b2daa16709225747cb102764c71ff752a145977b
[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 are all enabled by options; by default GHC
7 understands only plain Haskell 98.
8 </para>
9
10 <para>
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be &ldquo;stuck&rdquo;
15 on performance because of the implementation costs of Haskell's
16 &ldquo;high-level&rdquo; features&mdash;you can always code
17 &ldquo;under&rdquo; them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
19 </para>
20
21 <para>
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray&num;</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 &ldquo;Haskellised veneer&rdquo; over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
28 </para>
29
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
33
34 <indexterm><primary>language</primary><secondary>option</secondary>
35 </indexterm>
36 <indexterm><primary>options</primary><secondary>language</secondary>
37 </indexterm>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
39 </indexterm>
40
41 <para>These flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
43 98.</para>
44
45 <para>NB. turning on an option that enables special syntax
46 <emphasis>might</emphasis> cause working Haskell 98 code to fail
47 to compile, perhaps because it uses a variable name which has
48 become a reserved word. So, together with each option below, we
49 list the special syntax which is enabled by this option. We use
50 notation and nonterminal names from the Haskell 98 lexical syntax
51 (see the Haskell 98 Report). There are two classes of special
52 syntax:</para>
53
54 <itemizedlist>
55 <listitem>
56 <para>New reserved words and symbols: character sequences
57 which are no longer available for use as identifiers in the
58 program.</para>
59 </listitem>
60 <listitem>
61 <para>Other special syntax: sequences of characters that have
62 a different meaning when this particular option is turned
63 on.</para>
64 </listitem>
65 </itemizedlist>
66
67 <para>We are only listing syntax changes here that might affect
68 existing working programs (i.e. "stolen" syntax). Many of these
69 extensions will also enable new context-free syntax, but in all
70 cases programs written to use the new syntax would not be
71 compilable without the option enabled.</para>
72
73 <variablelist>
74
75 <varlistentry>
76 <term>
77 <option>-fglasgow-exts</option>:
78 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
79 </term>
80 <listitem>
81 <para>This simultaneously enables all of the extensions to
82 Haskell 98 described in <xref
83 linkend="ghc-language-features"/>, except where otherwise
84 noted. </para>
85
86 <para>New reserved words: <literal>forall</literal> (only in
87 types), <literal>mdo</literal>.</para>
88
89 <para>Other syntax stolen:
90 <replaceable>varid</replaceable>{<literal>&num;</literal>},
91 <replaceable>char</replaceable><literal>&num;</literal>,
92 <replaceable>string</replaceable><literal>&num;</literal>,
93 <replaceable>integer</replaceable><literal>&num;</literal>,
94 <replaceable>float</replaceable><literal>&num;</literal>,
95 <replaceable>float</replaceable><literal>&num;&num;</literal>,
96 <literal>(&num;</literal>, <literal>&num;)</literal>,
97 <literal>|)</literal>, <literal>{|</literal>.</para>
98 </listitem>
99 </varlistentry>
100
101 <varlistentry>
102 <term>
103 <option>-ffi</option> and <option>-fffi</option>:
104 <indexterm><primary><option>-ffi</option></primary></indexterm>
105 <indexterm><primary><option>-fffi</option></primary></indexterm>
106 </term>
107 <listitem>
108 <para>This option enables the language extension defined in the
109 Haskell 98 Foreign Function Interface Addendum.</para>
110
111 <para>New reserved words: <literal>foreign</literal>.</para>
112 </listitem>
113 </varlistentry>
114
115 <varlistentry>
116 <term>
117 <option>-fno-monomorphism-restriction</option>,<option>-fno-mono-pat-binds</option>:
118 </term>
119 <listitem>
120 <para> These two flags control how generalisation is done.
121 See <xref linkend="monomorphism"/>.
122 </para>
123 </listitem>
124 </varlistentry>
125
126 <varlistentry>
127 <term>
128 <option>-fextended-default-rules</option>:
129 <indexterm><primary><option>-fextended-default-rules</option></primary></indexterm>
130 </term>
131 <listitem>
132 <para> Use GHCi's extended default rules in a regular module (<xref linkend="extended-default-rules"/>).
133 Independent of the <option>-fglasgow-exts</option>
134 flag. </para>
135 </listitem>
136 </varlistentry>
137
138 <varlistentry>
139 <term>
140 <option>-fallow-overlapping-instances</option>
141 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
142 </term>
143 <term>
144 <option>-fallow-undecidable-instances</option>
145 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
146 </term>
147 <term>
148 <option>-fallow-incoherent-instances</option>
149 <indexterm><primary><option>-fallow-incoherent-instances</option></primary></indexterm>
150 </term>
151 <term>
152 <option>-fcontext-stack=N</option>
153 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
154 </term>
155 <listitem>
156 <para> See <xref linkend="instance-decls"/>. Only relevant
157 if you also use <option>-fglasgow-exts</option>.</para>
158 </listitem>
159 </varlistentry>
160
161 <varlistentry>
162 <term>
163 <option>-finline-phase</option>
164 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
165 </term>
166 <listitem>
167 <para>See <xref linkend="rewrite-rules"/>. Only relevant if
168 you also use <option>-fglasgow-exts</option>.</para>
169 </listitem>
170 </varlistentry>
171
172 <varlistentry>
173 <term>
174 <option>-farrows</option>
175 <indexterm><primary><option>-farrows</option></primary></indexterm>
176 </term>
177 <listitem>
178 <para>See <xref linkend="arrow-notation"/>. Independent of
179 <option>-fglasgow-exts</option>.</para>
180
181 <para>New reserved words/symbols: <literal>rec</literal>,
182 <literal>proc</literal>, <literal>-&lt;</literal>,
183 <literal>&gt;-</literal>, <literal>-&lt;&lt;</literal>,
184 <literal>&gt;&gt;-</literal>.</para>
185
186 <para>Other syntax stolen: <literal>(|</literal>,
187 <literal>|)</literal>.</para>
188 </listitem>
189 </varlistentry>
190
191 <varlistentry>
192 <term>
193 <option>-fgenerics</option>
194 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
195 </term>
196 <listitem>
197 <para>See <xref linkend="generic-classes"/>. Independent of
198 <option>-fglasgow-exts</option>.</para>
199 </listitem>
200 </varlistentry>
201
202 <varlistentry>
203 <term><option>-fno-implicit-prelude</option></term>
204 <listitem>
205 <para><indexterm><primary>-fno-implicit-prelude
206 option</primary></indexterm> GHC normally imports
207 <filename>Prelude.hi</filename> files for you. If you'd
208 rather it didn't, then give it a
209 <option>-fno-implicit-prelude</option> option. The idea is
210 that you can then import a Prelude of your own. (But don't
211 call it <literal>Prelude</literal>; the Haskell module
212 namespace is flat, and you must not conflict with any
213 Prelude module.)</para>
214
215 <para>Even though you have not imported the Prelude, most of
216 the built-in syntax still refers to the built-in Haskell
217 Prelude types and values, as specified by the Haskell
218 Report. For example, the type <literal>[Int]</literal>
219 still means <literal>Prelude.[] Int</literal>; tuples
220 continue to refer to the standard Prelude tuples; the
221 translation for list comprehensions continues to use
222 <literal>Prelude.map</literal> etc.</para>
223
224 <para>However, <option>-fno-implicit-prelude</option> does
225 change the handling of certain built-in syntax: see <xref
226 linkend="rebindable-syntax"/>.</para>
227 </listitem>
228 </varlistentry>
229
230 <varlistentry>
231 <term><option>-fimplicit-params</option></term>
232 <listitem>
233 <para>Enables implicit parameters (see <xref
234 linkend="implicit-parameters"/>). Currently also implied by
235 <option>-fglasgow-exts</option>.</para>
236
237 <para>Syntax stolen:
238 <literal>?<replaceable>varid</replaceable></literal>,
239 <literal>%<replaceable>varid</replaceable></literal>.</para>
240 </listitem>
241 </varlistentry>
242
243 <varlistentry>
244 <term><option>-fscoped-type-variables</option></term>
245 <listitem>
246 <para>Enables lexically-scoped type variables (see <xref
247 linkend="scoped-type-variables"/>). Implied by
248 <option>-fglasgow-exts</option>.</para>
249 </listitem>
250 </varlistentry>
251
252 <varlistentry>
253 <term><option>-fth</option></term>
254 <listitem>
255 <para>Enables Template Haskell (see <xref
256 linkend="template-haskell"/>). This flag must
257 be given explicitly; it is no longer implied by
258 <option>-fglasgow-exts</option>.</para>
259
260 <para>Syntax stolen: <literal>[|</literal>,
261 <literal>[e|</literal>, <literal>[p|</literal>,
262 <literal>[d|</literal>, <literal>[t|</literal>,
263 <literal>$(</literal>,
264 <literal>$<replaceable>varid</replaceable></literal>.</para>
265 </listitem>
266 </varlistentry>
267
268 </variablelist>
269 </sect1>
270
271 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
272 <!-- included from primitives.sgml -->
273 <!-- &primitives; -->
274 <sect1 id="primitives">
275 <title>Unboxed types and primitive operations</title>
276
277 <para>GHC is built on a raft of primitive data types and operations.
278 While you really can use this stuff to write fast code,
279 we generally find it a lot less painful, and more satisfying in the
280 long run, to use higher-level language features and libraries. With
281 any luck, the code you write will be optimised to the efficient
282 unboxed version in any case. And if it isn't, we'd like to know
283 about it.</para>
284
285 <para>We do not currently have good, up-to-date documentation about the
286 primitives, perhaps because they are mainly intended for internal use.
287 There used to be a long section about them here in the User Guide, but it
288 became out of date, and wrong information is worse than none.</para>
289
290 <para>The Real Truth about what primitive types there are, and what operations
291 work over those types, is held in the file
292 <filename>fptools/ghc/compiler/prelude/primops.txt.pp</filename>.
293 This file is used directly to generate GHC's primitive-operation definitions, so
294 it is always correct! It is also intended for processing into text.</para>
295
296 <para> Indeed,
297 the result of such processing is part of the description of the
298 <ulink
299 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
300 Core language</ulink>.
301 So that document is a good place to look for a type-set version.
302 We would be very happy if someone wanted to volunteer to produce an SGML
303 back end to the program that processes <filename>primops.txt</filename> so that
304 we could include the results here in the User Guide.</para>
305
306 <para>What follows here is a brief summary of some main points.</para>
307
308 <sect2 id="glasgow-unboxed">
309 <title>Unboxed types
310 </title>
311
312 <para>
313 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
314 </para>
315
316 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
317 that values of that type are represented by a pointer to a heap
318 object. The representation of a Haskell <literal>Int</literal>, for
319 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
320 type, however, is represented by the value itself, no pointers or heap
321 allocation are involved.
322 </para>
323
324 <para>
325 Unboxed types correspond to the &ldquo;raw machine&rdquo; types you
326 would use in C: <literal>Int&num;</literal> (long int),
327 <literal>Double&num;</literal> (double), <literal>Addr&num;</literal>
328 (void *), etc. The <emphasis>primitive operations</emphasis>
329 (PrimOps) on these types are what you might expect; e.g.,
330 <literal>(+&num;)</literal> is addition on
331 <literal>Int&num;</literal>s, and is the machine-addition that we all
332 know and love&mdash;usually one instruction.
333 </para>
334
335 <para>
336 Primitive (unboxed) types cannot be defined in Haskell, and are
337 therefore built into the language and compiler. Primitive types are
338 always unlifted; that is, a value of a primitive type cannot be
339 bottom. We use the convention that primitive types, values, and
340 operations have a <literal>&num;</literal> suffix.
341 </para>
342
343 <para>
344 Primitive values are often represented by a simple bit-pattern, such
345 as <literal>Int&num;</literal>, <literal>Float&num;</literal>,
346 <literal>Double&num;</literal>. But this is not necessarily the case:
347 a primitive value might be represented by a pointer to a
348 heap-allocated object. Examples include
349 <literal>Array&num;</literal>, the type of primitive arrays. A
350 primitive array is heap-allocated because it is too big a value to fit
351 in a register, and would be too expensive to copy around; in a sense,
352 it is accidental that it is represented by a pointer. If a pointer
353 represents a primitive value, then it really does point to that value:
354 no unevaluated thunks, no indirections&hellip;nothing can be at the
355 other end of the pointer than the primitive value.
356 A numerically-intensive program using unboxed types can
357 go a <emphasis>lot</emphasis> faster than its &ldquo;standard&rdquo;
358 counterpart&mdash;we saw a threefold speedup on one example.
359 </para>
360
361 <para>
362 There are some restrictions on the use of primitive types:
363 <itemizedlist>
364 <listitem><para>The main restriction
365 is that you can't pass a primitive value to a polymorphic
366 function or store one in a polymorphic data type. This rules out
367 things like <literal>[Int&num;]</literal> (i.e. lists of primitive
368 integers). The reason for this restriction is that polymorphic
369 arguments and constructor fields are assumed to be pointers: if an
370 unboxed integer is stored in one of these, the garbage collector would
371 attempt to follow it, leading to unpredictable space leaks. Or a
372 <function>seq</function> operation on the polymorphic component may
373 attempt to dereference the pointer, with disastrous results. Even
374 worse, the unboxed value might be larger than a pointer
375 (<literal>Double&num;</literal> for instance).
376 </para>
377 </listitem>
378 <listitem><para> You cannot bind a variable with an unboxed type
379 in a <emphasis>top-level</emphasis> binding.
380 </para></listitem>
381 <listitem><para> You cannot bind a variable with an unboxed type
382 in a <emphasis>recursive</emphasis> binding.
383 </para></listitem>
384 <listitem><para> You may bind unboxed variables in a (non-recursive,
385 non-top-level) pattern binding, but any such variable causes the entire
386 pattern-match
387 to become strict. For example:
388 <programlisting>
389 data Foo = Foo Int Int#
390
391 f x = let (Foo a b, w) = ..rhs.. in ..body..
392 </programlisting>
393 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
394 match
395 is strict, and the program behaves as if you had written
396 <programlisting>
397 data Foo = Foo Int Int#
398
399 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
400 </programlisting>
401 </para>
402 </listitem>
403 </itemizedlist>
404 </para>
405
406 </sect2>
407
408 <sect2 id="unboxed-tuples">
409 <title>Unboxed Tuples
410 </title>
411
412 <para>
413 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
414 they're available by default with <option>-fglasgow-exts</option>. An
415 unboxed tuple looks like this:
416 </para>
417
418 <para>
419
420 <programlisting>
421 (# e_1, ..., e_n #)
422 </programlisting>
423
424 </para>
425
426 <para>
427 where <literal>e&lowbar;1..e&lowbar;n</literal> are expressions of any
428 type (primitive or non-primitive). The type of an unboxed tuple looks
429 the same.
430 </para>
431
432 <para>
433 Unboxed tuples are used for functions that need to return multiple
434 values, but they avoid the heap allocation normally associated with
435 using fully-fledged tuples. When an unboxed tuple is returned, the
436 components are put directly into registers or on the stack; the
437 unboxed tuple itself does not have a composite representation. Many
438 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
439 tuples.
440 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
441 tuples to avoid unnecessary allocation during sequences of operations.
442 </para>
443
444 <para>
445 There are some pretty stringent restrictions on the use of unboxed tuples:
446 <itemizedlist>
447 <listitem>
448
449 <para>
450 Values of unboxed tuple types are subject to the same restrictions as
451 other unboxed types; i.e. they may not be stored in polymorphic data
452 structures or passed to polymorphic functions.
453
454 </para>
455 </listitem>
456 <listitem>
457
458 <para>
459 No variable can have an unboxed tuple type, nor may a constructor or function
460 argument have an unboxed tuple type. The following are all illegal:
461
462
463 <programlisting>
464 data Foo = Foo (# Int, Int #)
465
466 f :: (# Int, Int #) -&#62; (# Int, Int #)
467 f x = x
468
469 g :: (# Int, Int #) -&#62; Int
470 g (# a,b #) = a
471
472 h x = let y = (# x,x #) in ...
473 </programlisting>
474 </para>
475 </listitem>
476 </itemizedlist>
477 </para>
478 <para>
479 The typical use of unboxed tuples is simply to return multiple values,
480 binding those multiple results with a <literal>case</literal> expression, thus:
481 <programlisting>
482 f x y = (# x+1, y-1 #)
483 g x = case f x x of { (# a, b #) -&#62; a + b }
484 </programlisting>
485 You can have an unboxed tuple in a pattern binding, thus
486 <programlisting>
487 f x = let (# p,q #) = h x in ..body..
488 </programlisting>
489 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
490 the resulting binding is lazy like any other Haskell pattern binding. The
491 above example desugars like this:
492 <programlisting>
493 f x = let t = case h x o f{ (# p,q #) -> (p,q)
494 p = fst t
495 q = snd t
496 in ..body..
497 </programlisting>
498 Indeed, the bindings can even be recursive.
499 </para>
500
501 </sect2>
502 </sect1>
503
504
505 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
506
507 <sect1 id="syntax-extns">
508 <title>Syntactic extensions</title>
509
510 <!-- ====================== HIERARCHICAL MODULES ======================= -->
511
512 <sect2 id="hierarchical-modules">
513 <title>Hierarchical Modules</title>
514
515 <para>GHC supports a small extension to the syntax of module
516 names: a module name is allowed to contain a dot
517 <literal>&lsquo;.&rsquo;</literal>. This is also known as the
518 &ldquo;hierarchical module namespace&rdquo; extension, because
519 it extends the normally flat Haskell module namespace into a
520 more flexible hierarchy of modules.</para>
521
522 <para>This extension has very little impact on the language
523 itself; modules names are <emphasis>always</emphasis> fully
524 qualified, so you can just think of the fully qualified module
525 name as <quote>the module name</quote>. In particular, this
526 means that the full module name must be given after the
527 <literal>module</literal> keyword at the beginning of the
528 module; for example, the module <literal>A.B.C</literal> must
529 begin</para>
530
531 <programlisting>module A.B.C</programlisting>
532
533
534 <para>It is a common strategy to use the <literal>as</literal>
535 keyword to save some typing when using qualified names with
536 hierarchical modules. For example:</para>
537
538 <programlisting>
539 import qualified Control.Monad.ST.Strict as ST
540 </programlisting>
541
542 <para>For details on how GHC searches for source and interface
543 files in the presence of hierarchical modules, see <xref
544 linkend="search-path"/>.</para>
545
546 <para>GHC comes with a large collection of libraries arranged
547 hierarchically; see the accompanying library documentation.
548 There is an ongoing project to create and maintain a stable set
549 of <quote>core</quote> libraries used by several Haskell
550 compilers, and the libraries that GHC comes with represent the
551 current status of that project. For more details, see <ulink
552 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
553 Libraries</ulink>.</para>
554
555 </sect2>
556
557 <!-- ====================== PATTERN GUARDS ======================= -->
558
559 <sect2 id="pattern-guards">
560 <title>Pattern guards</title>
561
562 <para>
563 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
564 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.)
565 </para>
566
567 <para>
568 Suppose we have an abstract data type of finite maps, with a
569 lookup operation:
570
571 <programlisting>
572 lookup :: FiniteMap -> Int -> Maybe Int
573 </programlisting>
574
575 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
576 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
577 </para>
578
579 <programlisting>
580 clunky env var1 var2 | ok1 &amp;&amp; ok2 = val1 + val2
581 | otherwise = var1 + var2
582 where
583 m1 = lookup env var1
584 m2 = lookup env var2
585 ok1 = maybeToBool m1
586 ok2 = maybeToBool m2
587 val1 = expectJust m1
588 val2 = expectJust m2
589 </programlisting>
590
591 <para>
592 The auxiliary functions are
593 </para>
594
595 <programlisting>
596 maybeToBool :: Maybe a -&gt; Bool
597 maybeToBool (Just x) = True
598 maybeToBool Nothing = False
599
600 expectJust :: Maybe a -&gt; a
601 expectJust (Just x) = x
602 expectJust Nothing = error "Unexpected Nothing"
603 </programlisting>
604
605 <para>
606 What is <function>clunky</function> doing? The guard <literal>ok1 &amp;&amp;
607 ok2</literal> checks that both lookups succeed, using
608 <function>maybeToBool</function> to convert the <function>Maybe</function>
609 types to booleans. The (lazily evaluated) <function>expectJust</function>
610 calls extract the values from the results of the lookups, and binds the
611 returned values to <varname>val1</varname> and <varname>val2</varname>
612 respectively. If either lookup fails, then clunky takes the
613 <literal>otherwise</literal> case and returns the sum of its arguments.
614 </para>
615
616 <para>
617 This is certainly legal Haskell, but it is a tremendously verbose and
618 un-obvious way to achieve the desired effect. Arguably, a more direct way
619 to write clunky would be to use case expressions:
620 </para>
621
622 <programlisting>
623 clunky env var1 var1 = case lookup env var1 of
624 Nothing -&gt; fail
625 Just val1 -&gt; case lookup env var2 of
626 Nothing -&gt; fail
627 Just val2 -&gt; val1 + val2
628 where
629 fail = var1 + var2
630 </programlisting>
631
632 <para>
633 This is a bit shorter, but hardly better. Of course, we can rewrite any set
634 of pattern-matching, guarded equations as case expressions; that is
635 precisely what the compiler does when compiling equations! The reason that
636 Haskell provides guarded equations is because they allow us to write down
637 the cases we want to consider, one at a time, independently of each other.
638 This structure is hidden in the case version. Two of the right-hand sides
639 are really the same (<function>fail</function>), and the whole expression
640 tends to become more and more indented.
641 </para>
642
643 <para>
644 Here is how I would write clunky:
645 </para>
646
647 <programlisting>
648 clunky env var1 var1
649 | Just val1 &lt;- lookup env var1
650 , Just val2 &lt;- lookup env var2
651 = val1 + val2
652 ...other equations for clunky...
653 </programlisting>
654
655 <para>
656 The semantics should be clear enough. The qualifiers are matched in order.
657 For a <literal>&lt;-</literal> qualifier, which I call a pattern guard, the
658 right hand side is evaluated and matched against the pattern on the left.
659 If the match fails then the whole guard fails and the next equation is
660 tried. If it succeeds, then the appropriate binding takes place, and the
661 next qualifier is matched, in the augmented environment. Unlike list
662 comprehensions, however, the type of the expression to the right of the
663 <literal>&lt;-</literal> is the same as the type of the pattern to its
664 left. The bindings introduced by pattern guards scope over all the
665 remaining guard qualifiers, and over the right hand side of the equation.
666 </para>
667
668 <para>
669 Just as with list comprehensions, boolean expressions can be freely mixed
670 with among the pattern guards. For example:
671 </para>
672
673 <programlisting>
674 f x | [y] &lt;- x
675 , y > 3
676 , Just z &lt;- h y
677 = ...
678 </programlisting>
679
680 <para>
681 Haskell's current guards therefore emerge as a special case, in which the
682 qualifier list has just one element, a boolean expression.
683 </para>
684 </sect2>
685
686 <!-- ===================== Recursive do-notation =================== -->
687
688 <sect2 id="mdo-notation">
689 <title>The recursive do-notation
690 </title>
691
692 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
693 "A recursive do for Haskell",
694 Levent Erkok, John Launchbury",
695 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
696 </para>
697 <para>
698 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
699 that is, the variables bound in a do-expression are visible only in the textually following
700 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
701 group. It turns out that several applications can benefit from recursive bindings in
702 the do-notation, and this extension provides the necessary syntactic support.
703 </para>
704 <para>
705 Here is a simple (yet contrived) example:
706 </para>
707 <programlisting>
708 import Control.Monad.Fix
709
710 justOnes = mdo xs &lt;- Just (1:xs)
711 return xs
712 </programlisting>
713 <para>
714 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
715 </para>
716
717 <para>
718 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
719 </para>
720 <programlisting>
721 class Monad m => MonadFix m where
722 mfix :: (a -> m a) -> m a
723 </programlisting>
724 <para>
725 The function <literal>mfix</literal>
726 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
727 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
728 For details, see the above mentioned reference.
729 </para>
730 <para>
731 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
732 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
733 for Haskell's internal state monad (strict and lazy, respectively).
734 </para>
735 <para>
736 There are three important points in using the recursive-do notation:
737 <itemizedlist>
738 <listitem><para>
739 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
740 than <literal>do</literal>).
741 </para></listitem>
742
743 <listitem><para>
744 You should <literal>import Control.Monad.Fix</literal>.
745 (Note: Strictly speaking, this import is required only when you need to refer to the name
746 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
747 are encouraged to always import this module when using the mdo-notation.)
748 </para></listitem>
749
750 <listitem><para>
751 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
752 </para></listitem>
753 </itemizedlist>
754 </para>
755
756 <para>
757 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
758 contains up to date information on recursive monadic bindings.
759 </para>
760
761 <para>
762 Historical note: The old implementation of the mdo-notation (and most
763 of the existing documents) used the name
764 <literal>MonadRec</literal> for the class and the corresponding library.
765 This name is not supported by GHC.
766 </para>
767
768 </sect2>
769
770
771 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
772
773 <sect2 id="parallel-list-comprehensions">
774 <title>Parallel List Comprehensions</title>
775 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
776 </indexterm>
777 <indexterm><primary>parallel list comprehensions</primary>
778 </indexterm>
779
780 <para>Parallel list comprehensions are a natural extension to list
781 comprehensions. List comprehensions can be thought of as a nice
782 syntax for writing maps and filters. Parallel comprehensions
783 extend this to include the zipWith family.</para>
784
785 <para>A parallel list comprehension has multiple independent
786 branches of qualifier lists, each separated by a `|' symbol. For
787 example, the following zips together two lists:</para>
788
789 <programlisting>
790 [ (x, y) | x &lt;- xs | y &lt;- ys ]
791 </programlisting>
792
793 <para>The behavior of parallel list comprehensions follows that of
794 zip, in that the resulting list will have the same length as the
795 shortest branch.</para>
796
797 <para>We can define parallel list comprehensions by translation to
798 regular comprehensions. Here's the basic idea:</para>
799
800 <para>Given a parallel comprehension of the form: </para>
801
802 <programlisting>
803 [ e | p1 &lt;- e11, p2 &lt;- e12, ...
804 | q1 &lt;- e21, q2 &lt;- e22, ...
805 ...
806 ]
807 </programlisting>
808
809 <para>This will be translated to: </para>
810
811 <programlisting>
812 [ e | ((p1,p2), (q1,q2), ...) &lt;- zipN [(p1,p2) | p1 &lt;- e11, p2 &lt;- e12, ...]
813 [(q1,q2) | q1 &lt;- e21, q2 &lt;- e22, ...]
814 ...
815 ]
816 </programlisting>
817
818 <para>where `zipN' is the appropriate zip for the given number of
819 branches.</para>
820
821 </sect2>
822
823 <sect2 id="rebindable-syntax">
824 <title>Rebindable syntax</title>
825
826
827 <para>GHC allows most kinds of built-in syntax to be rebound by
828 the user, to facilitate replacing the <literal>Prelude</literal>
829 with a home-grown version, for example.</para>
830
831 <para>You may want to define your own numeric class
832 hierarchy. It completely defeats that purpose if the
833 literal "1" means "<literal>Prelude.fromInteger
834 1</literal>", which is what the Haskell Report specifies.
835 So the <option>-fno-implicit-prelude</option> flag causes
836 the following pieces of built-in syntax to refer to
837 <emphasis>whatever is in scope</emphasis>, not the Prelude
838 versions:
839
840 <itemizedlist>
841 <listitem>
842 <para>An integer literal <literal>368</literal> means
843 "<literal>fromInteger (368::Integer)</literal>", rather than
844 "<literal>Prelude.fromInteger (368::Integer)</literal>".
845 </para> </listitem>
846
847 <listitem><para>Fractional literals are handed in just the same way,
848 except that the translation is
849 <literal>fromRational (3.68::Rational)</literal>.
850 </para> </listitem>
851
852 <listitem><para>The equality test in an overloaded numeric pattern
853 uses whatever <literal>(==)</literal> is in scope.
854 </para> </listitem>
855
856 <listitem><para>The subtraction operation, and the
857 greater-than-or-equal test, in <literal>n+k</literal> patterns
858 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
859 </para></listitem>
860
861 <listitem>
862 <para>Negation (e.g. "<literal>- (f x)</literal>")
863 means "<literal>negate (f x)</literal>", both in numeric
864 patterns, and expressions.
865 </para></listitem>
866
867 <listitem>
868 <para>"Do" notation is translated using whatever
869 functions <literal>(>>=)</literal>,
870 <literal>(>>)</literal>, and <literal>fail</literal>,
871 are in scope (not the Prelude
872 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
873 comprehensions, are unaffected. </para></listitem>
874
875 <listitem>
876 <para>Arrow
877 notation (see <xref linkend="arrow-notation"/>)
878 uses whatever <literal>arr</literal>,
879 <literal>(>>>)</literal>, <literal>first</literal>,
880 <literal>app</literal>, <literal>(|||)</literal> and
881 <literal>loop</literal> functions are in scope. But unlike the
882 other constructs, the types of these functions must match the
883 Prelude types very closely. Details are in flux; if you want
884 to use this, ask!
885 </para></listitem>
886 </itemizedlist>
887 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
888 even if that is a little unexpected. For emample, the
889 static semantics of the literal <literal>368</literal>
890 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
891 <literal>fromInteger</literal> to have any of the types:
892 <programlisting>
893 fromInteger :: Integer -> Integer
894 fromInteger :: forall a. Foo a => Integer -> a
895 fromInteger :: Num a => a -> Integer
896 fromInteger :: Integer -> Bool -> Bool
897 </programlisting>
898 </para>
899
900 <para>Be warned: this is an experimental facility, with
901 fewer checks than usual. Use <literal>-dcore-lint</literal>
902 to typecheck the desugared program. If Core Lint is happy
903 you should be all right.</para>
904
905 </sect2>
906
907 <sect2 id="postfix-operators">
908 <title>Postfix operators</title>
909
910 <para>
911 GHC allows a small extension to the syntax of left operator sections, which
912 allows you to define postfix operators. The extension is this: the left section
913 <programlisting>
914 (e !)
915 </programlisting>
916 is equivalent (from the point of view of both type checking and execution) to the expression
917 <programlisting>
918 ((!) e)
919 </programlisting>
920 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
921 The strict Haskell 98 interpretation is that the section is equivalent to
922 <programlisting>
923 (\y -> (!) e y)
924 </programlisting>
925 That is, the operator must be a function of two arguments. GHC allows it to
926 take only one argument, and that in turn allows you to write the function
927 postfix.
928 </para>
929 <para>Since this extension goes beyond Haskell 98, it should really be enabled
930 by a flag; but in fact it is enabled all the time. (No Haskell 98 programs
931 change their behaviour, of course.)
932 </para>
933 <para>The extension does not extend to the left-hand side of function
934 definitions; you must define such a function in prefix form.</para>
935
936 </sect2>
937
938 </sect1>
939
940
941 <!-- TYPE SYSTEM EXTENSIONS -->
942 <sect1 id="type-extensions">
943 <title>Type system extensions</title>
944
945
946 <sect2>
947 <title>Data types and type synonyms</title>
948
949 <sect3 id="nullary-types">
950 <title>Data types with no constructors</title>
951
952 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
953 a data type with no constructors. For example:</para>
954
955 <programlisting>
956 data S -- S :: *
957 data T a -- T :: * -> *
958 </programlisting>
959
960 <para>Syntactically, the declaration lacks the "= constrs" part. The
961 type can be parameterised over types of any kind, but if the kind is
962 not <literal>*</literal> then an explicit kind annotation must be used
963 (see <xref linkend="sec-kinding"/>).</para>
964
965 <para>Such data types have only one value, namely bottom.
966 Nevertheless, they can be useful when defining "phantom types".</para>
967 </sect3>
968
969 <sect3 id="infix-tycons">
970 <title>Infix type constructors, classes, and type variables</title>
971
972 <para>
973 GHC allows type constructors, classes, and type variables to be operators, and
974 to be written infix, very much like expressions. More specifically:
975 <itemizedlist>
976 <listitem><para>
977 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
978 The lexical syntax is the same as that for data constructors.
979 </para></listitem>
980 <listitem><para>
981 Data type and type-synonym declarations can be written infix, parenthesised
982 if you want further arguments. E.g.
983 <screen>
984 data a :*: b = Foo a b
985 type a :+: b = Either a b
986 class a :=: b where ...
987
988 data (a :**: b) x = Baz a b x
989 type (a :++: b) y = Either (a,b) y
990 </screen>
991 </para></listitem>
992 <listitem><para>
993 Types, and class constraints, can be written infix. For example
994 <screen>
995 x :: Int :*: Bool
996 f :: (a :=: b) => a -> b
997 </screen>
998 </para></listitem>
999 <listitem><para>
1000 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1001 The lexical syntax is the same as that for variable operators, excluding "(.)",
1002 "(!)", and "(*)". In a binding position, the operator must be
1003 parenthesised. For example:
1004 <programlisting>
1005 type T (+) = Int + Int
1006 f :: T Either
1007 f = Left 3
1008
1009 liftA2 :: Arrow (~>)
1010 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1011 liftA2 = ...
1012 </programlisting>
1013 </para></listitem>
1014 <listitem><para>
1015 Back-quotes work
1016 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1017 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1018 </para></listitem>
1019 <listitem><para>
1020 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1021 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1022 sets the fixity for a data constructor and the corresponding type constructor. For example:
1023 <screen>
1024 infixl 7 T, :*:
1025 </screen>
1026 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1027 and similarly for <literal>:*:</literal>.
1028 <literal>Int `a` Bool</literal>.
1029 </para></listitem>
1030 <listitem><para>
1031 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1032 </para></listitem>
1033
1034 </itemizedlist>
1035 </para>
1036 </sect3>
1037
1038 <sect3 id="type-synonyms">
1039 <title>Liberalised type synonyms</title>
1040
1041 <para>
1042 Type synonyms are like macros at the type level, and
1043 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1044 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1045 <itemizedlist>
1046 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1047 in a type synonym, thus:
1048 <programlisting>
1049 type Discard a = forall b. Show b => a -> b -> (a, String)
1050
1051 f :: Discard a
1052 f x y = (x, show y)
1053
1054 g :: Discard Int -> (Int,String) -- A rank-2 type
1055 g f = f 3 True
1056 </programlisting>
1057 </para>
1058 </listitem>
1059
1060 <listitem><para>
1061 You can write an unboxed tuple in a type synonym:
1062 <programlisting>
1063 type Pr = (# Int, Int #)
1064
1065 h :: Int -> Pr
1066 h x = (# x, x #)
1067 </programlisting>
1068 </para></listitem>
1069
1070 <listitem><para>
1071 You can apply a type synonym to a forall type:
1072 <programlisting>
1073 type Foo a = a -> a -> Bool
1074
1075 f :: Foo (forall b. b->b)
1076 </programlisting>
1077 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1078 <programlisting>
1079 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1080 </programlisting>
1081 </para></listitem>
1082
1083 <listitem><para>
1084 You can apply a type synonym to a partially applied type synonym:
1085 <programlisting>
1086 type Generic i o = forall x. i x -> o x
1087 type Id x = x
1088
1089 foo :: Generic Id []
1090 </programlisting>
1091 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1092 <programlisting>
1093 foo :: forall x. x -> [x]
1094 </programlisting>
1095 </para></listitem>
1096
1097 </itemizedlist>
1098 </para>
1099
1100 <para>
1101 GHC currently does kind checking before expanding synonyms (though even that
1102 could be changed.)
1103 </para>
1104 <para>
1105 After expanding type synonyms, GHC does validity checking on types, looking for
1106 the following mal-formedness which isn't detected simply by kind checking:
1107 <itemizedlist>
1108 <listitem><para>
1109 Type constructor applied to a type involving for-alls.
1110 </para></listitem>
1111 <listitem><para>
1112 Unboxed tuple on left of an arrow.
1113 </para></listitem>
1114 <listitem><para>
1115 Partially-applied type synonym.
1116 </para></listitem>
1117 </itemizedlist>
1118 So, for example,
1119 this will be rejected:
1120 <programlisting>
1121 type Pr = (# Int, Int #)
1122
1123 h :: Pr -> Int
1124 h x = ...
1125 </programlisting>
1126 because GHC does not allow unboxed tuples on the left of a function arrow.
1127 </para>
1128 </sect3>
1129
1130
1131 <sect3 id="existential-quantification">
1132 <title>Existentially quantified data constructors
1133 </title>
1134
1135 <para>
1136 The idea of using existential quantification in data type declarations
1137 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1138 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1139 London, 1991). It was later formalised by Laufer and Odersky
1140 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1141 TOPLAS, 16(5), pp1411-1430, 1994).
1142 It's been in Lennart
1143 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1144 proved very useful. Here's the idea. Consider the declaration:
1145 </para>
1146
1147 <para>
1148
1149 <programlisting>
1150 data Foo = forall a. MkFoo a (a -> Bool)
1151 | Nil
1152 </programlisting>
1153
1154 </para>
1155
1156 <para>
1157 The data type <literal>Foo</literal> has two constructors with types:
1158 </para>
1159
1160 <para>
1161
1162 <programlisting>
1163 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1164 Nil :: Foo
1165 </programlisting>
1166
1167 </para>
1168
1169 <para>
1170 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1171 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1172 For example, the following expression is fine:
1173 </para>
1174
1175 <para>
1176
1177 <programlisting>
1178 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1179 </programlisting>
1180
1181 </para>
1182
1183 <para>
1184 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1185 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1186 isUpper</function> packages a character with a compatible function. These
1187 two things are each of type <literal>Foo</literal> and can be put in a list.
1188 </para>
1189
1190 <para>
1191 What can we do with a value of type <literal>Foo</literal>?. In particular,
1192 what happens when we pattern-match on <function>MkFoo</function>?
1193 </para>
1194
1195 <para>
1196
1197 <programlisting>
1198 f (MkFoo val fn) = ???
1199 </programlisting>
1200
1201 </para>
1202
1203 <para>
1204 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1205 are compatible, the only (useful) thing we can do with them is to
1206 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1207 </para>
1208
1209 <para>
1210
1211 <programlisting>
1212 f :: Foo -> Bool
1213 f (MkFoo val fn) = fn val
1214 </programlisting>
1215
1216 </para>
1217
1218 <para>
1219 What this allows us to do is to package heterogenous values
1220 together with a bunch of functions that manipulate them, and then treat
1221 that collection of packages in a uniform manner. You can express
1222 quite a bit of object-oriented-like programming this way.
1223 </para>
1224
1225 <sect4 id="existential">
1226 <title>Why existential?
1227 </title>
1228
1229 <para>
1230 What has this to do with <emphasis>existential</emphasis> quantification?
1231 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1232 </para>
1233
1234 <para>
1235
1236 <programlisting>
1237 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1238 </programlisting>
1239
1240 </para>
1241
1242 <para>
1243 But Haskell programmers can safely think of the ordinary
1244 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1245 adding a new existential quantification construct.
1246 </para>
1247
1248 </sect4>
1249
1250 <sect4>
1251 <title>Type classes</title>
1252
1253 <para>
1254 An easy extension is to allow
1255 arbitrary contexts before the constructor. For example:
1256 </para>
1257
1258 <para>
1259
1260 <programlisting>
1261 data Baz = forall a. Eq a => Baz1 a a
1262 | forall b. Show b => Baz2 b (b -> b)
1263 </programlisting>
1264
1265 </para>
1266
1267 <para>
1268 The two constructors have the types you'd expect:
1269 </para>
1270
1271 <para>
1272
1273 <programlisting>
1274 Baz1 :: forall a. Eq a => a -> a -> Baz
1275 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1276 </programlisting>
1277
1278 </para>
1279
1280 <para>
1281 But when pattern matching on <function>Baz1</function> the matched values can be compared
1282 for equality, and when pattern matching on <function>Baz2</function> the first matched
1283 value can be converted to a string (as well as applying the function to it).
1284 So this program is legal:
1285 </para>
1286
1287 <para>
1288
1289 <programlisting>
1290 f :: Baz -> String
1291 f (Baz1 p q) | p == q = "Yes"
1292 | otherwise = "No"
1293 f (Baz2 v fn) = show (fn v)
1294 </programlisting>
1295
1296 </para>
1297
1298 <para>
1299 Operationally, in a dictionary-passing implementation, the
1300 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1301 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1302 extract it on pattern matching.
1303 </para>
1304
1305 <para>
1306 Notice the way that the syntax fits smoothly with that used for
1307 universal quantification earlier.
1308 </para>
1309
1310 </sect4>
1311
1312 <sect4>
1313 <title>Record Constructors</title>
1314
1315 <para>
1316 GHC allows existentials to be used with records syntax as well. For example:
1317
1318 <programlisting>
1319 data Counter a = forall self. NewCounter
1320 { _this :: self
1321 , _inc :: self -> self
1322 , _display :: self -> IO ()
1323 , tag :: a
1324 }
1325 </programlisting>
1326 Here <literal>tag</literal> is a public field, with a well-typed selector
1327 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
1328 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
1329 <literal>_inc</literal> or <literal>_output</literal> as functions will raise a
1330 compile-time error. In other words, <emphasis>GHC defines a record selector function
1331 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
1332 (This example used an underscore in the fields for which record selectors
1333 will not be defined, but that is only programming style; GHC ignores them.)
1334 </para>
1335
1336 <para>
1337 To make use of these hidden fields, we need to create some helper functions:
1338
1339 <programlisting>
1340 inc :: Counter a -> Counter a
1341 inc (NewCounter x i d t) = NewCounter
1342 { _this = i x, _inc = i, _display = d, tag = t }
1343
1344 display :: Counter a -> IO ()
1345 display NewCounter{ _this = x, _display = d } = d x
1346 </programlisting>
1347
1348 Now we can define counters with different underlying implementations:
1349
1350 <programlisting>
1351 counterA :: Counter String
1352 counterA = NewCounter
1353 { _this = 0, _inc = (1+), _display = print, tag = "A" }
1354
1355 counterB :: Counter String
1356 counterB = NewCounter
1357 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
1358
1359 main = do
1360 display (inc counterA) -- prints "1"
1361 display (inc (inc counterB)) -- prints "##"
1362 </programlisting>
1363
1364 In GADT declarations (see <xref linkend="gadt"/>), the explicit
1365 <literal>forall</literal> may be omitted. For example, we can express
1366 the same <literal>Counter a</literal> using GADT:
1367
1368 <programlisting>
1369 data Counter a where
1370 NewCounter { _this :: self
1371 , _inc :: self -> self
1372 , _display :: self -> IO ()
1373 , tag :: a
1374 }
1375 :: Counter a
1376 </programlisting>
1377
1378 At the moment, record update syntax is only supported for Haskell 98 data types,
1379 so the following function does <emphasis>not</emphasis> work:
1380
1381 <programlisting>
1382 -- This is invalid; use explicit NewCounter instead for now
1383 setTag :: Counter a -> a -> Counter a
1384 setTag obj t = obj{ tag = t }
1385 </programlisting>
1386
1387 </para>
1388
1389 </sect4>
1390
1391
1392 <sect4>
1393 <title>Restrictions</title>
1394
1395 <para>
1396 There are several restrictions on the ways in which existentially-quantified
1397 constructors can be use.
1398 </para>
1399
1400 <para>
1401
1402 <itemizedlist>
1403 <listitem>
1404
1405 <para>
1406 When pattern matching, each pattern match introduces a new,
1407 distinct, type for each existential type variable. These types cannot
1408 be unified with any other type, nor can they escape from the scope of
1409 the pattern match. For example, these fragments are incorrect:
1410
1411
1412 <programlisting>
1413 f1 (MkFoo a f) = a
1414 </programlisting>
1415
1416
1417 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1418 is the result of <function>f1</function>. One way to see why this is wrong is to
1419 ask what type <function>f1</function> has:
1420
1421
1422 <programlisting>
1423 f1 :: Foo -> a -- Weird!
1424 </programlisting>
1425
1426
1427 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1428 this:
1429
1430
1431 <programlisting>
1432 f1 :: forall a. Foo -> a -- Wrong!
1433 </programlisting>
1434
1435
1436 The original program is just plain wrong. Here's another sort of error
1437
1438
1439 <programlisting>
1440 f2 (Baz1 a b) (Baz1 p q) = a==q
1441 </programlisting>
1442
1443
1444 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1445 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1446 from the two <function>Baz1</function> constructors.
1447
1448
1449 </para>
1450 </listitem>
1451 <listitem>
1452
1453 <para>
1454 You can't pattern-match on an existentially quantified
1455 constructor in a <literal>let</literal> or <literal>where</literal> group of
1456 bindings. So this is illegal:
1457
1458
1459 <programlisting>
1460 f3 x = a==b where { Baz1 a b = x }
1461 </programlisting>
1462
1463 Instead, use a <literal>case</literal> expression:
1464
1465 <programlisting>
1466 f3 x = case x of Baz1 a b -> a==b
1467 </programlisting>
1468
1469 In general, you can only pattern-match
1470 on an existentially-quantified constructor in a <literal>case</literal> expression or
1471 in the patterns of a function definition.
1472
1473 The reason for this restriction is really an implementation one.
1474 Type-checking binding groups is already a nightmare without
1475 existentials complicating the picture. Also an existential pattern
1476 binding at the top level of a module doesn't make sense, because it's
1477 not clear how to prevent the existentially-quantified type "escaping".
1478 So for now, there's a simple-to-state restriction. We'll see how
1479 annoying it is.
1480
1481 </para>
1482 </listitem>
1483 <listitem>
1484
1485 <para>
1486 You can't use existential quantification for <literal>newtype</literal>
1487 declarations. So this is illegal:
1488
1489
1490 <programlisting>
1491 newtype T = forall a. Ord a => MkT a
1492 </programlisting>
1493
1494
1495 Reason: a value of type <literal>T</literal> must be represented as a
1496 pair of a dictionary for <literal>Ord t</literal> and a value of type
1497 <literal>t</literal>. That contradicts the idea that
1498 <literal>newtype</literal> should have no concrete representation.
1499 You can get just the same efficiency and effect by using
1500 <literal>data</literal> instead of <literal>newtype</literal>. If
1501 there is no overloading involved, then there is more of a case for
1502 allowing an existentially-quantified <literal>newtype</literal>,
1503 because the <literal>data</literal> version does carry an
1504 implementation cost, but single-field existentially quantified
1505 constructors aren't much use. So the simple restriction (no
1506 existential stuff on <literal>newtype</literal>) stands, unless there
1507 are convincing reasons to change it.
1508
1509
1510 </para>
1511 </listitem>
1512 <listitem>
1513
1514 <para>
1515 You can't use <literal>deriving</literal> to define instances of a
1516 data type with existentially quantified data constructors.
1517
1518 Reason: in most cases it would not make sense. For example:&num;
1519
1520 <programlisting>
1521 data T = forall a. MkT [a] deriving( Eq )
1522 </programlisting>
1523
1524 To derive <literal>Eq</literal> in the standard way we would need to have equality
1525 between the single component of two <function>MkT</function> constructors:
1526
1527 <programlisting>
1528 instance Eq T where
1529 (MkT a) == (MkT b) = ???
1530 </programlisting>
1531
1532 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
1533 It's just about possible to imagine examples in which the derived instance
1534 would make sense, but it seems altogether simpler simply to prohibit such
1535 declarations. Define your own instances!
1536 </para>
1537 </listitem>
1538
1539 </itemizedlist>
1540
1541 </para>
1542
1543 </sect4>
1544 </sect3>
1545
1546 </sect2>
1547
1548
1549
1550 <sect2 id="multi-param-type-classes">
1551 <title>Class declarations</title>
1552
1553 <para>
1554 This section, and the next one, documents GHC's type-class extensions.
1555 There's lots of background in the paper <ulink
1556 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space" >Type
1557 classes: exploring the design space</ulink > (Simon Peyton Jones, Mark
1558 Jones, Erik Meijer).
1559 </para>
1560 <para>
1561 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
1562 </para>
1563
1564 <sect3>
1565 <title>Multi-parameter type classes</title>
1566 <para>
1567 Multi-parameter type classes are permitted. For example:
1568
1569
1570 <programlisting>
1571 class Collection c a where
1572 union :: c a -> c a -> c a
1573 ...etc.
1574 </programlisting>
1575
1576 </para>
1577 </sect3>
1578
1579 <sect3>
1580 <title>The superclasses of a class declaration</title>
1581
1582 <para>
1583 There are no restrictions on the context in a class declaration
1584 (which introduces superclasses), except that the class hierarchy must
1585 be acyclic. So these class declarations are OK:
1586
1587
1588 <programlisting>
1589 class Functor (m k) => FiniteMap m k where
1590 ...
1591
1592 class (Monad m, Monad (t m)) => Transform t m where
1593 lift :: m a -> (t m) a
1594 </programlisting>
1595
1596
1597 </para>
1598 <para>
1599 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
1600 of "acyclic" involves only the superclass relationships. For example,
1601 this is OK:
1602
1603
1604 <programlisting>
1605 class C a where {
1606 op :: D b => a -> b -> b
1607 }
1608
1609 class C a => D a where { ... }
1610 </programlisting>
1611
1612
1613 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1614 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1615 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1616 </para>
1617 </sect3>
1618
1619
1620
1621
1622 <sect3 id="class-method-types">
1623 <title>Class method types</title>
1624
1625 <para>
1626 Haskell 98 prohibits class method types to mention constraints on the
1627 class type variable, thus:
1628 <programlisting>
1629 class Seq s a where
1630 fromList :: [a] -> s a
1631 elem :: Eq a => a -> s a -> Bool
1632 </programlisting>
1633 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1634 contains the constraint <literal>Eq a</literal>, constrains only the
1635 class type variable (in this case <literal>a</literal>).
1636 GHC lifts this restriction.
1637 </para>
1638
1639
1640 </sect3>
1641 </sect2>
1642
1643 <sect2 id="functional-dependencies">
1644 <title>Functional dependencies
1645 </title>
1646
1647 <para> Functional dependencies are implemented as described by Mark Jones
1648 in &ldquo;<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>&rdquo;, Mark P. Jones,
1649 In Proceedings of the 9th European Symposium on Programming,
1650 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1651 .
1652 </para>
1653 <para>
1654 Functional dependencies are introduced by a vertical bar in the syntax of a
1655 class declaration; e.g.
1656 <programlisting>
1657 class (Monad m) => MonadState s m | m -> s where ...
1658
1659 class Foo a b c | a b -> c where ...
1660 </programlisting>
1661 There should be more documentation, but there isn't (yet). Yell if you need it.
1662 </para>
1663
1664 <sect3><title>Rules for functional dependencies </title>
1665 <para>
1666 In a class declaration, all of the class type variables must be reachable (in the sense
1667 mentioned in <xref linkend="type-restrictions"/>)
1668 from the free variables of each method type.
1669 For example:
1670
1671 <programlisting>
1672 class Coll s a where
1673 empty :: s
1674 insert :: s -> a -> s
1675 </programlisting>
1676
1677 is not OK, because the type of <literal>empty</literal> doesn't mention
1678 <literal>a</literal>. Functional dependencies can make the type variable
1679 reachable:
1680 <programlisting>
1681 class Coll s a | s -> a where
1682 empty :: s
1683 insert :: s -> a -> s
1684 </programlisting>
1685
1686 Alternatively <literal>Coll</literal> might be rewritten
1687
1688 <programlisting>
1689 class Coll s a where
1690 empty :: s a
1691 insert :: s a -> a -> s a
1692 </programlisting>
1693
1694
1695 which makes the connection between the type of a collection of
1696 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1697 Occasionally this really doesn't work, in which case you can split the
1698 class like this:
1699
1700
1701 <programlisting>
1702 class CollE s where
1703 empty :: s
1704
1705 class CollE s => Coll s a where
1706 insert :: s -> a -> s
1707 </programlisting>
1708 </para>
1709 </sect3>
1710
1711
1712 <sect3>
1713 <title>Background on functional dependencies</title>
1714
1715 <para>The following description of the motivation and use of functional dependencies is taken
1716 from the Hugs user manual, reproduced here (with minor changes) by kind
1717 permission of Mark Jones.
1718 </para>
1719 <para>
1720 Consider the following class, intended as part of a
1721 library for collection types:
1722 <programlisting>
1723 class Collects e ce where
1724 empty :: ce
1725 insert :: e -> ce -> ce
1726 member :: e -> ce -> Bool
1727 </programlisting>
1728 The type variable e used here represents the element type, while ce is the type
1729 of the container itself. Within this framework, we might want to define
1730 instances of this class for lists or characteristic functions (both of which
1731 can be used to represent collections of any equality type), bit sets (which can
1732 be used to represent collections of characters), or hash tables (which can be
1733 used to represent any collection whose elements have a hash function). Omitting
1734 standard implementation details, this would lead to the following declarations:
1735 <programlisting>
1736 instance Eq e => Collects e [e] where ...
1737 instance Eq e => Collects e (e -> Bool) where ...
1738 instance Collects Char BitSet where ...
1739 instance (Hashable e, Collects a ce)
1740 => Collects e (Array Int ce) where ...
1741 </programlisting>
1742 All this looks quite promising; we have a class and a range of interesting
1743 implementations. Unfortunately, there are some serious problems with the class
1744 declaration. First, the empty function has an ambiguous type:
1745 <programlisting>
1746 empty :: Collects e ce => ce
1747 </programlisting>
1748 By "ambiguous" we mean that there is a type variable e that appears on the left
1749 of the <literal>=&gt;</literal> symbol, but not on the right. The problem with
1750 this is that, according to the theoretical foundations of Haskell overloading,
1751 we cannot guarantee a well-defined semantics for any term with an ambiguous
1752 type.
1753 </para>
1754 <para>
1755 We can sidestep this specific problem by removing the empty member from the
1756 class declaration. However, although the remaining members, insert and member,
1757 do not have ambiguous types, we still run into problems when we try to use
1758 them. For example, consider the following two functions:
1759 <programlisting>
1760 f x y = insert x . insert y
1761 g = f True 'a'
1762 </programlisting>
1763 for which GHC infers the following types:
1764 <programlisting>
1765 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1766 g :: (Collects Bool c, Collects Char c) => c -> c
1767 </programlisting>
1768 Notice that the type for f allows the two parameters x and y to be assigned
1769 different types, even though it attempts to insert each of the two values, one
1770 after the other, into the same collection. If we're trying to model collections
1771 that contain only one type of value, then this is clearly an inaccurate
1772 type. Worse still, the definition for g is accepted, without causing a type
1773 error. As a result, the error in this code will not be flagged at the point
1774 where it appears. Instead, it will show up only when we try to use g, which
1775 might even be in a different module.
1776 </para>
1777
1778 <sect4><title>An attempt to use constructor classes</title>
1779
1780 <para>
1781 Faced with the problems described above, some Haskell programmers might be
1782 tempted to use something like the following version of the class declaration:
1783 <programlisting>
1784 class Collects e c where
1785 empty :: c e
1786 insert :: e -> c e -> c e
1787 member :: e -> c e -> Bool
1788 </programlisting>
1789 The key difference here is that we abstract over the type constructor c that is
1790 used to form the collection type c e, and not over that collection type itself,
1791 represented by ce in the original class declaration. This avoids the immediate
1792 problems that we mentioned above: empty has type <literal>Collects e c => c
1793 e</literal>, which is not ambiguous.
1794 </para>
1795 <para>
1796 The function f from the previous section has a more accurate type:
1797 <programlisting>
1798 f :: (Collects e c) => e -> e -> c e -> c e
1799 </programlisting>
1800 The function g from the previous section is now rejected with a type error as
1801 we would hope because the type of f does not allow the two arguments to have
1802 different types.
1803 This, then, is an example of a multiple parameter class that does actually work
1804 quite well in practice, without ambiguity problems.
1805 There is, however, a catch. This version of the Collects class is nowhere near
1806 as general as the original class seemed to be: only one of the four instances
1807 for <literal>Collects</literal>
1808 given above can be used with this version of Collects because only one of
1809 them---the instance for lists---has a collection type that can be written in
1810 the form c e, for some type constructor c, and element type e.
1811 </para>
1812 </sect4>
1813
1814 <sect4><title>Adding functional dependencies</title>
1815
1816 <para>
1817 To get a more useful version of the Collects class, Hugs provides a mechanism
1818 that allows programmers to specify dependencies between the parameters of a
1819 multiple parameter class (For readers with an interest in theoretical
1820 foundations and previous work: The use of dependency information can be seen
1821 both as a generalization of the proposal for `parametric type classes' that was
1822 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
1823 later framework for "improvement" of qualified types. The
1824 underlying ideas are also discussed in a more theoretical and abstract setting
1825 in a manuscript [implparam], where they are identified as one point in a
1826 general design space for systems of implicit parameterization.).
1827
1828 To start with an abstract example, consider a declaration such as:
1829 <programlisting>
1830 class C a b where ...
1831 </programlisting>
1832 which tells us simply that C can be thought of as a binary relation on types
1833 (or type constructors, depending on the kinds of a and b). Extra clauses can be
1834 included in the definition of classes to add information about dependencies
1835 between parameters, as in the following examples:
1836 <programlisting>
1837 class D a b | a -> b where ...
1838 class E a b | a -> b, b -> a where ...
1839 </programlisting>
1840 The notation <literal>a -&gt; b</literal> used here between the | and where
1841 symbols --- not to be
1842 confused with a function type --- indicates that the a parameter uniquely
1843 determines the b parameter, and might be read as "a determines b." Thus D is
1844 not just a relation, but actually a (partial) function. Similarly, from the two
1845 dependencies that are included in the definition of E, we can see that E
1846 represents a (partial) one-one mapping between types.
1847 </para>
1848 <para>
1849 More generally, dependencies take the form <literal>x1 ... xn -&gt; y1 ... ym</literal>,
1850 where x1, ..., xn, and y1, ..., yn are type variables with n&gt;0 and
1851 m&gt;=0, meaning that the y parameters are uniquely determined by the x
1852 parameters. Spaces can be used as separators if more than one variable appears
1853 on any single side of a dependency, as in <literal>t -&gt; a b</literal>. Note that a class may be
1854 annotated with multiple dependencies using commas as separators, as in the
1855 definition of E above. Some dependencies that we can write in this notation are
1856 redundant, and will be rejected because they don't serve any useful
1857 purpose, and may instead indicate an error in the program. Examples of
1858 dependencies like this include <literal>a -&gt; a </literal>,
1859 <literal>a -&gt; a a </literal>,
1860 <literal>a -&gt; </literal>, etc. There can also be
1861 some redundancy if multiple dependencies are given, as in
1862 <literal>a-&gt;b</literal>,
1863 <literal>b-&gt;c </literal>, <literal>a-&gt;c </literal>, and
1864 in which some subset implies the remaining dependencies. Examples like this are
1865 not treated as errors. Note that dependencies appear only in class
1866 declarations, and not in any other part of the language. In particular, the
1867 syntax for instance declarations, class constraints, and types is completely
1868 unchanged.
1869 </para>
1870 <para>
1871 By including dependencies in a class declaration, we provide a mechanism for
1872 the programmer to specify each multiple parameter class more precisely. The
1873 compiler, on the other hand, is responsible for ensuring that the set of
1874 instances that are in scope at any given point in the program is consistent
1875 with any declared dependencies. For example, the following pair of instance
1876 declarations cannot appear together in the same scope because they violate the
1877 dependency for D, even though either one on its own would be acceptable:
1878 <programlisting>
1879 instance D Bool Int where ...
1880 instance D Bool Char where ...
1881 </programlisting>
1882 Note also that the following declaration is not allowed, even by itself:
1883 <programlisting>
1884 instance D [a] b where ...
1885 </programlisting>
1886 The problem here is that this instance would allow one particular choice of [a]
1887 to be associated with more than one choice for b, which contradicts the
1888 dependency specified in the definition of D. More generally, this means that,
1889 in any instance of the form:
1890 <programlisting>
1891 instance D t s where ...
1892 </programlisting>
1893 for some particular types t and s, the only variables that can appear in s are
1894 the ones that appear in t, and hence, if the type t is known, then s will be
1895 uniquely determined.
1896 </para>
1897 <para>
1898 The benefit of including dependency information is that it allows us to define
1899 more general multiple parameter classes, without ambiguity problems, and with
1900 the benefit of more accurate types. To illustrate this, we return to the
1901 collection class example, and annotate the original definition of <literal>Collects</literal>
1902 with a simple dependency:
1903 <programlisting>
1904 class Collects e ce | ce -> e where
1905 empty :: ce
1906 insert :: e -> ce -> ce
1907 member :: e -> ce -> Bool
1908 </programlisting>
1909 The dependency <literal>ce -&gt; e</literal> here specifies that the type e of elements is uniquely
1910 determined by the type of the collection ce. Note that both parameters of
1911 Collects are of kind *; there are no constructor classes here. Note too that
1912 all of the instances of Collects that we gave earlier can be used
1913 together with this new definition.
1914 </para>
1915 <para>
1916 What about the ambiguity problems that we encountered with the original
1917 definition? The empty function still has type Collects e ce => ce, but it is no
1918 longer necessary to regard that as an ambiguous type: Although the variable e
1919 does not appear on the right of the => symbol, the dependency for class
1920 Collects tells us that it is uniquely determined by ce, which does appear on
1921 the right of the => symbol. Hence the context in which empty is used can still
1922 give enough information to determine types for both ce and e, without
1923 ambiguity. More generally, we need only regard a type as ambiguous if it
1924 contains a variable on the left of the => that is not uniquely determined
1925 (either directly or indirectly) by the variables on the right.
1926 </para>
1927 <para>
1928 Dependencies also help to produce more accurate types for user defined
1929 functions, and hence to provide earlier detection of errors, and less cluttered
1930 types for programmers to work with. Recall the previous definition for a
1931 function f:
1932 <programlisting>
1933 f x y = insert x y = insert x . insert y
1934 </programlisting>
1935 for which we originally obtained a type:
1936 <programlisting>
1937 f :: (Collects a c, Collects b c) => a -> b -> c -> c
1938 </programlisting>
1939 Given the dependency information that we have for Collects, however, we can
1940 deduce that a and b must be equal because they both appear as the second
1941 parameter in a Collects constraint with the same first parameter c. Hence we
1942 can infer a shorter and more accurate type for f:
1943 <programlisting>
1944 f :: (Collects a c) => a -> a -> c -> c
1945 </programlisting>
1946 In a similar way, the earlier definition of g will now be flagged as a type error.
1947 </para>
1948 <para>
1949 Although we have given only a few examples here, it should be clear that the
1950 addition of dependency information can help to make multiple parameter classes
1951 more useful in practice, avoiding ambiguity problems, and allowing more general
1952 sets of instance declarations.
1953 </para>
1954 </sect4>
1955 </sect3>
1956 </sect2>
1957
1958 <sect2 id="instance-decls">
1959 <title>Instance declarations</title>
1960
1961 <sect3 id="instance-rules">
1962 <title>Relaxed rules for instance declarations</title>
1963
1964 <para>An instance declaration has the form
1965 <screen>
1966 instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) =&gt; <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
1967 </screen>
1968 The part before the "<literal>=&gt;</literal>" is the
1969 <emphasis>context</emphasis>, while the part after the
1970 "<literal>=&gt;</literal>" is the <emphasis>head</emphasis> of the instance declaration.
1971 </para>
1972
1973 <para>
1974 In Haskell 98 the head of an instance declaration
1975 must be of the form <literal>C (T a1 ... an)</literal>, where
1976 <literal>C</literal> is the class, <literal>T</literal> is a type constructor,
1977 and the <literal>a1 ... an</literal> are distinct type variables.
1978 Furthermore, the assertions in the context of the instance declaration
1979 must be of the form <literal>C a</literal> where <literal>a</literal>
1980 is a type variable that occurs in the head.
1981 </para>
1982 <para>
1983 The <option>-fglasgow-exts</option> flag loosens these restrictions
1984 considerably. Firstly, multi-parameter type classes are permitted. Secondly,
1985 the context and head of the instance declaration can each consist of arbitrary
1986 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
1987 following rules:
1988 <orderedlist>
1989 <listitem><para>
1990 For each assertion in the context:
1991 <orderedlist>
1992 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
1993 <listitem><para>The assertion has fewer constructors and variables (taken together
1994 and counting repetitions) than the head</para></listitem>
1995 </orderedlist>
1996 </para></listitem>
1997
1998 <listitem><para>The coverage condition. For each functional dependency,
1999 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-&gt;</literal>
2000 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
2001 every type variable in
2002 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
2003 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
2004 substitution mapping each type variable in the class declaration to the
2005 corresponding type in the instance declaration.
2006 </para></listitem>
2007 </orderedlist>
2008 These restrictions ensure that context reduction terminates: each reduction
2009 step makes the problem smaller by at least one
2010 constructor. For example, the following would make the type checker
2011 loop if it wasn't excluded:
2012 <programlisting>
2013 instance C a => C a where ...
2014 </programlisting>
2015 For example, these are OK:
2016 <programlisting>
2017 instance C Int [a] -- Multiple parameters
2018 instance Eq (S [a]) -- Structured type in head
2019
2020 -- Repeated type variable in head
2021 instance C4 a a => C4 [a] [a]
2022 instance Stateful (ST s) (MutVar s)
2023
2024 -- Head can consist of type variables only
2025 instance C a
2026 instance (Eq a, Show b) => C2 a b
2027
2028 -- Non-type variables in context
2029 instance Show (s a) => Show (Sized s a)
2030 instance C2 Int a => C3 Bool [a]
2031 instance C2 Int a => C3 [a] b
2032 </programlisting>
2033 But these are not:
2034 <programlisting>
2035 -- Context assertion no smaller than head
2036 instance C a => C a where ...
2037 -- (C b b) has more more occurrences of b than the head
2038 instance C b b => Foo [b] where ...
2039 </programlisting>
2040 </para>
2041
2042 <para>
2043 The same restrictions apply to instances generated by
2044 <literal>deriving</literal> clauses. Thus the following is accepted:
2045 <programlisting>
2046 data MinHeap h a = H a (h a)
2047 deriving (Show)
2048 </programlisting>
2049 because the derived instance
2050 <programlisting>
2051 instance (Show a, Show (h a)) => Show (MinHeap h a)
2052 </programlisting>
2053 conforms to the above rules.
2054 </para>
2055
2056 <para>
2057 A useful idiom permitted by the above rules is as follows.
2058 If one allows overlapping instance declarations then it's quite
2059 convenient to have a "default instance" declaration that applies if
2060 something more specific does not:
2061 <programlisting>
2062 instance C a where
2063 op = ... -- Default
2064 </programlisting>
2065 </para>
2066 <para>You can find lots of background material about the reason for these
2067 restrictions in the paper <ulink
2068 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
2069 Understanding functional dependencies via Constraint Handling Rules</ulink>.
2070 </para>
2071 </sect3>
2072
2073 <sect3 id="undecidable-instances">
2074 <title>Undecidable instances</title>
2075
2076 <para>
2077 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
2078 For example, sometimes you might want to use the following to get the
2079 effect of a "class synonym":
2080 <programlisting>
2081 class (C1 a, C2 a, C3 a) => C a where { }
2082
2083 instance (C1 a, C2 a, C3 a) => C a where { }
2084 </programlisting>
2085 This allows you to write shorter signatures:
2086 <programlisting>
2087 f :: C a => ...
2088 </programlisting>
2089 instead of
2090 <programlisting>
2091 f :: (C1 a, C2 a, C3 a) => ...
2092 </programlisting>
2093 The restrictions on functional dependencies (<xref
2094 linkend="functional-dependencies"/>) are particularly troublesome.
2095 It is tempting to introduce type variables in the context that do not appear in
2096 the head, something that is excluded by the normal rules. For example:
2097 <programlisting>
2098 class HasConverter a b | a -> b where
2099 convert :: a -> b
2100
2101 data Foo a = MkFoo a
2102
2103 instance (HasConverter a b,Show b) => Show (Foo a) where
2104 show (MkFoo value) = show (convert value)
2105 </programlisting>
2106 This is dangerous territory, however. Here, for example, is a program that would make the
2107 typechecker loop:
2108 <programlisting>
2109 class D a
2110 class F a b | a->b
2111 instance F [a] [[a]]
2112 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
2113 </programlisting>
2114 Similarly, it can be tempting to lift the coverage condition:
2115 <programlisting>
2116 class Mul a b c | a b -> c where
2117 (.*.) :: a -> b -> c
2118
2119 instance Mul Int Int Int where (.*.) = (*)
2120 instance Mul Int Float Float where x .*. y = fromIntegral x * y
2121 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
2122 </programlisting>
2123 The third instance declaration does not obey the coverage condition;
2124 and indeed the (somewhat strange) definition:
2125 <programlisting>
2126 f = \ b x y -> if b then x .*. [y] else y
2127 </programlisting>
2128 makes instance inference go into a loop, because it requires the constraint
2129 <literal>(Mul a [b] b)</literal>.
2130 </para>
2131 <para>
2132 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
2133 the experimental flag <option>-fallow-undecidable-instances</option>
2134 <indexterm><primary>-fallow-undecidable-instances
2135 option</primary></indexterm>, you can use arbitrary
2136 types in both an instance context and instance head. Termination is ensured by having a
2137 fixed-depth recursion stack. If you exceed the stack depth you get a
2138 sort of backtrace, and the opportunity to increase the stack depth
2139 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
2140 </para>
2141
2142 </sect3>
2143
2144
2145 <sect3 id="instance-overlap">
2146 <title>Overlapping instances</title>
2147 <para>
2148 In general, <emphasis>GHC requires that that it be unambiguous which instance
2149 declaration
2150 should be used to resolve a type-class constraint</emphasis>. This behaviour
2151 can be modified by two flags: <option>-fallow-overlapping-instances</option>
2152 <indexterm><primary>-fallow-overlapping-instances
2153 </primary></indexterm>
2154 and <option>-fallow-incoherent-instances</option>
2155 <indexterm><primary>-fallow-incoherent-instances
2156 </primary></indexterm>, as this section discusses. Both these
2157 flags are dynamic flags, and can be set on a per-module basis, using
2158 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
2159 <para>
2160 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
2161 it tries to match every instance declaration against the
2162 constraint,
2163 by instantiating the head of the instance declaration. For example, consider
2164 these declarations:
2165 <programlisting>
2166 instance context1 => C Int a where ... -- (A)
2167 instance context2 => C a Bool where ... -- (B)
2168 instance context3 => C Int [a] where ... -- (C)
2169 instance context4 => C Int [Int] where ... -- (D)
2170 </programlisting>
2171 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
2172 but (C) and (D) do not. When matching, GHC takes
2173 no account of the context of the instance declaration
2174 (<literal>context1</literal> etc).
2175 GHC's default behaviour is that <emphasis>exactly one instance must match the
2176 constraint it is trying to resolve</emphasis>.
2177 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
2178 including both declarations (A) and (B), say); an error is only reported if a
2179 particular constraint matches more than one.
2180 </para>
2181
2182 <para>
2183 The <option>-fallow-overlapping-instances</option> flag instructs GHC to allow
2184 more than one instance to match, provided there is a most specific one. For
2185 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
2186 (C) and (D), but the last is more specific, and hence is chosen. If there is no
2187 most-specific match, the program is rejected.
2188 </para>
2189 <para>
2190 However, GHC is conservative about committing to an overlapping instance. For example:
2191 <programlisting>
2192 f :: [b] -> [b]
2193 f x = ...
2194 </programlisting>
2195 Suppose that from the RHS of <literal>f</literal> we get the constraint
2196 <literal>C Int [b]</literal>. But
2197 GHC does not commit to instance (C), because in a particular
2198 call of <literal>f</literal>, <literal>b</literal> might be instantiate
2199 to <literal>Int</literal>, in which case instance (D) would be more specific still.
2200 So GHC rejects the program. If you add the flag <option>-fallow-incoherent-instances</option>,
2201 GHC will instead pick (C), without complaining about
2202 the problem of subsequent instantiations.
2203 </para>
2204 <para>
2205 The willingness to be overlapped or incoherent is a property of
2206 the <emphasis>instance declaration</emphasis> itself, controlled by the
2207 presence or otherwise of the <option>-fallow-overlapping-instances</option>
2208 and <option>-fallow-incoherent-instances</option> flags when that mdodule is
2209 being defined. Neither flag is required in a module that imports and uses the
2210 instance declaration. Specifically, during the lookup process:
2211 <itemizedlist>
2212 <listitem><para>
2213 An instance declaration is ignored during the lookup process if (a) a more specific
2214 match is found, and (b) the instance declaration was compiled with
2215 <option>-fallow-overlapping-instances</option>. The flag setting for the
2216 more-specific instance does not matter.
2217 </para></listitem>
2218 <listitem><para>
2219 Suppose an instance declaration does not matche the constraint being looked up, but
2220 does unify with it, so that it might match when the constraint is further
2221 instantiated. Usually GHC will regard this as a reason for not committing to
2222 some other constraint. But if the instance declaration was compiled with
2223 <option>-fallow-incoherent-instances</option>, GHC will skip the "does-it-unify?"
2224 check for that declaration.
2225 </para></listitem>
2226 </itemizedlist>
2227 These rules make it possible for a library author to design a library that relies on
2228 overlapping instances without the library client having to know.
2229 </para>
2230 <para>
2231 If an instance declaration is compiled without
2232 <option>-fallow-overlapping-instances</option>,
2233 then that instance can never be overlapped. This could perhaps be
2234 inconvenient. Perhaps the rule should instead say that the
2235 <emphasis>overlapping</emphasis> instance declaration should be compiled in
2236 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
2237 at a usage site should be permitted regardless of how the instance declarations
2238 are compiled, if the <option>-fallow-overlapping-instances</option> flag is
2239 used at the usage site. (Mind you, the exact usage site can occasionally be
2240 hard to pin down.) We are interested to receive feedback on these points.
2241 </para>
2242 <para>The <option>-fallow-incoherent-instances</option> flag implies the
2243 <option>-fallow-overlapping-instances</option> flag, but not vice versa.
2244 </para>
2245 </sect3>
2246
2247 <sect3>
2248 <title>Type synonyms in the instance head</title>
2249
2250 <para>
2251 <emphasis>Unlike Haskell 98, instance heads may use type
2252 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
2253 As always, using a type synonym is just shorthand for
2254 writing the RHS of the type synonym definition. For example:
2255
2256
2257 <programlisting>
2258 type Point = (Int,Int)
2259 instance C Point where ...
2260 instance C [Point] where ...
2261 </programlisting>
2262
2263
2264 is legal. However, if you added
2265
2266
2267 <programlisting>
2268 instance C (Int,Int) where ...
2269 </programlisting>
2270
2271
2272 as well, then the compiler will complain about the overlapping
2273 (actually, identical) instance declarations. As always, type synonyms
2274 must be fully applied. You cannot, for example, write:
2275
2276
2277 <programlisting>
2278 type P a = [[a]]
2279 instance Monad P where ...
2280 </programlisting>
2281
2282
2283 This design decision is independent of all the others, and easily
2284 reversed, but it makes sense to me.
2285
2286 </para>
2287 </sect3>
2288
2289
2290 </sect2>
2291
2292 <sect2 id="type-restrictions">
2293 <title>Type signatures</title>
2294
2295 <sect3><title>The context of a type signature</title>
2296 <para>
2297 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
2298 the form <emphasis>(class type-variable)</emphasis> or
2299 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
2300 these type signatures are perfectly OK
2301 <programlisting>
2302 g :: Eq [a] => ...
2303 g :: Ord (T a ()) => ...
2304 </programlisting>
2305 </para>
2306 <para>
2307 GHC imposes the following restrictions on the constraints in a type signature.
2308 Consider the type:
2309
2310 <programlisting>
2311 forall tv1..tvn (c1, ...,cn) => type
2312 </programlisting>
2313
2314 (Here, we write the "foralls" explicitly, although the Haskell source
2315 language omits them; in Haskell 98, all the free type variables of an
2316 explicit source-language type signature are universally quantified,
2317 except for the class type variables in a class declaration. However,
2318 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
2319 </para>
2320
2321 <para>
2322
2323 <orderedlist>
2324 <listitem>
2325
2326 <para>
2327 <emphasis>Each universally quantified type variable
2328 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
2329
2330 A type variable <literal>a</literal> is "reachable" if it it appears
2331 in the same constraint as either a type variable free in in
2332 <literal>type</literal>, or another reachable type variable.
2333 A value with a type that does not obey
2334 this reachability restriction cannot be used without introducing
2335 ambiguity; that is why the type is rejected.
2336 Here, for example, is an illegal type:
2337
2338
2339 <programlisting>
2340 forall a. Eq a => Int
2341 </programlisting>
2342
2343
2344 When a value with this type was used, the constraint <literal>Eq tv</literal>
2345 would be introduced where <literal>tv</literal> is a fresh type variable, and
2346 (in the dictionary-translation implementation) the value would be
2347 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
2348 can never know which instance of <literal>Eq</literal> to use because we never
2349 get any more information about <literal>tv</literal>.
2350 </para>
2351 <para>
2352 Note
2353 that the reachability condition is weaker than saying that <literal>a</literal> is
2354 functionally dependent on a type variable free in
2355 <literal>type</literal> (see <xref
2356 linkend="functional-dependencies"/>). The reason for this is there
2357 might be a "hidden" dependency, in a superclass perhaps. So
2358 "reachable" is a conservative approximation to "functionally dependent".
2359 For example, consider:
2360 <programlisting>
2361 class C a b | a -> b where ...
2362 class C a b => D a b where ...
2363 f :: forall a b. D a b => a -> a
2364 </programlisting>
2365 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
2366 but that is not immediately apparent from <literal>f</literal>'s type.
2367 </para>
2368 </listitem>
2369 <listitem>
2370
2371 <para>
2372 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
2373 universally quantified type variables <literal>tvi</literal></emphasis>.
2374
2375 For example, this type is OK because <literal>C a b</literal> mentions the
2376 universally quantified type variable <literal>b</literal>:
2377
2378
2379 <programlisting>
2380 forall a. C a b => burble
2381 </programlisting>
2382
2383
2384 The next type is illegal because the constraint <literal>Eq b</literal> does not
2385 mention <literal>a</literal>:
2386
2387
2388 <programlisting>
2389 forall a. Eq b => burble
2390 </programlisting>
2391
2392
2393 The reason for this restriction is milder than the other one. The
2394 excluded types are never useful or necessary (because the offending
2395 context doesn't need to be witnessed at this point; it can be floated
2396 out). Furthermore, floating them out increases sharing. Lastly,
2397 excluding them is a conservative choice; it leaves a patch of
2398 territory free in case we need it later.
2399
2400 </para>
2401 </listitem>
2402
2403 </orderedlist>
2404
2405 </para>
2406 </sect3>
2407
2408 <sect3 id="hoist">
2409 <title>For-all hoisting</title>
2410 <para>
2411 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms"/>) at the right hand
2412 end of an arrow, thus:
2413 <programlisting>
2414 type Discard a = forall b. a -> b -> a
2415
2416 g :: Int -> Discard Int
2417 g x y z = x+y
2418 </programlisting>
2419 Simply expanding the type synonym would give
2420 <programlisting>
2421 g :: Int -> (forall b. Int -> b -> Int)
2422 </programlisting>
2423 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2424 <programlisting>
2425 g :: forall b. Int -> Int -> b -> Int
2426 </programlisting>
2427 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2428 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2429 performs the transformation:</emphasis>
2430 <programlisting>
2431 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2432 ==>
2433 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2434 </programlisting>
2435 (In fact, GHC tries to retain as much synonym information as possible for use in
2436 error messages, but that is a usability issue.) This rule applies, of course, whether
2437 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2438 valid way to write <literal>g</literal>'s type signature:
2439 <programlisting>
2440 g :: Int -> Int -> forall b. b -> Int
2441 </programlisting>
2442 </para>
2443 <para>
2444 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2445 example:
2446 <programlisting>
2447 type Foo a = (?x::Int) => Bool -> a
2448 g :: Foo (Foo Int)
2449 </programlisting>
2450 means
2451 <programlisting>
2452 g :: (?x::Int) => Bool -> Bool -> Int
2453 </programlisting>
2454 </para>
2455 </sect3>
2456
2457
2458 </sect2>
2459
2460 <sect2 id="implicit-parameters">
2461 <title>Implicit parameters</title>
2462
2463 <para> Implicit parameters are implemented as described in
2464 "Implicit parameters: dynamic scoping with static types",
2465 J Lewis, MB Shields, E Meijer, J Launchbury,
2466 27th ACM Symposium on Principles of Programming Languages (POPL'00),
2467 Boston, Jan 2000.
2468 </para>
2469
2470 <para>(Most of the following, stil rather incomplete, documentation is
2471 due to Jeff Lewis.)</para>
2472
2473 <para>Implicit parameter support is enabled with the option
2474 <option>-fimplicit-params</option>.</para>
2475
2476 <para>
2477 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
2478 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
2479 context. In Haskell, all variables are statically bound. Dynamic
2480 binding of variables is a notion that goes back to Lisp, but was later
2481 discarded in more modern incarnations, such as Scheme. Dynamic binding
2482 can be very confusing in an untyped language, and unfortunately, typed
2483 languages, in particular Hindley-Milner typed languages like Haskell,
2484 only support static scoping of variables.
2485 </para>
2486 <para>
2487 However, by a simple extension to the type class system of Haskell, we
2488 can support dynamic binding. Basically, we express the use of a
2489 dynamically bound variable as a constraint on the type. These
2490 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
2491 function uses a dynamically-bound variable <literal>?x</literal>
2492 of type <literal>t'</literal>". For
2493 example, the following expresses the type of a sort function,
2494 implicitly parameterized by a comparison function named <literal>cmp</literal>.
2495 <programlisting>
2496 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2497 </programlisting>
2498 The dynamic binding constraints are just a new form of predicate in the type class system.
2499 </para>
2500 <para>
2501 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
2502 where <literal>x</literal> is
2503 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
2504 Use of this construct also introduces a new
2505 dynamic-binding constraint in the type of the expression.
2506 For example, the following definition
2507 shows how we can define an implicitly parameterized sort function in
2508 terms of an explicitly parameterized <literal>sortBy</literal> function:
2509 <programlisting>
2510 sortBy :: (a -> a -> Bool) -> [a] -> [a]
2511
2512 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
2513 sort = sortBy ?cmp
2514 </programlisting>
2515 </para>
2516
2517 <sect3>
2518 <title>Implicit-parameter type constraints</title>
2519 <para>
2520 Dynamic binding constraints behave just like other type class
2521 constraints in that they are automatically propagated. Thus, when a
2522 function is used, its implicit parameters are inherited by the
2523 function that called it. For example, our <literal>sort</literal> function might be used
2524 to pick out the least value in a list:
2525 <programlisting>
2526 least :: (?cmp :: a -> a -> Bool) => [a] -> a
2527 least xs = head (sort xs)
2528 </programlisting>
2529 Without lifting a finger, the <literal>?cmp</literal> parameter is
2530 propagated to become a parameter of <literal>least</literal> as well. With explicit
2531 parameters, the default is that parameters must always be explicit
2532 propagated. With implicit parameters, the default is to always
2533 propagate them.
2534 </para>
2535 <para>
2536 An implicit-parameter type constraint differs from other type class constraints in the
2537 following way: All uses of a particular implicit parameter must have
2538 the same type. This means that the type of <literal>(?x, ?x)</literal>
2539 is <literal>(?x::a) => (a,a)</literal>, and not
2540 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
2541 class constraints.
2542 </para>
2543
2544 <para> You can't have an implicit parameter in the context of a class or instance
2545 declaration. For example, both these declarations are illegal:
2546 <programlisting>
2547 class (?x::Int) => C a where ...
2548 instance (?x::a) => Foo [a] where ...
2549 </programlisting>
2550 Reason: exactly which implicit parameter you pick up depends on exactly where
2551 you invoke a function. But the ``invocation'' of instance declarations is done
2552 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
2553 Easiest thing is to outlaw the offending types.</para>
2554 <para>
2555 Implicit-parameter constraints do not cause ambiguity. For example, consider:
2556 <programlisting>
2557 f :: (?x :: [a]) => Int -> Int
2558 f n = n + length ?x
2559
2560 g :: (Read a, Show a) => String -> String
2561 g s = show (read s)
2562 </programlisting>
2563 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
2564 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
2565 quite unambiguous, and fixes the type <literal>a</literal>.
2566 </para>
2567 </sect3>
2568
2569 <sect3>
2570 <title>Implicit-parameter bindings</title>
2571
2572 <para>
2573 An implicit parameter is <emphasis>bound</emphasis> using the standard
2574 <literal>let</literal> or <literal>where</literal> binding forms.
2575 For example, we define the <literal>min</literal> function by binding
2576 <literal>cmp</literal>.
2577 <programlisting>
2578 min :: [a] -> a
2579 min = let ?cmp = (&lt;=) in least
2580 </programlisting>
2581 </para>
2582 <para>
2583 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
2584 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
2585 (including in a list comprehension, or do-notation, or pattern guards),
2586 or a <literal>where</literal> clause.
2587 Note the following points:
2588 <itemizedlist>
2589 <listitem><para>
2590 An implicit-parameter binding group must be a
2591 collection of simple bindings to implicit-style variables (no
2592 function-style bindings, and no type signatures); these bindings are
2593 neither polymorphic or recursive.
2594 </para></listitem>
2595 <listitem><para>
2596 You may not mix implicit-parameter bindings with ordinary bindings in a
2597 single <literal>let</literal>
2598 expression; use two nested <literal>let</literal>s instead.
2599 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
2600 </para></listitem>
2601
2602 <listitem><para>
2603 You may put multiple implicit-parameter bindings in a
2604 single binding group; but they are <emphasis>not</emphasis> treated
2605 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
2606 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
2607 parameter. The bindings are not nested, and may be re-ordered without changing
2608 the meaning of the program.
2609 For example, consider:
2610 <programlisting>
2611 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
2612 </programlisting>
2613 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
2614 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2615 <programlisting>
2616 f :: (?x::Int) => Int -> Int
2617 </programlisting>
2618 </para></listitem>
2619 </itemizedlist>
2620 </para>
2621
2622 </sect3>
2623
2624 <sect3><title>Implicit parameters and polymorphic recursion</title>
2625
2626 <para>
2627 Consider these two definitions:
2628 <programlisting>
2629 len1 :: [a] -> Int
2630 len1 xs = let ?acc = 0 in len_acc1 xs
2631
2632 len_acc1 [] = ?acc
2633 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
2634
2635 ------------
2636
2637 len2 :: [a] -> Int
2638 len2 xs = let ?acc = 0 in len_acc2 xs
2639
2640 len_acc2 :: (?acc :: Int) => [a] -> Int
2641 len_acc2 [] = ?acc
2642 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
2643 </programlisting>
2644 The only difference between the two groups is that in the second group
2645 <literal>len_acc</literal> is given a type signature.
2646 In the former case, <literal>len_acc1</literal> is monomorphic in its own
2647 right-hand side, so the implicit parameter <literal>?acc</literal> is not
2648 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
2649 has a type signature, the recursive call is made to the
2650 <emphasis>polymoprhic</emphasis> version, which takes <literal>?acc</literal>
2651 as an implicit parameter. So we get the following results in GHCi:
2652 <programlisting>
2653 Prog> len1 "hello"
2654 0
2655 Prog> len2 "hello"
2656 5
2657 </programlisting>
2658 Adding a type signature dramatically changes the result! This is a rather
2659 counter-intuitive phenomenon, worth watching out for.
2660 </para>
2661 </sect3>
2662
2663 <sect3><title>Implicit parameters and monomorphism</title>
2664
2665 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
2666 Haskell Report) to implicit parameters. For example, consider:
2667 <programlisting>
2668 f :: Int -> Int
2669 f v = let ?x = 0 in
2670 let y = ?x + v in
2671 let ?x = 5 in
2672 y
2673 </programlisting>
2674 Since the binding for <literal>y</literal> falls under the Monomorphism
2675 Restriction it is not generalised, so the type of <literal>y</literal> is
2676 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
2677 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
2678 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
2679 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
2680 <literal>y</literal> in the body of the <literal>let</literal> will see the
2681 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
2682 <literal>14</literal>.
2683 </para>
2684 </sect3>
2685 </sect2>
2686
2687 <!-- ======================= COMMENTED OUT ========================
2688
2689 We intend to remove linear implicit parameters, so I'm at least removing
2690 them from the 6.6 user manual
2691
2692 <sect2 id="linear-implicit-parameters">
2693 <title>Linear implicit parameters</title>
2694 <para>
2695 Linear implicit parameters are an idea developed by Koen Claessen,
2696 Mark Shields, and Simon PJ. They address the long-standing
2697 problem that monads seem over-kill for certain sorts of problem, notably:
2698 </para>
2699 <itemizedlist>
2700 <listitem> <para> distributing a supply of unique names </para> </listitem>
2701 <listitem> <para> distributing a supply of random numbers </para> </listitem>
2702 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2703 </itemizedlist>
2704
2705 <para>
2706 Linear implicit parameters are just like ordinary implicit parameters,
2707 except that they are "linear"; that is, they cannot be copied, and
2708 must be explicitly "split" instead. Linear implicit parameters are
2709 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2710 (The '/' in the '%' suggests the split!)
2711 </para>
2712 <para>
2713 For example:
2714 <programlisting>
2715 import GHC.Exts( Splittable )
2716
2717 data NameSupply = ...
2718
2719 splitNS :: NameSupply -> (NameSupply, NameSupply)
2720 newName :: NameSupply -> Name
2721
2722 instance Splittable NameSupply where
2723 split = splitNS
2724
2725
2726 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2727 f env (Lam x e) = Lam x' (f env e)
2728 where
2729 x' = newName %ns
2730 env' = extend env x x'
2731 ...more equations for f...
2732 </programlisting>
2733 Notice that the implicit parameter %ns is consumed
2734 <itemizedlist>
2735 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2736 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2737 </itemizedlist>
2738 </para>
2739 <para>
2740 So the translation done by the type checker makes
2741 the parameter explicit:
2742 <programlisting>
2743 f :: NameSupply -> Env -> Expr -> Expr
2744 f ns env (Lam x e) = Lam x' (f ns1 env e)
2745 where
2746 (ns1,ns2) = splitNS ns
2747 x' = newName ns2
2748 env = extend env x x'
2749 </programlisting>
2750 Notice the call to 'split' introduced by the type checker.
2751 How did it know to use 'splitNS'? Because what it really did
2752 was to introduce a call to the overloaded function 'split',
2753 defined by the class <literal>Splittable</literal>:
2754 <programlisting>
2755 class Splittable a where
2756 split :: a -> (a,a)
2757 </programlisting>
2758 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2759 split for name supplies. But we can simply write
2760 <programlisting>
2761 g x = (x, %ns, %ns)
2762 </programlisting>
2763 and GHC will infer
2764 <programlisting>
2765 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2766 </programlisting>
2767 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2768 <literal>GHC.Exts</literal>.
2769 </para>
2770 <para>
2771 Other points:
2772 <itemizedlist>
2773 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2774 are entirely distinct implicit parameters: you
2775 can use them together and they won't intefere with each other. </para>
2776 </listitem>
2777
2778 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2779
2780 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2781 in the context of a class or instance declaration. </para></listitem>
2782 </itemizedlist>
2783 </para>
2784
2785 <sect3><title>Warnings</title>
2786
2787 <para>
2788 The monomorphism restriction is even more important than usual.
2789 Consider the example above:
2790 <programlisting>
2791 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2792 f env (Lam x e) = Lam x' (f env e)
2793 where
2794 x' = newName %ns
2795 env' = extend env x x'
2796 </programlisting>
2797 If we replaced the two occurrences of x' by (newName %ns), which is
2798 usually a harmless thing to do, we get:
2799 <programlisting>
2800 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2801 f env (Lam x e) = Lam (newName %ns) (f env e)
2802 where
2803 env' = extend env x (newName %ns)
2804 </programlisting>
2805 But now the name supply is consumed in <emphasis>three</emphasis> places
2806 (the two calls to newName,and the recursive call to f), so
2807 the result is utterly different. Urk! We don't even have
2808 the beta rule.
2809 </para>
2810 <para>
2811 Well, this is an experimental change. With implicit
2812 parameters we have already lost beta reduction anyway, and
2813 (as John Launchbury puts it) we can't sensibly reason about
2814 Haskell programs without knowing their typing.
2815 </para>
2816
2817 </sect3>
2818
2819 <sect3><title>Recursive functions</title>
2820 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2821 Consider
2822 <programlisting>
2823 foo :: %x::T => Int -> [Int]
2824 foo 0 = []
2825 foo n = %x : foo (n-1)
2826 </programlisting>
2827 where T is some type in class Splittable.</para>
2828 <para>
2829 Do you get a list of all the same T's or all different T's
2830 (assuming that split gives two distinct T's back)?
2831 </para><para>
2832 If you supply the type signature, taking advantage of polymorphic
2833 recursion, you get what you'd probably expect. Here's the
2834 translated term, where the implicit param is made explicit:
2835 <programlisting>
2836 foo x 0 = []
2837 foo x n = let (x1,x2) = split x
2838 in x1 : foo x2 (n-1)
2839 </programlisting>
2840 But if you don't supply a type signature, GHC uses the Hindley
2841 Milner trick of using a single monomorphic instance of the function
2842 for the recursive calls. That is what makes Hindley Milner type inference
2843 work. So the translation becomes
2844 <programlisting>
2845 foo x = let
2846 foom 0 = []
2847 foom n = x : foom (n-1)
2848 in
2849 foom
2850 </programlisting>
2851 Result: 'x' is not split, and you get a list of identical T's. So the
2852 semantics of the program depends on whether or not foo has a type signature.
2853 Yikes!
2854 </para><para>
2855 You may say that this is a good reason to dislike linear implicit parameters
2856 and you'd be right. That is why they are an experimental feature.
2857 </para>
2858 </sect3>
2859
2860 </sect2>
2861
2862 ================ END OF Linear Implicit Parameters commented out -->
2863
2864 <sect2 id="sec-kinding">
2865 <title>Explicitly-kinded quantification</title>
2866
2867 <para>
2868 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2869 to give the kind explicitly as (machine-checked) documentation,
2870 just as it is nice to give a type signature for a function. On some occasions,
2871 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2872 John Hughes had to define the data type:
2873 <screen>
2874 data Set cxt a = Set [a]
2875 | Unused (cxt a -> ())
2876 </screen>
2877 The only use for the <literal>Unused</literal> constructor was to force the correct
2878 kind for the type variable <literal>cxt</literal>.
2879 </para>
2880 <para>
2881 GHC now instead allows you to specify the kind of a type variable directly, wherever
2882 a type variable is explicitly bound. Namely:
2883 <itemizedlist>
2884 <listitem><para><literal>data</literal> declarations:
2885 <screen>
2886 data Set (cxt :: * -> *) a = Set [a]
2887 </screen></para></listitem>
2888 <listitem><para><literal>type</literal> declarations:
2889 <screen>
2890 type T (f :: * -> *) = f Int
2891 </screen></para></listitem>
2892 <listitem><para><literal>class</literal> declarations:
2893 <screen>
2894 class (Eq a) => C (f :: * -> *) a where ...
2895 </screen></para></listitem>
2896 <listitem><para><literal>forall</literal>'s in type signatures:
2897 <screen>
2898 f :: forall (cxt :: * -> *). Set cxt Int
2899 </screen></para></listitem>
2900 </itemizedlist>
2901 </para>
2902
2903 <para>
2904 The parentheses are required. Some of the spaces are required too, to
2905 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2906 will get a parse error, because "<literal>::*->*</literal>" is a
2907 single lexeme in Haskell.
2908 </para>
2909
2910 <para>
2911 As part of the same extension, you can put kind annotations in types
2912 as well. Thus:
2913 <screen>
2914 f :: (Int :: *) -> Int
2915 g :: forall a. a -> (a :: *)
2916 </screen>
2917 The syntax is
2918 <screen>
2919 atype ::= '(' ctype '::' kind ')
2920 </screen>
2921 The parentheses are required.
2922 </para>
2923 </sect2>
2924
2925
2926 <sect2 id="universal-quantification">
2927 <title>Arbitrary-rank polymorphism
2928 </title>
2929
2930 <para>
2931 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2932 allows us to say exactly what this means. For example:
2933 </para>
2934 <para>
2935 <programlisting>
2936 g :: b -> b
2937 </programlisting>
2938 means this:
2939 <programlisting>
2940 g :: forall b. (b -> b)
2941 </programlisting>
2942 The two are treated identically.
2943 </para>
2944
2945 <para>
2946 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2947 explicit universal quantification in
2948 types.
2949 For example, all the following types are legal:
2950 <programlisting>
2951 f1 :: forall a b. a -> b -> a
2952 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2953
2954 f2 :: (forall a. a->a) -> Int -> Int
2955 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2956
2957 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2958 </programlisting>
2959 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2960 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2961 The <literal>forall</literal> makes explicit the universal quantification that
2962 is implicitly added by Haskell.
2963 </para>
2964 <para>
2965 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2966 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
2967 shows, the polymorphic type on the left of the function arrow can be overloaded.
2968 </para>
2969 <para>
2970 The function <literal>f3</literal> has a rank-3 type;
2971 it has rank-2 types on the left of a function arrow.
2972 </para>
2973 <para>
2974 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2975 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2976 that restriction has now been lifted.)
2977 In particular, a forall-type (also called a "type scheme"),
2978 including an operational type class context, is legal:
2979 <itemizedlist>
2980 <listitem> <para> On the left of a function arrow </para> </listitem>
2981 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist"/>) </para> </listitem>
2982 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2983 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2984 field type signatures.</para> </listitem>
2985 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2986 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
2987 </itemizedlist>
2988 There is one place you cannot put a <literal>forall</literal>:
2989 you cannot instantiate a type variable with a forall-type. So you cannot
2990 make a forall-type the argument of a type constructor. So these types are illegal:
2991 <programlisting>
2992 x1 :: [forall a. a->a]
2993 x2 :: (forall a. a->a, Int)
2994 x3 :: Maybe (forall a. a->a)
2995 </programlisting>
2996 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2997 a type variable any more!
2998 </para>
2999
3000
3001 <sect3 id="univ">
3002 <title>Examples
3003 </title>
3004
3005 <para>
3006 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
3007 the types of the constructor arguments. Here are several examples:
3008 </para>
3009
3010 <para>
3011
3012 <programlisting>
3013 data T a = T1 (forall b. b -> b -> b) a
3014
3015 data MonadT m = MkMonad { return :: forall a. a -> m a,
3016 bind :: forall a b. m a -> (a -> m b) -> m b
3017 }
3018
3019 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
3020 </programlisting>
3021
3022 </para>
3023
3024 <para>
3025 The constructors have rank-2 types:
3026 </para>
3027
3028 <para>
3029
3030 <programlisting>
3031 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
3032 MkMonad :: forall m. (forall a. a -> m a)
3033 -> (forall a b. m a -> (a -> m b) -> m b)
3034 -> MonadT m
3035 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
3036 </programlisting>
3037
3038 </para>
3039
3040 <para>
3041 Notice that you don't need to use a <literal>forall</literal> if there's an
3042 explicit context. For example in the first argument of the
3043 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
3044 prefixed to the argument type. The implicit <literal>forall</literal>
3045 quantifies all type variables that are not already in scope, and are
3046 mentioned in the type quantified over.
3047 </para>
3048
3049 <para>
3050 As for type signatures, implicit quantification happens for non-overloaded
3051 types too. So if you write this:
3052
3053 <programlisting>
3054 data T a = MkT (Either a b) (b -> b)
3055 </programlisting>
3056
3057 it's just as if you had written this:
3058
3059 <programlisting>
3060 data T a = MkT (forall b. Either a b) (forall b. b -> b)
3061 </programlisting>
3062
3063 That is, since the type variable <literal>b</literal> isn't in scope, it's
3064 implicitly universally quantified. (Arguably, it would be better
3065 to <emphasis>require</emphasis> explicit quantification on constructor arguments
3066 where that is what is wanted. Feedback welcomed.)
3067 </para>
3068
3069 <para>
3070 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
3071 the constructor to suitable values, just as usual. For example,
3072 </para>
3073
3074 <para>
3075
3076 <programlisting>
3077 a1 :: T Int
3078 a1 = T1 (\xy->x) 3
3079
3080 a2, a3 :: Swizzle
3081 a2 = MkSwizzle sort
3082 a3 = MkSwizzle reverse
3083
3084 a4 :: MonadT Maybe
3085 a4 = let r x = Just x
3086 b m k = case m of
3087 Just y -> k y
3088 Nothing -> Nothing
3089 in
3090 MkMonad r b
3091
3092 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
3093 mkTs f x y = [T1 f x, T1 f y]
3094 </programlisting>
3095
3096 </para>
3097
3098 <para>
3099 The type of the argument can, as usual, be more general than the type
3100 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
3101 does not need the <literal>Ord</literal> constraint.)
3102 </para>
3103
3104 <para>
3105 When you use pattern matching, the bound variables may now have
3106 polymorphic types. For example:
3107 </para>
3108
3109 <para>
3110
3111 <programlisting>
3112 f :: T a -> a -> (a, Char)
3113 f (T1 w k) x = (w k x, w 'c' 'd')
3114
3115 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
3116 g (MkSwizzle s) xs f = s (map f (s xs))
3117
3118 h :: MonadT m -> [m a] -> m [a]
3119 h m [] = return m []
3120 h m (x:xs) = bind m x $ \y ->
3121 bind m (h m xs) $ \ys ->
3122 return m (y:ys)
3123 </programlisting>
3124
3125 </para>
3126
3127 <para>
3128 In the function <function>h</function> we use the record selectors <literal>return</literal>
3129 and <literal>bind</literal> to extract the polymorphic bind and return functions
3130 from the <literal>MonadT</literal> data structure, rather than using pattern
3131 matching.
3132 </para>
3133 </sect3>
3134
3135 <sect3>
3136 <title>Type inference</title>
3137
3138 <para>
3139 In general, type inference for arbitrary-rank types is undecidable.
3140 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
3141 to get a decidable algorithm by requiring some help from the programmer.
3142 We do not yet have a formal specification of "some help" but the rule is this:
3143 </para>
3144 <para>
3145 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
3146 provides an explicit polymorphic type for x, or GHC's type inference will assume
3147 that x's type has no foralls in it</emphasis>.
3148 </para>
3149 <para>
3150 What does it mean to "provide" an explicit type for x? You can do that by
3151 giving a type signature for x directly, using a pattern type signature
3152 (<xref linkend="scoped-type-variables"/>), thus:
3153 <programlisting>
3154 \ f :: (forall a. a->a) -> (f True, f 'c')
3155 </programlisting>
3156 Alternatively, you can give a type signature to the enclosing
3157 context, which GHC can "push down" to find the type for the variable:
3158 <programlisting>
3159 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
3160 </programlisting>
3161 Here the type signature on the expression can be pushed inwards
3162 to give a type signature for f. Similarly, and more commonly,
3163 one can give a type signature for the function itself:
3164 <programlisting>
3165 h :: (forall a. a->a) -> (Bool,Char)
3166 h f = (f True, f 'c')
3167 </programlisting>
3168 You don't need to give a type signature if the lambda bound variable
3169 is a constructor argument. Here is an example we saw earlier:
3170 <programlisting>
3171 f :: T a -> a -> (a, Char)
3172 f (T1 w k) x = (w k x, w 'c' 'd')
3173 </programlisting>
3174 Here we do not need to give a type signature to <literal>w</literal>, because
3175 it is an argument of constructor <literal>T1</literal> and that tells GHC all
3176 it needs to know.
3177 </para>
3178
3179 </sect3>
3180
3181
3182 <sect3 id="implicit-quant">
3183 <title>Implicit quantification</title>
3184
3185 <para>
3186 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
3187 user-written types, if and only if there is no explicit <literal>forall</literal>,
3188 GHC finds all the type variables mentioned in the type that are not already
3189 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
3190 equivalent:
3191 <programlisting>
3192 f :: a -> a
3193 f :: forall a. a -> a
3194
3195 g (x::a) = let
3196 h :: a -> b -> b
3197 h x y = y
3198 in ...
3199 g (x::a) = let
3200 h :: forall b. a -> b -> b
3201 h x y = y
3202 in ...
3203 </programlisting>
3204 </para>
3205 <para>
3206 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
3207 point. For example:
3208 <programlisting>
3209 f :: (a -> a) -> Int
3210 -- MEANS
3211 f :: forall a. (a -> a) -> Int
3212 -- NOT
3213 f :: (forall a. a -> a) -> Int
3214
3215
3216 g :: (Ord a => a -> a) -> Int
3217 -- MEANS the illegal type
3218 g :: forall a. (Ord a => a -> a) -> Int
3219 -- NOT
3220 g :: (forall a. Ord a => a -> a) -> Int
3221 </programlisting>
3222 The latter produces an illegal type, which you might think is silly,
3223 but at least the rule is simple. If you want the latter type, you
3224 can write your for-alls explicitly. Indeed, doing so is strongly advised
3225 for rank-2 types.
3226 </para>
3227 </sect3>
3228 </sect2>
3229
3230
3231 <sect2 id="impredicative-polymorphism">
3232 <title>Impredicative polymorphism
3233 </title>
3234 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>. This means
3235 that you can call a polymorphic function at a polymorphic type, and
3236 parameterise data structures over polymorphic types. For example:
3237 <programlisting>
3238 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
3239 f (Just g) = Just (g [3], g "hello")
3240 f Nothing = Nothing
3241 </programlisting>
3242 Notice here that the <literal>Maybe</literal> type is parameterised by the
3243 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
3244 [a])</literal>.
3245 </para>
3246 <para>The technical details of this extension are described in the paper
3247 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy">Boxy types:
3248 type inference for higher-rank types and impredicativity</ulink>,
3249 which appeared at ICFP 2006.
3250 </para>
3251 </sect2>
3252
3253 <sect2 id="scoped-type-variables">
3254 <title>Lexically scoped type variables
3255 </title>
3256
3257 <para>
3258 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
3259 which some type signatures are simply impossible to write. For example:
3260 <programlisting>
3261 f :: forall a. [a] -> [a]
3262 f xs = ys ++ ys
3263 where
3264 ys :: [a]
3265 ys = reverse xs
3266 </programlisting>
3267 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope; it scopes over
3268 the entire definition of <literal>f</literal>.
3269 In particular, it is in scope at the type signature for <varname>ys</varname>.
3270 In Haskell 98 it is not possible to declare
3271 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
3272 it becomes possible to do so.
3273 </para>
3274 <para>Lexically-scoped type variables are enabled by
3275 <option>-fglasgow-exts</option>.
3276 </para>
3277 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
3278 variables work, compared to earlier releases. Read this section
3279 carefully!</para>
3280
3281 <sect3>
3282 <title>Overview</title>
3283
3284 <para>The design follows the following principles
3285 <itemizedlist>
3286 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
3287 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
3288 design.)</para></listitem>
3289 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
3290 type variables. This means that every programmer-written type signature
3291 (includin one that contains free scoped type variables) denotes a
3292 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
3293 checker, and no inference is involved.</para></listitem>
3294 <listitem><para>Lexical type variables may be alpha-renamed freely, without
3295 changing the program.</para></listitem>
3296 </itemizedlist>
3297 </para>
3298 <para>
3299 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
3300 <itemizedlist>
3301 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
3302 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
3303 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
3304 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
3305 </itemizedlist>
3306 </para>
3307 <para>
3308 In Haskell, a programmer-written type signature is implicitly quantifed over
3309 its free type variables (<ulink
3310 url="http://haskell.org/onlinereport/decls.html#sect4.1.2">Section
3311 4.1.2</ulink>
3312 of the Haskel Report).
3313 Lexically scoped type variables affect this implicit quantification rules
3314 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
3315 quantified. For example, if type variable <literal>a</literal> is in scope,
3316 then
3317 <programlisting>
3318 (e :: a -> a) means (e :: a -> a)
3319 (e :: b -> b) means (e :: forall b. b->b)
3320 (e :: a -> b) means (e :: forall b. a->b)
3321 </programlisting>
3322 </para>
3323
3324
3325 </sect3>
3326
3327
3328 <sect3 id="decl-type-sigs">
3329 <title>Declaration type signatures</title>
3330 <para>A declaration type signature that has <emphasis>explicit</emphasis>
3331 quantification (using <literal>forall</literal>) brings into scope the
3332 explicitly-quantified
3333 type variables, in the definition of the named function(s). For example:
3334 <programlisting>
3335 f :: forall a. [a] -> [a]
3336 f (x:xs) = xs ++ [ x :: a ]
3337 </programlisting>
3338 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
3339 the definition of "<literal>f</literal>".
3340 </para>
3341 <para>This only happens if the quantification in <literal>f</literal>'s type
3342 signature is explicit. For example:
3343 <programlisting>
3344 g :: [a] -> [a]
3345 g (x:xs) = xs ++ [ x :: a ]
3346 </programlisting>
3347 This program will be rejected, because "<literal>a</literal>" does not scope
3348 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
3349 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
3350 quantification rules.
3351 </para>
3352 </sect3>
3353
3354 <sect3 id="exp-type-sigs">
3355 <title>Expression type signatures</title>
3356
3357 <para>An expression type signature that has <emphasis>explicit</emphasis>
3358 quantification (using <literal>forall</literal>) brings into scope the
3359 explicitly-quantified
3360 type variables, in the annotated expression. For example:
3361 <programlisting>
3362 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
3363 </programlisting>
3364 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
3365 type variable <literal>s</literal> into scope, in the annotated expression
3366 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
3367 </para>
3368
3369 </sect3>
3370
3371 <sect3 id="pattern-type-sigs">
3372 <title>Pattern type signatures</title>
3373 <para>
3374 A type signature may occur in any pattern; this is a <emphasis>pattern type
3375 signature</emphasis>.
3376 For example:
3377 <programlisting>
3378 -- f and g assume that 'a' is already in scope
3379 f = \(x::Int, y::a) -> x
3380 g (x::a) = x
3381 h ((x,y) :: (Int,Bool)) = (y,x)
3382 </programlisting>
3383 In the case where all the type variables in the pattern type sigature are
3384 already in scope (i.e. bound by the enclosing context), matters are simple: the
3385 signature simply constrains the type of the pattern in the obvious way.
3386 </para>
3387 <para>
3388 There is only one situation in which you can write a pattern type signature that
3389 mentions a type variable that is not already in scope, namely in pattern match
3390 of an existential data constructor. For example:
3391 <programlisting>
3392 data T = forall a. MkT [a]
3393
3394 k :: T -> T
3395 k (MkT [t::a]) = MkT t3
3396 where
3397 t3::[a] = [t,t,t]
3398 </programlisting>
3399 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
3400 variable that is not already in scope. Indeed, it cannot already be in scope,
3401 because it is bound by the pattern match. GHC's rule is that in this situation
3402 (and only then), a pattern type signature can mention a type variable that is
3403 not already in scope; the effect is to bring it into scope, standing for the
3404 existentially-bound type variable.
3405 </para>
3406 <para>
3407 If this seems a little odd, we think so too. But we must have
3408 <emphasis>some</emphasis> way to bring such type variables into scope, else we
3409 could not name existentially-bound type variables in subequent type signatures.
3410 </para>
3411 <para>
3412 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
3413 signature is allowed to mention a lexical variable that is not already in
3414 scope.
3415 For example, both <literal>f</literal> and <literal>g</literal> would be
3416 illegal if <literal>a</literal> was not already in scope.
3417 </para>
3418
3419
3420 </sect3>
3421
3422 <!-- ==================== Commented out part about result type signatures
3423
3424 <sect3 id="result-type-sigs">
3425 <title>Result type signatures</title>
3426
3427 <para>
3428 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
3429
3430 <programlisting>
3431 {- f assumes that 'a' is already in scope -}
3432 f x y :: [a] = [x,y,x]
3433
3434 g = \ x :: [Int] -> [3,4]
3435
3436 h :: forall a. [a] -> a
3437 h xs = case xs of
3438 (y:ys) :: a -> y
3439 </programlisting>
3440 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
3441 the result of the function. Similarly, the body of the lambda in the RHS of
3442 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
3443 alternative in <literal>h</literal> is <literal>a</literal>.
3444 </para>
3445 <para> A result type signature never brings new type variables into scope.</para>
3446 <para>
3447 There are a couple of syntactic wrinkles. First, notice that all three
3448 examples would parse quite differently with parentheses:
3449 <programlisting>
3450 {- f assumes that 'a' is already in scope -}
3451 f x (y :: [a]) = [x,y,x]
3452
3453 g = \ (x :: [Int]) -> [3,4]
3454
3455 h :: forall a. [a] -> a
3456 h xs = case xs of
3457 ((y:ys) :: a) -> y
3458 </programlisting>
3459 Now the signature is on the <emphasis>pattern</emphasis>; and
3460 <literal>h</literal> would certainly be ill-typed (since the pattern
3461 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
3462
3463 Second, to avoid ambiguity, the type after the &ldquo;<literal>::</literal>&rdquo; in a result
3464 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
3465 token or a parenthesised type of some sort). To see why,
3466 consider how one would parse this:
3467 <programlisting>
3468 \ x :: a -> b -> x
3469 </programlisting>
3470 </para>
3471 </sect3>
3472
3473 -->
3474
3475 <sect3 id="cls-inst-scoped-tyvars">
3476 <title>Class and instance declarations</title>
3477 <para>
3478
3479 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
3480 scope over the methods defined in the <literal>where</literal> part. For example:
3481
3482
3483 <programlisting>
3484 class C a where
3485 op :: [a] -> a
3486
3487 op xs = let ys::[a]
3488 ys = reverse xs
3489 in
3490 head ys
3491 </programlisting>
3492 </para>
3493 </sect3>
3494
3495 </sect2>
3496
3497 <sect2 id="deriving-typeable">
3498 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
3499
3500 <para>
3501 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3502 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3503 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3504 classes <literal>Eq</literal>, <literal>Ord</literal>,
3505 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3506 </para>
3507 <para>
3508 GHC extends this list with two more classes that may be automatically derived
3509 (provided the <option>-fglasgow-exts</option> flag is specified):
3510 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
3511 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively, and the
3512 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3513 </para>
3514 <para>An instance of <literal>Typeable</literal> can only be derived if the
3515 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3516 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3517 described in
3518 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3519 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3520 </ulink>.
3521 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3522 are used, and only <literal>Typeable1</literal> up to
3523 <literal>Typeable7</literal> are provided in the library.)
3524 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3525 class, whose kind suits that of the data type constructor, and
3526 then writing the data type instance by hand.
3527 </para>
3528 </sect2>
3529
3530 <sect2 id="newtype-deriving">
3531 <title>Generalised derived instances for newtypes</title>
3532
3533 <para>
3534 When you define an abstract type using <literal>newtype</literal>, you may want
3535 the new type to inherit some instances from its representation. In
3536 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3537 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3538 other classes you have to write an explicit instance declaration. For
3539 example, if you define
3540
3541 <programlisting>
3542 newtype Dollars = Dollars Int
3543 </programlisting>
3544
3545 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3546 explicitly define an instance of <literal>Num</literal>:
3547
3548 <programlisting>
3549 instance Num Dollars where
3550 Dollars a + Dollars b = Dollars (a+b)
3551 ...
3552 </programlisting>
3553 All the instance does is apply and remove the <literal>newtype</literal>
3554 constructor. It is particularly galling that, since the constructor
3555 doesn't appear at run-time, this instance declaration defines a
3556 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3557 dictionary, only slower!
3558 </para>
3559
3560
3561 <sect3> <title> Generalising the deriving clause </title>
3562 <para>
3563 GHC now permits such instances to be derived instead, so one can write
3564 <programlisting>
3565 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3566 </programlisting>
3567
3568 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3569 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3570 derives an instance declaration of the form
3571
3572 <programlisting>
3573 instance Num Int => Num Dollars
3574 </programlisting>
3575
3576 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3577 </para>
3578 <para>
3579
3580 We can also derive instances of constructor classes in a similar
3581 way. For example, suppose we have implemented state and failure monad
3582 transformers, such that
3583
3584 <programlisting>
3585 instance Monad m => Monad (State s m)
3586 instance Monad m => Monad (Failure m)
3587 </programlisting>
3588 In Haskell 98, we can define a parsing monad by
3589 <programlisting>
3590 type Parser tok m a = State [tok] (Failure m) a
3591 </programlisting>
3592
3593 which is automatically a monad thanks to the instance declarations
3594 above. With the extension, we can make the parser type abstract,
3595 without needing to write an instance of class <literal>Monad</literal>, via
3596
3597 <programlisting>
3598 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3599 deriving Monad
3600 </programlisting>
3601 In this case the derived instance declaration is of the form
3602 <programlisting>
3603 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3604 </programlisting>
3605
3606 Notice that, since <literal>Monad</literal> is a constructor class, the
3607 instance is a <emphasis>partial application</emphasis> of the new type, not the
3608 entire left hand side. We can imagine that the type declaration is
3609 ``eta-converted'' to generate the context of the instance
3610 declaration.
3611 </para>
3612 <para>
3613
3614 We can even derive instances of multi-parameter classes, provided the
3615 newtype is the last class parameter. In this case, a ``partial
3616 application'' of the class appears in the <literal>deriving</literal>
3617 clause. For example, given the class
3618
3619 <programlisting>
3620 class StateMonad s m | m -> s where ...
3621 instance Monad m => StateMonad s (State s m) where ...
3622 </programlisting>
3623 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3624 <programlisting>
3625 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3626 deriving (Monad, StateMonad [tok])
3627 </programlisting>
3628
3629 The derived instance is obtained by completing the application of the
3630 class to the new type:
3631
3632 <programlisting>
3633 instance StateMonad [tok] (State [tok] (Failure m)) =>
3634 StateMonad [tok] (Parser tok m)
3635 </programlisting>
3636 </para>
3637 <para>
3638
3639 As a result of this extension, all derived instances in newtype
3640 declarations are treated uniformly (and implemented just by reusing
3641 the dictionary for the representation type), <emphasis>except</emphasis>
3642 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3643 the newtype and its representation.
3644 </para>
3645 </sect3>
3646
3647 <sect3> <title> A more precise specification </title>
3648 <para>
3649 Derived instance declarations are constructed as follows. Consider the
3650 declaration (after expansion of any type synonyms)
3651
3652 <programlisting>
3653 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3654 </programlisting>
3655
3656 where
3657 <itemizedlist>
3658 <listitem><para>
3659 The <literal>ci</literal> are partial applications of
3660 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3661 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3662 </para></listitem>
3663 <listitem><para>
3664 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3665 </para></listitem>
3666 <listitem><para>
3667 The type <literal>t</literal> is an arbitrary type.
3668 </para></listitem>
3669 <listitem><para>
3670 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3671 nor in the <literal>ci</literal>, and
3672 </para></listitem>
3673 <listitem><para>
3674 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3675 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3676 should not "look through" the type or its constructor. You can still
3677 derive these classes for a newtype, but it happens in the usual way, not
3678 via this new mechanism.
3679 </para></listitem>
3680 </itemizedlist>
3681 Then, for each <literal>ci</literal>, the derived instance
3682 declaration is:
3683 <programlisting>
3684 instance ci t => ci (T v1...vk)
3685 </programlisting>
3686 As an example which does <emphasis>not</emphasis> work, consider
3687 <programlisting>
3688 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3689 </programlisting>
3690 Here we cannot derive the instance
3691 <programlisting>
3692 instance Monad (State s m) => Monad (NonMonad m)
3693 </programlisting>
3694
3695 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3696 and so cannot be "eta-converted" away. It is a good thing that this
3697 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3698 not, in fact, a monad --- for the same reason. Try defining
3699 <literal>>>=</literal> with the correct type: you won't be able to.
3700 </para>
3701 <para>
3702
3703 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3704 important, since we can only derive instances for the last one. If the
3705 <literal>StateMonad</literal> class above were instead defined as
3706
3707 <programlisting>
3708 class StateMonad m s | m -> s where ...
3709 </programlisting>
3710
3711 then we would not have been able to derive an instance for the
3712 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3713 classes usually have one "main" parameter for which deriving new
3714 instances is most interesting.
3715 </para>
3716 <para>Lastly, all of this applies only for classes other than
3717 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3718 and <literal>Data</literal>, for which the built-in derivation applies (section
3719 4.3.3. of the Haskell Report).
3720 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3721 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3722 the standard method is used or the one described here.)
3723 </para>
3724 </sect3>
3725
3726 </sect2>
3727
3728 <sect2 id="stand-alone-deriving">
3729 <title>Stand-alone deriving declarations</title>
3730
3731 <para>
3732 GHC now allows stand-alone <literal>deriving</literal> declarations:
3733 </para>
3734
3735 <programlisting>
3736 data Foo = Bar Int | Baz String
3737
3738 deriving Eq for Foo
3739 </programlisting>
3740
3741 <para>Deriving instances of multi-parameter type classes for newtypes is
3742 also allowed:</para>
3743
3744 <programlisting>
3745 newtype Foo a = MkFoo (State Int a)
3746
3747 deriving (MonadState Int) for Foo
3748 </programlisting>
3749
3750 <para>
3751 </para>
3752
3753 </sect2>
3754
3755 <sect2 id="typing-binds">
3756 <title>Generalised typing of mutually recursive bindings</title>
3757
3758 <para>
3759 The Haskell Report specifies that a group of bindings (at top level, or in a
3760 <literal>let</literal> or <literal>where</literal>) should be sorted into
3761 strongly-connected components, and then type-checked in dependency order
3762 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
3763 Report, Section 4.5.1</ulink>).
3764 As each group is type-checked, any binders of the group that
3765 have
3766 an explicit type signature are put in the type environment with the specified
3767 polymorphic type,
3768 and all others are monomorphic until the group is generalised
3769 (<ulink url="http://haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
3770 </para>
3771
3772 <para>Following a suggestion of Mark Jones, in his paper
3773 <ulink url="http://www.cse.ogi.edu/~mpj/thih/">Typing Haskell in
3774 Haskell</ulink>,
3775 GHC implements a more general scheme. If <option>-fglasgow-exts</option> is
3776 specified:
3777 <emphasis>the dependency analysis ignores references to variables that have an explicit
3778 type signature</emphasis>.
3779 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
3780 typecheck. For example, consider:
3781 <programlisting>
3782 f :: Eq a =&gt; a -> Bool
3783 f x = (x == x) || g True || g "Yes"
3784
3785 g y = (y &lt;= y) || f True
3786 </programlisting>
3787 This is rejected by Haskell 98, but under Jones's scheme the definition for
3788 <literal>g</literal> is typechecked first, separately from that for
3789 <literal>f</literal>,
3790 because the reference to <literal>f</literal> in <literal>g</literal>'s right
3791 hand side is ingored by the dependency analysis. Then <literal>g</literal>'s
3792 type is generalised, to get
3793 <programlisting>
3794 g :: Ord a =&gt; a -> Bool
3795 </programlisting>
3796 Now, the defintion for <literal>f</literal> is typechecked, with this type for
3797 <literal>g</literal> in the type environment.
3798 </para>
3799
3800 <para>
3801 The same refined dependency analysis also allows the type signatures of
3802 mutually-recursive functions to have different contexts, something that is illegal in
3803 Haskell 98 (Section 4.5.2, last sentence). With
3804 <option>-fglasgow-exts</option>
3805 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
3806 type signatures; in practice this means that only variables bound by the same
3807 pattern binding must have the same context. For example, this is fine:
3808 <programlisting>
3809 f :: Eq a =&gt; a -> Bool
3810 f x = (x == x) || g True
3811
3812 g :: Ord a =&gt; a -> Bool
3813 g y = (y &lt;= y) || f True
3814 </programlisting>
3815 </para>
3816 </sect2>
3817
3818 </sect1>
3819 <!-- ==================== End of type system extensions ================= -->
3820
3821 <!-- ====================== Generalised algebraic data types ======================= -->
3822
3823 <sect1 id="gadt">
3824 <title>Generalised Algebraic Data Types (GADTs)</title>
3825
3826 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types by allowing you
3827 to give the type signatures of constructors explicitly. For example:
3828 <programlisting>
3829 data Term a where
3830 Lit :: Int -> Term Int
3831 Succ :: Term Int -> Term Int
3832 IsZero :: Term Int -> Term Bool
3833 If :: Term Bool -> Term a -> Term a -> Term a
3834 Pair :: Term a -> Term b -> Term (a,b)
3835 </programlisting>
3836 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
3837 case with ordinary vanilla data types. Now we can write a well-typed <literal>eval</literal> function
3838 for these <literal>Terms</literal>:
3839 <programlisting>
3840 eval :: Term a -> a
3841 eval (Lit i) = i
3842 eval (Succ t) = 1 + eval t
3843 eval (IsZero t) = eval t == 0
3844 eval (If b e1 e2) = if eval b then eval e1 else eval e2
3845 eval (Pair e1 e2) = (eval e1, eval e2)
3846 </programlisting>
3847 These and many other examples are given in papers by Hongwei Xi, and
3848 Tim Sheard. There is a longer introduction
3849 <ulink url="http://haskell.org/haskellwiki/GADT">on the wiki</ulink>,
3850 and Ralf Hinze's
3851 <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
3852 may use different notation to that implemented in GHC.
3853 </para>
3854 <para>
3855 The rest of this section outlines the extensions to GHC that support GADTs.
3856 It is far from comprehensive, but the design closely follows that described in
3857 the paper <ulink
3858 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/index.htm">Simple
3859 unification-based type inference for GADTs</ulink>,
3860 which appeared in ICFP 2006.
3861 <itemizedlist>
3862 <listitem><para>
3863 Data type declarations have a 'where' form, as exemplified above. The type signature of
3864 each constructor is independent, and is implicitly universally quantified as usual. Unlike a normal
3865 Haskell data type declaration, the type variable(s) in the "<literal>data Term a where</literal>" header
3866 have no scope. Indeed, one can write a kind signature instead:
3867 <programlisting>
3868 data Term :: * -> * where ...
3869 </programlisting>
3870 or even a mixture of the two:
3871 <programlisting>
3872 data Foo a :: (* -> *) -> * where ...
3873 </programlisting>
3874 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
3875 like this:
3876 <programlisting>
3877 data Foo a (b :: * -> *) where ...
3878 </programlisting>
3879 </para></listitem>
3880
3881 <listitem><para>
3882 There are no restrictions on the type of the data constructor, except that the result
3883 type must begin with the type constructor being defined. For example, in the <literal>Term</literal> data
3884 type above, the type of each constructor must end with <literal> ... -> Term ...</literal>.
3885 </para></listitem>
3886
3887 <listitem><para>
3888 You can use record syntax on a GADT-style data type declaration:
3889
3890 <programlisting>
3891 data Term a where
3892 Lit { val :: Int } :: Term Int
3893 Succ { num :: Term Int } :: Term Int
3894 Pred { num :: Term Int } :: Term Int
3895 IsZero { arg :: Term Int } :: Term Bool
3896 Pair { arg1 :: Term a
3897 , arg2 :: Term b
3898 } :: Term (a,b)
3899 If { cnd :: Term Bool
3900 , tru :: Term a
3901 , fls :: Term a
3902 } :: Term a
3903 </programlisting>
3904 For every constructor that has a field <literal>f</literal>, (a) the type of
3905 field <literal>f</literal> must be the same; and (b) the
3906 result type of the constructor must be the same; both modulo alpha conversion.
3907 Hence, in our example, we cannot merge the <literal>num</literal> and <literal>arg</literal>
3908 fields above into a
3909 single name. Although their field types are both <literal>Term Int</literal>,
3910 their selector functions actually have different types:
3911
3912 <programlisting>
3913 num :: Term Int -> Term Int
3914 arg :: Term Bool -> Term Int
3915 </programlisting>
3916
3917 At the moment, record updates are not yet possible with GADT, so support is
3918 limited to record construction, selection and pattern matching:
3919
3920 <programlisting>
3921 someTerm :: Term Bool
3922 someTerm = IsZero { arg = Succ { num = Lit { val = 0 } } }
3923
3924 eval :: Term a -> a
3925 eval Lit { val = i } = i
3926 eval Succ { num = t } = eval t + 1
3927 eval Pred { num = t } = eval t - 1
3928 eval IsZero { arg = t } = eval t == 0
3929 eval Pair { arg1 = t1, arg2 = t2 } = (eval t1, eval t2)
3930 eval t@If{} = if eval (cnd t) then eval (tru t) else eval (fls t)
3931 </programlisting>
3932
3933 </para></listitem>
3934
3935 <listitem><para>
3936 You can use strictness annotations, in the obvious places
3937 in the constructor type:
3938 <programlisting>
3939 data Term a where
3940 Lit :: !Int -> Term Int
3941 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
3942 Pair :: Term a -> Term b -> Term (a,b)
3943 </programlisting>
3944 </para></listitem>
3945
3946 <listitem><para>
3947 You can use a <literal>deriving</literal> clause on a GADT-style data type
3948 declaration, but only if the data type could also have been declared in
3949 Haskell-98 syntax. For example, these two declarations are equivalent
3950 <programlisting>
3951 data Maybe1 a where {
3952 Nothing1 :: Maybe1 a ;
3953 Just1 :: a -> Maybe1 a
3954 } deriving( Eq, Ord )
3955
3956 data Maybe2 a = Nothing2 | Just2 a
3957 deriving( Eq, Ord )
3958 </programlisting>
3959 This simply allows you to declare a vanilla Haskell-98 data type using the
3960 <literal>where</literal> form without losing the <literal>deriving</literal> clause.
3961 </para></listitem>
3962
3963 <listitem><para>
3964 Pattern matching causes type refinement. For example, in the right hand side of the equation
3965 <programlisting>
3966 eval :: Term a -> a
3967 eval (Lit i) = ...
3968 </programlisting>
3969 the type <literal>a</literal> is refined to <literal>Int</literal>. (That's the whole point!)
3970 A precise specification of the type rules is beyond what this user manual aspires to, but there is a paper
3971 about the ideas: "Wobbly types: practical type inference for generalised algebraic data types", on Simon PJ's home page.</para>
3972
3973 <para> The general principle is this: <emphasis>type refinement is only carried out based on user-supplied type annotations</emphasis>.
3974 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens, and lots of obscure error messages will
3975 occur. However, the refinement is quite general. For example, if we had:
3976 <programlisting>
3977 eval :: Term a -> a -> a
3978 eval (Lit i) j = i+j
3979 </programlisting>
3980 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
3981 of the constructor <literal>Lit</literal>, and that refinement also applies to the type of <literal>j</literal>, and
3982 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
3983 </para>
3984 </listitem>
3985 </itemizedlist>
3986 </para>
3987
3988 <para>Notice that GADTs generalise existential types. For example, these two declarations are equivalent:
3989 <programlisting>
3990 data T a = forall b. MkT b (b->a)
3991 data T' a where { MKT :: b -> (b->a) -> T' a }
3992 </programlisting>
3993 </para>
3994 </sect1>
3995
3996 <!-- ====================== End of Generalised algebraic data types ======================= -->
3997
3998 <!-- ====================== TEMPLATE HASKELL ======================= -->
3999
4000 <sect1 id="template-haskell">
4001 <title>Template Haskell</title>
4002
4003 <para>Template Haskell allows you to do compile-time meta-programming in
4004 Haskell.
4005 The background to
4006 the main technical innovations is discussed in "<ulink
4007 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
4008 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
4009 </para>
4010 <para>
4011 There is a Wiki page about
4012 Template Haskell at <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
4013 http://www.haskell.org/th/</ulink>, and that is the best place to look for
4014 further details.
4015 You may also
4016 consult the <ulink
4017 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
4018 Haskell library reference material</ulink>
4019 (search for the type ExpQ).
4020 [Temporary: many changes to the original design are described in
4021 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
4022 Not all of these changes are in GHC 6.6.]
4023 </para>
4024
4025 <para> The first example from that paper is set out below as a worked example to help get you started.
4026 </para>
4027
4028 <para>
4029 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
4030 Tim Sheard is going to expand it.)
4031 </para>
4032
4033 <sect2>
4034 <title>Syntax</title>
4035
4036 <para> Template Haskell has the following new syntactic
4037 constructions. You need to use the flag
4038 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
4039 </indexterm>to switch these syntactic extensions on
4040 (<option>-fth</option> is no longer implied by
4041 <option>-fglasgow-exts</option>).</para>
4042
4043 <itemizedlist>
4044 <listitem><para>
4045 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
4046 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
4047 There must be no space between the "$" and the identifier or parenthesis. This use
4048 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
4049 of "." as an infix operator. If you want the infix operator, put spaces around it.
4050 </para>
4051 <para> A splice can occur in place of
4052 <itemizedlist>
4053 <listitem><para> an expression; the spliced expression must
4054 have type <literal>Q Exp</literal></para></listitem>
4055 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
4056 <listitem><para> [Planned, but not implemented yet.] a
4057 type; the spliced expression must have type <literal>Q Typ</literal>.</para></listitem>
4058 </itemizedlist>
4059 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
4060 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
4061 as in the paper.)
4062 </para></listitem>
4063
4064
4065 <listitem><para>
4066 A expression quotation is written in Oxford brackets, thus:
4067 <itemizedlist>
4068 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
4069 the quotation has type <literal>Expr</literal>.</para></listitem>
4070 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
4071 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
4072 <listitem><para> [Planned, but not implemented yet.] <literal>[t| ... |]</literal>, where the "..." is a type;
4073 the quotation has type <literal>Type</literal>.</para></listitem>
4074 </itemizedlist></para></listitem>
4075
4076 <listitem><para>
4077 Reification is written thus:
4078 <itemizedlist>
4079 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
4080 has type <literal>Dec</literal>. </para></listitem>
4081 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
4082 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
4083 <listitem><para> Still to come: fixities </para></listitem>
4084
4085 </itemizedlist></para>
4086 </listitem>
4087
4088
4089 </itemizedlist>
4090 </sect2>
4091
4092 <sect2> <title> Using Template Haskell </title>
4093 <para>
4094 <itemizedlist>
4095 <listitem><para>
4096 The data types and monadic constructor functions for Template Haskell are in the library
4097 <literal>Language.Haskell.THSyntax</literal>.
4098 </para></listitem>
4099
4100 <listitem><para>
4101 You can only run a function at compile time if it is imported from another module. That is,
4102 you can't define a function in a module, and call it from within a splice in the same module.
4103 (It would make sense to do so, but it's hard to implement.)
4104 </para></listitem>
4105
4106 <listitem><para>
4107 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
4108 </para></listitem>
4109 <listitem><para>
4110 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
4111 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
4112 compiles and runs a program, and then looks at the result. So it's important that
4113 the program it compiles produces results whose representations are identical to
4114 those of the compiler itself.
4115 </para></listitem>
4116 </itemizedlist>
4117 </para>
4118 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
4119 or file-at-a-time). There used to be a restriction to the former two, but that restriction