
3602 have no scope. Indeed, one can write a kind signature instead:
3603 <programlisting>
3604 data Set :: * -> * where ...
3605 </programlisting>
3606 or even a mixture of the two:
3607 <programlisting>
3608 data Bar a :: (* -> *) -> * where ...
3609 </programlisting>
3610 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3611 like this:
3612 <programlisting>
3613 data Bar a (b :: * -> *) where ...
3614 </programlisting>
3615 </para></listitem>
3616
3617
3618 <listitem><para>
3619 You can use strictness annotations, in the obvious places
3620 in the constructor type:
3621 <programlisting>
3622 data Term a where
3623 Lit :: !Int -> Term Int
3624 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3625 Pair :: Term a -> Term b -> Term (a,b)
3626 </programlisting>
3627 </para></listitem>
3628
3629 <listitem><para>
3630 You can use a <literal>deriving</literal> clause on a GADT-style data type
3631 declaration. For example, these two declarations are equivalent
3632 <programlisting>
3633 data Maybe1 a where {
3634 Nothing1 :: Maybe1 a ;
3635 Just1 :: a -> Maybe1 a
3636 } deriving( Eq, Ord )
3637
3638 data Maybe2 a = Nothing2 | Just2 a
3639 deriving( Eq, Ord )
3640 </programlisting>
3641 </para></listitem>
3642
3643 <listitem><para>
3644 The type signature may have quantified type variables that do not appear
3645 in the result type:
3646 <programlisting>
3647 data Foo where
3648 MkFoo :: a -> (a->Bool) -> Foo
3649 Nil :: Foo
3650 </programlisting>
3651 Here the type variable <literal>a</literal> does not appear in the result type
3652 of either constructor.
3653 Although it is universally quantified in the type of the constructor, such
3654 a type variable is often called "existential".
3655 Indeed, the above declaration declares precisely the same type as
3656 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
3657 </para><para>
3658 The type may contain a class context too, of course:
3659 <programlisting>
3660 data Showable where
3661 MkShowable :: Show a => a -> Showable
3662 </programlisting>
3663 </para></listitem>
3664
3665 <listitem><para>
3666 You can use record syntax on a GADT-style data type declaration:
3667
3668 <programlisting>
3669 data Person where
3670 Adult :: { name :: String, children :: [Person] } -> Person
3671 Child :: Show a => { name :: !String, funny :: a } -> Person
3672 </programlisting>
3673 As usual, for every constructor that has a field <literal>f</literal>, the type of
3674 field <literal>f</literal> must be the same (modulo alpha conversion).
3675 The <literal>Child</literal> constructor above shows that the signature
3676 may have a context, existentially-quantified variables, and strictness annotations,
3677 just as in the non-record case. (NB: the "type" that follows the double-colon
3678 is not really a type, because of the record syntax and strictness annotations.
3679 A "type" of this form can appear only in a constructor signature.)
3680 </para></listitem>
3681
3682 <listitem><para>
3683 Record updates are allowed with GADT-style declarations,
3684 only fields that have the following property: the type of the field
3685 mentions no existential type variables.
3686 </para></listitem>
3687
3688 <listitem><para>
3689 As in the case of existentials declared using the Haskell-98-like record syntax
3690 (<xref linkend="existential-records"/>),
3691 record-selector functions are generated only for those fields that have well-typed
3692 selectors.
3693 Here is the example of that section, in GADT-style syntax:
3694 <programlisting>
3695 data Counter a where
3696 NewCounter :: { _this :: self
3697 , _inc :: self -> self
3698 , _display :: self -> IO ()
3699 , tag :: a
3700 } -> Counter a
3701 </programlisting>
3702 As before, only one selector function is generated here, that for <literal>tag</literal>.
3703 Nevertheless, you can still use all the field names in pattern matching and record construction.
3704 </para></listitem>
3705
3706 <listitem><para>
3707 In a GADT-style data type declaration there is no obvious way to specify that a data constructor
3708 should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
3709 (Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
3710 So GHC implements the following design: a data constructor declared in a GADT-style data type
3711 declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
3712 (b) it has two arguments, (c) it has a programmer-supplied fixity declaration. For example
3713 <programlisting>
3714 infix 6 (:--:)
3715 data T a where
3716 (:--:) :: Int -> Bool -> T Int
3717 </programlisting>
3718 </para></listitem>
3719 </itemizedlist></para>
3720 </sect2>
3721
3722 <sect2 id="gadt">
3723 <title>Generalised Algebraic Data Types (GADTs)</title>
3724
3725 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
3726 by allowing constructors to have richer return types. Here is an example:
3727 <programlisting>
3728 data Term a where
3729 Lit :: Int -> Term Int
3730 Succ :: Term Int -> Term Int
3731 IsZero :: Term Int -> Term Bool
3732 If :: Term Bool -> Term a -> Term a -> Term a
3733 Pair :: Term a -> Term b -> Term (a,b)
3734 </programlisting>
3735 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3736 case with ordinary data types. This generality allows us to
3737 write a well-typed <literal>eval</literal> function
3738 for these <literal>Terms</literal>:
3739 <programlisting>
3740 eval :: Term a -> a
3741 eval (Lit i) = i
3742 eval (Succ t) = 1 + eval t
3743 eval (IsZero t) = eval t == 0
3744 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3745 eval (Pair e1 e2) = (eval e1, eval e2)
3746 </programlisting>
3747 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
3748 For example, in the right hand side of the equation
3749 <programlisting>
3750 eval :: Term a -> a
3751 eval (Lit i) = ...
3752 </programlisting>
3753 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
3754 A precise specification of the type rules is beyond what this user manual aspires to,
3755 but the design closely follows that described in
3756 the paper <ulink
3757 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
3758 unification-based type inference for GADTs</ulink>,
3759 (ICFP 2006).
3760 The general principle is this: <emphasis>type refinement is only carried out
3761 based on user-supplied type annotations</emphasis>.
3762 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
3763 and lots of obscure error messages will
3764 occur. However, the refinement is quite general. For example, if we had:
3765 <programlisting>
3766 eval :: Term a -> a -> a
3767 eval (Lit i) j = i+j
3768 </programlisting>
3769 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3770 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
3771 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3772 </para>
3773 <para>
3774 These and many other examples are given in papers by Hongwei Xi, and
3775 Tim Sheard. There is a longer introduction
3776 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3777 and Ralf Hinze's
3778 <ulink url="http://www.cs.ox.ac.uk/ralf.hinze/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
3779 may use different notation to that implemented in GHC.
3780 </para>
3781 <para>
3782 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
3783 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XGADTSyntax</option>
3784 and <option>-XMonoLocalBinds</option>.
3785 <itemizedlist>
3786 <listitem><para>
3787 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
3788 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
3789 The result type of each constructor must begin with the type constructor being defined,
3790 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
3791 For example, in the <literal>Term</literal> data
3792 type above, the type of each constructor must end with <literal>Term ty</literal>, but
3793 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
3794 constructor).
3795 </para></listitem>
3796
3797 <listitem><para>
3798 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
3799 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
3800 whose result type is not just <literal>T a b</literal>.
3801 </para></listitem>
3802
3803 <listitem><para>
3804 You cannot use a <literal>deriving</literal> clause for a GADT; only for
3805 an ordinary data type.
3806 </para></listitem>
3807
3808 <listitem><para>
3809 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
3810 For example:
3811 <programlisting>
3812 data Term a where
3813 Lit :: { val :: Int } -> Term Int
3814 Succ :: { num :: Term Int } -> Term Int
3815 Pred :: { num :: Term Int } -> Term Int
3816 IsZero :: { arg :: Term Int } -> Term Bool
3817 Pair :: { arg1 :: Term a
3818 , arg2 :: Term b
3819 } -> Term (a,b)
3820 If :: { cnd :: Term Bool
3821 , tru :: Term a
3822 , fls :: Term a
3823 } -> Term a
3824 </programlisting>
3825 However, for GADTs there is the following additional constraint:
3826 every constructor that has a field <literal>f</literal> must have
3827 the same result type (modulo alpha conversion)
3828 Hence, in the above example, we cannot merge the <literal>num</literal>
3829 and <literal>arg</literal> fields above into a
3830 single name. Although their field types are both <literal>Term Int</literal>,
3831 their selector functions actually have different types:
3832
3833 <programlisting>
3834 num :: Term Int -> Term Int
3835 arg :: Term Bool -> Term Int
3836 </programlisting>
3837 </para></listitem>
3838
3839 <listitem><para>
3840 When pattern-matching against data constructors drawn from a GADT,
3841 for example in a <literal>case</literal> expression, the following rules apply:
3842 <itemizedlist>
3843 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
3844 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
3845 <listitem><para>The type of any free variable mentioned in any of
3846 the <literal>case</literal> alternatives must be rigid.</para></listitem>
3847 </itemizedlist>
3848 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
3849 way to ensure that a variable a rigid type is to give it a type signature.
3850 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
3851 Simple unification-based type inference for GADTs
3852 </ulink>. The criteria implemented by GHC are given in the Appendix.
3853
3854 </para></listitem>
3855
3856 </itemizedlist>
3857 </para>
3858
3859 </sect2>
3860 </sect1>
3861
3862 <!-- ====================== End of Generalised algebraic data types ======================= -->
3863
3864 <sect1 id="deriving">
3865 <title>Extensions to the "deriving" mechanism</title>
3866
3867 <sect2 id="deriving-inferred">
3868 <title>Inferred context for deriving clauses</title>
3869
3870 <para>
3871 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
3872 legal. For example:
3873 <programlisting>
3874 data T0 f a = MkT0 a deriving( Eq )
3875 data T1 f a = MkT1 (f a) deriving( Eq )
3876 data T2 f a = MkT2 (f (f a)) deriving( Eq )
3877 </programlisting>
3878 The natural generated <literal>Eq</literal> code would result in these instance declarations:
3879 <programlisting>
3880 instance Eq a => Eq (T0 f a) where ...
3881 instance Eq (f a) => Eq (T1 f a) where ...
3882 instance Eq (f (f a)) => Eq (T2 f a) where ...
3883 </programlisting>
3884 The first of these is obviously fine. The second is still fine, although less obviously.
3885 The third is not Haskell 98, and risks losing termination of instances.
3886 </para>
3887 <para>
3888 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
3889 each constraint in the inferred instance context must consist only of type variables,
3890 with no repetitions.
3891 </para>
3892 <para>
3893 This rule is applied regardless of flags. If you want a more exotic context, you can write
3894 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
3895 </para>
3896 </sect2>
3897
3898 <sect2 id="stand-alone-deriving">
3899 <title>Stand-alone deriving declarations</title>
3900
3901 <para>
3902 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
3903 <programlisting>
3904 data Foo a = Bar a | Baz String
3905
3906 deriving instance Eq a => Eq (Foo a)
3907 </programlisting>
3908 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
3909 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
3910 </para>
3911 <para>
3912 However, standalone deriving differs from a <literal>deriving</literal> clause in a number
3913 of important ways:
3914 <itemizedlist>
3915 <listitem><para>The standalone deriving declaration does not need to be in the
3916 same module as the data type declaration. (But be aware of the dangers of
3917 orphan instances (<xref linkend="orphan-modules"/>).
3918 </para></listitem>
3919
3920 <listitem><para>
3921 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
3922 exactly as you would in an ordinary instance declaration.
3923 (In contrast, in a <literal>deriving</literal> clause
3924 attached to a data type declaration, the context is inferred.)
3925 </para></listitem>
3926
3927 <listitem><para>
3928 Unlike a <literal>deriving</literal>
3929 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
3930 than the data type (assuming you also use
3931 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
3932 for example
3933 <programlisting>
3934 data Foo a = Bar a | Baz String
3935
3936 deriving instance Eq a => Eq (Foo [a])
3937 deriving instance Eq a => Eq (Foo (Maybe a))
3938 </programlisting>
3939 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
3940 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
3941 </para></listitem>
3942
3943 <listitem><para>
3944 Unlike a <literal>deriving</literal>
3945 declaration attached to a <literal>data</literal> declaration,
3946 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
3947 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
3948 your problem. (GHC will show you the offending code if it has a type error.)
3949 </para>
3950 <para>
3951 The merit of this is that you can derive instances for GADTs and other exotic
3952 data types, providing only that the boilerplate code does indeed typecheck. For example:
3953 <programlisting>
3954 data T a where
3955 T1 :: T Int
3956 T2 :: T Bool
3957
3958 deriving instance Show (T a)
3959 </programlisting>
3960 In this example, you cannot say <literal>... deriving( Show )</literal> on the
3961 data type declaration for <literal>T</literal>,
3962 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
3963 the instance declaration using stand-alone deriving.
3964 </para>
3965 <para>
3966 The down-side is that,
3967 if the boilerplate code fails to typecheck, you will get an error message about that
3968 code, which you did not write. Whereas, with a <literal>deriving</literal> clause
3969 the side-conditions are necessarily more conservative, but any error message
3970 may be more comprehensible.
3971 </para>
3972 </listitem>
3973 </itemizedlist></para>
3974
3975 <para>
3976 In other ways, however, a standalone deriving obeys the same rules as ordinary deriving:
3977 <itemizedlist>
3978 <listitem><para>
3979 A <literal>deriving instance</literal> declaration
3980 must obey the same rules concerning form and termination as ordinary instance declarations,
3981 controlled by the same flags; see <xref linkend="instance-decls"/>.
3982 </para></listitem>
3983
3984 <listitem>
3985 <para>The stand-alone syntax is generalised for newtypes in exactly the same
3986 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3987 For example:
3988 <programlisting>
3989 newtype Foo a = MkFoo (State Int a)
3990
3991 deriving instance MonadState Int Foo
3992 </programlisting>
3993 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3994 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3995 </para></listitem>
3996 </itemizedlist></para>
3997
3998 </sect2>
3999
4000 <sect2 id="deriving-extra">
4001 <title>Deriving instances of extra classes (<literal>Data</literal>, etc)</title>
4002
4003 <para>
4004 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
4005 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
4006 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
4007 classes <literal>Eq</literal>, <literal>Ord</literal>,
4008 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
4009 </para>
4010 <para>
4011 GHC extends this list with several more classes that may be automatically derived:
4012 <itemizedlist>
4013 <listitem><para> With <option>-XDeriveGeneric</option>, you can derive
4014 instances of the classes <literal>Generic</literal> and
4015 <literal>Generic1</literal>, defined in <literal>GHC.Generics</literal>.
4016 You can use these to define generic functions,
4017 as described in <xref linkend="generic-programming"/>.
4018 </para></listitem>
4019
4020 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
4021 the class <literal>Functor</literal>,
4022 defined in <literal>GHC.Base</literal>.
4023 </para></listitem>
4024
4025 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of
4026 the class <literal>Data</literal>,
4027 defined in <literal>Data.Data</literal>. See <xref linkend="deriving-typeable"/> for
4028 deriving <literal>Typeable</literal>.
4029 </para></listitem>
4030
4031 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
4032 the class <literal>Foldable</literal>,
4033 defined in <literal>Data.Foldable</literal>.
4034 </para></listitem>
4035
4036 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
4037 the class <literal>Traversable</literal>,
4038 defined in <literal>Data.Traversable</literal>. Since the <literal>Traversable</literal>
4039 instance dictates the instances of <literal>Functor</literal> and
4040 <literal>Foldable</literal>, you'll probably want to derive them too, so
4041 <option>-XDeriveTraversable</option> implies
4042 <option>-XDeriveFunctor</option> and <option>-XDeriveFoldable</option>.
4043 </para></listitem>
4044 </itemizedlist>
4045 You can also use a standalone deriving declaration instead
4046 (see <xref linkend="stand-alone-deriving"/>).
4047 </para>
4048 <para>
4049 In each case the appropriate class must be in scope before it
4050 can be mentioned in the <literal>deriving</literal> clause.
4051 </para>
4052 </sect2>
4053
4054 <sect2 id="deriving-typeable">
4055 <title>Deriving <literal>Typeable</literal> instances</title>
4056
4057 <para>The class <literal>Typeable</literal> is very special:
4058 <itemizedlist>
4059 <listitem><para>
4060 <literal>Typeable</literal> is kind-polymorphic (see
4061 <xref linkend="kind-polymorphism"/>).
4062 </para></listitem>
4063
4064 <listitem><para>
4065 Only derived instances of <literal>Typeable</literal> are allowed;
4066 i.e. handwritten instances are forbidden. This ensures that the
4067 programmer cannot subert the type system by writing bogus instances.
4068 </para></listitem>
4069
4070 <listitem><para>
4071 With <option>-XDeriveDataTypeable</option>
4072 GHC allows you to derive instances of <literal>Typeable</literal> for data types or newtypes,
4073 using a <literal>deriving</literal> clause, or using
4074 a standalone deriving declaration (<xref linkend="stand-alone-deriving"/>).
4075 </para></listitem>
4076
4077 <listitem><para>
4078 With <option>-XDataKinds</option>, deriving <literal>Typeable</literal> for a data
4079 type (whether via a deriving clause or standalone deriving)
4080 also derives <literal>Typeable</literal> for the promoted data constructors (<xref linkend="promotion"/>).
4081 </para></listitem>
4082
4083 <listitem><para>
4084 However, using standalone deriving, you can <emphasis>also</emphasis> derive
4085 a <literal>Typeable</literal> instance for a data family.
4086 You may not add a <literal>deriving(Typeable)</literal> clause to a
4087 <literal>data instance</literal> declaration; instead you must use a
4088 standalone deriving declaration for the data family.