Link from 7.6.3.4 to 7.7.2.6 in the user guide.
[ghc.git] / docs / users_guide / glasgow_exts.xml
1 <?xml version="1.0" encoding="iso-8859-1"?>
2 <para>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They can all be enabled or disabled by commandline flags
7 or language pragmas. By default GHC understands the most recent Haskell
8 version it supports, plus a handful of extensions.
9 </para>
10
11 <para>
12 Some of the Glasgow extensions serve to give you access to the
13 underlying facilities with which we implement Haskell. Thus, you can
14 get at the Raw Iron, if you are willing to write some non-portable
15 code at a more primitive level. You need not be &ldquo;stuck&rdquo;
16 on performance because of the implementation costs of Haskell's
17 &ldquo;high-level&rdquo; features&mdash;you can always code
18 &ldquo;under&rdquo; them. In an extreme case, you can write all your
19 time-critical code in C, and then just glue it together with Haskell!
20 </para>
21
22 <para>
23 Before you get too carried away working at the lowest level (e.g.,
24 sloshing <literal>MutableByteArray&num;</literal>s around your
25 program), you may wish to check if there are libraries that provide a
26 &ldquo;Haskellised veneer&rdquo; over the features you want. The
27 separate <ulink url="../libraries/index.html">libraries
28 documentation</ulink> describes all the libraries that come with GHC.
29 </para>
30
31 <!-- LANGUAGE OPTIONS -->
32 <sect1 id="options-language">
33 <title>Language options</title>
34
35 <indexterm><primary>language</primary><secondary>option</secondary>
36 </indexterm>
37 <indexterm><primary>options</primary><secondary>language</secondary>
38 </indexterm>
39 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
40 </indexterm>
41
42 <para>The language option flags control what variation of the language are
43 permitted.</para>
44
45 <para>Language options can be controlled in two ways:
46 <itemizedlist>
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
50 <listitem><para>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
53 </listitem>
54 </itemizedlist></para>
55
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 &what_glasgow_exts_does;
60 Enabling these options is the <emphasis>only</emphasis>
61 effect of <option>-fglasgow-exts</option>.
62 We are trying to move away from this portmanteau flag,
63 and towards enabling features individually.</para>
64
65 </sect1>
66
67 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
68 <sect1 id="primitives">
69 <title>Unboxed types and primitive operations</title>
70
71 <para>GHC is built on a raft of primitive data types and operations;
72 "primitive" in the sense that they cannot be defined in Haskell itself.
73 While you really can use this stuff to write fast code,
74 we generally find it a lot less painful, and more satisfying in the
75 long run, to use higher-level language features and libraries. With
76 any luck, the code you write will be optimised to the efficient
77 unboxed version in any case. And if it isn't, we'd like to know
78 about it.</para>
79
80 <para>All these primitive data types and operations are exported by the
81 library <literal>GHC.Prim</literal>, for which there is
82 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
83 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
84 </para>
85
86 <para>
87 If you want to mention any of the primitive data types or operations in your
88 program, you must first import <literal>GHC.Prim</literal> to bring them
89 into scope. Many of them have names ending in "&num;", and to mention such
90 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
91 </para>
92
93 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
94 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
95 we briefly summarise here. </para>
96
97 <sect2 id="glasgow-unboxed">
98 <title>Unboxed types</title>
99
100 <para>
101 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
102 </para>
103
104 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
105 that values of that type are represented by a pointer to a heap
106 object. The representation of a Haskell <literal>Int</literal>, for
107 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
108 type, however, is represented by the value itself, no pointers or heap
109 allocation are involved.
110 </para>
111
112 <para>
113 Unboxed types correspond to the &ldquo;raw machine&rdquo; types you
114 would use in C: <literal>Int&num;</literal> (long int),
115 <literal>Double&num;</literal> (double), <literal>Addr&num;</literal>
116 (void *), etc. The <emphasis>primitive operations</emphasis>
117 (PrimOps) on these types are what you might expect; e.g.,
118 <literal>(+&num;)</literal> is addition on
119 <literal>Int&num;</literal>s, and is the machine-addition that we all
120 know and love&mdash;usually one instruction.
121 </para>
122
123 <para>
124 Primitive (unboxed) types cannot be defined in Haskell, and are
125 therefore built into the language and compiler. Primitive types are
126 always unlifted; that is, a value of a primitive type cannot be
127 bottom. We use the convention (but it is only a convention)
128 that primitive types, values, and
129 operations have a <literal>&num;</literal> suffix (see <xref linkend="magic-hash"/>).
130 For some primitive types we have special syntax for literals, also
131 described in the <link linkend="magic-hash">same section</link>.
132 </para>
133
134 <para>
135 Primitive values are often represented by a simple bit-pattern, such
136 as <literal>Int&num;</literal>, <literal>Float&num;</literal>,
137 <literal>Double&num;</literal>. But this is not necessarily the case:
138 a primitive value might be represented by a pointer to a
139 heap-allocated object. Examples include
140 <literal>Array&num;</literal>, the type of primitive arrays. A
141 primitive array is heap-allocated because it is too big a value to fit
142 in a register, and would be too expensive to copy around; in a sense,
143 it is accidental that it is represented by a pointer. If a pointer
144 represents a primitive value, then it really does point to that value:
145 no unevaluated thunks, no indirections&hellip;nothing can be at the
146 other end of the pointer than the primitive value.
147 A numerically-intensive program using unboxed types can
148 go a <emphasis>lot</emphasis> faster than its &ldquo;standard&rdquo;
149 counterpart&mdash;we saw a threefold speedup on one example.
150 </para>
151
152 <para>
153 There are some restrictions on the use of primitive types:
154 <itemizedlist>
155 <listitem><para>The main restriction
156 is that you can't pass a primitive value to a polymorphic
157 function or store one in a polymorphic data type. This rules out
158 things like <literal>[Int&num;]</literal> (i.e. lists of primitive
159 integers). The reason for this restriction is that polymorphic
160 arguments and constructor fields are assumed to be pointers: if an
161 unboxed integer is stored in one of these, the garbage collector would
162 attempt to follow it, leading to unpredictable space leaks. Or a
163 <function>seq</function> operation on the polymorphic component may
164 attempt to dereference the pointer, with disastrous results. Even
165 worse, the unboxed value might be larger than a pointer
166 (<literal>Double&num;</literal> for instance).
167 </para>
168 </listitem>
169 <listitem><para> You cannot define a newtype whose representation type
170 (the argument type of the data constructor) is an unboxed type. Thus,
171 this is illegal:
172 <programlisting>
173 newtype A = MkA Int#
174 </programlisting>
175 </para></listitem>
176 <listitem><para> You cannot bind a variable with an unboxed type
177 in a <emphasis>top-level</emphasis> binding.
178 </para></listitem>
179 <listitem><para> You cannot bind a variable with an unboxed type
180 in a <emphasis>recursive</emphasis> binding.
181 </para></listitem>
182 <listitem><para> You may bind unboxed variables in a (non-recursive,
183 non-top-level) pattern binding, but you must make any such pattern-match
184 strict. For example, rather than:
185 <programlisting>
186 data Foo = Foo Int Int#
187
188 f x = let (Foo a b, w) = ..rhs.. in ..body..
189 </programlisting>
190 you must write:
191 <programlisting>
192 data Foo = Foo Int Int#
193
194 f x = let !(Foo a b, w) = ..rhs.. in ..body..
195 </programlisting>
196 since <literal>b</literal> has type <literal>Int#</literal>.
197 </para>
198 </listitem>
199 </itemizedlist>
200 </para>
201
202 </sect2>
203
204 <sect2 id="unboxed-tuples">
205 <title>Unboxed tuples</title>
206
207 <para>
208 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>;
209 they are a syntactic extension enabled by the language flag <option>-XUnboxedTuples</option>. An
210 unboxed tuple looks like this:
211 </para>
212
213 <para>
214
215 <programlisting>
216 (# e_1, ..., e_n #)
217 </programlisting>
218
219 </para>
220
221 <para>
222 where <literal>e&lowbar;1..e&lowbar;n</literal> are expressions of any
223 type (primitive or non-primitive). The type of an unboxed tuple looks
224 the same.
225 </para>
226
227 <para>
228 Note that when unboxed tuples are enabled,
229 <literal>(#</literal> is a single lexeme, so for example when using
230 operators like <literal>#</literal> and <literal>#-</literal> you need
231 to write <literal>( # )</literal> and <literal>( #- )</literal> rather than
232 <literal>(#)</literal> and <literal>(#-)</literal>.
233 </para>
234
235 <para>
236 Unboxed tuples are used for functions that need to return multiple
237 values, but they avoid the heap allocation normally associated with
238 using fully-fledged tuples. When an unboxed tuple is returned, the
239 components are put directly into registers or on the stack; the
240 unboxed tuple itself does not have a composite representation. Many
241 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
242 tuples.
243 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
244 tuples to avoid unnecessary allocation during sequences of operations.
245 </para>
246
247 <para>
248 There are some restrictions on the use of unboxed tuples:
249 <itemizedlist>
250
251 <listitem>
252 <para>
253 Values of unboxed tuple types are subject to the same restrictions as
254 other unboxed types; i.e. they may not be stored in polymorphic data
255 structures or passed to polymorphic functions.
256 </para>
257 </listitem>
258
259 <listitem>
260 <para>
261 The typical use of unboxed tuples is simply to return multiple values,
262 binding those multiple results with a <literal>case</literal> expression, thus:
263 <programlisting>
264 f x y = (# x+1, y-1 #)
265 g x = case f x x of { (# a, b #) -&#62; a + b }
266 </programlisting>
267 You can have an unboxed tuple in a pattern binding, thus
268 <programlisting>
269 f x = let (# p,q #) = h x in ..body..
270 </programlisting>
271 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
272 the resulting binding is lazy like any other Haskell pattern binding. The
273 above example desugars like this:
274 <programlisting>
275 f x = let t = case h x of { (# p,q #) -> (p,q) }
276 p = fst t
277 q = snd t
278 in ..body..
279 </programlisting>
280 Indeed, the bindings can even be recursive.
281 </para>
282 </listitem>
283 </itemizedlist>
284
285 </para>
286
287 </sect2>
288 </sect1>
289
290
291 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
292
293 <sect1 id="syntax-extns">
294 <title>Syntactic extensions</title>
295
296 <sect2 id="unicode-syntax">
297 <title>Unicode syntax</title>
298 <para>The language
299 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
300 enables Unicode characters to be used to stand for certain ASCII
301 character sequences. The following alternatives are provided:</para>
302
303 <informaltable>
304 <tgroup cols="2" align="left" colsep="1" rowsep="1">
305 <thead>
306 <row>
307 <entry>ASCII</entry>
308 <entry>Unicode alternative</entry>
309 <entry>Code point</entry>
310 <entry>Name</entry>
311 </row>
312 </thead>
313
314 <!--
315 to find the DocBook entities for these characters, find
316 the Unicode code point (e.g. 0x2237), and grep for it in
317 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
318 your system. Some of these Unicode code points don't have
319 equivalent DocBook entities.
320 -->
321
322 <tbody>
323 <row>
324 <entry><literal>::</literal></entry>
325 <entry>::</entry> <!-- no special char, apparently -->
326 <entry>0x2237</entry>
327 <entry>PROPORTION</entry>
328 </row>
329 </tbody>
330 <tbody>
331 <row>
332 <entry><literal>=&gt;</literal></entry>
333 <entry>&rArr;</entry>
334 <entry>0x21D2</entry>
335 <entry>RIGHTWARDS DOUBLE ARROW</entry>
336 </row>
337 </tbody>
338 <tbody>
339 <row>
340 <entry><literal>forall</literal></entry>
341 <entry>&forall;</entry>
342 <entry>0x2200</entry>
343 <entry>FOR ALL</entry>
344 </row>
345 </tbody>
346 <tbody>
347 <row>
348 <entry><literal>-&gt;</literal></entry>
349 <entry>&rarr;</entry>
350 <entry>0x2192</entry>
351 <entry>RIGHTWARDS ARROW</entry>
352 </row>
353 </tbody>
354 <tbody>
355 <row>
356 <entry><literal>&lt;-</literal></entry>
357 <entry>&larr;</entry>
358 <entry>0x2190</entry>
359 <entry>LEFTWARDS ARROW</entry>
360 </row>
361 </tbody>
362
363 <tbody>
364 <row>
365 <entry>-&lt;</entry>
366 <entry>&larrtl;</entry>
367 <entry>0x2919</entry>
368 <entry>LEFTWARDS ARROW-TAIL</entry>
369 </row>
370 </tbody>
371
372 <tbody>
373 <row>
374 <entry>&gt;-</entry>
375 <entry>&rarrtl;</entry>
376 <entry>0x291A</entry>
377 <entry>RIGHTWARDS ARROW-TAIL</entry>
378 </row>
379 </tbody>
380
381 <tbody>
382 <row>
383 <entry>-&lt;&lt;</entry>
384 <entry></entry>
385 <entry>0x291B</entry>
386 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
387 </row>
388 </tbody>
389
390 <tbody>
391 <row>
392 <entry>&gt;&gt;-</entry>
393 <entry></entry>
394 <entry>0x291C</entry>
395 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
396 </row>
397 </tbody>
398
399 <tbody>
400 <row>
401 <entry>*</entry>
402 <entry>&starf;</entry>
403 <entry>0x2605</entry>
404 <entry>BLACK STAR</entry>
405 </row>
406 </tbody>
407
408 </tgroup>
409 </informaltable>
410 </sect2>
411
412 <sect2 id="magic-hash">
413 <title>The magic hash</title>
414 <para>The language extension <option>-XMagicHash</option> allows "&num;" as a
415 postfix modifier to identifiers. Thus, "x&num;" is a valid variable, and "T&num;" is
416 a valid type constructor or data constructor.</para>
417
418 <para>The hash sign does not change semantics at all. We tend to use variable
419 names ending in "&num;" for unboxed values or types (e.g. <literal>Int&num;</literal>),
420 but there is no requirement to do so; they are just plain ordinary variables.
421 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
422 For example, to bring <literal>Int&num;</literal> into scope you must
423 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
424 the <option>-XMagicHash</option> extension
425 then allows you to <emphasis>refer</emphasis> to the <literal>Int&num;</literal>
426 that is now in scope. Note that with this option, the meaning of <literal>x&num;y = 0</literal>
427 is changed: it defines a function <literal>x&num;</literal> taking a single argument <literal>y</literal>;
428 to define the operator <literal>&num;</literal>, put a space: <literal>x &num; y = 0</literal>.
429
430 </para>
431 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
432 <itemizedlist>
433 <listitem><para> <literal>'x'&num;</literal> has type <literal>Char&num;</literal></para> </listitem>
434 <listitem><para> <literal>&quot;foo&quot;&num;</literal> has type <literal>Addr&num;</literal></para> </listitem>
435 <listitem><para> <literal>3&num;</literal> has type <literal>Int&num;</literal>. In general,
436 any Haskell integer lexeme followed by a <literal>&num;</literal> is an <literal>Int&num;</literal> literal, e.g.
437 <literal>-0x3A&num;</literal> as well as <literal>32&num;</literal>.</para></listitem>
438 <listitem><para> <literal>3&num;&num;</literal> has type <literal>Word&num;</literal>. In general,
439 any non-negative Haskell integer lexeme followed by <literal>&num;&num;</literal>
440 is a <literal>Word&num;</literal>. </para> </listitem>
441 <listitem><para> <literal>3.2&num;</literal> has type <literal>Float&num;</literal>.</para> </listitem>
442 <listitem><para> <literal>3.2&num;&num;</literal> has type <literal>Double&num;</literal></para> </listitem>
443 </itemizedlist>
444 </para>
445 </sect2>
446
447 <sect2 id="negative-literals">
448 <title>Negative literals</title>
449 <para>
450 The literal <literal>-123</literal> is, according to
451 Haskell98 and Haskell 2010, desugared as
452 <literal>negate (fromInteger 123)</literal>.
453 The language extension <option>-XNegativeLiterals</option>
454 means that it is instead desugared as
455 <literal>fromInteger (-123)</literal>.
456 </para>
457
458 <para>
459 This can make a difference when the positive and negative range of
460 a numeric data type don't match up. For example,
461 in 8-bit arithmetic -128 is representable, but +128 is not.
462 So <literal>negate (fromInteger 128)</literal> will elicit an
463 unexpected integer-literal-overflow message.
464 </para>
465 </sect2>
466
467 <sect2 id="num-decimals">
468 <title>Fractional looking integer literals</title>
469 <para>
470 Haskell 2010 and Haskell 98 define floating literals with
471 the syntax <literal>1.2e6</literal>. These literals have the
472 type <literal>Fractional a => a</literal>.
473 </para>
474
475 <para>
476 The language extension <option>-XNumDecimals</option> allows
477 you to also use the floating literal syntax for instances of
478 <literal>Integral</literal>, and have values like
479 <literal>(1.2e6 :: Num a => a)</literal>
480 </para>
481 </sect2>
482
483 <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 both
881 defining them <emphasis>and</emphasis> 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. Currently, they also don't work in GHCi, but that is a
1029 technical restriction that will be lifted in later versions.
1030 </para>
1031 <para>
1032 The variables in the left-hand side of the definition are bound by
1033 the pattern on the right-hand side. For implicitly bidirectional
1034 pattern synonyms, all the variables of the right-hand side must also
1035 occur on the left-hand side; also, wildcard patterns and view
1036 patterns are not allowed. For unidirectional and
1037 explicitly-bidirectional pattern synonyms, there is no restriction
1038 on the right-hand side pattern.
1039 </para>
1040
1041 <para>
1042 Pattern synonyms cannot be defined recursively.
1043 </para>
1044 </sect3>
1045
1046 <sect3 id="patsyn-impexp"> <title>Import and export of pattern synonyms</title>
1047
1048 <para>
1049 The name of the pattern synonym itself is in the same namespace as
1050 proper data constructors. In an export or import specification,
1051 you must prefix pattern
1052 names with the <literal>pattern</literal> keyword, e.g.:
1053 <programlisting>
1054 module Example (pattern Single) where
1055 pattern Single x = [x]
1056 </programlisting>
1057 Without the <literal>pattern</literal> prefix, <literal>Single</literal> would
1058 be interpreted as a type constructor in the export list.
1059 </para>
1060 <para>
1061 You may also use the <literal>pattern</literal> keyword in an import/export
1062 specification to import or export an ordinary data constructor. For example:
1063 <programlisting>
1064 import Data.Maybe( pattern Just )
1065 </programlisting>
1066 would bring into scope the data constructor <literal>Just</literal> from the
1067 <literal>Maybe</literal> type, without also bringing the type constructor
1068 <literal>Maybe</literal> into scope.
1069 </para>
1070 </sect3>
1071
1072 <sect3> <title>Typing of pattern synonyms</title>
1073
1074 <para>
1075 Given a pattern synonym definition of the form
1076 </para>
1077 <programlisting>
1078 pattern P var1 var2 ... varN &lt;- pat
1079 </programlisting>
1080 <para>
1081 it is assigned a <emphasis>pattern type</emphasis> of the form
1082 </para>
1083 <programlisting>
1084 pattern CProv => P t1 t2 ... tN :: CReq => t
1085 </programlisting>
1086 <para>
1087 where <replaceable>CProv</replaceable> and
1088 <replaceable>CReq</replaceable> are type contexts, and
1089 <replaceable>t1</replaceable>, <replaceable>t2</replaceable>, ...,
1090 <replaceable>tN</replaceable> and <replaceable>t</replaceable> are
1091 types.
1092 </para>
1093
1094 <para>
1095 A pattern synonym of this type can be used in a pattern if the
1096 instatiated (monomorphic) type satisfies the constraints of
1097 <replaceable>CReq</replaceable>. In this case, it extends the context
1098 available in the right-hand side of the match with
1099 <replaceable>CProv</replaceable>, just like how an existentially-typed
1100 data constructor can extend the context.
1101 </para>
1102
1103 <para>
1104 For example, in the following program:
1105 </para>
1106 <programlisting>
1107 {-# LANGUAGE PatternSynonyms, GADTs #-}
1108 module ShouldCompile where
1109
1110 data T a where
1111 MkT :: (Show b) => a -> b -> T a
1112
1113 pattern ExNumPat x = MkT 42 x
1114 </programlisting>
1115
1116 <para>
1117 the pattern type of <literal>ExNumPat</literal> is
1118 </para>
1119
1120 <programlisting>
1121 pattern (Show b) => ExNumPat b :: (Num a, Eq a) => T a
1122 </programlisting>
1123
1124 <para>
1125 and so can be used in a function definition like the following:
1126 </para>
1127
1128 <programlisting>
1129 f :: (Num t, Eq t) => T t -> String
1130 f (ExNumPat x) = show x
1131 </programlisting>
1132
1133 <para>
1134 For bidirectional pattern synonyms, uses as expressions have the type
1135 </para>
1136 <programlisting>
1137 (CProv, CReq) => t1 -> t2 -> ... -> tN -> t
1138 </programlisting>
1139
1140 <para>
1141 So in the previous example, <literal>ExNumPat</literal>,
1142 when used in an expression, has type
1143 </para>
1144 <programlisting>
1145 ExNumPat :: (Show b, Num a, Eq a) => b -> T t
1146 </programlisting>
1147 </sect3>
1148
1149 <sect3><title>Matching of pattern synonyms</title>
1150
1151 <para>
1152 A pattern synonym occurrence in a pattern is evaluated by first
1153 matching against the pattern synonym itself, and then on the argument
1154 patterns. For example, in the following program, <literal>f</literal>
1155 and <literal>f'</literal> are equivalent:
1156 </para>
1157
1158 <programlisting>
1159 pattern Pair x y &lt;- [x, y]
1160
1161 f (Pair True True) = True
1162 f _ = False
1163
1164 f' [x, y] | True &lt;- x, True &lt;- y = True
1165 f' _ = False
1166 </programlisting>
1167
1168 <para>
1169 Note that the strictness of <literal>f</literal> differs from that
1170 of <literal>g</literal> defined below:
1171 <programlisting>
1172 g [True, True] = True
1173 g _ = False
1174
1175 *Main> f (False:undefined)
1176 *** Exception: Prelude.undefined
1177 *Main> g (False:undefined)
1178 False
1179 </programlisting>
1180 </para>
1181 </sect3>
1182
1183 </sect2>
1184
1185 <!-- ===================== n+k patterns =================== -->
1186
1187 <sect2 id="n-k-patterns">
1188 <title>n+k patterns</title>
1189 <indexterm><primary><option>-XNPlusKPatterns</option></primary></indexterm>
1190
1191 <para>
1192 <literal>n+k</literal> pattern support is disabled by default. To enable
1193 it, you can use the <option>-XNPlusKPatterns</option> flag.
1194 </para>
1195
1196 </sect2>
1197
1198 <!-- ===================== Traditional record syntax =================== -->
1199
1200 <sect2 id="traditional-record-syntax">
1201 <title>Traditional record syntax</title>
1202 <indexterm><primary><option>-XNoTraditionalRecordSyntax</option></primary></indexterm>
1203
1204 <para>
1205 Traditional record syntax, such as <literal>C {f = x}</literal>, is enabled by default.
1206 To disable it, you can use the <option>-XNoTraditionalRecordSyntax</option> flag.
1207 </para>
1208
1209 </sect2>
1210
1211 <!-- ===================== Recursive do-notation =================== -->
1212
1213 <sect2 id="recursive-do-notation">
1214 <title>The recursive do-notation
1215 </title>
1216
1217 <para>
1218 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
1219 that is, the variables bound in a do-expression are visible only in the textually following
1220 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
1221 group.
1222 </para>
1223
1224 <para>
1225 It turns out that such recursive bindings do indeed make sense for a variety of monads, but
1226 not all. In particular, recursion in this sense requires a fixed-point operator for the underlying
1227 monad, captured by the <literal>mfix</literal> method of the <literal>MonadFix</literal> class, defined in <literal>Control.Monad.Fix</literal> as follows:
1228 <programlisting>
1229 class Monad m => MonadFix m where
1230 mfix :: (a -> m a) -> m a
1231 </programlisting>
1232 Haskell's
1233 <literal>Maybe</literal>, <literal>[]</literal> (list), <literal>ST</literal> (both strict and lazy versions),
1234 <literal>IO</literal>, and many other monads have <literal>MonadFix</literal> instances. On the negative
1235 side, the continuation monad, with the signature <literal>(a -> r) -> r</literal>, does not.
1236 </para>
1237
1238 <para>
1239 For monads that do belong to the <literal>MonadFix</literal> class, GHC provides
1240 an extended version of the do-notation that allows recursive bindings.
1241 The <option>-XRecursiveDo</option> (language pragma: <literal>RecursiveDo</literal>)
1242 provides the necessary syntactic support, introducing the keywords <literal>mdo</literal> and
1243 <literal>rec</literal> for higher and lower levels of the notation respectively. Unlike
1244 bindings in a <literal>do</literal> expression, those introduced by <literal>mdo</literal> and <literal>rec</literal>
1245 are recursively defined, much like in an ordinary let-expression. Due to the new
1246 keyword <literal>mdo</literal>, we also call this notation the <emphasis>mdo-notation</emphasis>.
1247 </para>
1248
1249 <para>
1250 Here is a simple (albeit contrived) example:
1251 <programlisting>
1252 {-# LANGUAGE RecursiveDo #-}
1253 justOnes = mdo { xs &lt;- Just (1:xs)
1254 ; return (map negate xs) }
1255 </programlisting>
1256 or equivalently
1257 <programlisting>
1258 {-# LANGUAGE RecursiveDo #-}
1259 justOnes = do { rec { xs &lt;- Just (1:xs) }
1260 ; return (map negate xs) }
1261 </programlisting>
1262 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
1263 </para>
1264
1265 <para>
1266 GHC's implementation the mdo-notation closely follows the original translation as described in the paper
1267 <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for Haskell</ulink>, which
1268 in turn is based on the work <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion
1269 in Monadic Computations</ulink>. Furthermore, GHC extends the syntax described in the former paper
1270 with a lower level syntax flagged by the <literal>rec</literal> keyword, as we describe next.
1271 </para>
1272
1273 <sect3>
1274 <title>Recursive binding groups</title>
1275
1276 <para>
1277 The flag <option>-XRecursiveDo</option> also introduces a new keyword <literal>rec</literal>, which wraps a
1278 mutually-recursive group of monadic statements inside a <literal>do</literal> expression, producing a single statement.
1279 Similar to a <literal>let</literal> statement inside a <literal>do</literal>, variables bound in
1280 the <literal>rec</literal> are visible throughout the <literal>rec</literal> group, and below it. For example, compare
1281 <programlisting>
1282 do { a &lt;- getChar do { a &lt;- getChar
1283 ; let { r1 = f a r2 ; rec { r1 &lt;- f a r2
1284 ; ; r2 = g r1 } ; ; r2 &lt;- g r1 }
1285 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
1286 </programlisting>
1287 In both cases, <literal>r1</literal> and <literal>r2</literal> are available both throughout
1288 the <literal>let</literal> or <literal>rec</literal> block, and in the statements that follow it.
1289 The difference is that <literal>let</literal> is non-monadic, while <literal>rec</literal> is monadic.
1290 (In Haskell <literal>let</literal> is really <literal>letrec</literal>, of course.)
1291 </para>
1292
1293 <para>
1294 The semantics of <literal>rec</literal> is fairly straightforward. Whenever GHC finds a <literal>rec</literal>
1295 group, it will compute its set of bound variables, and will introduce an appropriate call
1296 to the underlying monadic value-recursion operator <literal>mfix</literal>, belonging to the
1297 <literal>MonadFix</literal> class. Here is an example:
1298 <programlisting>
1299 rec { b &lt;- f a c ===> (b,c) &lt;- mfix (\ ~(b,c) -> do { b &lt;- f a c
1300 ; c &lt;- f b a } ; c &lt;- f b a
1301 ; return (b,c) })
1302 </programlisting>
1303 As usual, the meta-variables <literal>b</literal>, <literal>c</literal> etc., can be arbitrary patterns.
1304 In general, the statement <literal>rec <replaceable>ss</replaceable></literal> is desugared to the statement
1305 <programlisting>
1306 <replaceable>vs</replaceable> &lt;- mfix (\ ~<replaceable>vs</replaceable> -&gt; do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
1307 </programlisting>
1308 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
1309 </para>
1310
1311 <para>
1312 Note in particular that the translation for a <literal>rec</literal> block only involves wrapping a call
1313 to <literal>mfix</literal>: it performs no other analysis on the bindings. The latter is the task
1314 for the <literal>mdo</literal> notation, which is described next.
1315 </para>
1316 </sect3>
1317
1318 <sect3>
1319 <title>The <literal>mdo</literal> notation</title>
1320
1321 <para>
1322 A <literal>rec</literal>-block tells the compiler where precisely the recursive knot should be tied. It turns out that
1323 the placement of the recursive knots can be rather delicate: in particular, we would like the knots to be wrapped
1324 around as minimal groups as possible. This process is known as <emphasis>segmentation</emphasis>, and is described
1325 in detail in Secton 3.2 of <ulink url="https://sites.google.com/site/leventerkok/recdo.pdf">A recursive do for
1326 Haskell</ulink>. Segmentation improves polymorphism and reduces the size of the recursive knot. Most importantly, it avoids
1327 unnecessary interference caused by a fundamental issue with the so-called <emphasis>right-shrinking</emphasis>
1328 axiom for monadic recursion. In brief, most monads of interest (IO, strict state, etc.) do <emphasis>not</emphasis>
1329 have recursion operators that satisfy this axiom, and thus not performing segmentation can cause unnecessary
1330 interference, changing the termination behavior of the resulting translation.
1331 (Details can be found in Sections 3.1 and 7.2.2 of
1332 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.)
1333 </para>
1334
1335 <para>
1336 The <literal>mdo</literal> notation removes the burden of placing
1337 explicit <literal>rec</literal> blocks in the code. Unlike an
1338 ordinary <literal>do</literal> expression, in which variables bound by
1339 statements are only in scope for later statements, variables bound in
1340 an <literal>mdo</literal> expression are in scope for all statements
1341 of the expression. The compiler then automatically identifies minimal
1342 mutually recursively dependent segments of statements, treating them as
1343 if the user had wrapped a <literal>rec</literal> qualifier around them.
1344 </para>
1345
1346 <para>
1347 The definition is syntactic:
1348 </para>
1349 <itemizedlist>
1350 <listitem>
1351 <para>
1352 A generator <replaceable>g</replaceable>
1353 <emphasis>depends</emphasis> on a textually following generator
1354 <replaceable>g'</replaceable>, if
1355 </para>
1356 <itemizedlist>
1357 <listitem>
1358 <para>
1359 <replaceable>g'</replaceable> defines a variable that
1360 is used by <replaceable>g</replaceable>, or
1361 </para>
1362 </listitem>
1363 <listitem>
1364 <para>
1365 <replaceable>g'</replaceable> textually appears between
1366 <replaceable>g</replaceable> and
1367 <replaceable>g''</replaceable>, where <replaceable>g</replaceable>
1368 depends on <replaceable>g''</replaceable>.
1369 </para>
1370 </listitem>
1371 </itemizedlist>
1372 </listitem>
1373 <listitem>
1374 <para>
1375 A <emphasis>segment</emphasis> of a given
1376 <literal>mdo</literal>-expression is a minimal sequence of generators
1377 such that no generator of the sequence depends on an outside
1378 generator. As a special case, although it is not a generator,
1379 the final expression in an <literal>mdo</literal>-expression is
1380 considered to form a segment by itself.
1381 </para>
1382 </listitem>
1383 </itemizedlist>
1384 <para>
1385 Segments in this sense are
1386 related to <emphasis>strongly-connected components</emphasis> analysis,
1387 with the exception that bindings in a segment cannot be reordered and
1388 must be contiguous.
1389 </para>
1390
1391 <para>
1392 Here is an example <literal>mdo</literal>-expression, and its translation to <literal>rec</literal> blocks:
1393 <programlisting>
1394 mdo { a &lt;- getChar ===> do { a &lt;- getChar
1395 ; b &lt;- f a c ; rec { b &lt;- f a c
1396 ; c &lt;- f b a ; ; c &lt;- f b a }
1397 ; z &lt;- h a b ; z &lt;- h a b
1398 ; d &lt;- g d e ; rec { d &lt;- g d e
1399 ; e &lt;- g a z ; ; e &lt;- g a z }
1400 ; putChar c } ; putChar c }
1401 </programlisting>
1402 Note that a given <literal>mdo</literal> expression can cause the creation of multiple <literal>rec</literal> blocks.
1403 If there are no recursive dependencies, <literal>mdo</literal> will introduce no <literal>rec</literal> blocks. In this
1404 latter case an <literal>mdo</literal> expression is precisely the same as a <literal>do</literal> expression, as one
1405 would expect.
1406 </para>
1407
1408 <para>
1409 In summary, given an <literal>mdo</literal> expression, GHC first performs segmentation, introducing
1410 <literal>rec</literal> blocks to wrap over minimal recursive groups. Then, each resulting
1411 <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal> as described
1412 in the previous section. The original <literal>mdo</literal>-expression typechecks exactly when the desugared
1413 version would do so.
1414 </para>
1415
1416 <para>
1417 Here are some other important points in using the recursive-do notation:
1418
1419 <itemizedlist>
1420 <listitem>
1421 <para>
1422 It is enabled with the flag <literal>-XRecursiveDo</literal>, or the <literal>LANGUAGE RecursiveDo</literal>
1423 pragma. (The same flag enables both <literal>mdo</literal>-notation, and the use of <literal>rec</literal>
1424 blocks inside <literal>do</literal> expressions.)
1425 </para>
1426 </listitem>
1427 <listitem>
1428 <para>
1429 <literal>rec</literal> blocks can also be used inside <literal>mdo</literal>-expressions, which will be
1430 treated as a single statement. However, it is good style to either use <literal>mdo</literal> or
1431 <literal>rec</literal> blocks in a single expression.
1432 </para>
1433 </listitem>
1434 <listitem>
1435 <para>
1436 If recursive bindings are required for a monad, then that monad must be declared an instance of
1437 the <literal>MonadFix</literal> class.
1438 </para>
1439 </listitem>
1440 <listitem>
1441 <para>
1442 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1443 Furthermore, the <literal>Control.Monad.ST</literal> and <literal>Control.Monad.ST.Lazy</literal>
1444 modules provide the instances of the <literal>MonadFix</literal> class for Haskell's internal
1445 state monad (strict and lazy, respectively).
1446 </para>
1447 </listitem>
1448 <listitem>
1449 <para>
1450 Like <literal>let</literal> and <literal>where</literal> bindings, name shadowing is not allowed within
1451 an <literal>mdo</literal>-expression or a <literal>rec</literal>-block; that is, all the names bound in
1452 a single <literal>rec</literal> must be distinct. (GHC will complain if this is not the case.)
1453 </para>
1454 </listitem>
1455 </itemizedlist>
1456 </para>
1457 </sect3>
1458
1459
1460 </sect2>
1461
1462
1463 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1464
1465 <sect2 id="parallel-list-comprehensions">
1466 <title>Parallel List Comprehensions</title>
1467 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1468 </indexterm>
1469 <indexterm><primary>parallel list comprehensions</primary>
1470 </indexterm>
1471
1472 <para>Parallel list comprehensions are a natural extension to list
1473 comprehensions. List comprehensions can be thought of as a nice
1474 syntax for writing maps and filters. Parallel comprehensions
1475 extend this to include the zipWith family.</para>
1476
1477 <para>A parallel list comprehension has multiple independent
1478 branches of qualifier lists, each separated by a `|' symbol. For
1479 example, the following zips together two lists:</para>
1480
1481 <programlisting>
1482 [ (x, y) | x &lt;- xs | y &lt;- ys ]
1483 </programlisting>
1484
1485 <para>The behaviour of parallel list comprehensions follows that of
1486 zip, in that the resulting list will have the same length as the
1487 shortest branch.</para>
1488
1489 <para>We can define parallel list comprehensions by translation to
1490 regular comprehensions. Here's the basic idea:</para>
1491
1492 <para>Given a parallel comprehension of the form: </para>
1493
1494 <programlisting>
1495 [ e | p1 &lt;- e11, p2 &lt;- e12, ...
1496 | q1 &lt;- e21, q2 &lt;- e22, ...
1497 ...
1498 ]
1499 </programlisting>
1500
1501 <para>This will be translated to: </para>
1502
1503 <programlisting>
1504 [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
1505 [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
1506 ...
1507 ]
1508 </programlisting>
1509
1510 <para>where `zipN' is the appropriate zip for the given number of
1511 branches.</para>
1512
1513 </sect2>
1514
1515 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1516
1517 <sect2 id="generalised-list-comprehensions">
1518 <title>Generalised (SQL-Like) List Comprehensions</title>
1519 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1520 </indexterm>
1521 <indexterm><primary>extended list comprehensions</primary>
1522 </indexterm>
1523 <indexterm><primary>group</primary></indexterm>
1524 <indexterm><primary>sql</primary></indexterm>
1525
1526
1527 <para>Generalised list comprehensions are a further enhancement to the
1528 list comprehension syntactic sugar to allow operations such as sorting
1529 and grouping which are familiar from SQL. They are fully described in the
1530 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1531 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1532 except that the syntax we use differs slightly from the paper.</para>
1533 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1534 <para>Here is an example:
1535 <programlisting>
1536 employees = [ ("Simon", "MS", 80)
1537 , ("Erik", "MS", 100)
1538 , ("Phil", "Ed", 40)
1539 , ("Gordon", "Ed", 45)
1540 , ("Paul", "Yale", 60)]
1541
1542 output = [ (the dept, sum salary)
1543 | (name, dept, salary) &lt;- employees
1544 , then group by dept using groupWith
1545 , then sortWith by (sum salary)
1546 , then take 5 ]
1547 </programlisting>
1548 In this example, the list <literal>output</literal> would take on
1549 the value:
1550
1551 <programlisting>
1552 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1553 </programlisting>
1554 </para>
1555 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1556 (The functions <literal>sortWith</literal> and <literal>groupWith</literal> are not keywords; they are ordinary
1557 functions that are exported by <literal>GHC.Exts</literal>.)</para>
1558
1559 <para>There are five new forms of comprehension qualifier,
1560 all introduced by the (existing) keyword <literal>then</literal>:
1561 <itemizedlist>
1562 <listitem>
1563
1564 <programlisting>
1565 then f
1566 </programlisting>
1567
1568 This statement requires that <literal>f</literal> have the type <literal>
1569 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1570 motivating example, as this form is used to apply <literal>take 5</literal>.
1571
1572 </listitem>
1573
1574
1575 <listitem>
1576 <para>
1577 <programlisting>
1578 then f by e
1579 </programlisting>
1580
1581 This form is similar to the previous one, but allows you to create a function
1582 which will be passed as the first argument to f. As a consequence f must have
1583 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1584 from the type, this function lets f &quot;project out&quot; some information
1585 from the elements of the list it is transforming.</para>
1586
1587 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1588 is supplied with a function that lets it find out the <literal>sum salary</literal>
1589 for any item in the list comprehension it transforms.</para>
1590
1591 </listitem>
1592
1593
1594 <listitem>
1595
1596 <programlisting>
1597 then group by e using f
1598 </programlisting>
1599
1600 <para>This is the most general of the grouping-type statements. In this form,
1601 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1602 As with the <literal>then f by e</literal> case above, the first argument
1603 is a function supplied to f by the compiler which lets it compute e on every
1604 element of the list being transformed. However, unlike the non-grouping case,
1605 f additionally partitions the list into a number of sublists: this means that
1606 at every point after this statement, binders occurring before it in the comprehension
1607 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1608 this, let's look at an example:</para>
1609
1610 <programlisting>
1611 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1612 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1613 groupRuns f = groupBy (\x y -> f x == f y)
1614
1615 output = [ (the x, y)
1616 | x &lt;- ([1..3] ++ [1..2])
1617 , y &lt;- [4..6]
1618 , then group by x using groupRuns ]
1619 </programlisting>
1620
1621 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1622
1623 <programlisting>
1624 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1625 </programlisting>
1626
1627 <para>Note that we have used the <literal>the</literal> function to change the type
1628 of x from a list to its original numeric type. The variable y, in contrast, is left
1629 unchanged from the list form introduced by the grouping.</para>
1630
1631 </listitem>
1632
1633 <listitem>
1634
1635 <programlisting>
1636 then group using f
1637 </programlisting>
1638
1639 <para>With this form of the group statement, f is required to simply have the type
1640 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1641 comprehension so far directly. An example of this form is as follows:</para>
1642
1643 <programlisting>
1644 output = [ x
1645 | y &lt;- [1..5]
1646 , x &lt;- "hello"
1647 , then group using inits]
1648 </programlisting>
1649
1650 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1651
1652 <programlisting>
1653 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1654 </programlisting>
1655
1656 </listitem>
1657 </itemizedlist>
1658 </para>
1659 </sect2>
1660
1661 <!-- ===================== MONAD COMPREHENSIONS ===================== -->
1662
1663 <sect2 id="monad-comprehensions">
1664 <title>Monad comprehensions</title>
1665 <indexterm><primary>monad comprehensions</primary></indexterm>
1666
1667 <para>
1668 Monad comprehensions generalise the list comprehension notation,
1669 including parallel comprehensions
1670 (<xref linkend="parallel-list-comprehensions"/>) and
1671 transform comprehensions (<xref linkend="generalised-list-comprehensions"/>)
1672 to work for any monad.
1673 </para>
1674
1675 <para>Monad comprehensions support:</para>
1676
1677 <itemizedlist>
1678 <listitem>
1679 <para>
1680 Bindings:
1681 </para>
1682
1683 <programlisting>
1684 [ x + y | x &lt;- Just 1, y &lt;- Just 2 ]
1685 </programlisting>
1686
1687 <para>
1688 Bindings are translated with the <literal>(&gt;&gt;=)</literal> and
1689 <literal>return</literal> functions to the usual do-notation:
1690 </para>
1691
1692 <programlisting>
1693 do x &lt;- Just 1
1694 y &lt;- Just 2
1695 return (x+y)
1696 </programlisting>
1697
1698 </listitem>
1699 <listitem>
1700 <para>
1701 Guards:
1702 </para>
1703
1704 <programlisting>
1705 [ x | x &lt;- [1..10], x &lt;= 5 ]
1706 </programlisting>
1707
1708 <para>
1709 Guards are translated with the <literal>guard</literal> function,
1710 which requires a <literal>MonadPlus</literal> instance:
1711 </para>
1712
1713 <programlisting>
1714 do x &lt;- [1..10]
1715 guard (x &lt;= 5)
1716 return x
1717 </programlisting>
1718
1719 </listitem>
1720 <listitem>
1721 <para>
1722 Transform statements (as with <literal>-XTransformListComp</literal>):
1723 </para>
1724
1725 <programlisting>
1726 [ x+y | x &lt;- [1..10], y &lt;- [1..x], then take 2 ]
1727 </programlisting>
1728
1729 <para>
1730 This translates to:
1731 </para>
1732
1733 <programlisting>
1734 do (x,y) &lt;- take 2 (do x &lt;- [1..10]
1735 y &lt;- [1..x]
1736 return (x,y))
1737 return (x+y)
1738 </programlisting>
1739
1740 </listitem>
1741 <listitem>
1742 <para>
1743 Group statements (as with <literal>-XTransformListComp</literal>):
1744 </para>
1745
1746 <programlisting>
1747 [ x | x &lt;- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
1748 [ x | x &lt;- [1,1,2,2,3], then group using myGroup ]
1749 </programlisting>
1750
1751 </listitem>
1752 <listitem>
1753 <para>
1754 Parallel statements (as with <literal>-XParallelListComp</literal>):
1755 </para>
1756
1757 <programlisting>
1758 [ (x+y) | x &lt;- [1..10]
1759 | y &lt;- [11..20]
1760 ]
1761 </programlisting>
1762
1763 <para>
1764 Parallel statements are translated using the
1765 <literal>mzip</literal> function, which requires a
1766 <literal>MonadZip</literal> instance defined in
1767 <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
1768 </para>
1769
1770 <programlisting>
1771 do (x,y) &lt;- mzip (do x &lt;- [1..10]
1772 return x)
1773 (do y &lt;- [11..20]
1774 return y)
1775 return (x+y)
1776 </programlisting>
1777
1778 </listitem>
1779 </itemizedlist>
1780
1781 <para>
1782 All these features are enabled by default if the
1783 <literal>MonadComprehensions</literal> extension is enabled. The types
1784 and more detailed examples on how to use comprehensions are explained
1785 in the previous chapters <xref
1786 linkend="generalised-list-comprehensions"/> and <xref
1787 linkend="parallel-list-comprehensions"/>. In general you just have
1788 to replace the type <literal>[a]</literal> with the type
1789 <literal>Monad m => m a</literal> for monad comprehensions.
1790 </para>
1791
1792 <para>
1793 Note: Even though most of these examples are using the list monad,
1794 monad comprehensions work for any monad.
1795 The <literal>base</literal> package offers all necessary instances for
1796 lists, which make <literal>MonadComprehensions</literal> backward
1797 compatible to built-in, transform and parallel list comprehensions.
1798 </para>
1799 <para> More formally, the desugaring is as follows. We write <literal>D[ e | Q]</literal>
1800 to mean the desugaring of the monad comprehension <literal>[ e | Q]</literal>:
1801 <programlisting>
1802 Expressions: e
1803 Declarations: d
1804 Lists of qualifiers: Q,R,S
1805
1806 -- Basic forms
1807 D[ e | ] = return e
1808 D[ e | p &lt;- e, Q ] = e &gt;&gt;= \p -&gt; D[ e | Q ]
1809 D[ e | e, Q ] = guard e &gt;&gt; \p -&gt; D[ e | Q ]
1810 D[ e | let d, Q ] = let d in D[ e | Q ]
1811
1812 -- Parallel comprehensions (iterate for multiple parallel branches)
1813 D[ e | (Q | R), S ] = mzip D[ Qv | Q ] D[ Rv | R ] &gt;&gt;= \(Qv,Rv) -&gt; D[ e | S ]
1814
1815 -- Transform comprehensions
1816 D[ e | Q then f, R ] = f D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1817
1818 D[ e | Q then f by b, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \Qv -&gt; D[ e | R ]
1819
1820 D[ e | Q then group using f, R ] = f D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1821 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1822 Qv -&gt; D[ e | R ]
1823
1824 D[ e | Q then group by b using f, R ] = f (\Qv -&gt; b) D[ Qv | Q ] &gt;&gt;= \ys -&gt;
1825 case (fmap selQv1 ys, ..., fmap selQvn ys) of
1826 Qv -&gt; D[ e | R ]
1827
1828 where Qv is the tuple of variables bound by Q (and used subsequently)
1829 selQvi is a selector mapping Qv to the ith component of Qv
1830
1831 Operator Standard binding Expected type
1832 --------------------------------------------------------------------
1833 return GHC.Base t1 -&gt; m t2
1834 (&gt;&gt;=) GHC.Base m1 t1 -&gt; (t2 -&gt; m2 t3) -&gt; m3 t3
1835 (&gt;&gt;) GHC.Base m1 t1 -&gt; m2 t2 -&gt; m3 t3
1836 guard Control.Monad t1 -&gt; m t2
1837 fmap GHC.Base forall a b. (a-&gt;b) -&gt; n a -&gt; n b
1838 mzip Control.Monad.Zip forall a b. m a -&gt; m b -&gt; m (a,b)
1839 </programlisting>
1840 The comprehension should typecheck when its desugaring would typecheck.
1841 </para>
1842 <para>
1843 Monad comprehensions support rebindable syntax (<xref linkend="rebindable-syntax"/>).
1844 Without rebindable
1845 syntax, the operators from the "standard binding" module are used; with
1846 rebindable syntax, the operators are looked up in the current lexical scope.
1847 For example, parallel comprehensions will be typechecked and desugared
1848 using whatever "<literal>mzip</literal>" is in scope.
1849 </para>
1850 <para>
1851 The rebindable operators must have the "Expected type" given in the
1852 table above. These types are surprisingly general. For example, you can
1853 use a bind operator with the type
1854 <programlisting>
1855 (>>=) :: T x y a -> (a -> T y z b) -> T x z b
1856 </programlisting>
1857 In the case of transform comprehensions, notice that the groups are
1858 parameterised over some arbitrary type <literal>n</literal> (provided it
1859 has an <literal>fmap</literal>, as well as
1860 the comprehension being over an arbitrary monad.
1861 </para>
1862 </sect2>
1863
1864 <!-- ===================== REBINDABLE SYNTAX =================== -->
1865
1866 <sect2 id="rebindable-syntax">
1867 <title>Rebindable syntax and the implicit Prelude import</title>
1868
1869 <para><indexterm><primary>-XNoImplicitPrelude
1870 option</primary></indexterm> GHC normally imports
1871 <filename>Prelude.hi</filename> files for you. If you'd
1872 rather it didn't, then give it a
1873 <option>-XNoImplicitPrelude</option> option. The idea is
1874 that you can then import a Prelude of your own. (But don't
1875 call it <literal>Prelude</literal>; the Haskell module
1876 namespace is flat, and you must not conflict with any
1877 Prelude module.)</para>
1878
1879 <para>Suppose you are importing a Prelude of your own
1880 in order to define your own numeric class
1881 hierarchy. It completely defeats that purpose if the
1882 literal "1" means "<literal>Prelude.fromInteger
1883 1</literal>", which is what the Haskell Report specifies.
1884 So the <option>-XRebindableSyntax</option>
1885 flag causes
1886 the following pieces of built-in syntax to refer to
1887 <emphasis>whatever is in scope</emphasis>, not the Prelude
1888 versions:
1889 <itemizedlist>
1890 <listitem>
1891 <para>An integer literal <literal>368</literal> means
1892 "<literal>fromInteger (368::Integer)</literal>", rather than
1893 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1894 </para> </listitem>
1895
1896 <listitem><para>Fractional literals are handed in just the same way,
1897 except that the translation is
1898 <literal>fromRational (3.68::Rational)</literal>.
1899 </para> </listitem>
1900
1901 <listitem><para>The equality test in an overloaded numeric pattern
1902 uses whatever <literal>(==)</literal> is in scope.
1903 </para> </listitem>
1904
1905 <listitem><para>The subtraction operation, and the
1906 greater-than-or-equal test, in <literal>n+k</literal> patterns
1907 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1908 </para></listitem>
1909
1910 <listitem>
1911 <para>Negation (e.g. "<literal>- (f x)</literal>")
1912 means "<literal>negate (f x)</literal>", both in numeric
1913 patterns, and expressions.
1914 </para></listitem>
1915
1916 <listitem>
1917 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1918 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1919 </para></listitem>
1920
1921 <listitem>
1922 <para>"Do" notation is translated using whatever
1923 functions <literal>(>>=)</literal>,
1924 <literal>(>>)</literal>, and <literal>fail</literal>,
1925 are in scope (not the Prelude
1926 versions). List comprehensions, <literal>mdo</literal>
1927 (<xref linkend="recursive-do-notation"/>), and parallel array
1928 comprehensions, are unaffected. </para></listitem>
1929
1930 <listitem>
1931 <para>Arrow
1932 notation (see <xref linkend="arrow-notation"/>)
1933 uses whatever <literal>arr</literal>,
1934 <literal>(>>>)</literal>, <literal>first</literal>,
1935 <literal>app</literal>, <literal>(|||)</literal> and
1936 <literal>loop</literal> functions are in scope. But unlike the
1937 other constructs, the types of these functions must match the
1938 Prelude types very closely. Details are in flux; if you want
1939 to use this, ask!
1940 </para></listitem>
1941 </itemizedlist>
1942 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1943 </para>
1944 <para>
1945 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1946 even if that is a little unexpected. For example, the
1947 static semantics of the literal <literal>368</literal>
1948 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1949 <literal>fromInteger</literal> to have any of the types:
1950 <programlisting>
1951 fromInteger :: Integer -> Integer
1952 fromInteger :: forall a. Foo a => Integer -> a
1953 fromInteger :: Num a => a -> Integer
1954 fromInteger :: Integer -> Bool -> Bool
1955 </programlisting>
1956 </para>
1957
1958 <para>Be warned: this is an experimental facility, with
1959 fewer checks than usual. Use <literal>-dcore-lint</literal>
1960 to typecheck the desugared program. If Core Lint is happy
1961 you should be all right.</para>
1962
1963 </sect2>
1964
1965 <sect2 id="postfix-operators">
1966 <title>Postfix operators</title>
1967
1968 <para>
1969 The <option>-XPostfixOperators</option> flag enables a small
1970 extension to the syntax of left operator sections, which allows you to
1971 define postfix operators. The extension is this: the left section
1972 <programlisting>
1973 (e !)
1974 </programlisting>
1975 is equivalent (from the point of view of both type checking and execution) to the expression
1976 <programlisting>
1977 ((!) e)
1978 </programlisting>
1979 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1980 The strict Haskell 98 interpretation is that the section is equivalent to
1981 <programlisting>
1982 (\y -> (!) e y)
1983 </programlisting>
1984 That is, the operator must be a function of two arguments. GHC allows it to
1985 take only one argument, and that in turn allows you to write the function
1986 postfix.
1987 </para>
1988 <para>The extension does not extend to the left-hand side of function
1989 definitions; you must define such a function in prefix form.</para>
1990
1991 </sect2>
1992
1993 <sect2 id="tuple-sections">
1994 <title>Tuple sections</title>
1995
1996 <para>
1997 The <option>-XTupleSections</option> flag enables Python-style partially applied
1998 tuple constructors. For example, the following program
1999 <programlisting>
2000 (, True)
2001 </programlisting>
2002 is considered to be an alternative notation for the more unwieldy alternative
2003 <programlisting>
2004 \x -> (x, True)
2005 </programlisting>
2006 You can omit any combination of arguments to the tuple, as in the following
2007 <programlisting>
2008 (, "I", , , "Love", , 1337)
2009 </programlisting>
2010 which translates to
2011 <programlisting>
2012 \a b c d -> (a, "I", b, c, "Love", d, 1337)
2013 </programlisting>
2014 </para>
2015
2016 <para>
2017 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
2018 will also be available for them, like so
2019 <programlisting>
2020 (# , True #)
2021 </programlisting>
2022 Because there is no unboxed unit tuple, the following expression
2023 <programlisting>
2024 (# #)
2025 </programlisting>
2026 continues to stand for the unboxed singleton tuple data constructor.
2027 </para>
2028
2029 </sect2>
2030
2031 <sect2 id="lambda-case">
2032 <title>Lambda-case</title>
2033 <para>
2034 The <option>-XLambdaCase</option> flag enables expressions of the form
2035 <programlisting>
2036 \case { p1 -> e1; ...; pN -> eN }
2037 </programlisting>
2038 which is equivalent to
2039 <programlisting>
2040 \freshName -> case freshName of { p1 -> e1; ...; pN -> eN }
2041 </programlisting>
2042 Note that <literal>\case</literal> starts a layout, so you can write
2043 <programlisting>
2044 \case
2045 p1 -> e1
2046 ...
2047 pN -> eN
2048 </programlisting>
2049 </para>
2050 </sect2>
2051
2052 <sect2 id="empty-case">
2053 <title>Empty case alternatives</title>
2054 <para>
2055 The <option>-XEmptyCase</option> flag enables
2056 case expressions, or lambda-case expressions, that have no alternatives,
2057 thus:
2058 <programlisting>
2059 case e of { } -- No alternatives
2060 or
2061 \case { } -- -XLambdaCase is also required
2062 </programlisting>
2063 This can be useful when you know that the expression being scrutinised
2064 has no non-bottom values. For example:
2065 <programlisting>
2066 data Void
2067 f :: Void -> Int
2068 f x = case x of { }
2069 </programlisting>
2070 With dependently-typed features it is more useful
2071 (see <ulink url="http://ghc.haskell.org/trac/ghc/ticket/2431">Trac</ulink>).
2072 For example, consider these two candidate definitions of <literal>absurd</literal>:
2073 <programlisting>
2074 data a :==: b where
2075 Refl :: a :==: a
2076
2077 absurd :: True :~: False -> a
2078 absurd x = error "absurd" -- (A)
2079 absurd x = case x of {} -- (B)
2080 </programlisting>
2081 We much prefer (B). Why? Because GHC can figure out that <literal>(True :~: False)</literal>
2082 is an empty type. So (B) has no partiality and GHC should be able to compile with
2083 <option>-fwarn-incomplete-patterns</option>. (Though the pattern match checking is not
2084 yet clever enough to do that.)
2085 On the other hand (A) looks dangerous, and GHC doesn't check to make
2086 sure that, in fact, the function can never get called.
2087 </para>
2088 </sect2>
2089
2090 <sect2 id="multi-way-if">
2091 <title>Multi-way if-expressions</title>
2092 <para>
2093 With <option>-XMultiWayIf</option> flag GHC accepts conditional expressions
2094 with multiple branches:
2095 <programlisting>
2096 if | guard1 -> expr1
2097 | ...
2098 | guardN -> exprN
2099 </programlisting>
2100 which is roughly equivalent to
2101 <programlisting>
2102 case () of
2103 _ | guard1 -> expr1
2104 ...
2105 _ | guardN -> exprN
2106 </programlisting>
2107 </para>
2108
2109 <para>Multi-way if expressions introduce a new layout context. So the
2110 example above is equivalent to:
2111 <programlisting>
2112 if { | guard1 -> expr1
2113 ; | ...
2114 ; | guardN -> exprN
2115 }
2116 </programlisting>
2117 The following behaves as expected:
2118 <programlisting>
2119 if | guard1 -> if | guard2 -> expr2
2120 | guard3 -> expr3
2121 | guard4 -> expr4
2122 </programlisting>
2123 because layout translates it as
2124 <programlisting>
2125 if { | guard1 -> if { | guard2 -> expr2
2126 ; | guard3 -> expr3
2127 }
2128 ; | guard4 -> expr4
2129 }
2130 </programlisting>
2131 Layout with multi-way if works in the same way as other layout
2132 contexts, except that the semi-colons between guards in a multi-way if
2133 are optional. So it is not necessary to line up all the guards at the
2134 same column; this is consistent with the way guards work in function
2135 definitions and case expressions.
2136 </para>
2137 </sect2>
2138
2139 <sect2 id="disambiguate-fields">
2140 <title>Record field disambiguation</title>
2141 <para>
2142 In record construction and record pattern matching
2143 it is entirely unambiguous which field is referred to, even if there are two different
2144 data types in scope with a common field name. For example:
2145 <programlisting>
2146 module M where
2147 data S = MkS { x :: Int, y :: Bool }
2148
2149 module Foo where
2150 import M
2151
2152 data T = MkT { x :: Int }
2153
2154 ok1 (MkS { x = n }) = n+1 -- Unambiguous
2155 ok2 n = MkT { x = n+1 } -- Unambiguous
2156
2157 bad1 k = k { x = 3 } -- Ambiguous
2158 bad2 k = x k -- Ambiguous
2159 </programlisting>
2160 Even though there are two <literal>x</literal>'s in scope,
2161 it is clear that the <literal>x</literal> in the pattern in the
2162 definition of <literal>ok1</literal> can only mean the field
2163 <literal>x</literal> from type <literal>S</literal>. Similarly for
2164 the function <literal>ok2</literal>. However, in the record update
2165 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
2166 it is not clear which of the two types is intended.
2167 </para>
2168 <para>
2169 Haskell 98 regards all four as ambiguous, but with the
2170 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
2171 the former two. The rules are precisely the same as those for instance
2172 declarations in Haskell 98, where the method names on the left-hand side
2173 of the method bindings in an instance declaration refer unambiguously
2174 to the method of that class (provided they are in scope at all), even
2175 if there are other variables in scope with the same name.
2176 This reduces the clutter of qualified names when you import two
2177 records from different modules that use the same field name.
2178 </para>
2179 <para>
2180 Some details:
2181 <itemizedlist>
2182 <listitem><para>
2183 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For example:
2184 <programlisting>
2185 module Foo where
2186 import M
2187 x=True
2188 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
2189 </programlisting>
2190 </para></listitem>
2191
2192 <listitem><para>
2193 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualified</emphasis>
2194 field names even if the corresponding selector is only in scope <emphasis>qualified</emphasis>
2195 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
2196 <programlisting>
2197 module Foo where
2198 import qualified M -- Note qualified
2199
2200 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
2201 </programlisting>
2202 Since the constructor <literal>MkS</literal> is only in scope qualified, you must
2203 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
2204 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
2205 is not. (In effect, it is qualified by the constructor.)
2206 </para></listitem>
2207 </itemizedlist>
2208 </para>
2209
2210 </sect2>
2211
2212 <!-- ===================== Record puns =================== -->
2213
2214 <sect2 id="record-puns">
2215 <title>Record puns
2216 </title>
2217
2218 <para>
2219 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
2220 </para>
2221
2222 <para>
2223 When using records, it is common to write a pattern that binds a
2224 variable with the same name as a record field, such as:
2225
2226 <programlisting>
2227 data C = C {a :: Int}
2228 f (C {a = a}) = a
2229 </programlisting>
2230 </para>
2231
2232 <para>
2233 Record punning permits the variable name to be elided, so one can simply
2234 write
2235
2236 <programlisting>
2237 f (C {a}) = a
2238 </programlisting>
2239
2240 to mean the same pattern as above. That is, in a record pattern, the
2241 pattern <literal>a</literal> expands into the pattern <literal>a =
2242 a</literal> for the same name <literal>a</literal>.
2243 </para>
2244
2245 <para>
2246 Note that:
2247 <itemizedlist>
2248 <listitem><para>
2249 Record punning can also be used in an expression, writing, for example,
2250 <programlisting>
2251 let a = 1 in C {a}
2252 </programlisting>
2253 instead of
2254 <programlisting>
2255 let a = 1 in C {a = a}
2256 </programlisting>
2257 The expansion is purely syntactic, so the expanded right-hand side
2258 expression refers to the nearest enclosing variable that is spelled the
2259 same as the field name.
2260 </para></listitem>
2261
2262 <listitem><para>
2263 Puns and other patterns can be mixed in the same record:
2264 <programlisting>
2265 data C = C {a :: Int, b :: Int}
2266 f (C {a, b = 4}) = a
2267 </programlisting>
2268 </para></listitem>
2269
2270 <listitem><para>
2271 Puns can be used wherever record patterns occur (e.g. in
2272 <literal>let</literal> bindings or at the top-level).
2273 </para></listitem>
2274
2275 <listitem><para>
2276 A pun on a qualified field name is expanded by stripping off the module qualifier.
2277 For example:
2278 <programlisting>
2279 f (C {M.a}) = a
2280 </programlisting>
2281 means
2282 <programlisting>
2283 f (M.C {M.a = a}) = a
2284 </programlisting>
2285 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
2286 is only in scope in qualified form.)
2287 </para></listitem>
2288 </itemizedlist>
2289 </para>
2290
2291
2292 </sect2>
2293
2294 <!-- ===================== Record wildcards =================== -->
2295
2296 <sect2 id="record-wildcards">
2297 <title>Record wildcards
2298 </title>
2299
2300 <para>
2301 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
2302 This flag implies <literal>-XDisambiguateRecordFields</literal>.
2303 </para>
2304
2305 <para>
2306 For records with many fields, it can be tiresome to write out each field
2307 individually in a record pattern, as in
2308 <programlisting>
2309 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
2310 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
2311 </programlisting>
2312 </para>
2313
2314 <para>
2315 Record wildcard syntax permits a "<literal>..</literal>" in a record
2316 pattern, where each elided field <literal>f</literal> is replaced by the
2317 pattern <literal>f = f</literal>. For example, the above pattern can be
2318 written as
2319 <programlisting>
2320 f (C {a = 1, ..}) = b + c + d
2321 </programlisting>
2322 </para>
2323
2324 <para>
2325 More details:
2326 <itemizedlist>
2327 <listitem><para>
2328 Record wildcards in patterns can be mixed with other patterns, including puns
2329 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
2330 = 1, b, ..})</literal>. Additionally, record wildcards can be used
2331 wherever record patterns occur, including in <literal>let</literal>
2332 bindings and at the top-level. For example, the top-level binding
2333 <programlisting>
2334 C {a = 1, ..} = e
2335 </programlisting>
2336 defines <literal>b</literal>, <literal>c</literal>, and
2337 <literal>d</literal>.
2338 </para></listitem>
2339
2340 <listitem><para>
2341 Record wildcards can also be used in an expression, when constructing a record. For example,
2342 <programlisting>
2343 let {a = 1; b = 2; c = 3; d = 4} in C {..}
2344 </programlisting>
2345 in place of
2346 <programlisting>
2347 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
2348 </programlisting>
2349 The expansion is purely syntactic, so the record wildcard
2350 expression refers to the nearest enclosing variables that are spelled
2351 the same as the omitted field names.
2352 </para></listitem>
2353
2354 <listitem><para>
2355 Record wildcards may <emphasis>not</emphasis> be used in record <emphasis>updates</emphasis>. For example this
2356 is illegal:
2357 <programlisting>
2358 f r = r { x = 3, .. }
2359 </programlisting>
2360 </para></listitem>
2361
2362 <listitem><para>
2363 For both pattern and expression wildcards, the "<literal>..</literal>" expands to the missing
2364 <emphasis>in-scope</emphasis> record fields.
2365 Specifically the expansion of "<literal>C {..}</literal>" includes
2366 <literal>f</literal> if and only if:
2367 <itemizedlist>
2368 <listitem><para>
2369 <literal>f</literal> is a record field of constructor <literal>C</literal>.
2370 </para></listitem>
2371 <listitem><para>
2372 The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
2373 </para></listitem>
2374 <listitem><para>
2375 In the case of expressions (but not patterns),
2376 the variable <literal>f</literal> is in scope unqualified,
2377 apart from the binding of the record selector itself.
2378 </para></listitem>
2379 </itemizedlist>
2380 These rules restrict record wildcards to the situations in which the user
2381 could have written the expanded version.
2382 For example
2383 <programlisting>
2384 module M where
2385 data R = R { a,b,c :: Int }
2386 module X where
2387 import M( R(a,c) )
2388 f b = R { .. }
2389 </programlisting>
2390 The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
2391 omitting <literal>b</literal> since the record field is not in scope,
2392 and omitting <literal>c</literal> since the variable <literal>c</literal>
2393 is not in scope (apart from the binding of the
2394 record selector <literal>c</literal>, of course).
2395 </para></listitem>
2396 </itemizedlist>
2397 </para>
2398
2399 </sect2>
2400
2401 <!-- ===================== Local fixity declarations =================== -->
2402
2403 <sect2 id="local-fixity-declarations">
2404 <title>Local Fixity Declarations
2405 </title>
2406
2407 <para>A careful reading of the Haskell 98 Report reveals that fixity
2408 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
2409 <literal>infixr</literal>) are permitted to appear inside local bindings
2410 such those introduced by <literal>let</literal> and
2411 <literal>where</literal>. However, the Haskell Report does not specify
2412 the semantics of such bindings very precisely.
2413 </para>
2414
2415 <para>In GHC, a fixity declaration may accompany a local binding:
2416 <programlisting>
2417 let f = ...
2418 infixr 3 `f`
2419 in
2420 ...
2421 </programlisting>
2422 and the fixity declaration applies wherever the binding is in scope.
2423 For example, in a <literal>let</literal>, it applies in the right-hand
2424 sides of other <literal>let</literal>-bindings and the body of the
2425 <literal>let</literal>C. Or, in recursive <literal>do</literal>
2426 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
2427 declarations of a <literal>let</literal> statement scope over other
2428 statements in the group, just as the bound name does.
2429 </para>
2430
2431 <para>
2432 Moreover, a local fixity declaration *must* accompany a local binding of
2433 that name: it is not possible to revise the fixity of name bound
2434 elsewhere, as in
2435 <programlisting>
2436 let infixr 9 $ in ...
2437 </programlisting>
2438
2439 Because local fixity declarations are technically Haskell 98, no flag is
2440 necessary to enable them.
2441 </para>
2442 </sect2>
2443
2444 <sect2 id="package-imports">
2445 <title>Import and export extensions</title>
2446
2447 <sect3>
2448 <title>Hiding things the imported module doesn't export</title>
2449
2450 <para>
2451 Technically in Haskell 2010 this is illegal:
2452 <programlisting>
2453 module A( f ) where
2454 f = True
2455
2456 module B where
2457 import A hiding( g ) -- A does not export g
2458 g = f
2459 </programlisting>
2460 The <literal>import A hiding( g )</literal> in module <literal>B</literal>
2461 is technically an error (<ulink url="http://www.haskell.org/onlinereport/haskell2010/haskellch5.html#x11-1020005.3.1">Haskell Report, 5.3.1</ulink>)
2462 because <literal>A</literal> does not export <literal>g</literal>.
2463 However GHC allows it, in the interests of supporting backward compatibility; for example, a newer version of
2464 <literal>A</literal> might export <literal>g</literal>, and you want <literal>B</literal> to work
2465 in either case.
2466 </para>
2467 <para>
2468 The warning <literal>-fwarn-dodgy-imports</literal>, which is off by default but included with <literal>-W</literal>,
2469 warns if you hide something that the imported module does not export.
2470 </para>
2471 </sect3>
2472
2473 <sect3>
2474 <title id="package-qualified-imports">Package-qualified imports</title>
2475
2476 <para>With the <option>-XPackageImports</option> flag, GHC allows
2477 import declarations to be qualified by the package name that the
2478 module is intended to be imported from. For example:</para>
2479
2480 <programlisting>
2481 import "network" Network.Socket
2482 </programlisting>
2483
2484 <para>would import the module <literal>Network.Socket</literal> from
2485 the package <literal>network</literal> (any version). This may
2486 be used to disambiguate an import when the same module is
2487 available from multiple packages, or is present in both the
2488 current package being built and an external package.</para>
2489
2490 <para>The special package name <literal>this</literal> can be used to
2491 refer to the current package being built.</para>
2492
2493 <para>Note: you probably don't need to use this feature, it was
2494 added mainly so that we can build backwards-compatible versions of
2495 packages when APIs change. It can lead to fragile dependencies in
2496 the common case: modules occasionally move from one package to
2497 another, rendering any package-qualified imports broken.
2498 See also <xref linkend="package-thinning-and-renaming" /> for
2499 an alternative way of disambiguating between module names.</para>
2500 </sect3>
2501
2502 <sect3 id="safe-imports-ext">
2503 <title>Safe imports</title>
2504
2505 <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
2506 and <option>-XUnsafe</option> language flags, GHC extends
2507 the import declaration syntax to take an optional <literal>safe</literal>
2508 keyword after the <literal>import</literal> keyword. This feature
2509 is part of the Safe Haskell GHC extension. For example:</para>
2510
2511 <programlisting>
2512 import safe qualified Network.Socket as NS
2513 </programlisting>
2514
2515 <para>would import the module <literal>Network.Socket</literal>
2516 with compilation only succeeding if Network.Socket can be
2517 safely imported. For a description of when a import is
2518 considered safe see <xref linkend="safe-haskell"/></para>
2519
2520 </sect3>
2521
2522 <sect3 id="explicit-namespaces">
2523 <title>Explicit namespaces in import/export</title>
2524
2525 <para> In an import or export list, such as
2526 <programlisting>
2527 module M( f, (++) ) where ...
2528 import N( f, (++) )
2529 ...
2530 </programlisting>
2531 the entities <literal>f</literal> and <literal>(++)</literal> are <emphasis>values</emphasis>.
2532 However, with type operators (<xref linkend="type-operators"/>) it becomes possible
2533 to declare <literal>(++)</literal> as a <emphasis>type constructor</emphasis>. In that
2534 case, how would you export or import it?
2535 </para>
2536 <para>
2537 The <option>-XExplicitNamespaces</option> extension allows you to prefix the name of
2538 a type constructor in an import or export list with "<literal>type</literal>" to
2539 disambiguate this case, thus:
2540 <programlisting>
2541 module M( f, type (++) ) where ...
2542 import N( f, type (++) )
2543 ...
2544 module N( f, type (++) ) where
2545 data family a ++ b = L a | R b
2546 </programlisting>
2547 The extension <option>-XExplicitNamespaces</option>
2548 is implied by <option>-XTypeOperators</option> and (for some reason) by <option>-XTypeFamilies</option>.
2549 </para>
2550 <para>
2551 In addition, with <option>-XPatternSynonyms</option> you can prefix the name of
2552 a data constructor in an import or export list with the keyword <literal>pattern</literal>,
2553 to allow the import or export of a data constructor without its parent type constructor
2554 (see <xref linkend="patsyn-impexp"/>).
2555 </para>
2556 </sect3>
2557
2558 </sect2>
2559
2560 <sect2 id="syntax-stolen">
2561 <title>Summary of stolen syntax</title>
2562
2563 <para>Turning on an option that enables special syntax
2564 <emphasis>might</emphasis> cause working Haskell 98 code to fail
2565 to compile, perhaps because it uses a variable name which has
2566 become a reserved word. This section lists the syntax that is
2567 "stolen" by language extensions.
2568 We use
2569 notation and nonterminal names from the Haskell 98 lexical syntax
2570 (see the Haskell 98 Report).
2571 We only list syntax changes here that might affect
2572 existing working programs (i.e. "stolen" syntax). Many of these
2573 extensions will also enable new context-free syntax, but in all
2574 cases programs written to use the new syntax would not be
2575 compilable without the option enabled.</para>
2576
2577 <para>There are two classes of special
2578 syntax:
2579
2580 <itemizedlist>
2581 <listitem>
2582 <para>New reserved words and symbols: character sequences
2583 which are no longer available for use as identifiers in the
2584 program.</para>
2585 </listitem>
2586 <listitem>
2587 <para>Other special syntax: sequences of characters that have
2588 a different meaning when this particular option is turned
2589 on.</para>
2590 </listitem>
2591 </itemizedlist>
2592
2593 The following syntax is stolen:
2594
2595 <variablelist>
2596 <varlistentry>
2597 <term>
2598 <literal>forall</literal>
2599 <indexterm><primary><literal>forall</literal></primary></indexterm>
2600 </term>
2601 <listitem><para>
2602 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
2603 <option>-XScopedTypeVariables</option>,
2604 <option>-XLiberalTypeSynonyms</option>,
2605 <option>-XRankNTypes</option>,
2606 <option>-XExistentialQuantification</option>
2607 </para></listitem>
2608 </varlistentry>
2609
2610 <varlistentry>
2611 <term>
2612 <literal>mdo</literal>
2613 <indexterm><primary><literal>mdo</literal></primary></indexterm>
2614 </term>
2615 <listitem><para>
2616 Stolen by: <option>-XRecursiveDo</option>
2617 </para></listitem>
2618 </varlistentry>
2619
2620 <varlistentry>
2621 <term>
2622 <literal>foreign</literal>
2623 <indexterm><primary><literal>foreign</literal></primary></indexterm>
2624 </term>
2625 <listitem><para>
2626 Stolen by: <option>-XForeignFunctionInterface</option>
2627 </para></listitem>
2628 </varlistentry>
2629
2630 <varlistentry>
2631 <term>
2632 <literal>rec</literal>,
2633 <literal>proc</literal>, <literal>-&lt;</literal>,
2634 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
2635 <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
2636 <literal>|)</literal> brackets
2637 <indexterm><primary><literal>proc</literal></primary></indexterm>
2638 </term>
2639 <listitem><para>
2640 Stolen by: <option>-XArrows</option>
2641 </para></listitem>
2642 </varlistentry>
2643
2644 <varlistentry>
2645 <term>
2646 <literal>?<replaceable>varid</replaceable></literal>
2647 <indexterm><primary>implicit parameters</primary></indexterm>
2648 </term>
2649 <listitem><para>
2650 Stolen by: <option>-XImplicitParams</option>
2651 </para></listitem>
2652 </varlistentry>
2653
2654 <varlistentry>
2655 <term>
2656 <literal>[|</literal>,
2657 <literal>[e|</literal>, <literal>[p|</literal>,
2658 <literal>[d|</literal>, <literal>[t|</literal>,
2659 <literal>$(</literal>,
2660 <literal>$$(</literal>,
2661 <literal>[||</literal>,
2662 <literal>[e||</literal>,
2663 <literal>$<replaceable>varid</replaceable></literal>,
2664 <literal>$$<replaceable>varid</replaceable></literal>
2665 <indexterm><primary>Template Haskell</primary></indexterm>
2666 </term>
2667 <listitem><para>
2668 Stolen by: <option>-XTemplateHaskell</option>
2669 </para></listitem>
2670 </varlistentry>
2671
2672 <varlistentry>
2673 <term>
2674 <literal>[<replaceable>varid</replaceable>|</literal>
2675 <indexterm><primary>quasi-quotation</primary></indexterm>
2676 </term>
2677 <listitem><para>
2678 Stolen by: <option>-XQuasiQuotes</option>
2679 </para></listitem>
2680 </varlistentry>
2681
2682 <varlistentry>
2683 <term>
2684 <replaceable>varid</replaceable>{<literal>&num;</literal>},
2685 <replaceable>char</replaceable><literal>&num;</literal>,
2686 <replaceable>string</replaceable><literal>&num;</literal>,
2687 <replaceable>integer</replaceable><literal>&num;</literal>,
2688 <replaceable>float</replaceable><literal>&num;</literal>,
2689 <replaceable>float</replaceable><literal>&num;&num;</literal>
2690 </term>
2691 <listitem><para>
2692 Stolen by: <option>-XMagicHash</option>
2693 </para></listitem>
2694 </varlistentry>
2695
2696 <varlistentry>
2697 <term>
2698 <literal>(&num;</literal>, <literal>&num;)</literal>
2699 </term>
2700 <listitem><para>
2701 Stolen by: <option>-XUnboxedTuples</option>
2702 </para></listitem>
2703 </varlistentry>
2704
2705 <varlistentry>
2706 <term>
2707 <replaceable>varid</replaceable><literal>!</literal><replaceable>varid</replaceable>
2708 </term>
2709 <listitem><para>
2710 Stolen by: <option>-XBangPatterns</option>
2711 </para></listitem>
2712 </varlistentry>
2713
2714 <varlistentry>
2715 <term>
2716 <literal>pattern</literal>
2717 </term>
2718 <listitem><para>
2719 Stolen by: <option>-XPatternSynonyms</option>
2720 </para></listitem>
2721 </varlistentry>
2722 </variablelist>
2723 </para>
2724 </sect2>
2725 </sect1>
2726
2727
2728 <!-- TYPE SYSTEM EXTENSIONS -->
2729 <sect1 id="data-type-extensions">
2730 <title>Extensions to data types and type synonyms</title>
2731
2732 <sect2 id="nullary-types">
2733 <title>Data types with no constructors</title>
2734
2735 <para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
2736 GHC lets you declare a data type with no constructors. For example:</para>
2737
2738 <programlisting>
2739 data S -- S :: *
2740 data T a -- T :: * -> *
2741 </programlisting>
2742
2743 <para>Syntactically, the declaration lacks the "= constrs" part. The
2744 type can be parameterised over types of any kind, but if the kind is
2745 not <literal>*</literal> then an explicit kind annotation must be used
2746 (see <xref linkend="kinding"/>).</para>
2747
2748 <para>Such data types have only one value, namely bottom.
2749 Nevertheless, they can be useful when defining "phantom types".</para>
2750 </sect2>
2751
2752 <sect2 id="datatype-contexts">
2753 <title>Data type contexts</title>
2754
2755 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2756
2757 <programlisting>
2758 data Eq a => Set a = NilSet | ConsSet a (Set a)
2759 </programlisting>
2760
2761 <para>give constructors with types:</para>
2762
2763 <programlisting>
2764 NilSet :: Set a
2765 ConsSet :: Eq a => a -> Set a -> Set a
2766 </programlisting>
2767
2768 <para>This is widely considered a misfeature, and is going to be removed from
2769 the language. In GHC, it is controlled by the deprecated extension
2770 <literal>DatatypeContexts</literal>.</para>
2771 </sect2>
2772
2773 <sect2 id="infix-tycons">
2774 <title>Infix type constructors, classes, and type variables</title>
2775
2776 <para>
2777 GHC allows type constructors, classes, and type variables to be operators, and
2778 to be written infix, very much like expressions. More specifically:
2779 <itemizedlist>
2780 <listitem><para>
2781 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
2782 The lexical syntax is the same as that for data constructors.
2783 </para></listitem>
2784 <listitem><para>
2785 Data type and type-synonym declarations can be written infix, parenthesised
2786 if you want further arguments. E.g.
2787 <screen>
2788 data a :*: b = Foo a b
2789 type a :+: b = Either a b
2790 class a :=: b where ...
2791
2792 data (a :**: b) x = Baz a b x
2793 type (a :++: b) y = Either (a,b) y
2794 </screen>
2795 </para></listitem>
2796 <listitem><para>
2797 Types, and class constraints, can be written infix. For example
2798 <screen>
2799 x :: Int :*: Bool
2800 f :: (a :=: b) => a -> b
2801 </screen>
2802 </para></listitem>
2803 <listitem><para>
2804 Back-quotes work
2805 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
2806 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
2807 </para></listitem>
2808 <listitem><para>
2809 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
2810 one cannot distinguish between the two in a fixity declaration; a fixity declaration
2811 sets the fixity for a data constructor and the corresponding type constructor. For example:
2812 <screen>
2813 infixl 7 T, :*:
2814 </screen>
2815 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
2816 and similarly for <literal>:*:</literal>.
2817 <literal>Int `a` Bool</literal>.
2818 </para></listitem>
2819 <listitem><para>
2820 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
2821 </para></listitem>
2822
2823 </itemizedlist>
2824 </para>
2825 </sect2>
2826
2827 <sect2 id="type-operators">
2828 <title>Type operators</title>
2829 <para>
2830 In types, an operator symbol like <literal>(+)</literal> is normally treated as a type
2831 <emphasis>variable</emphasis>, just like <literal>a</literal>. Thus in Haskell 98 you can say
2832 <programlisting>
2833 type T (+) = ((+), (+))
2834 -- Just like: type T a = (a,a)
2835
2836 f :: T Int -> Int
2837 f (x,y)= x
2838 </programlisting>
2839 As you can see, using operators in this way is not very useful, and Haskell 98 does not even
2840 allow you to write them infix.
2841 </para>
2842 <para>
2843 The language <option>-XTypeOperators</option> changes this behaviour:
2844 <itemizedlist>
2845 <listitem><para>
2846 Operator symbols become type <emphasis>constructors</emphasis> rather than
2847 type <emphasis>variables</emphasis>.
2848 </para></listitem>
2849 <listitem><para>
2850 Operator symbols in types can be written infix, both in definitions and uses.
2851 for example:
2852 <programlisting>
2853 data a + b = Plus a b
2854 type Foo = Int + Bool
2855 </programlisting>
2856 </para></listitem>
2857 <listitem><para>
2858 There is now some potential ambiguity in import and export lists; for example
2859 if you write <literal>import M( (+) )</literal> do you mean the
2860 <emphasis>function</emphasis> <literal>(+)</literal> or the
2861 <emphasis>type constructor</emphasis> <literal>(+)</literal>?
2862 The default is the former, but with <option>-XExplicitNamespaces</option> (which is implied
2863 by <option>-XExplicitTypeOperators</option>) GHC allows you to specify the latter
2864 by preceding it with the keyword <literal>type</literal>, thus:
2865 <programlisting>
2866 import M( type (+) )
2867 </programlisting>
2868 See <xref linkend="explicit-namespaces"/>.
2869 </para></listitem>
2870 <listitem><para>
2871 The fixity of a type operator may be set using the usual fixity declarations
2872 but, as in <xref linkend="infix-tycons"/>, the function and type constructor share
2873 a single fixity.
2874 </para></listitem>
2875 </itemizedlist>
2876 </para>
2877 </sect2>
2878
2879 <sect2 id="type-synonyms">
2880 <title>Liberalised type synonyms</title>
2881
2882 <para>
2883 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
2884 on individual synonym declarations.
2885 With the <option>-XLiberalTypeSynonyms</option> extension,
2886 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2887 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
2888
2889 <itemizedlist>
2890 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2891 in a type synonym, thus:
2892 <programlisting>
2893 type Discard a = forall b. Show b => a -> b -> (a, String)
2894
2895 f :: Discard a
2896 f x y = (x, show y)
2897
2898 g :: Discard Int -> (Int,String) -- A rank-2 type
2899 g f = f 3 True
2900 </programlisting>
2901 </para>
2902 </listitem>
2903
2904 <listitem><para>
2905 If you also use <option>-XUnboxedTuples</option>,
2906 you can write an unboxed tuple in a type synonym:
2907 <programlisting>
2908 type Pr = (# Int, Int #)
2909
2910 h :: Int -> Pr
2911 h x = (# x, x #)
2912 </programlisting>
2913 </para></listitem>
2914
2915 <listitem><para>
2916 You can apply a type synonym to a forall type:
2917 <programlisting>
2918 type Foo a = a -> a -> Bool
2919
2920 f :: Foo (forall b. b->b)
2921 </programlisting>
2922 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2923 <programlisting>
2924 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2925 </programlisting>
2926 </para></listitem>
2927
2928 <listitem><para>
2929 You can apply a type synonym to a partially applied type synonym:
2930 <programlisting>
2931 type Generic i o = forall x. i x -> o x
2932 type Id x = x
2933
2934 foo :: Generic Id []
2935 </programlisting>
2936 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2937 <programlisting>
2938 foo :: forall x. x -> [x]
2939 </programlisting>
2940 </para></listitem>
2941
2942 </itemizedlist>
2943 </para>
2944
2945 <para>
2946 GHC currently does kind checking before expanding synonyms (though even that
2947 could be changed.)
2948 </para>
2949 <para>
2950 After expanding type synonyms, GHC does validity checking on types, looking for
2951 the following mal-formedness which isn't detected simply by kind checking:
2952 <itemizedlist>
2953 <listitem><para>
2954 Type constructor applied to a type involving for-alls (if <literal>XImpredicativeTypes</literal>
2955 is off)
2956 </para></listitem>
2957 <listitem><para>
2958 Partially-applied type synonym.
2959 </para></listitem>
2960 </itemizedlist>
2961 So, for example, this will be rejected:
2962 <programlisting>
2963 type Pr = forall a. a
2964
2965 h :: [Pr]
2966 h = ...
2967 </programlisting>
2968 because GHC does not allow type constructors applied to for-all types.
2969 </para>
2970 </sect2>
2971
2972
2973 <sect2 id="existential-quantification">
2974 <title>Existentially quantified data constructors
2975 </title>
2976
2977 <para>
2978 The idea of using existential quantification in data type declarations
2979 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2980 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2981 London, 1991). It was later formalised by Laufer and Odersky
2982 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2983 TOPLAS, 16(5), pp1411-1430, 1994).
2984 It's been in Lennart
2985 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2986 proved very useful. Here's the idea. Consider the declaration:
2987 </para>
2988
2989 <para>
2990
2991 <programlisting>
2992 data Foo = forall a. MkFoo a (a -> Bool)
2993 | Nil
2994 </programlisting>
2995
2996 </para>
2997
2998 <para>
2999 The data type <literal>Foo</literal> has two constructors with types:
3000 </para>
3001
3002 <para>
3003
3004 <programlisting>
3005 MkFoo :: forall a. a -> (a -> Bool) -> Foo
3006 Nil :: Foo
3007 </programlisting>
3008
3009 </para>
3010
3011 <para>
3012 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
3013 does not appear in the data type itself, which is plain <literal>Foo</literal>.
3014 For example, the following expression is fine:
3015 </para>
3016
3017 <para>
3018
3019 <programlisting>
3020 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
3021 </programlisting>
3022
3023 </para>
3024
3025 <para>
3026 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
3027 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
3028 isUpper</function> packages a character with a compatible function. These
3029 two things are each of type <literal>Foo</literal> and can be put in a list.
3030 </para>
3031
3032 <para>
3033 What can we do with a value of type <literal>Foo</literal>?. In particular,
3034 what happens when we pattern-match on <function>MkFoo</function>?
3035 </para>
3036
3037 <para>
3038
3039 <programlisting>
3040 f (MkFoo val fn) = ???
3041 </programlisting>
3042
3043 </para>
3044
3045 <para>
3046 Since all we know about <literal>val</literal> and <function>fn</function> is that they
3047 are compatible, the only (useful) thing we can do with them is to
3048 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
3049 </para>
3050
3051 <para>
3052
3053 <programlisting>
3054 f :: Foo -> Bool
3055 f (MkFoo val fn) = fn val
3056 </programlisting>
3057
3058 </para>
3059
3060 <para>
3061 What this allows us to do is to package heterogeneous values
3062 together with a bunch of functions that manipulate them, and then treat
3063 that collection of packages in a uniform manner. You can express
3064 quite a bit of object-oriented-like programming this way.
3065 </para>
3066
3067 <sect3 id="existential">
3068 <title>Why existential?
3069 </title>
3070
3071 <para>
3072 What has this to do with <emphasis>existential</emphasis> quantification?
3073 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
3074 </para>
3075
3076 <para>
3077
3078 <programlisting>
3079 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
3080 </programlisting>
3081
3082 </para>
3083
3084 <para>
3085 But Haskell programmers can safely think of the ordinary
3086 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
3087 adding a new existential quantification construct.
3088 </para>
3089
3090 </sect3>
3091
3092 <sect3 id="existential-with-context">
3093 <title>Existentials and type classes</title>
3094
3095 <para>
3096 An easy extension is to allow
3097 arbitrary contexts before the constructor. For example:
3098 </para>
3099
3100 <para>
3101
3102 <programlisting>
3103 data Baz = forall a. Eq a => Baz1 a a
3104 | forall b. Show b => Baz2 b (b -> b)
3105 </programlisting>
3106
3107 </para>
3108
3109 <para>
3110 The two constructors have the types you'd expect:
3111 </para>
3112
3113 <para>
3114
3115 <programlisting>
3116 Baz1 :: forall a. Eq a => a -> a -> Baz
3117 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
3118 </programlisting>
3119
3120 </para>
3121
3122 <para>
3123 But when pattern matching on <function>Baz1</function> the matched values can be compared
3124 for equality, and when pattern matching on <function>Baz2</function> the first matched
3125 value can be converted to a string (as well as applying the function to it).
3126 So this program is legal:
3127 </para>
3128
3129 <para>
3130
3131 <programlisting>
3132 f :: Baz -> String
3133 f (Baz1 p q) | p == q = "Yes"
3134 | otherwise = "No"
3135 f (Baz2 v fn) = show (fn v)
3136 </programlisting>
3137
3138 </para>
3139
3140 <para>
3141 Operationally, in a dictionary-passing implementation, the
3142 constructors <function>Baz1</function> and <function>Baz2</function> must store the
3143 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
3144 extract it on pattern matching.
3145 </para>
3146
3147 </sect3>
3148
3149 <sect3 id="existential-records">
3150 <title>Record Constructors</title>
3151
3152 <para>
3153 GHC allows existentials to be used with records syntax as well. For example:
3154
3155 <programlisting>
3156 data Counter a = forall self. NewCounter
3157 { _this :: self
3158 , _inc :: self -> self
3159 , _display :: self -> IO ()
3160 , tag :: a
3161 }
3162 </programlisting>
3163 Here <literal>tag</literal> is a public field, with a well-typed selector
3164 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
3165 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
3166 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
3167 compile-time error. In other words, <emphasis>GHC defines a record selector function
3168 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
3169 (This example used an underscore in the fields for which record selectors
3170 will not be defined, but that is only programming style; GHC ignores them.)
3171 </para>
3172
3173 <para>
3174 To make use of these hidden fields, we need to create some helper functions:
3175
3176 <programlisting>
3177 inc :: Counter a -> Counter a
3178 inc (NewCounter x i d t) = NewCounter
3179 { _this = i x, _inc = i, _display = d, tag = t }
3180
3181 display :: Counter a -> IO ()
3182 display NewCounter{ _this = x, _display = d } = d x
3183 </programlisting>
3184
3185 Now we can define counters with different underlying implementations:
3186
3187 <programlisting>
3188 counterA :: Counter String
3189 counterA = NewCounter
3190 { _this = 0, _inc = (1+), _display = print, tag = "A" }
3191
3192 counterB :: Counter String
3193 counterB = NewCounter
3194 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
3195
3196 main = do
3197 display (inc counterA) -- prints "1"
3198 display (inc (inc counterB)) -- prints "##"
3199 </programlisting>
3200
3201 Record update syntax is supported for existentials (and GADTs):
3202 <programlisting>
3203 setTag :: Counter a -> a -> Counter a
3204 setTag obj t = obj{ tag = t }
3205 </programlisting>
3206 The rule for record update is this: <emphasis>
3207 the types of the updated fields may
3208 mention only the universally-quantified type variables
3209 of the data constructor. For GADTs, the field may mention only types
3210 that appear as a simple type-variable argument in the constructor's result
3211 type</emphasis>. For example:
3212 <programlisting>
3213 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
3214 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
3215 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
3216 -- existentially quantified)
3217
3218 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
3219 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
3220 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
3221 -- type-variable argument in G1's result type)
3222 </programlisting>
3223 </para>
3224
3225 </sect3>
3226
3227
3228 <sect3>
3229 <title>Restrictions</title>
3230
3231 <para>
3232 There are several restrictions on the ways in which existentially-quantified
3233 constructors can be use.
3234 </para>
3235
3236 <para>
3237
3238 <itemizedlist>
3239 <listitem>
3240
3241 <para>
3242 When pattern matching, each pattern match introduces a new,
3243 distinct, type for each existential type variable. These types cannot
3244 be unified with any other type, nor can they escape from the scope of
3245 the pattern match. For example, these fragments are incorrect:
3246
3247
3248 <programlisting>
3249 f1 (MkFoo a f) = a
3250 </programlisting>
3251
3252
3253 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
3254 is the result of <function>f1</function>. One way to see why this is wrong is to
3255 ask what type <function>f1</function> has:
3256
3257
3258 <programlisting>
3259 f1 :: Foo -> a -- Weird!
3260 </programlisting>
3261
3262
3263 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
3264 this:
3265
3266
3267 <programlisting>
3268 f1 :: forall a. Foo -> a -- Wrong!
3269 </programlisting>
3270
3271
3272 The original program is just plain wrong. Here's another sort of error
3273
3274
3275 <programlisting>
3276 f2 (Baz1 a b) (Baz1 p q) = a==q
3277 </programlisting>
3278
3279
3280 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
3281 <literal>a==q</literal> is wrong because it equates the two distinct types arising
3282 from the two <function>Baz1</function> constructors.
3283
3284
3285 </para>
3286 </listitem>
3287 <listitem>
3288
3289 <para>
3290 You can't pattern-match on an existentially quantified
3291 constructor in a <literal>let</literal> or <literal>where</literal> group of
3292 bindings. So this is illegal:
3293
3294
3295 <programlisting>
3296 f3 x = a==b where { Baz1 a b = x }
3297 </programlisting>
3298
3299 Instead, use a <literal>case</literal> expression:
3300
3301 <programlisting>
3302 f3 x = case x of Baz1 a b -> a==b
3303 </programlisting>
3304
3305 In general, you can only pattern-match
3306 on an existentially-quantified constructor in a <literal>case</literal> expression or
3307 in the patterns of a function definition.
3308
3309 The reason for this restriction is really an implementation one.
3310 Type-checking binding groups is already a nightmare without
3311 existentials complicating the picture. Also an existential pattern
3312 binding at the top level of a module doesn't make sense, because it's
3313 not clear how to prevent the existentially-quantified type "escaping".
3314 So for now, there's a simple-to-state restriction. We'll see how
3315 annoying it is.
3316
3317 </para>
3318 </listitem>
3319 <listitem>
3320
3321 <para>
3322 You can't use existential quantification for <literal>newtype</literal>
3323 declarations. So this is illegal:
3324
3325
3326 <programlisting>
3327 newtype T = forall a. Ord a => MkT a
3328 </programlisting>
3329
3330
3331 Reason: a value of type <literal>T</literal> must be represented as a
3332 pair of a dictionary for <literal>Ord t</literal> and a value of type
3333 <literal>t</literal>. That contradicts the idea that
3334 <literal>newtype</literal> should have no concrete representation.
3335 You can get just the same efficiency and effect by using
3336 <literal>data</literal> instead of <literal>newtype</literal>. If
3337 there is no overloading involved, then there is more of a case for
3338 allowing an existentially-quantified <literal>newtype</literal>,
3339 because the <literal>data</literal> version does carry an
3340 implementation cost, but single-field existentially quantified
3341 constructors aren't much use. So the simple restriction (no
3342 existential stuff on <literal>newtype</literal>) stands, unless there
3343 are convincing reasons to change it.
3344
3345
3346 </para>
3347 </listitem>
3348 <listitem>
3349
3350 <para>
3351 You can't use <literal>deriving</literal> to define instances of a
3352 data type with existentially quantified data constructors.
3353
3354 Reason: in most cases it would not make sense. For example:;
3355
3356 <programlisting>
3357 data T = forall a. MkT [a] deriving( Eq )
3358 </programlisting>
3359
3360 To derive <literal>Eq</literal> in the standard way we would need to have equality
3361 between the single component of two <function>MkT</function> constructors:
3362
3363 <programlisting>
3364 instance Eq T where
3365 (MkT a) == (MkT b) = ???
3366 </programlisting>
3367
3368 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
3369 It's just about possible to imagine examples in which the derived instance
3370 would make sense, but it seems altogether simpler simply to prohibit such
3371 declarations. Define your own instances!
3372 </para>
3373 </listitem>
3374
3375 </itemizedlist>
3376
3377 </para>
3378
3379 </sect3>
3380 </sect2>
3381
3382 <!-- ====================== Generalised algebraic data types ======================= -->
3383
3384 <sect2 id="gadt-style">
3385 <title>Declaring data types with explicit constructor signatures</title>
3386
3387 <para>When the <literal>GADTSyntax</literal> extension is enabled,
3388 GHC allows you to declare an algebraic data type by
3389 giving the type signatures of constructors explicitly. For example:
3390 <programlisting>
3391 data Maybe a where
3392 Nothing :: Maybe a
3393 Just :: a -> Maybe a
3394 </programlisting>
3395 The form is called a "GADT-style declaration"
3396 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
3397 can only be declared using this form.</para>
3398 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
3399 For example, these two declarations are equivalent:
3400 <programlisting>
3401 data Foo = forall a. MkFoo a (a -> Bool)
3402 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
3403 </programlisting>
3404 </para>
3405 <para>Any data type that can be declared in standard Haskell-98 syntax
3406 can also be declared using GADT-style syntax.
3407 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
3408 they treat class constraints on the data constructors differently.
3409 Specifically, if the constructor is given a type-class context, that
3410 context is made available by pattern matching. For example:
3411 <programlisting>
3412 data Set a where
3413 MkSet :: Eq a => [a] -> Set a
3414
3415 makeSet :: Eq a => [a] -> Set a
3416 makeSet xs = MkSet (nub xs)
3417
3418 insert :: a -> Set a -> Set a
3419 insert a (MkSet as) | a `elem` as = MkSet as
3420 | otherwise = MkSet (a:as)
3421 </programlisting>
3422 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
3423 gives rise to a <literal>(Eq a)</literal>
3424 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
3425 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
3426 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
3427 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
3428 when pattern-matching that dictionary becomes available for the right-hand side of the match.
3429 In the example, the equality dictionary is used to satisfy the equality constraint
3430 generated by the call to <literal>elem</literal>, so that the type of
3431 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
3432 </para>
3433 <para>
3434 For example, one possible application is to reify dictionaries:
3435 <programlisting>
3436 data NumInst a where
3437 MkNumInst :: Num a => NumInst a
3438
3439 intInst :: NumInst Int
3440 intInst = MkNumInst
3441
3442 plus :: NumInst a -> a -> a -> a
3443 plus MkNumInst p q = p + q
3444 </programlisting>
3445 Here, a value of type <literal>NumInst a</literal> is equivalent
3446 to an explicit <literal>(Num a)</literal> dictionary.
3447 </para>
3448 <para>
3449 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
3450 For example, the <literal>NumInst</literal> data type above could equivalently be declared
3451 like this:
3452 <programlisting>
3453 data NumInst a
3454 = Num a => MkNumInst (NumInst a)
3455 </programlisting>
3456 Notice that, unlike the situation when declaring an existential, there is
3457 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
3458 data type's universally quantified type variable <literal>a</literal>.
3459 A constructor may have both universal and existential type variables: for example,
3460 the following two declarations are equivalent:
3461 <programlisting>
3462 data T1 a
3463 = forall b. (Num a, Eq b) => MkT1 a b
3464 data T2 a where
3465 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
3466 </programlisting>
3467 </para>
3468 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
3469 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
3470 In Haskell 98 the definition
3471 <programlisting>
3472 data Eq a => Set' a = MkSet' [a]
3473 </programlisting>
3474 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
3475 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
3476 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
3477 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
3478 GHC's behaviour is much more useful, as well as much more intuitive.
3479 </para>
3480
3481 <para>
3482 The rest of this section gives further details about GADT-style data
3483 type declarations.
3484
3485 <itemizedlist>
3486 <listitem><para>
3487 The result type of each data constructor must begin with the type constructor being defined.
3488 If the result type of all constructors
3489 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
3490 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
3491 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
3492 </para></listitem>
3493
3494 <listitem><para>
3495 As with other type signatures, you can give a single signature for several data constructors.
3496 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
3497 <programlisting>
3498 data T a where
3499 T1,T2 :: a -> T a
3500 T3 :: T a
3501 </programlisting>
3502 </para></listitem>
3503
3504 <listitem><para>
3505 The type signature of
3506 each constructor is independent, and is implicitly universally quantified as usual.
3507 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
3508 have no scope, and different constructors may have different universally-quantified type variables:
3509 <programlisting>
3510 data T a where -- The 'a' has no scope
3511 T1,T2 :: b -> T b -- Means forall b. b -> T b
3512 T3 :: T a -- Means forall a. T a
3513 </programlisting>
3514 </para></listitem>
3515
3516 <listitem><para>
3517 A constructor signature may mention type class constraints, which can differ for
3518 different constructors. For example, this is fine:
3519 <programlisting>
3520 data T a where
3521 T1 :: Eq b => b -> b -> T b
3522 T2 :: (Show c, Ix c) => c -> [c] -> T c
3523 </programlisting>
3524 When pattern matching, these constraints are made available to discharge constraints
3525 in the body of the match. For example:
3526 <programlisting>
3527 f :: T a -> String
3528 f (T1 x y) | x==y = "yes"
3529 | otherwise = "no"
3530 f (T2 a b) = show a
3531 </programlisting>
3532 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
3533 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
3534 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
3535 </para></listitem>
3536
3537 <listitem><para>
3538 Unlike a Haskell-98-style
3539 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
3540 have no scope. Indeed, one can write a kind signature instead:
3541 <programlisting>
3542 data Set :: * -> * where ...
3543 </programlisting>
3544 or even a mixture of the two:
3545 <programlisting>
3546 data Bar a :: (* -> *) -> * where ...
3547 </programlisting>
3548 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3549 like this:
3550 <programlisting>
3551 data Bar a (b :: * -> *) where ...
3552 </programlisting>
3553 </para></listitem>
3554
3555
3556 <listitem><para>
3557 You can use strictness annotations, in the obvious places
3558 in the constructor type:
3559 <programlisting>
3560 data Term a where
3561 Lit :: !Int -> Term Int
3562 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3563 Pair :: Term a -> Term b -> Term (a,b)
3564 </programlisting>
3565 </para></listitem>
3566
3567 <listitem><para>
3568 You can use a <literal>deriving</literal> clause on a GADT-style data type
3569 declaration. For example, these two declarations are equivalent
3570 <programlisting>
3571 data Maybe1 a where {
3572 Nothing1 :: Maybe1 a ;
3573 Just1 :: a -> Maybe1 a
3574 } deriving( Eq, Ord )
3575
3576 data Maybe2 a = Nothing2 | Just2 a
3577 deriving( Eq, Ord )
3578 </programlisting>
3579 </para></listitem>
3580
3581 <listitem><para>
3582 The type signature may have quantified type variables that do not appear
3583 in the result type:
3584 <programlisting>
3585 data Foo where
3586 MkFoo :: a -> (a->Bool) -> Foo
3587 Nil :: Foo
3588 </programlisting>
3589 Here the type variable <literal>a</literal> does not appear in the result type
3590 of either constructor.
3591 Although it is universally quantified in the type of the constructor, such
3592 a type variable is often called "existential".
3593 Indeed, the above declaration declares precisely the same type as
3594 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
3595 </para><para>
3596 The type may contain a class context too, of course:
3597 <programlisting>
3598 data Showable where
3599 MkShowable :: Show a => a -> Showable
3600 </programlisting>
3601 </para></listitem>
3602
3603 <listitem><para>
3604 You can use record syntax on a GADT-style data type declaration:
3605
3606 <programlisting>
3607 data Person where
3608 Adult :: { name :: String, children :: [Person] } -> Person
3609 Child :: Show a => { name :: !String, funny :: a } -> Person
3610 </programlisting>
3611 As usual, for every constructor that has a field <literal>f</literal>, the type of
3612 field <literal>f</literal> must be the same (modulo alpha conversion).
3613 The <literal>Child</literal> constructor above shows that the signature
3614 may have a context, existentially-quantified variables, and strictness annotations,
3615 just as in the non-record case. (NB: the "type" that follows the double-colon
3616 is not really a type, because of the record syntax and strictness annotations.
3617 A "type" of this form can appear only in a constructor signature.)
3618 </para></listitem>
3619
3620 <listitem><para>
3621 Record updates are allowed with GADT-style declarations,
3622 only fields that have the following property: the type of the field
3623 mentions no existential type variables.
3624 </para></listitem>
3625
3626 <listitem><para>
3627 As in the case of existentials declared using the Haskell-98-like record syntax
3628 (<xref linkend="existential-records"/>),
3629 record-selector functions are generated only for those fields that have well-typed
3630 selectors.
3631 Here is the example of that section, in GADT-style syntax:
3632 <programlisting>
3633 data Counter a where
3634 NewCounter :: { _this :: self
3635 , _inc :: self -> self
3636 , _display :: self -> IO ()
3637 , tag :: a
3638 } -> Counter a
3639 </programlisting>
3640 As before, only one selector function is generated here, that for <literal>tag</literal>.
3641 Nevertheless, you can still use all the field names in pattern matching and record construction.
3642 </para></listitem>
3643
3644 <listitem><para>
3645 In a GADT-style data type declaration there is no obvious way to specify that a data constructor
3646 should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
3647 (Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
3648 So GHC implements the following design: a data constructor declared in a GADT-style data type
3649 declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
3650 (b) it has two arguments, (c) it has a programmer-supplied fixity declaration. For example
3651 <programlisting>
3652 infix 6 (:--:)
3653 data T a where
3654 (:--:) :: Int -> Bool -> T Int
3655 </programlisting>
3656 </para></listitem>
3657 </itemizedlist></para>
3658 </sect2>
3659
3660 <sect2 id="gadt">
3661 <title>Generalised Algebraic Data Types (GADTs)</title>
3662
3663 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
3664 by allowing constructors to have richer return types. Here is an example:
3665 <programlisting>
3666 data Term a where
3667 Lit :: Int -> Term Int
3668 Succ :: Term Int -> Term Int
3669 IsZero :: Term Int -> Term Bool
3670 If :: Term Bool -> Term a -> Term a -> Term a
3671 Pair :: Term a -> Term b -> Term (a,b)
3672 </programlisting>
3673 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3674 case with ordinary data types. This generality allows us to
3675 write a well-typed <literal>eval</literal> function
3676 for these <literal>Terms</literal>:
3677 <programlisting>
3678 eval :: Term a -> a
3679 eval (Lit i) = i
3680 eval (Succ t) = 1 + eval t
3681 eval (IsZero t) = eval t == 0
3682 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3683 eval (Pair e1 e2) = (eval e1, eval e2)
3684 </programlisting>
3685 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
3686 For example, in the right hand side of the equation
3687 <programlisting>
3688 eval :: Term a -> a
3689 eval (Lit i) = ...
3690 </programlisting>
3691 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
3692 A precise specification of the type rules is beyond what this user manual aspires to,
3693 but the design closely follows that described in
3694 the paper <ulink
3695 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
3696 unification-based type inference for GADTs</ulink>,
3697 (ICFP 2006).
3698 The general principle is this: <emphasis>type refinement is only carried out
3699 based on user-supplied type annotations</emphasis>.
3700 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
3701 and lots of obscure error messages will
3702 occur. However, the refinement is quite general. For example, if we had:
3703 <programlisting>
3704 eval :: Term a -> a -> a
3705 eval (Lit i) j = i+j
3706 </programlisting>
3707 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3708 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
3709 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3710 </para>
3711 <para>
3712 These and many other examples are given in papers by Hongwei Xi, and
3713 Tim Sheard. There is a longer introduction
3714 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3715 and Ralf Hinze's
3716 <ulink url="http://www.informatik.uni-bonn.de/~ralf/publications/With.pdf">Fun with phantom types</ulink> also has a number of examples. Note that papers
3717 may use different notation to that implemented in GHC.
3718 </para>
3719 <para>
3720 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
3721 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XGADTSyntax</option>
3722 and <option>-XMonoLocalBinds</option>.
3723 <itemizedlist>
3724 <listitem><para>
3725 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
3726 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
3727 The result type of each constructor must begin with the type constructor being defined,
3728 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
3729 For example, in the <literal>Term</literal> data
3730 type above, the type of each constructor must end with <literal>Term ty</literal>, but
3731 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
3732 constructor).
3733 </para></listitem>
3734
3735 <listitem><para>
3736 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
3737 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
3738 whose result type is not just <literal>T a b</literal>.
3739 </para></listitem>
3740
3741 <listitem><para>
3742 You cannot use a <literal>deriving</literal> clause for a GADT; only for
3743 an ordinary data type.
3744 </para></listitem>
3745
3746 <listitem><para>
3747 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
3748 For example:
3749 <programlisting>
3750 data Term a where
3751 Lit :: { val :: Int } -> Term Int
3752 Succ :: { num :: Term Int } -> Term Int
3753 Pred :: { num :: Term Int } -> Term Int
3754 IsZero :: { arg :: Term Int } -> Term Bool
3755 Pair :: { arg1 :: Term a
3756 , arg2 :: Term b
3757 } -> Term (a,b)
3758 If :: { cnd :: Term Bool
3759 , tru :: Term a
3760 , fls :: Term a
3761 } -> Term a
3762 </programlisting>
3763 However, for GADTs there is the following additional constraint:
3764 every constructor that has a field <literal>f</literal> must have
3765 the same result type (modulo alpha conversion)
3766 Hence, in the above example, we cannot merge the <literal>num</literal>
3767 and <literal>arg</literal> fields above into a
3768 single name. Although their field types are both <literal>Term Int</literal>,
3769 their selector functions actually have different types:
3770
3771 <programlisting>
3772 num :: Term Int -> Term Int
3773 arg :: Term Bool -> Term Int
3774 </programlisting>
3775 </para></listitem>
3776
3777 <listitem><para>
3778 When pattern-matching against data constructors drawn from a GADT,
3779 for example in a <literal>case</literal> expression, the following rules apply:
3780 <itemizedlist>
3781 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
3782 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
3783 <listitem><para>The type of any free variable mentioned in any of
3784 the <literal>case</literal> alternatives must be rigid.</para></listitem>
3785 </itemizedlist>
3786 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
3787 way to ensure that a variable a rigid type is to give it a type signature.
3788 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
3789 Simple unification-based type inference for GADTs
3790 </ulink>. The criteria implemented by GHC are given in the Appendix.
3791
3792 </para></listitem>
3793
3794 </itemizedlist>
3795 </para>
3796
3797 </sect2>
3798 </sect1>
3799
3800 <!-- ====================== End of Generalised algebraic data types ======================= -->
3801
3802 <sect1 id="deriving">
3803 <title>Extensions to the "deriving" mechanism</title>
3804
3805 <sect2 id="deriving-inferred">
3806 <title>Inferred context for deriving clauses</title>
3807
3808 <para>
3809 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
3810 legal. For example:
3811 <programlisting>
3812 data T0 f a = MkT0 a deriving( Eq )
3813 data T1 f a = MkT1 (f a) deriving( Eq )
3814 data T2 f a = MkT2 (f (f a)) deriving( Eq )
3815 </programlisting>
3816 The natural generated <literal>Eq</literal> code would result in these instance declarations:
3817 <programlisting>
3818 instance Eq a => Eq (T0 f a) where ...
3819 instance Eq (f a) => Eq (T1 f a) where ...
3820 instance Eq (f (f a)) => Eq (T2 f a) where ...
3821 </programlisting>
3822 The first of these is obviously fine. The second is still fine, although less obviously.
3823 The third is not Haskell 98, and risks losing termination of instances.
3824 </para>
3825 <para>
3826 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
3827 each constraint in the inferred instance context must consist only of type variables,
3828 with no repetitions.
3829 </para>
3830 <para>
3831 This rule is applied regardless of flags. If you want a more exotic context, you can write
3832 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
3833 </para>
3834 </sect2>
3835
3836 <sect2 id="stand-alone-deriving">
3837 <title>Stand-alone deriving declarations</title>
3838
3839 <para>
3840 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
3841 <programlisting>
3842 data Foo a = Bar a | Baz String
3843
3844 deriving instance Eq a => Eq (Foo a)
3845 </programlisting>
3846 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
3847 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
3848 </para>
3849 <para>
3850 However, standalone deriving differs from a <literal>deriving</literal> clause in a number
3851 of important ways:
3852 <itemizedlist>
3853 <listitem><para>The standalone deriving declaration does not need to be in the
3854 same module as the data type declaration. (But be aware of the dangers of
3855 orphan instances (<xref linkend="orphan-modules"/>).
3856 </para></listitem>
3857
3858 <listitem><para>
3859 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
3860 exactly as you would in an ordinary instance declaration.
3861 (In contrast, in a <literal>deriving</literal> clause
3862 attached to a data type declaration, the context is inferred.)
3863 </para></listitem>
3864
3865 <listitem><para>
3866 Unlike a <literal>deriving</literal>
3867 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
3868 than the data type (assuming you also use
3869 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
3870 for example
3871 <programlisting>
3872 data Foo a = Bar a | Baz String
3873
3874 deriving instance Eq a => Eq (Foo [a])
3875 deriving instance Eq a => Eq (Foo (Maybe a))
3876 </programlisting>
3877 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
3878 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
3879 </para></listitem>
3880
3881 <listitem><para>
3882 Unlike a <literal>deriving</literal>
3883 declaration attached to a <literal>data</literal> declaration,
3884 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
3885 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
3886 your problem. (GHC will show you the offending code if it has a type error.)
3887 </para>
3888 <para>
3889 The merit of this is that you can derive instances for GADTs and other exotic
3890 data types, providing only that the boilerplate code does indeed typecheck. For example:
3891 <programlisting>
3892 data T a where
3893 T1 :: T Int
3894 T2 :: T Bool
3895
3896 deriving instance Show (T a)
3897 </programlisting>
3898 In this example, you cannot say <literal>... deriving( Show )</literal> on the
3899 data type declaration for <literal>T</literal>,
3900 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
3901 the instance declaration using stand-alone deriving.
3902 </para>
3903 <para>
3904 The down-side is that,
3905 if the boilerplate code fails to typecheck, you will get an error message about that
3906 code, which you did not write. Whereas, with a <literal>deriving</literal> clause
3907 the side-conditions are necessarily more conservative, but any error message
3908 may be more comprehensible.
3909 </para>
3910 </listitem>
3911 </itemizedlist></para>
3912
3913 <para>
3914 In other ways, however, a standalone deriving obeys the same rules as ordinary deriving:
3915 <itemizedlist>
3916 <listitem><para>
3917 A <literal>deriving instance</literal> declaration
3918 must obey the same rules concerning form and termination as ordinary instance declarations,
3919 controlled by the same flags; see <xref linkend="instance-decls"/>.
3920 </para></listitem>
3921
3922 <listitem>
3923 <para>The stand-alone syntax is generalised for newtypes in exactly the same
3924 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3925 For example:
3926 <programlisting>
3927 newtype Foo a = MkFoo (State Int a)
3928
3929 deriving instance MonadState Int Foo
3930 </programlisting>
3931 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3932 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3933 </para></listitem>
3934 </itemizedlist></para>
3935
3936 </sect2>
3937
3938 <sect2 id="deriving-extra">
3939 <title>Deriving instances of extra classes (<literal>Data</literal>, etc)</title>
3940
3941 <para>
3942 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3943 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3944 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3945 classes <literal>Eq</literal>, <literal>Ord</literal>,
3946 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3947 </para>
3948 <para>
3949 GHC extends this list with several more classes that may be automatically derived:
3950 <itemizedlist>
3951 <listitem><para> With <option>-XDeriveGeneric</option>, you can derive
3952 instances of the classes <literal>Generic</literal> and
3953 <literal>Generic1</literal>, defined in <literal>GHC.Generics</literal>.
3954 You can use these to define generic functions,
3955 as described in <xref linkend="generic-programming"/>.
3956 </para></listitem>
3957
3958 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3959 the class <literal>Functor</literal>,
3960 defined in <literal>GHC.Base</literal>.
3961 </para></listitem>
3962
3963 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of
3964 the class <literal>Data</literal>,
3965 defined in <literal>Data.Data</literal>. See <xref linkend="deriving-typeable"/> for
3966 deriving <literal>Typeable</literal>.
3967 </para></listitem>
3968
3969 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3970 the class <literal>Foldable</literal>,
3971 defined in <literal>Data.Foldable</literal>.
3972 </para></listitem>
3973
3974 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3975 the class <literal>Traversable</literal>,
3976 defined in <literal>Data.Traversable</literal>. Since the <literal>Traversable</literal>
3977 instance dictates the instances of <literal>Functor</literal> and
3978 <literal>Foldable</literal>, you'll probably want to derive them too, so
3979 <option>-XDeriveTraversable</option> implies
3980 <option>-XDeriveFunctor</option> and <option>-XDeriveFoldable</option>.
3981 </para></listitem>
3982 </itemizedlist>
3983 You can also use a standalone deriving declaration instead
3984 (see <xref linkend="stand-alone-deriving"/>).
3985 </para>
3986 <para>
3987 In each case the appropriate class must be in scope before it
3988 can be mentioned in the <literal>deriving</literal> clause.
3989 </para>
3990 </sect2>
3991
3992 <sect2 id="deriving-typeable">
3993 <title>Deriving <literal>Typeable</literal> instances</title>
3994
3995 <para>The class <literal>Typeable</literal> is very special:
3996 <itemizedlist>
3997 <listitem><para>
3998 <literal>Typeable</literal> is kind-polymorphic (see
3999 <xref linkend="kind-polymorphism"/>).
4000 </para></listitem>
4001
4002 <listitem><para>
4003 Only derived instances of <literal>Typeable</literal> are allowed;
4004 i.e. handwritten instances are forbidden. This ensures that the
4005 programmer cannot subert the type system by writing bogus instances.
4006 </para></listitem>
4007
4008 <listitem><para>
4009 With <option>-XDeriveDataTypeable</option>
4010 GHC allows you to derive instances of <literal>Typeable</literal> for data types or newtypes,
4011 using a <literal>deriving</literal> clause, or using
4012 a standalone deriving declaration (<xref linkend="stand-alone-deriving"/>).
4013 </para></listitem>
4014
4015 <listitem><para>
4016 With <option>-XDataKinds</option>, deriving <literal>Typeable</literal> for a data
4017 type (whether via a deriving clause or standalone deriving)
4018 also derives <literal>Typeable</literal> for the promoted data constructors (<xref linkend="promotion"/>).
4019 </para></listitem>
4020
4021 <listitem><para>
4022 However, using standalone deriving, you can <emphasis>also</emphasis> derive
4023 a <literal>Typeable</literal> instance for a data family.
4024 You may not add a <literal>deriving(Typeable)</literal> clause to a
4025 <literal>data instance</literal> declaration; instead you must use a
4026 standalone deriving declaration for the data family.
4027 </para></listitem>
4028
4029 <listitem><para>
4030 Using standalone deriving, you can <emphasis>also</emphasis> derive
4031 a <literal>Typeable</literal> instance for a type class.
4032 </para></listitem>
4033
4034 <listitem><para>
4035 The flag <option>-XAutoDeriveTypeable</option> triggers the generation
4036 of derived <literal>Typeable</literal> instances for every datatype, data family,
4037 and type class declaration in the module it is used, unless a manually-specified one is
4038 already provided.
4039 This flag implies <option>-XDeriveDataTypeable</option>.
4040 </para></listitem>
4041 </itemizedlist>
4042
4043 </para>
4044
4045 </sect2>
4046
4047 <sect2 id="newtype-deriving">
4048 <title>Generalised derived instances for newtypes</title>
4049
4050 <para>
4051 When you define an abstract type using <literal>newtype</literal>, you may want
4052 the new type to inherit some instances from its representation. In
4053 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
4054 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
4055 other classes you have to write an explicit instance declaration. For
4056 example, if you define
4057
4058 <programlisting>
4059 newtype Dollars = Dollars Int
4060 </programlisting>
4061
4062 and you want to use arithmetic on <literal>Dollars</literal>, you have to
4063 explicitly define an instance of <literal>Num</literal>:
4064
4065 <programlisting>
4066 instance Num Dollars where
4067 Dollars a + Dollars b = Dollars (a+b)
4068 ...
4069 </programlisting>
4070 All the instance does is apply and remove the <literal>newtype</literal>
4071 constructor. It is particularly galling that, since the constructor
4072 doesn't appear at run-time, this instance declaration defines a
4073 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
4074 dictionary, only slower!
4075 </para>
4076
4077
4078 <sect3 id="generalized-newtype-deriving"> <title> Generalising the deriving clause </title>
4079 <para>
4080 GHC now permits such instances to be derived instead,
4081 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
4082 so one can write
4083 <programlisting>
4084 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
4085 </programlisting>
4086
4087 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
4088 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
4089 derives an instance declaration of the form
4090
4091 <programlisting>
4092 instance Num Int => Num Dollars
4093 </programlisting>
4094
4095 which just adds or removes the <literal>newtype</literal> constructor according to the type.
4096 </para>
4097 <para>
4098
4099 We can also derive instances of constructor classes in a similar
4100 way. For example, suppose we have implemented state and failure monad
4101 transformers, such that
4102
4103 <programlisting>
4104 instance Monad m => Monad (State s m)