Complete work on new OVERLAPPABLE/OVERLAPPING pragmas (Trac #9242)
[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 Wildcards 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 expressions, writing, 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 The "<literal>..</literal>" expands to the missing
2356 <emphasis>in-scope</emphasis> record fields.
2357 Specifically the expansion of "<literal>C {..}</literal>" includes
2358 <literal>f</literal> if and only if:
2359 <itemizedlist>
2360 <listitem><para>
2361 <literal>f</literal> is a record field of constructor <literal>C</literal>.
2362 </para></listitem>
2363 <listitem><para>
2364 The record field <literal>f</literal> is in scope somehow (either qualified or unqualified).
2365 </para></listitem>
2366 <listitem><para>
2367 In the case of expressions (but not patterns),
2368 the variable <literal>f</literal> is in scope unqualified,
2369 apart from the binding of the record selector itself.
2370 </para></listitem>
2371 </itemizedlist>
2372 For example
2373 <programlisting>
2374 module M where
2375 data R = R { a,b,c :: Int }
2376 module X where
2377 import M( R(a,c) )
2378 f b = R { .. }
2379 </programlisting>
2380 The <literal>R{..}</literal> expands to <literal>R{M.a=a}</literal>,
2381 omitting <literal>b</literal> since the record field is not in scope,
2382 and omitting <literal>c</literal> since the variable <literal>c</literal>
2383 is not in scope (apart from the binding of the
2384 record selector <literal>c</literal>, of course).
2385 </para></listitem>
2386 </itemizedlist>
2387 </para>
2388
2389 </sect2>
2390
2391 <!-- ===================== Local fixity declarations =================== -->
2392
2393 <sect2 id="local-fixity-declarations">
2394 <title>Local Fixity Declarations
2395 </title>
2396
2397 <para>A careful reading of the Haskell 98 Report reveals that fixity
2398 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
2399 <literal>infixr</literal>) are permitted to appear inside local bindings
2400 such those introduced by <literal>let</literal> and
2401 <literal>where</literal>. However, the Haskell Report does not specify
2402 the semantics of such bindings very precisely.
2403 </para>
2404
2405 <para>In GHC, a fixity declaration may accompany a local binding:
2406 <programlisting>
2407 let f = ...
2408 infixr 3 `f`
2409 in
2410 ...
2411 </programlisting>
2412 and the fixity declaration applies wherever the binding is in scope.
2413 For example, in a <literal>let</literal>, it applies in the right-hand
2414 sides of other <literal>let</literal>-bindings and the body of the
2415 <literal>let</literal>C. Or, in recursive <literal>do</literal>
2416 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
2417 declarations of a <literal>let</literal> statement scope over other
2418 statements in the group, just as the bound name does.
2419 </para>
2420
2421 <para>
2422 Moreover, a local fixity declaration *must* accompany a local binding of
2423 that name: it is not possible to revise the fixity of name bound
2424 elsewhere, as in
2425 <programlisting>
2426 let infixr 9 $ in ...
2427 </programlisting>
2428
2429 Because local fixity declarations are technically Haskell 98, no flag is
2430 necessary to enable them.
2431 </para>
2432 </sect2>
2433
2434 <sect2 id="package-imports">
2435 <title>Import and export extensions</title>
2436
2437 <sect3>
2438 <title>Hiding things the imported module doesn't export</title>
2439
2440 <para>
2441 Technically in Haskell 2010 this is illegal:
2442 <programlisting>
2443 module A( f ) where
2444 f = True
2445
2446 module B where
2447 import A hiding( g ) -- A does not export g
2448 g = f
2449 </programlisting>
2450 The <literal>import A hiding( g )</literal> in module <literal>B</literal>
2451 is technically an error (<ulink url="http://www.haskell.org/onlinereport/haskell2010/haskellch5.html#x11-1020005.3.1">Haskell Report, 5.3.1</ulink>)
2452 because <literal>A</literal> does not export <literal>g</literal>.
2453 However GHC allows it, in the interests of supporting backward compatibility; for example, a newer version of
2454 <literal>A</literal> might export <literal>g</literal>, and you want <literal>B</literal> to work
2455 in either case.
2456 </para>
2457 <para>
2458 The warning <literal>-fwarn-dodgy-imports</literal>, which is off by default but included with <literal>-W</literal>,
2459 warns if you hide something that the imported module does not export.
2460 </para>
2461 </sect3>
2462
2463 <sect3>
2464 <title>Package-qualified imports</title>
2465
2466 <para>With the <option>-XPackageImports</option> flag, GHC allows
2467 import declarations to be qualified by the package name that the
2468 module is intended to be imported from. For example:</para>
2469
2470 <programlisting>
2471 import "network" Network.Socket
2472 </programlisting>
2473
2474 <para>would import the module <literal>Network.Socket</literal> from
2475 the package <literal>network</literal> (any version). This may
2476 be used to disambiguate an import when the same module is
2477 available from multiple packages, or is present in both the
2478 current package being built and an external package.</para>
2479
2480 <para>The special package name <literal>this</literal> can be used to
2481 refer to the current package being built.</para>
2482
2483 <para>Note: you probably don't need to use this feature, it was
2484 added mainly so that we can build backwards-compatible versions of
2485 packages when APIs change. It can lead to fragile dependencies in
2486 the common case: modules occasionally move from one package to
2487 another, rendering any package-qualified imports broken.</para>
2488 </sect3>
2489
2490 <sect3 id="safe-imports-ext">
2491 <title>Safe imports</title>
2492
2493 <para>With the <option>-XSafe</option>, <option>-XTrustworthy</option>
2494 and <option>-XUnsafe</option> language flags, GHC extends
2495 the import declaration syntax to take an optional <literal>safe</literal>
2496 keyword after the <literal>import</literal> keyword. This feature
2497 is part of the Safe Haskell GHC extension. For example:</para>
2498
2499 <programlisting>
2500 import safe qualified Network.Socket as NS
2501 </programlisting>
2502
2503 <para>would import the module <literal>Network.Socket</literal>
2504 with compilation only succeeding if Network.Socket can be
2505 safely imported. For a description of when a import is
2506 considered safe see <xref linkend="safe-haskell"/></para>
2507
2508 </sect3>
2509
2510 <sect3 id="explicit-namespaces">
2511 <title>Explicit namespaces in import/export</title>
2512
2513 <para> In an import or export list, such as
2514 <programlisting>
2515 module M( f, (++) ) where ...
2516 import N( f, (++) )
2517 ...
2518 </programlisting>
2519 the entities <literal>f</literal> and <literal>(++)</literal> are <emphasis>values</emphasis>.
2520 However, with type operators (<xref linkend="type-operators"/>) it becomes possible
2521 to declare <literal>(++)</literal> as a <emphasis>type constructor</emphasis>. In that
2522 case, how would you export or import it?
2523 </para>
2524 <para>
2525 The <option>-XExplicitNamespaces</option> extension allows you to prefix the name of
2526 a type constructor in an import or export list with "<literal>type</literal>" to
2527 disambiguate this case, thus:
2528 <programlisting>
2529 module M( f, type (++) ) where ...
2530 import N( f, type (++) )
2531 ...
2532 module N( f, type (++) ) where
2533 data family a ++ b = L a | R b
2534 </programlisting>
2535 The extension <option>-XExplicitNamespaces</option>
2536 is implied by <option>-XTypeOperators</option> and (for some reason) by <option>-XTypeFamilies</option>.
2537 </para>
2538 <para>
2539 In addition, with <option>-XPatternSynonyms</option> you can prefix the name of
2540 a data constructor in an import or export list with the keyword <literal>pattern</literal>,
2541 to allow the import or export of a data constructor without its parent type constructor
2542 (see <xref linkend="patsyn-impexp"/>).
2543 </para>
2544 </sect3>
2545
2546 </sect2>
2547
2548 <sect2 id="syntax-stolen">
2549 <title>Summary of stolen syntax</title>
2550
2551 <para>Turning on an option that enables special syntax
2552 <emphasis>might</emphasis> cause working Haskell 98 code to fail
2553 to compile, perhaps because it uses a variable name which has
2554 become a reserved word. This section lists the syntax that is
2555 "stolen" by language extensions.
2556 We use
2557 notation and nonterminal names from the Haskell 98 lexical syntax
2558 (see the Haskell 98 Report).
2559 We only list syntax changes here that might affect
2560 existing working programs (i.e. "stolen" syntax). Many of these
2561 extensions will also enable new context-free syntax, but in all
2562 cases programs written to use the new syntax would not be
2563 compilable without the option enabled.</para>
2564
2565 <para>There are two classes of special
2566 syntax:
2567
2568 <itemizedlist>
2569 <listitem>
2570 <para>New reserved words and symbols: character sequences
2571 which are no longer available for use as identifiers in the
2572 program.</para>
2573 </listitem>
2574 <listitem>
2575 <para>Other special syntax: sequences of characters that have
2576 a different meaning when this particular option is turned
2577 on.</para>
2578 </listitem>
2579 </itemizedlist>
2580
2581 The following syntax is stolen:
2582
2583 <variablelist>
2584 <varlistentry>
2585 <term>
2586 <literal>forall</literal>
2587 <indexterm><primary><literal>forall</literal></primary></indexterm>
2588 </term>
2589 <listitem><para>
2590 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
2591 <option>-XScopedTypeVariables</option>,
2592 <option>-XLiberalTypeSynonyms</option>,
2593 <option>-XRankNTypes</option>,
2594 <option>-XExistentialQuantification</option>
2595 </para></listitem>
2596 </varlistentry>
2597
2598 <varlistentry>
2599 <term>
2600 <literal>mdo</literal>
2601 <indexterm><primary><literal>mdo</literal></primary></indexterm>
2602 </term>
2603 <listitem><para>
2604 Stolen by: <option>-XRecursiveDo</option>
2605 </para></listitem>
2606 </varlistentry>
2607
2608 <varlistentry>
2609 <term>
2610 <literal>foreign</literal>
2611 <indexterm><primary><literal>foreign</literal></primary></indexterm>
2612 </term>
2613 <listitem><para>
2614 Stolen by: <option>-XForeignFunctionInterface</option>
2615 </para></listitem>
2616 </varlistentry>
2617
2618 <varlistentry>
2619 <term>
2620 <literal>rec</literal>,
2621 <literal>proc</literal>, <literal>-&lt;</literal>,
2622 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
2623 <literal>&gt;&gt;-</literal>, and <literal>(|</literal>,
2624 <literal>|)</literal> brackets
2625 <indexterm><primary><literal>proc</literal></primary></indexterm>
2626 </term>
2627 <listitem><para>
2628 Stolen by: <option>-XArrows</option>
2629 </para></listitem>
2630 </varlistentry>
2631
2632 <varlistentry>
2633 <term>
2634 <literal>?<replaceable>varid</replaceable></literal>
2635 <indexterm><primary>implicit parameters</primary></indexterm>
2636 </term>
2637 <listitem><para>
2638 Stolen by: <option>-XImplicitParams</option>
2639 </para></listitem>
2640 </varlistentry>
2641
2642 <varlistentry>
2643 <term>
2644 <literal>[|</literal>,
2645 <literal>[e|</literal>, <literal>[p|</literal>,
2646 <literal>[d|</literal>, <literal>[t|</literal>,
2647 <literal>$(</literal>,
2648 <literal>$$(</literal>,
2649 <literal>[||</literal>,
2650 <literal>[e||</literal>,
2651 <literal>$<replaceable>varid</replaceable></literal>,
2652 <literal>$$<replaceable>varid</replaceable></literal>
2653 <indexterm><primary>Template Haskell</primary></indexterm>
2654 </term>
2655 <listitem><para>
2656 Stolen by: <option>-XTemplateHaskell</option>
2657 </para></listitem>
2658 </varlistentry>
2659
2660 <varlistentry>
2661 <term>
2662 <literal>[<replaceable>varid</replaceable>|</literal>
2663 <indexterm><primary>quasi-quotation</primary></indexterm>
2664 </term>
2665 <listitem><para>
2666 Stolen by: <option>-XQuasiQuotes</option>
2667 </para></listitem>
2668 </varlistentry>
2669
2670 <varlistentry>
2671 <term>
2672 <replaceable>varid</replaceable>{<literal>&num;</literal>},
2673 <replaceable>char</replaceable><literal>&num;</literal>,
2674 <replaceable>string</replaceable><literal>&num;</literal>,
2675 <replaceable>integer</replaceable><literal>&num;</literal>,
2676 <replaceable>float</replaceable><literal>&num;</literal>,
2677 <replaceable>float</replaceable><literal>&num;&num;</literal>
2678 </term>
2679 <listitem><para>
2680 Stolen by: <option>-XMagicHash</option>
2681 </para></listitem>
2682 </varlistentry>
2683
2684 <varlistentry>
2685 <term>
2686 <literal>(&num;</literal>, <literal>&num;)</literal>
2687 </term>
2688 <listitem><para>
2689 Stolen by: <option>-XUnboxedTuples</option>
2690 </para></listitem>
2691 </varlistentry>
2692
2693 <varlistentry>
2694 <term>
2695 <replaceable>varid</replaceable><literal>!</literal><replaceable>varid</replaceable>
2696 </term>
2697 <listitem><para>
2698 Stolen by: <option>-XBangPatterns</option>
2699 </para></listitem>
2700 </varlistentry>
2701
2702 <varlistentry>
2703 <term>
2704 <literal>pattern</literal>
2705 </term>
2706 <listitem><para>
2707 Stolen by: <option>-XPatternSynonyms</option>
2708 </para></listitem>
2709 </varlistentry>
2710 </variablelist>
2711 </para>
2712 </sect2>
2713 </sect1>
2714
2715
2716 <!-- TYPE SYSTEM EXTENSIONS -->
2717 <sect1 id="data-type-extensions">
2718 <title>Extensions to data types and type synonyms</title>
2719
2720 <sect2 id="nullary-types">
2721 <title>Data types with no constructors</title>
2722
2723 <para>With the <option>-XEmptyDataDecls</option> flag (or equivalent LANGUAGE pragma),
2724 GHC lets you declare a data type with no constructors. For example:</para>
2725
2726 <programlisting>
2727 data S -- S :: *
2728 data T a -- T :: * -> *
2729 </programlisting>
2730
2731 <para>Syntactically, the declaration lacks the "= constrs" part. The
2732 type can be parameterised over types of any kind, but if the kind is
2733 not <literal>*</literal> then an explicit kind annotation must be used
2734 (see <xref linkend="kinding"/>).</para>
2735
2736 <para>Such data types have only one value, namely bottom.
2737 Nevertheless, they can be useful when defining "phantom types".</para>
2738 </sect2>
2739
2740 <sect2 id="datatype-contexts">
2741 <title>Data type contexts</title>
2742
2743 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2744
2745 <programlisting>
2746 data Eq a => Set a = NilSet | ConsSet a (Set a)
2747 </programlisting>
2748
2749 <para>give constructors with types:</para>
2750
2751 <programlisting>
2752 NilSet :: Set a
2753 ConsSet :: Eq a => a -> Set a -> Set a
2754 </programlisting>
2755
2756 <para>This is widely considered a misfeature, and is going to be removed from
2757 the language. In GHC, it is controlled by the deprecated extension
2758 <literal>DatatypeContexts</literal>.</para>
2759 </sect2>
2760
2761 <sect2 id="infix-tycons">
2762 <title>Infix type constructors, classes, and type variables</title>
2763
2764 <para>
2765 GHC allows type constructors, classes, and type variables to be operators, and
2766 to be written infix, very much like expressions. More specifically:
2767 <itemizedlist>
2768 <listitem><para>
2769 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
2770 The lexical syntax is the same as that for data constructors.
2771 </para></listitem>
2772 <listitem><para>
2773 Data type and type-synonym declarations can be written infix, parenthesised
2774 if you want further arguments. E.g.
2775 <screen>
2776 data a :*: b = Foo a b
2777 type a :+: b = Either a b
2778 class a :=: b where ...
2779
2780 data (a :**: b) x = Baz a b x
2781 type (a :++: b) y = Either (a,b) y
2782 </screen>
2783 </para></listitem>
2784 <listitem><para>
2785 Types, and class constraints, can be written infix. For example
2786 <screen>
2787 x :: Int :*: Bool
2788 f :: (a :=: b) => a -> b
2789 </screen>
2790 </para></listitem>
2791 <listitem><para>
2792 Back-quotes work
2793 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
2794 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
2795 </para></listitem>
2796 <listitem><para>
2797 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
2798 one cannot distinguish between the two in a fixity declaration; a fixity declaration
2799 sets the fixity for a data constructor and the corresponding type constructor. For example:
2800 <screen>
2801 infixl 7 T, :*:
2802 </screen>
2803 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
2804 and similarly for <literal>:*:</literal>.
2805 <literal>Int `a` Bool</literal>.
2806 </para></listitem>
2807 <listitem><para>
2808 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
2809 </para></listitem>
2810
2811 </itemizedlist>
2812 </para>
2813 </sect2>
2814
2815 <sect2 id="type-operators">
2816 <title>Type operators</title>
2817 <para>
2818 In types, an operator symbol like <literal>(+)</literal> is normally treated as a type
2819 <emphasis>variable</emphasis>, just like <literal>a</literal>. Thus in Haskell 98 you can say
2820 <programlisting>
2821 type T (+) = ((+), (+))
2822 -- Just like: type T a = (a,a)
2823
2824 f :: T Int -> Int
2825 f (x,y)= x
2826 </programlisting>
2827 As you can see, using operators in this way is not very useful, and Haskell 98 does not even
2828 allow you to write them infix.
2829 </para>
2830 <para>
2831 The language <option>-XTypeOperators</option> changes this behaviour:
2832 <itemizedlist>
2833 <listitem><para>
2834 Operator symbols become type <emphasis>constructors</emphasis> rather than
2835 type <emphasis>variables</emphasis>.
2836 </para></listitem>
2837 <listitem><para>
2838 Operator symbols in types can be written infix, both in definitions and uses.
2839 for example:
2840 <programlisting>
2841 data a + b = Plus a b
2842 type Foo = Int + Bool
2843 </programlisting>
2844 </para></listitem>
2845 <listitem><para>
2846 There is now some potential ambiguity in import and export lists; for example
2847 if you write <literal>import M( (+) )</literal> do you mean the
2848 <emphasis>function</emphasis> <literal>(+)</literal> or the
2849 <emphasis>type constructor</emphasis> <literal>(+)</literal>?
2850 The default is the former, but with <option>-XExplicitNamespaces</option> (which is implied
2851 by <option>-XExplicitTypeOperators</option>) GHC allows you to specify the latter
2852 by preceding it with the keyword <literal>type</literal>, thus:
2853 <programlisting>
2854 import M( type (+) )
2855 </programlisting>
2856 See <xref linkend="explicit-namespaces"/>.
2857 </para></listitem>
2858 <listitem><para>
2859 The fixity of a type operator may be set using the usual fixity declarations
2860 but, as in <xref linkend="infix-tycons"/>, the function and type constructor share
2861 a single fixity.
2862 </para></listitem>
2863 </itemizedlist>
2864 </para>
2865 </sect2>
2866
2867 <sect2 id="type-synonyms">
2868 <title>Liberalised type synonyms</title>
2869
2870 <para>
2871 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
2872 on individual synonym declarations.
2873 With the <option>-XLiberalTypeSynonyms</option> extension,
2874 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2875 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
2876
2877 <itemizedlist>
2878 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2879 in a type synonym, thus:
2880 <programlisting>
2881 type Discard a = forall b. Show b => a -> b -> (a, String)
2882
2883 f :: Discard a
2884 f x y = (x, show y)
2885
2886 g :: Discard Int -> (Int,String) -- A rank-2 type
2887 g f = f 3 True
2888 </programlisting>
2889 </para>
2890 </listitem>
2891
2892 <listitem><para>
2893 If you also use <option>-XUnboxedTuples</option>,
2894 you can write an unboxed tuple in a type synonym:
2895 <programlisting>
2896 type Pr = (# Int, Int #)
2897
2898 h :: Int -> Pr
2899 h x = (# x, x #)
2900 </programlisting>
2901 </para></listitem>
2902
2903 <listitem><para>
2904 You can apply a type synonym to a forall type:
2905 <programlisting>
2906 type Foo a = a -> a -> Bool
2907
2908 f :: Foo (forall b. b->b)
2909 </programlisting>
2910 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2911 <programlisting>
2912 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2913 </programlisting>
2914 </para></listitem>
2915
2916 <listitem><para>
2917 You can apply a type synonym to a partially applied type synonym:
2918 <programlisting>
2919 type Generic i o = forall x. i x -> o x
2920 type Id x = x
2921
2922 foo :: Generic Id []
2923 </programlisting>
2924 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2925 <programlisting>
2926 foo :: forall x. x -> [x]
2927 </programlisting>
2928 </para></listitem>
2929
2930 </itemizedlist>
2931 </para>
2932
2933 <para>
2934 GHC currently does kind checking before expanding synonyms (though even that
2935 could be changed.)
2936 </para>
2937 <para>
2938 After expanding type synonyms, GHC does validity checking on types, looking for
2939 the following mal-formedness which isn't detected simply by kind checking:
2940 <itemizedlist>
2941 <listitem><para>
2942 Type constructor applied to a type involving for-alls (if <literal>XImpredicativeTypes</literal>
2943 is off)
2944 </para></listitem>
2945 <listitem><para>
2946 Partially-applied type synonym.
2947 </para></listitem>
2948 </itemizedlist>
2949 So, for example, this will be rejected:
2950 <programlisting>
2951 type Pr = forall a. a
2952
2953 h :: [Pr]
2954 h = ...
2955 </programlisting>
2956 because GHC does not allow type constructors applied to for-all types.
2957 </para>
2958 </sect2>
2959
2960
2961 <sect2 id="existential-quantification">
2962 <title>Existentially quantified data constructors
2963 </title>
2964
2965 <para>
2966 The idea of using existential quantification in data type declarations
2967 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2968 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2969 London, 1991). It was later formalised by Laufer and Odersky
2970 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2971 TOPLAS, 16(5), pp1411-1430, 1994).
2972 It's been in Lennart
2973 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2974 proved very useful. Here's the idea. Consider the declaration:
2975 </para>
2976
2977 <para>
2978
2979 <programlisting>
2980 data Foo = forall a. MkFoo a (a -> Bool)
2981 | Nil
2982 </programlisting>
2983
2984 </para>
2985
2986 <para>
2987 The data type <literal>Foo</literal> has two constructors with types:
2988 </para>
2989
2990 <para>
2991
2992 <programlisting>
2993 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2994 Nil :: Foo
2995 </programlisting>
2996
2997 </para>
2998
2999 <para>
3000 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
3001 does not appear in the data type itself, which is plain <literal>Foo</literal>.
3002 For example, the following expression is fine:
3003 </para>
3004
3005 <para>
3006
3007 <programlisting>
3008 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
3009 </programlisting>
3010
3011 </para>
3012
3013 <para>
3014 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
3015 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
3016 isUpper</function> packages a character with a compatible function. These
3017 two things are each of type <literal>Foo</literal> and can be put in a list.
3018 </para>
3019
3020 <para>
3021 What can we do with a value of type <literal>Foo</literal>?. In particular,
3022 what happens when we pattern-match on <function>MkFoo</function>?
3023 </para>
3024
3025 <para>
3026
3027 <programlisting>
3028 f (MkFoo val fn) = ???
3029 </programlisting>
3030
3031 </para>
3032
3033 <para>
3034 Since all we know about <literal>val</literal> and <function>fn</function> is that they
3035 are compatible, the only (useful) thing we can do with them is to
3036 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
3037 </para>
3038
3039 <para>
3040
3041 <programlisting>
3042 f :: Foo -> Bool
3043 f (MkFoo val fn) = fn val
3044 </programlisting>
3045
3046 </para>
3047
3048 <para>
3049 What this allows us to do is to package heterogeneous values
3050 together with a bunch of functions that manipulate them, and then treat
3051 that collection of packages in a uniform manner. You can express
3052 quite a bit of object-oriented-like programming this way.
3053 </para>
3054
3055 <sect3 id="existential">
3056 <title>Why existential?
3057 </title>
3058
3059 <para>
3060 What has this to do with <emphasis>existential</emphasis> quantification?
3061 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
3062 </para>
3063
3064 <para>
3065
3066 <programlisting>
3067 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
3068 </programlisting>
3069
3070 </para>
3071
3072 <para>
3073 But Haskell programmers can safely think of the ordinary
3074 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
3075 adding a new existential quantification construct.
3076 </para>
3077
3078 </sect3>
3079
3080 <sect3 id="existential-with-context">
3081 <title>Existentials and type classes</title>
3082
3083 <para>
3084 An easy extension is to allow
3085 arbitrary contexts before the constructor. For example:
3086 </para>
3087
3088 <para>
3089
3090 <programlisting>
3091 data Baz = forall a. Eq a => Baz1 a a
3092 | forall b. Show b => Baz2 b (b -> b)
3093 </programlisting>
3094
3095 </para>
3096
3097 <para>
3098 The two constructors have the types you'd expect:
3099 </para>
3100
3101 <para>
3102
3103 <programlisting>
3104 Baz1 :: forall a. Eq a => a -> a -> Baz
3105 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
3106 </programlisting>
3107
3108 </para>
3109
3110 <para>
3111 But when pattern matching on <function>Baz1</function> the matched values can be compared
3112 for equality, and when pattern matching on <function>Baz2</function> the first matched
3113 value can be converted to a string (as well as applying the function to it).
3114 So this program is legal:
3115 </para>
3116
3117 <para>
3118
3119 <programlisting>
3120 f :: Baz -> String
3121 f (Baz1 p q) | p == q = "Yes"
3122 | otherwise = "No"
3123 f (Baz2 v fn) = show (fn v)
3124 </programlisting>
3125
3126 </para>
3127
3128 <para>
3129 Operationally, in a dictionary-passing implementation, the
3130 constructors <function>Baz1</function> and <function>Baz2</function> must store the
3131 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
3132 extract it on pattern matching.
3133 </para>
3134
3135 </sect3>
3136
3137 <sect3 id="existential-records">
3138 <title>Record Constructors</title>
3139
3140 <para>
3141 GHC allows existentials to be used with records syntax as well. For example:
3142
3143 <programlisting>
3144 data Counter a = forall self. NewCounter
3145 { _this :: self
3146 , _inc :: self -> self
3147 , _display :: self -> IO ()
3148 , tag :: a
3149 }
3150 </programlisting>
3151 Here <literal>tag</literal> is a public field, with a well-typed selector
3152 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
3153 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
3154 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
3155 compile-time error. In other words, <emphasis>GHC defines a record selector function
3156 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
3157 (This example used an underscore in the fields for which record selectors
3158 will not be defined, but that is only programming style; GHC ignores them.)
3159 </para>
3160
3161 <para>
3162 To make use of these hidden fields, we need to create some helper functions:
3163
3164 <programlisting>
3165 inc :: Counter a -> Counter a
3166 inc (NewCounter x i d t) = NewCounter
3167 { _this = i x, _inc = i, _display = d, tag = t }
3168
3169 display :: Counter a -> IO ()
3170 display NewCounter{ _this = x, _display = d } = d x
3171 </programlisting>
3172
3173 Now we can define counters with different underlying implementations:
3174
3175 <programlisting>
3176 counterA :: Counter String
3177 counterA = NewCounter
3178 { _this = 0, _inc = (1+), _display = print, tag = "A" }
3179
3180 counterB :: Counter String
3181 counterB = NewCounter
3182 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
3183
3184 main = do
3185 display (inc counterA) -- prints "1"
3186 display (inc (inc counterB)) -- prints "##"
3187 </programlisting>
3188
3189 Record update syntax is supported for existentials (and GADTs):
3190 <programlisting>
3191 setTag :: Counter a -> a -> Counter a
3192 setTag obj t = obj{ tag = t }
3193 </programlisting>
3194 The rule for record update is this: <emphasis>
3195 the types of the updated fields may
3196 mention only the universally-quantified type variables
3197 of the data constructor. For GADTs, the field may mention only types
3198 that appear as a simple type-variable argument in the constructor's result
3199 type</emphasis>. For example:
3200 <programlisting>
3201 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
3202 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
3203 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
3204 -- existentially quantified)
3205
3206 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
3207 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
3208 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
3209 -- type-variable argument in G1's result type)
3210 </programlisting>
3211 </para>
3212
3213 </sect3>
3214
3215
3216 <sect3>
3217 <title>Restrictions</title>
3218
3219 <para>
3220 There are several restrictions on the ways in which existentially-quantified
3221 constructors can be use.
3222 </para>
3223
3224 <para>
3225
3226 <itemizedlist>
3227 <listitem>
3228
3229 <para>
3230 When pattern matching, each pattern match introduces a new,
3231 distinct, type for each existential type variable. These types cannot
3232 be unified with any other type, nor can they escape from the scope of
3233 the pattern match. For example, these fragments are incorrect:
3234
3235
3236 <programlisting>
3237 f1 (MkFoo a f) = a
3238 </programlisting>
3239
3240
3241 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
3242 is the result of <function>f1</function>. One way to see why this is wrong is to
3243 ask what type <function>f1</function> has:
3244
3245
3246 <programlisting>
3247 f1 :: Foo -> a -- Weird!
3248 </programlisting>
3249
3250
3251 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
3252 this:
3253
3254
3255 <programlisting>
3256 f1 :: forall a. Foo -> a -- Wrong!
3257 </programlisting>
3258
3259
3260 The original program is just plain wrong. Here's another sort of error
3261
3262
3263 <programlisting>
3264 f2 (Baz1 a b) (Baz1 p q) = a==q
3265 </programlisting>
3266
3267
3268 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
3269 <literal>a==q</literal> is wrong because it equates the two distinct types arising
3270 from the two <function>Baz1</function> constructors.
3271
3272
3273 </para>
3274 </listitem>
3275 <listitem>
3276
3277 <para>
3278 You can't pattern-match on an existentially quantified
3279 constructor in a <literal>let</literal> or <literal>where</literal> group of
3280 bindings. So this is illegal:
3281
3282
3283 <programlisting>
3284 f3 x = a==b where { Baz1 a b = x }
3285 </programlisting>
3286
3287 Instead, use a <literal>case</literal> expression:
3288
3289 <programlisting>
3290 f3 x = case x of Baz1 a b -> a==b
3291 </programlisting>
3292
3293 In general, you can only pattern-match
3294 on an existentially-quantified constructor in a <literal>case</literal> expression or
3295 in the patterns of a function definition.
3296
3297 The reason for this restriction is really an implementation one.
3298 Type-checking binding groups is already a nightmare without
3299 existentials complicating the picture. Also an existential pattern
3300 binding at the top level of a module doesn't make sense, because it's
3301 not clear how to prevent the existentially-quantified type "escaping".
3302 So for now, there's a simple-to-state restriction. We'll see how
3303 annoying it is.
3304
3305 </para>
3306 </listitem>
3307 <listitem>
3308
3309 <para>
3310 You can't use existential quantification for <literal>newtype</literal>
3311 declarations. So this is illegal:
3312
3313
3314 <programlisting>
3315 newtype T = forall a. Ord a => MkT a
3316 </programlisting>
3317
3318
3319 Reason: a value of type <literal>T</literal> must be represented as a
3320 pair of a dictionary for <literal>Ord t</literal> and a value of type
3321 <literal>t</literal>. That contradicts the idea that
3322 <literal>newtype</literal> should have no concrete representation.
3323 You can get just the same efficiency and effect by using
3324 <literal>data</literal> instead of <literal>newtype</literal>. If
3325 there is no overloading involved, then there is more of a case for
3326 allowing an existentially-quantified <literal>newtype</literal>,
3327 because the <literal>data</literal> version does carry an
3328 implementation cost, but single-field existentially quantified
3329 constructors aren't much use. So the simple restriction (no
3330 existential stuff on <literal>newtype</literal>) stands, unless there
3331 are convincing reasons to change it.
3332
3333
3334 </para>
3335 </listitem>
3336 <listitem>
3337
3338 <para>
3339 You can't use <literal>deriving</literal> to define instances of a
3340 data type with existentially quantified data constructors.
3341
3342 Reason: in most cases it would not make sense. For example:;
3343
3344 <programlisting>
3345 data T = forall a. MkT [a] deriving( Eq )
3346 </programlisting>
3347
3348 To derive <literal>Eq</literal> in the standard way we would need to have equality
3349 between the single component of two <function>MkT</function> constructors:
3350
3351 <programlisting>
3352 instance Eq T where
3353 (MkT a) == (MkT b) = ???
3354 </programlisting>
3355
3356 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
3357 It's just about possible to imagine examples in which the derived instance
3358 would make sense, but it seems altogether simpler simply to prohibit such
3359 declarations. Define your own instances!
3360 </para>
3361 </listitem>
3362
3363 </itemizedlist>
3364
3365 </para>
3366
3367 </sect3>
3368 </sect2>
3369
3370 <!-- ====================== Generalised algebraic data types ======================= -->
3371
3372 <sect2 id="gadt-style">
3373 <title>Declaring data types with explicit constructor signatures</title>
3374
3375 <para>When the <literal>GADTSyntax</literal> extension is enabled,
3376 GHC allows you to declare an algebraic data type by
3377 giving the type signatures of constructors explicitly. For example:
3378 <programlisting>
3379 data Maybe a where
3380 Nothing :: Maybe a
3381 Just :: a -> Maybe a
3382 </programlisting>
3383 The form is called a "GADT-style declaration"
3384 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
3385 can only be declared using this form.</para>
3386 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
3387 For example, these two declarations are equivalent:
3388 <programlisting>
3389 data Foo = forall a. MkFoo a (a -> Bool)
3390 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
3391 </programlisting>
3392 </para>
3393 <para>Any data type that can be declared in standard Haskell-98 syntax
3394 can also be declared using GADT-style syntax.
3395 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
3396 they treat class constraints on the data constructors differently.
3397 Specifically, if the constructor is given a type-class context, that
3398 context is made available by pattern matching. For example:
3399 <programlisting>
3400 data Set a where
3401 MkSet :: Eq a => [a] -> Set a
3402
3403 makeSet :: Eq a => [a] -> Set a
3404 makeSet xs = MkSet (nub xs)
3405
3406 insert :: a -> Set a -> Set a
3407 insert a (MkSet as) | a `elem` as = MkSet as
3408 | otherwise = MkSet (a:as)
3409 </programlisting>
3410 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
3411 gives rise to a <literal>(Eq a)</literal>
3412 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
3413 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
3414 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
3415 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
3416 when pattern-matching that dictionary becomes available for the right-hand side of the match.
3417 In the example, the equality dictionary is used to satisfy the equality constraint
3418 generated by the call to <literal>elem</literal>, so that the type of
3419 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
3420 </para>
3421 <para>
3422 For example, one possible application is to reify dictionaries:
3423 <programlisting>
3424 data NumInst a where
3425 MkNumInst :: Num a => NumInst a
3426
3427 intInst :: NumInst Int
3428 intInst = MkNumInst
3429
3430 plus :: NumInst a -> a -> a -> a
3431 plus MkNumInst p q = p + q
3432 </programlisting>
3433 Here, a value of type <literal>NumInst a</literal> is equivalent
3434 to an explicit <literal>(Num a)</literal> dictionary.
3435 </para>
3436 <para>
3437 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
3438 For example, the <literal>NumInst</literal> data type above could equivalently be declared
3439 like this:
3440 <programlisting>
3441 data NumInst a
3442 = Num a => MkNumInst (NumInst a)
3443 </programlisting>
3444 Notice that, unlike the situation when declaring an existential, there is
3445 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
3446 data type's universally quantified type variable <literal>a</literal>.
3447 A constructor may have both universal and existential type variables: for example,
3448 the following two declarations are equivalent:
3449 <programlisting>
3450 data T1 a
3451 = forall b. (Num a, Eq b) => MkT1 a b
3452 data T2 a where
3453 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
3454 </programlisting>
3455 </para>
3456 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
3457 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
3458 In Haskell 98 the definition
3459 <programlisting>
3460 data Eq a => Set' a = MkSet' [a]
3461 </programlisting>
3462 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
3463 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
3464 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
3465 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
3466 GHC's behaviour is much more useful, as well as much more intuitive.
3467 </para>
3468
3469 <para>
3470 The rest of this section gives further details about GADT-style data
3471 type declarations.
3472
3473 <itemizedlist>
3474 <listitem><para>
3475 The result type of each data constructor must begin with the type constructor being defined.
3476 If the result type of all constructors
3477 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
3478 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
3479 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
3480 </para></listitem>
3481
3482 <listitem><para>
3483 As with other type signatures, you can give a single signature for several data constructors.
3484 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
3485 <programlisting>
3486 data T a where
3487 T1,T2 :: a -> T a
3488 T3 :: T a
3489 </programlisting>
3490 </para></listitem>
3491
3492 <listitem><para>
3493 The type signature of
3494 each constructor is independent, and is implicitly universally quantified as usual.
3495 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
3496 have no scope, and different constructors may have different universally-quantified type variables:
3497 <programlisting>
3498 data T a where -- The 'a' has no scope
3499 T1,T2 :: b -> T b -- Means forall b. b -> T b
3500 T3 :: T a -- Means forall a. T a
3501 </programlisting>
3502 </para></listitem>
3503
3504 <listitem><para>
3505 A constructor signature may mention type class constraints, which can differ for
3506 different constructors. For example, this is fine:
3507 <programlisting>
3508 data T a where
3509 T1 :: Eq b => b -> b -> T b
3510 T2 :: (Show c, Ix c) => c -> [c] -> T c
3511 </programlisting>
3512 When pattern matching, these constraints are made available to discharge constraints
3513 in the body of the match. For example:
3514 <programlisting>
3515 f :: T a -> String
3516 f (T1 x y) | x==y = "yes"
3517 | otherwise = "no"
3518 f (T2 a b) = show a
3519 </programlisting>
3520 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
3521 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
3522 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
3523 </para></listitem>
3524
3525 <listitem><para>
3526 Unlike a Haskell-98-style
3527 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
3528 have no scope. Indeed, one can write a kind signature instead:
3529 <programlisting>
3530 data Set :: * -> * where ...
3531 </programlisting>
3532 or even a mixture of the two:
3533 <programlisting>
3534 data Bar a :: (* -> *) -> * where ...
3535 </programlisting>
3536 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3537 like this:
3538 <programlisting>
3539 data Bar a (b :: * -> *) where ...
3540 </programlisting>
3541 </para></listitem>
3542
3543
3544 <listitem><para>
3545 You can use strictness annotations, in the obvious places
3546 in the constructor type:
3547 <programlisting>
3548 data Term a where
3549 Lit :: !Int -> Term Int
3550 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3551 Pair :: Term a -> Term b -> Term (a,b)
3552 </programlisting>
3553 </para></listitem>
3554
3555 <listitem><para>
3556 You can use a <literal>deriving</literal> clause on a GADT-style data type
3557 declaration. For example, these two declarations are equivalent
3558 <programlisting>
3559 data Maybe1 a where {
3560 Nothing1 :: Maybe1 a ;
3561 Just1 :: a -> Maybe1 a
3562 } deriving( Eq, Ord )
3563
3564 data Maybe2 a = Nothing2 | Just2 a
3565 deriving( Eq, Ord )
3566 </programlisting>
3567 </para></listitem>
3568
3569 <listitem><para>
3570 The type signature may have quantified type variables that do not appear
3571 in the result type:
3572 <programlisting>
3573 data Foo where
3574 MkFoo :: a -> (a->Bool) -> Foo
3575 Nil :: Foo
3576 </programlisting>
3577 Here the type variable <literal>a</literal> does not appear in the result type
3578 of either constructor.
3579 Although it is universally quantified in the type of the constructor, such
3580 a type variable is often called "existential".
3581 Indeed, the above declaration declares precisely the same type as
3582 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
3583 </para><para>
3584 The type may contain a class context too, of course:
3585 <programlisting>
3586 data Showable where
3587 MkShowable :: Show a => a -> Showable
3588 </programlisting>
3589 </para></listitem>
3590
3591 <listitem><para>
3592 You can use record syntax on a GADT-style data type declaration:
3593
3594 <programlisting>
3595 data Person where
3596 Adult :: { name :: String, children :: [Person] } -> Person
3597 Child :: Show a => { name :: !String, funny :: a } -> Person
3598 </programlisting>
3599 As usual, for every constructor that has a field <literal>f</literal>, the type of
3600 field <literal>f</literal> must be the same (modulo alpha conversion).
3601 The <literal>Child</literal> constructor above shows that the signature
3602 may have a context, existentially-quantified variables, and strictness annotations,
3603 just as in the non-record case. (NB: the "type" that follows the double-colon
3604 is not really a type, because of the record syntax and strictness annotations.
3605 A "type" of this form can appear only in a constructor signature.)
3606 </para></listitem>
3607
3608 <listitem><para>
3609 Record updates are allowed with GADT-style declarations,
3610 only fields that have the following property: the type of the field
3611 mentions no existential type variables.
3612 </para></listitem>
3613
3614 <listitem><para>
3615 As in the case of existentials declared using the Haskell-98-like record syntax
3616 (<xref linkend="existential-records"/>),
3617 record-selector functions are generated only for those fields that have well-typed
3618 selectors.
3619 Here is the example of that section, in GADT-style syntax:
3620 <programlisting>
3621 data Counter a where
3622 NewCounter :: { _this :: self
3623 , _inc :: self -> self
3624 , _display :: self -> IO ()
3625 , tag :: a
3626 } -> Counter a
3627 </programlisting>
3628 As before, only one selector function is generated here, that for <literal>tag</literal>.
3629 Nevertheless, you can still use all the field names in pattern matching and record construction.
3630 </para></listitem>
3631
3632 <listitem><para>
3633 In a GADT-style data type declaration there is no obvious way to specify that a data constructor
3634 should be infix, which makes a difference if you derive <literal>Show</literal> for the type.
3635 (Data constructors declared infix are displayed infix by the derived <literal>show</literal>.)
3636 So GHC implements the following design: a data constructor declared in a GADT-style data type
3637 declaration is displayed infix by <literal>Show</literal> iff (a) it is an operator symbol,
3638 (b) it has two arguments, (c) it has a programmer-supplied fixity declaration. For example
3639 <programlisting>
3640 infix 6 (:--:)
3641 data T a where
3642 (:--:) :: Int -> Bool -> T Int
3643 </programlisting>
3644 </para></listitem>
3645 </itemizedlist></para>
3646 </sect2>
3647
3648 <sect2 id="gadt">
3649 <title>Generalised Algebraic Data Types (GADTs)</title>
3650
3651 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
3652 by allowing constructors to have richer return types. Here is an example:
3653 <programlisting>
3654 data Term a where
3655 Lit :: Int -> Term Int
3656 Succ :: Term Int -> Term Int
3657 IsZero :: Term Int -> Term Bool
3658 If :: Term Bool -> Term a -> Term a -> Term a
3659 Pair :: Term a -> Term b -> Term (a,b)
3660 </programlisting>
3661 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3662 case with ordinary data types. This generality allows us to
3663 write a well-typed <literal>eval</literal> function
3664 for these <literal>Terms</literal>:
3665 <programlisting>
3666 eval :: Term a -> a
3667 eval (Lit i) = i
3668 eval (Succ t) = 1 + eval t
3669 eval (IsZero t) = eval t == 0
3670 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3671 eval (Pair e1 e2) = (eval e1, eval e2)
3672 </programlisting>
3673 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
3674 For example, in the right hand side of the equation
3675 <programlisting>
3676 eval :: Term a -> a
3677 eval (Lit i) = ...
3678 </programlisting>
3679 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
3680 A precise specification of the type rules is beyond what this user manual aspires to,
3681 but the design closely follows that described in
3682 the paper <ulink
3683 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
3684 unification-based type inference for GADTs</ulink>,
3685 (ICFP 2006).
3686 The general principle is this: <emphasis>type refinement is only carried out
3687 based on user-supplied type annotations</emphasis>.
3688 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
3689 and lots of obscure error messages will
3690 occur. However, the refinement is quite general. For example, if we had:
3691 <programlisting>
3692 eval :: Term a -> a -> a
3693 eval (Lit i) j = i+j
3694 </programlisting>
3695 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3696 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
3697 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3698 </para>
3699 <para>
3700 These and many other examples are given in papers by Hongwei Xi, and
3701 Tim Sheard. There is a longer introduction
3702 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3703 and Ralf Hinze's
3704 <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
3705 may use different notation to that implemented in GHC.
3706 </para>
3707 <para>
3708 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
3709 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
3710 <itemizedlist>
3711 <listitem><para>
3712 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
3713 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
3714 The result type of each constructor must begin with the type constructor being defined,
3715 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
3716 For example, in the <literal>Term</literal> data
3717 type above, the type of each constructor must end with <literal>Term ty</literal>, but
3718 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
3719 constructor).
3720 </para></listitem>
3721
3722 <listitem><para>
3723 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
3724 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
3725 whose result type is not just <literal>T a b</literal>.
3726 </para></listitem>
3727
3728 <listitem><para>
3729 You cannot use a <literal>deriving</literal> clause for a GADT; only for
3730 an ordinary data type.
3731 </para></listitem>
3732
3733 <listitem><para>
3734 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
3735 For example:
3736 <programlisting>
3737 data Term a where
3738 Lit :: { val :: Int } -> Term Int
3739 Succ :: { num :: Term Int } -> Term Int
3740 Pred :: { num :: Term Int } -> Term Int
3741 IsZero :: { arg :: Term Int } -> Term Bool
3742 Pair :: { arg1 :: Term a
3743 , arg2 :: Term b
3744 } -> Term (a,b)
3745 If :: { cnd :: Term Bool
3746 , tru :: Term a
3747 , fls :: Term a
3748 } -> Term a
3749 </programlisting>
3750 However, for GADTs there is the following additional constraint:
3751 every constructor that has a field <literal>f</literal> must have
3752 the same result type (modulo alpha conversion)
3753 Hence, in the above example, we cannot merge the <literal>num</literal>
3754 and <literal>arg</literal> fields above into a
3755 single name. Although their field types are both <literal>Term Int</literal>,
3756 their selector functions actually have different types:
3757
3758 <programlisting>
3759 num :: Term Int -> Term Int
3760 arg :: Term Bool -> Term Int
3761 </programlisting>
3762 </para></listitem>
3763
3764 <listitem><para>
3765 When pattern-matching against data constructors drawn from a GADT,
3766 for example in a <literal>case</literal> expression, the following rules apply:
3767 <itemizedlist>
3768 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
3769 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
3770 <listitem><para>The type of any free variable mentioned in any of
3771 the <literal>case</literal> alternatives must be rigid.</para></listitem>
3772 </itemizedlist>
3773 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
3774 way to ensure that a variable a rigid type is to give it a type signature.
3775 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
3776 Simple unification-based type inference for GADTs
3777 </ulink>. The criteria implemented by GHC are given in the Appendix.
3778
3779 </para></listitem>
3780
3781 </itemizedlist>
3782 </para>
3783
3784 </sect2>
3785 </sect1>
3786
3787 <!-- ====================== End of Generalised algebraic data types ======================= -->
3788
3789 <sect1 id="deriving">
3790 <title>Extensions to the "deriving" mechanism</title>
3791
3792 <sect2 id="deriving-inferred">
3793 <title>Inferred context for deriving clauses</title>
3794
3795 <para>
3796 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
3797 legal. For example:
3798 <programlisting>
3799 data T0 f a = MkT0 a deriving( Eq )
3800 data T1 f a = MkT1 (f a) deriving( Eq )
3801 data T2 f a = MkT2 (f (f a)) deriving( Eq )
3802 </programlisting>
3803 The natural generated <literal>Eq</literal> code would result in these instance declarations:
3804 <programlisting>
3805 instance Eq a => Eq (T0 f a) where ...
3806 instance Eq (f a) => Eq (T1 f a) where ...
3807 instance Eq (f (f a)) => Eq (T2 f a) where ...
3808 </programlisting>
3809 The first of these is obviously fine. The second is still fine, although less obviously.
3810 The third is not Haskell 98, and risks losing termination of instances.
3811 </para>
3812 <para>
3813 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
3814 each constraint in the inferred instance context must consist only of type variables,
3815 with no repetitions.
3816 </para>
3817 <para>
3818 This rule is applied regardless of flags. If you want a more exotic context, you can write
3819 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
3820 </para>
3821 </sect2>
3822
3823 <sect2 id="stand-alone-deriving">
3824 <title>Stand-alone deriving declarations</title>
3825
3826 <para>
3827 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
3828 <programlisting>
3829 data Foo a = Bar a | Baz String
3830
3831 deriving instance Eq a => Eq (Foo a)
3832 </programlisting>
3833 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
3834 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
3835 </para>
3836 <para>
3837 However, standalone deriving differs from a <literal>deriving</literal> clause in a number
3838 of important ways:
3839 <itemizedlist>
3840 <listitem><para>The standalone deriving declaration does not need to be in the
3841 same module as the data type declaration. (But be aware of the dangers of
3842 orphan instances (<xref linkend="orphan-modules"/>).
3843 </para></listitem>
3844
3845 <listitem><para>
3846 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
3847 exactly as you would in an ordinary instance declaration.
3848 (In contrast, in a <literal>deriving</literal> clause
3849 attached to a data type declaration, the context is inferred.)
3850 </para></listitem>
3851
3852 <listitem><para>
3853 Unlike a <literal>deriving</literal>
3854 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
3855 than the data type (assuming you also use
3856 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
3857 for example
3858 <programlisting>
3859 data Foo a = Bar a | Baz String
3860
3861 deriving instance Eq a => Eq (Foo [a])
3862 deriving instance Eq a => Eq (Foo (Maybe a))
3863 </programlisting>
3864 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
3865 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
3866 </para></listitem>
3867
3868 <listitem><para>
3869 Unlike a <literal>deriving</literal>
3870 declaration attached to a <literal>data</literal> declaration,
3871 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
3872 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
3873 your problem. (GHC will show you the offending code if it has a type error.)
3874 </para>
3875 <para>
3876 The merit of this is that you can derive instances for GADTs and other exotic
3877 data types, providing only that the boilerplate code does indeed typecheck. For example:
3878 <programlisting>
3879 data T a where
3880 T1 :: T Int
3881 T2 :: T Bool
3882
3883 deriving instance Show (T a)
3884 </programlisting>
3885 In this example, you cannot say <literal>... deriving( Show )</literal> on the
3886 data type declaration for <literal>T</literal>,
3887 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
3888 the instance declaration using stand-alone deriving.
3889 </para>
3890 <para>
3891 The down-side is that,
3892 if the boilerplate code fails to typecheck, you will get an error message about that
3893 code, which you did not write. Whereas, with a <literal>deriving</literal> clause
3894 the side-conditions are necessarily more conservative, but any error message
3895 may be more comprehensible.
3896 </para>
3897 </listitem>
3898 </itemizedlist></para>
3899
3900 <para>
3901 In other ways, however, a standalone deriving obeys the same rules as ordinary deriving:
3902 <itemizedlist>
3903 <listitem><para>
3904 A <literal>deriving instance</literal> declaration
3905 must obey the same rules concerning form and termination as ordinary instance declarations,
3906 controlled by the same flags; see <xref linkend="instance-decls"/>.
3907 </para></listitem>
3908
3909 <listitem>
3910 <para>The stand-alone syntax is generalised for newtypes in exactly the same
3911 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3912 For example:
3913 <programlisting>
3914 newtype Foo a = MkFoo (State Int a)
3915
3916 deriving instance MonadState Int Foo
3917 </programlisting>
3918 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3919 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3920 </para></listitem>
3921 </itemizedlist></para>
3922
3923 </sect2>
3924
3925 <sect2 id="deriving-extra">
3926 <title>Deriving instances of extra classes (<literal>Data</literal>, etc)</title>
3927
3928 <para>
3929 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3930 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3931 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3932 classes <literal>Eq</literal>, <literal>Ord</literal>,
3933 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3934 </para>
3935 <para>
3936 GHC extends this list with several more classes that may be automatically derived:
3937 <itemizedlist>
3938 <listitem><para> With <option>-XDeriveGeneric</option>, you can derive
3939 instances of the classes <literal>Generic</literal> and
3940 <literal>Generic1</literal>, defined in <literal>GHC.Generics</literal>.
3941 You can use these to define generic functions,
3942 as described in <xref linkend="generic-programming"/>.
3943 </para></listitem>
3944
3945 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3946 the class <literal>Functor</literal>,
3947 defined in <literal>GHC.Base</literal>.
3948 </para></listitem>
3949
3950 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of
3951 the class <literal>Data</literal>,
3952 defined in <literal>Data.Data</literal>. See <xref linkend="deriving-typeable"/> for
3953 deriving <literal>Typeable</literal>.
3954 </para></listitem>
3955
3956 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3957 the class <literal>Foldable</literal>,
3958 defined in <literal>Data.Foldable</literal>.
3959 </para></listitem>
3960
3961 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3962 the class <literal>Traversable</literal>,
3963 defined in <literal>Data.Traversable</literal>. Since the <literal>Traversable</literal>
3964 instance dictates the instances of <literal>Functor</literal> and
3965 <literal>Foldable</literal>, you'll probably want to derive them too, so
3966 <option>-XDeriveTraversable</option> implies
3967 <option>-XDeriveFunctor</option> and <option>-XDeriveFoldable</option>.
3968 </para></listitem>
3969 </itemizedlist>
3970 You can also use a standalone deriving declaration instead
3971 (see <xref linkend="stand-alone-deriving"/>).
3972 </para>
3973 <para>
3974 In each case the appropriate class must be in scope before it
3975 can be mentioned in the <literal>deriving</literal> clause.
3976 </para>
3977 </sect2>
3978
3979 <sect2 id="deriving-typeable">
3980 <title>Deriving <literal>Typeable</literal> instances</title>
3981
3982 <para>The class <literal>Typeable</literal> is very special:
3983 <itemizedlist>
3984 <listitem><para>
3985 <literal>Typeable</literal> is kind-polymorphic (see
3986 <xref linkend="kind-polymorphism"/>).
3987 </para></listitem>
3988
3989 <listitem><para>
3990 Only derived instances of <literal>Typeable</literal> are allowed;
3991 i.e. handwritten instances are forbidden. This ensures that the
3992 programmer cannot subert the type system by writing bogus instances.
3993 </para></listitem>
3994
3995 <listitem><para>
3996 With <option>-XDeriveDataTypeable</option>
3997 GHC allows you to derive instances of <literal>Typeable</literal> for data types or newtypes,
3998 using a <literal>deriving</literal> clause, or using
3999 a standalone deriving declaration (<xref linkend="stand-alone-deriving"/>).
4000 </para></listitem>
4001
4002 <listitem><para>
4003 With <option>-XDataKinds</option>, deriving <literal>Typeable</literal> for a data
4004 type (whether via a deriving clause or standalone deriving)
4005 also derives <literal>Typeable</literal> for the promoted data constructors (<xref linkend="promotion"/>).
4006 </para></listitem>
4007
4008 <listitem><para>
4009 However, using standalone deriving, you can <emphasis>also</emphasis> derive
4010 a <literal>Typeable</literal> instance for a data family.
4011 You may not add a <literal>deriving(Typeable)</literal> clause to a
4012 <literal>data instance</literal> declaration; instead you must use a
4013 standalone deriving declaration for the data family.
4014 </para></listitem>
4015
4016 <listitem><para>
4017 Using standalone deriving, you can <emphasis>also</emphasis> derive
4018 a <literal>Typeable</literal> instance for a type class.
4019 </para></listitem>
4020
4021 <listitem><para>
4022 The flag <option>-XAutoDeriveTypeable</option> triggers the generation
4023 of derived <literal>Typeable</literal> instances for every datatype, data family,
4024 and type class declaration in the module it is used, unless a manually-specified one is
4025 already provided.
4026 This flag implies <option>-XDeriveDataTypeable</option>.
4027 </para></listitem>
4028 </itemizedlist>
4029
4030 </para>
4031
4032 </sect2>
4033
4034 <sect2 id="newtype-deriving">
4035 <title>Generalised derived instances for newtypes</title>
4036
4037 <para>
4038 When you define an abstract type using <literal>newtype</literal>, you may want
4039 the new type to inherit some instances from its representation. In
4040 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
4041 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
4042 other classes you have to write an explicit instance declaration. For
4043 example, if you define
4044
4045 <programlisting>
4046 newtype Dollars = Dollars Int
4047 </programlisting>
4048
4049 and you want to use arithmetic on <literal>Dollars</literal>, you have to
4050 explicitly define an instance of <literal>Num</literal>:
4051
4052 <programlisting>
4053 instance Num Dollars where
4054 Dollars a + Dollars b = Dollars (a+b)
4055 ...
4056 </programlisting>
4057 All the instance does is apply and remove the <literal>newtype</literal>
4058 constructor. It is particularly galling that, since the constructor
4059 doesn't appear at run-time, this instance declaration defines a
4060 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
4061 dictionary, only slower!
4062 </para>
4063
4064
4065 <sect3 id="generalized-newtype-deriving"> <title> Generalising the deriving clause </title>
4066 <para>
4067 GHC now permits such instances to be derived instead,
4068 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
4069 so one can write
4070 <programlisting>
4071 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
4072 </programlisting>
4073
4074 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
4075 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
4076 derives an instance declaration of the form
4077
4078 <programlisting>
4079 instance Num Int => Num Dollars
4080 </programlisting>
4081
4082 which just adds or removes the <literal>newtype</literal> constructor according to the type.
4083 </para>
4084 <para>
4085
4086 We can also derive instances of constructor classes in a similar
4087 way. For example, suppose we have implemented state and failure monad
4088 transformers, such that
4089
4090 <programlisting>
4091 instance Monad m => Monad (State s m)
4092 instance Monad m => Monad (Failure m)
4093 </programlisting>
4094 In Haskell 98, we can define a parsing monad by
4095 <programlisting>
4096 type Parser tok m a = State [tok] (Failure m) a
4097 </programlisting>
4098
4099 which is automatically a monad thanks to the instance declarations
4100 above. With the extension, we can make the parser type abstract,
4101 without needing to write an instance of class <literal>Monad</literal>, via
4102
4103 <programlisting>
4104 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
4105 deriving Monad
4106 </programlisting>