1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They can all be enabled or disabled by commandline flags
7 or language pragmas. By default GHC understands the most recent Haskell
8 version it supports, plus a handful of extensions.
12 Some of the Glasgow extensions serve to give you access to the
13 underlying facilities with which we implement Haskell. Thus, you can
14 get at the Raw Iron, if you are willing to write some non-portable
15 code at a more primitive level. You need not be “stuck”
16 on performance because of the implementation costs of Haskell's
17 “high-level” features—you can always code
18 “under” them. In an extreme case, you can write all your
19 time-critical code in C, and then just glue it together with Haskell!
23 Before you get too carried away working at the lowest level (e.g.,
24 sloshing <literal>MutableByteArray#</literal>s around your
25 program), you may wish to check if there are libraries that provide a
26 “Haskellised veneer” over the features you want. The
27 separate <ulink url="../libraries/index.html">libraries
28 documentation</ulink> describes all the libraries that come with GHC.
31 <!-- LANGUAGE OPTIONS -->
32 <sect1 id="options-language">
33 <title>Language options</title>
35 <indexterm><primary>language</primary><secondary>option</secondary>
37 <indexterm><primary>options</primary><secondary>language</secondary>
39 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
42 <para>The language option flags control what variation of the language are
45 <para>Language options can be controlled in two ways:
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
54 </itemizedlist></para>
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 &what_glasgow_exts_does;
60 Enabling these options is the <emphasis>only</emphasis>
61 effect of <option>-fglasgow-exts</option>.
62 We are trying to move away from this portmanteau flag,
63 and towards enabling features individually.</para>
67 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
68 <sect1 id="primitives">
69 <title>Unboxed types and primitive operations</title>
71 <para>GHC is built on a raft of primitive data types and operations;
72 "primitive" in the sense that they cannot be defined in Haskell itself.
73 While you really can use this stuff to write fast code,
74 we generally find it a lot less painful, and more satisfying in the
75 long run, to use higher-level language features and libraries. With
76 any luck, the code you write will be optimised to the efficient
77 unboxed version in any case. And if it isn't, we'd like to know
80 <para>All these primitive data types and operations are exported by the
81 library <literal>GHC.Prim</literal>, for which there is
82 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
83 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
86 If you want to mention any of the primitive data types or operations in your
87 program, you must first import <literal>GHC.Prim</literal> to bring them
88 into scope. Many of them have names ending in "#", and to mention such
89 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
92 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
93 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
94 we briefly summarise here. </para>
96 <sect2 id="glasgow-unboxed">
101 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
104 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
105 that values of that type are represented by a pointer to a heap
106 object. The representation of a Haskell <literal>Int</literal>, for
107 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
108 type, however, is represented by the value itself, no pointers or heap
109 allocation are involved.
113 Unboxed types correspond to the “raw machine” types you
114 would use in C: <literal>Int#</literal> (long int),
115 <literal>Double#</literal> (double), <literal>Addr#</literal>
116 (void *), etc. The <emphasis>primitive operations</emphasis>
117 (PrimOps) on these types are what you might expect; e.g.,
118 <literal>(+#)</literal> is addition on
119 <literal>Int#</literal>s, and is the machine-addition that we all
120 know and love—usually one instruction.
124 Primitive (unboxed) types cannot be defined in Haskell, and are
125 therefore built into the language and compiler. Primitive types are
126 always unlifted; that is, a value of a primitive type cannot be
127 bottom. We use the convention (but it is only a convention)
128 that primitive types, values, and
129 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
130 For some primitive types we have special syntax for literals, also
131 described in the <link linkend="magic-hash">same section</link>.
135 Primitive values are often represented by a simple bit-pattern, such
136 as <literal>Int#</literal>, <literal>Float#</literal>,
137 <literal>Double#</literal>. But this is not necessarily the case:
138 a primitive value might be represented by a pointer to a
139 heap-allocated object. Examples include
140 <literal>Array#</literal>, the type of primitive arrays. A
141 primitive array is heap-allocated because it is too big a value to fit
142 in a register, and would be too expensive to copy around; in a sense,
143 it is accidental that it is represented by a pointer. If a pointer
144 represents a primitive value, then it really does point to that value:
145 no unevaluated thunks, no indirections…nothing can be at the
146 other end of the pointer than the primitive value.
147 A numerically-intensive program using unboxed types can
148 go a <emphasis>lot</emphasis> faster than its “standard”
149 counterpart—we saw a threefold speedup on one example.
153 There are some restrictions on the use of primitive types:
155 <listitem><para>The main restriction
156 is that you can't pass a primitive value to a polymorphic
157 function or store one in a polymorphic data type. This rules out
158 things like <literal>[Int#]</literal> (i.e. lists of primitive
159 integers). The reason for this restriction is that polymorphic
160 arguments and constructor fields are assumed to be pointers: if an
161 unboxed integer is stored in one of these, the garbage collector would
162 attempt to follow it, leading to unpredictable space leaks. Or a
163 <function>seq</function> operation on the polymorphic component may
164 attempt to dereference the pointer, with disastrous results. Even
165 worse, the unboxed value might be larger than a pointer
166 (<literal>Double#</literal> for instance).
169 <listitem><para> You cannot define a newtype whose representation type
170 (the argument type of the data constructor) is an unboxed type. Thus,
176 <listitem><para> You cannot bind a variable with an unboxed type
177 in a <emphasis>top-level</emphasis> binding.
179 <listitem><para> You cannot bind a variable with an unboxed type
180 in a <emphasis>recursive</emphasis> binding.
182 <listitem><para> You may bind unboxed variables in a (non-recursive,
183 non-top-level) pattern binding, but you must make any such pattern-match
184 strict. For example, rather than:
186 data Foo = Foo Int Int#
188 f x = let (Foo a b, w) = ..rhs.. in ..body..
192 data Foo = Foo Int Int#
194 f x = let !(Foo a b, w) = ..rhs.. in ..body..
196 since <literal>b</literal> has type <literal>Int#</literal>.
204 <sect2 id="unboxed-tuples">
205 <title>Unboxed Tuples
209 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
210 they're available by default with <option>-fglasgow-exts</option>. An
211 unboxed tuple looks like this:
223 where <literal>e_1..e_n</literal> are expressions of any
224 type (primitive or non-primitive). The type of an unboxed tuple looks
229 Unboxed tuples are used for functions that need to return multiple
230 values, but they avoid the heap allocation normally associated with
231 using fully-fledged tuples. When an unboxed tuple is returned, the
232 components are put directly into registers or on the stack; the
233 unboxed tuple itself does not have a composite representation. Many
234 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
236 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
237 tuples to avoid unnecessary allocation during sequences of operations.
241 There are some pretty stringent restrictions on the use of unboxed tuples:
246 Values of unboxed tuple types are subject to the same restrictions as
247 other unboxed types; i.e. they may not be stored in polymorphic data
248 structures or passed to polymorphic functions.
255 No variable can have an unboxed tuple type, nor may a constructor or function
256 argument have an unboxed tuple type. The following are all illegal:
260 data Foo = Foo (# Int, Int #)
262 f :: (# Int, Int #) -> (# Int, Int #)
265 g :: (# Int, Int #) -> Int
268 h x = let y = (# x,x #) in ...
275 The typical use of unboxed tuples is simply to return multiple values,
276 binding those multiple results with a <literal>case</literal> expression, thus:
278 f x y = (# x+1, y-1 #)
279 g x = case f x x of { (# a, b #) -> a + b }
281 You can have an unboxed tuple in a pattern binding, thus
283 f x = let (# p,q #) = h x in ..body..
285 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
286 the resulting binding is lazy like any other Haskell pattern binding. The
287 above example desugars like this:
289 f x = let t = case h x o f{ (# p,q #) -> (p,q)
294 Indeed, the bindings can even be recursive.
301 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
303 <sect1 id="syntax-extns">
304 <title>Syntactic extensions</title>
306 <sect2 id="unicode-syntax">
307 <title>Unicode syntax</title>
309 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
310 enables Unicode characters to be used to stand for certain ASCII
311 character sequences. The following alternatives are provided:</para>
314 <tgroup cols="2" align="left" colsep="1" rowsep="1">
318 <entry>Unicode alternative</entry>
319 <entry>Code point</entry>
325 to find the DocBook entities for these characters, find
326 the Unicode code point (e.g. 0x2237), and grep for it in
327 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
328 your system. Some of these Unicode code points don't have
329 equivalent DocBook entities.
334 <entry><literal>::</literal></entry>
335 <entry>::</entry> <!-- no special char, apparently -->
336 <entry>0x2237</entry>
337 <entry>PROPORTION</entry>
342 <entry><literal>=></literal></entry>
343 <entry>⇒</entry>
344 <entry>0x21D2</entry>
345 <entry>RIGHTWARDS DOUBLE ARROW</entry>
350 <entry><literal>forall</literal></entry>
351 <entry>∀</entry>
352 <entry>0x2200</entry>
353 <entry>FOR ALL</entry>
358 <entry><literal>-></literal></entry>
359 <entry>→</entry>
360 <entry>0x2192</entry>
361 <entry>RIGHTWARDS ARROW</entry>
366 <entry><literal><-</literal></entry>
367 <entry>←</entry>
368 <entry>0x2190</entry>
369 <entry>LEFTWARDS ARROW</entry>
376 <entry>↢</entry>
377 <entry>0x2919</entry>
378 <entry>LEFTWARDS ARROW-TAIL</entry>
385 <entry>↣</entry>
386 <entry>0x291A</entry>
387 <entry>RIGHTWARDS ARROW-TAIL</entry>
393 <entry>-<<</entry>
395 <entry>0x291B</entry>
396 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
402 <entry>>>-</entry>
404 <entry>0x291C</entry>
405 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
412 <entry>★</entry>
413 <entry>0x2605</entry>
414 <entry>BLACK STAR</entry>
422 <sect2 id="magic-hash">
423 <title>The magic hash</title>
424 <para>The language extension <option>-XMagicHash</option> allows "#" as a
425 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
426 a valid type constructor or data constructor.</para>
428 <para>The hash sign does not change sematics at all. We tend to use variable
429 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
430 but there is no requirement to do so; they are just plain ordinary variables.
431 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
432 For example, to bring <literal>Int#</literal> into scope you must
433 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
434 the <option>-XMagicHash</option> extension
435 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
436 that is now in scope.</para>
437 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
439 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
440 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
441 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
442 any Haskell integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
443 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
444 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
445 any non-negative Haskell integer lexeme followed by <literal>##</literal>
446 is a <literal>Word#</literal>. </para> </listitem>
447 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
448 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
453 <!-- ====================== HIERARCHICAL MODULES ======================= -->
456 <sect2 id="hierarchical-modules">
457 <title>Hierarchical Modules</title>
459 <para>GHC supports a small extension to the syntax of module
460 names: a module name is allowed to contain a dot
461 <literal>‘.’</literal>. This is also known as the
462 “hierarchical module namespace” extension, because
463 it extends the normally flat Haskell module namespace into a
464 more flexible hierarchy of modules.</para>
466 <para>This extension has very little impact on the language
467 itself; modules names are <emphasis>always</emphasis> fully
468 qualified, so you can just think of the fully qualified module
469 name as <quote>the module name</quote>. In particular, this
470 means that the full module name must be given after the
471 <literal>module</literal> keyword at the beginning of the
472 module; for example, the module <literal>A.B.C</literal> must
475 <programlisting>module A.B.C</programlisting>
478 <para>It is a common strategy to use the <literal>as</literal>
479 keyword to save some typing when using qualified names with
480 hierarchical modules. For example:</para>
483 import qualified Control.Monad.ST.Strict as ST
486 <para>For details on how GHC searches for source and interface
487 files in the presence of hierarchical modules, see <xref
488 linkend="search-path"/>.</para>
490 <para>GHC comes with a large collection of libraries arranged
491 hierarchically; see the accompanying <ulink
492 url="../libraries/index.html">library
493 documentation</ulink>. More libraries to install are available
495 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
498 <!-- ====================== PATTERN GUARDS ======================= -->
500 <sect2 id="pattern-guards">
501 <title>Pattern guards</title>
504 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
505 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.)
509 Suppose we have an abstract data type of finite maps, with a
513 lookup :: FiniteMap -> Int -> Maybe Int
516 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
517 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
521 clunky env var1 var2 | ok1 && ok2 = val1 + val2
522 | otherwise = var1 + var2
533 The auxiliary functions are
537 maybeToBool :: Maybe a -> Bool
538 maybeToBool (Just x) = True
539 maybeToBool Nothing = False
541 expectJust :: Maybe a -> a
542 expectJust (Just x) = x
543 expectJust Nothing = error "Unexpected Nothing"
547 What is <function>clunky</function> doing? The guard <literal>ok1 &&
548 ok2</literal> checks that both lookups succeed, using
549 <function>maybeToBool</function> to convert the <function>Maybe</function>
550 types to booleans. The (lazily evaluated) <function>expectJust</function>
551 calls extract the values from the results of the lookups, and binds the
552 returned values to <varname>val1</varname> and <varname>val2</varname>
553 respectively. If either lookup fails, then clunky takes the
554 <literal>otherwise</literal> case and returns the sum of its arguments.
558 This is certainly legal Haskell, but it is a tremendously verbose and
559 un-obvious way to achieve the desired effect. Arguably, a more direct way
560 to write clunky would be to use case expressions:
564 clunky env var1 var2 = case lookup env var1 of
566 Just val1 -> case lookup env var2 of
568 Just val2 -> val1 + val2
574 This is a bit shorter, but hardly better. Of course, we can rewrite any set
575 of pattern-matching, guarded equations as case expressions; that is
576 precisely what the compiler does when compiling equations! The reason that
577 Haskell provides guarded equations is because they allow us to write down
578 the cases we want to consider, one at a time, independently of each other.
579 This structure is hidden in the case version. Two of the right-hand sides
580 are really the same (<function>fail</function>), and the whole expression
581 tends to become more and more indented.
585 Here is how I would write clunky:
590 | Just val1 <- lookup env var1
591 , Just val2 <- lookup env var2
593 ...other equations for clunky...
597 The semantics should be clear enough. The qualifiers are matched in order.
598 For a <literal><-</literal> qualifier, which I call a pattern guard, the
599 right hand side is evaluated and matched against the pattern on the left.
600 If the match fails then the whole guard fails and the next equation is
601 tried. If it succeeds, then the appropriate binding takes place, and the
602 next qualifier is matched, in the augmented environment. Unlike list
603 comprehensions, however, the type of the expression to the right of the
604 <literal><-</literal> is the same as the type of the pattern to its
605 left. The bindings introduced by pattern guards scope over all the
606 remaining guard qualifiers, and over the right hand side of the equation.
610 Just as with list comprehensions, boolean expressions can be freely mixed
611 with among the pattern guards. For example:
622 Haskell's current guards therefore emerge as a special case, in which the
623 qualifier list has just one element, a boolean expression.
627 <!-- ===================== View patterns =================== -->
629 <sect2 id="view-patterns">
634 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
635 More information and examples of view patterns can be found on the
636 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
641 View patterns are somewhat like pattern guards that can be nested inside
642 of other patterns. They are a convenient way of pattern-matching
643 against values of abstract types. For example, in a programming language
644 implementation, we might represent the syntax of the types of the
653 view :: Type -> TypeView
655 -- additional operations for constructing Typ's ...
658 The representation of Typ is held abstract, permitting implementations
659 to use a fancy representation (e.g., hash-consing to manage sharing).
661 Without view patterns, using this signature a little inconvenient:
663 size :: Typ -> Integer
664 size t = case view t of
666 Arrow t1 t2 -> size t1 + size t2
669 It is necessary to iterate the case, rather than using an equational
670 function definition. And the situation is even worse when the matching
671 against <literal>t</literal> is buried deep inside another pattern.
675 View patterns permit calling the view function inside the pattern and
676 matching against the result:
678 size (view -> Unit) = 1
679 size (view -> Arrow t1 t2) = size t1 + size t2
682 That is, we add a new form of pattern, written
683 <replaceable>expression</replaceable> <literal>-></literal>
684 <replaceable>pattern</replaceable> that means "apply the expression to
685 whatever we're trying to match against, and then match the result of
686 that application against the pattern". The expression can be any Haskell
687 expression of function type, and view patterns can be used wherever
692 The semantics of a pattern <literal>(</literal>
693 <replaceable>exp</replaceable> <literal>-></literal>
694 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
700 <para>The variables bound by the view pattern are the variables bound by
701 <replaceable>pat</replaceable>.
705 Any variables in <replaceable>exp</replaceable> are bound occurrences,
706 but variables bound "to the left" in a pattern are in scope. This
707 feature permits, for example, one argument to a function to be used in
708 the view of another argument. For example, the function
709 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
710 written using view patterns as follows:
713 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
714 ...other equations for clunky...
719 More precisely, the scoping rules are:
723 In a single pattern, variables bound by patterns to the left of a view
724 pattern expression are in scope. For example:
726 example :: Maybe ((String -> Integer,Integer), String) -> Bool
727 example Just ((f,_), f -> 4) = True
730 Additionally, in function definitions, variables bound by matching earlier curried
731 arguments may be used in view pattern expressions in later arguments:
733 example :: (String -> Integer) -> String -> Bool
734 example f (f -> 4) = True
736 That is, the scoping is the same as it would be if the curried arguments
737 were collected into a tuple.
743 In mutually recursive bindings, such as <literal>let</literal>,
744 <literal>where</literal>, or the top level, view patterns in one
745 declaration may not mention variables bound by other declarations. That
746 is, each declaration must be self-contained. For example, the following
747 program is not allowed:
753 (For some amplification on this design choice see
754 <ulink url="http://hackage.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
763 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
764 <replaceable>T1</replaceable> <literal>-></literal>
765 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
766 a <replaceable>T2</replaceable>, then the whole view pattern matches a
767 <replaceable>T1</replaceable>.
770 <listitem><para> Matching: To the equations in Section 3.17.3 of the
771 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
772 Report</ulink>, add the following:
774 case v of { (e -> p) -> e1 ; _ -> e2 }
776 case (e v) of { p -> e1 ; _ -> e2 }
778 That is, to match a variable <replaceable>v</replaceable> against a pattern
779 <literal>(</literal> <replaceable>exp</replaceable>
780 <literal>-></literal> <replaceable>pat</replaceable>
781 <literal>)</literal>, evaluate <literal>(</literal>
782 <replaceable>exp</replaceable> <replaceable> v</replaceable>
783 <literal>)</literal> and match the result against
784 <replaceable>pat</replaceable>.
787 <listitem><para> Efficiency: When the same view function is applied in
788 multiple branches of a function definition or a case expression (e.g.,
789 in <literal>size</literal> above), GHC makes an attempt to collect these
790 applications into a single nested case expression, so that the view
791 function is only applied once. Pattern compilation in GHC follows the
792 matrix algorithm described in Chapter 4 of <ulink
793 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
794 Implementation of Functional Programming Languages</ulink>. When the
795 top rows of the first column of a matrix are all view patterns with the
796 "same" expression, these patterns are transformed into a single nested
797 case. This includes, for example, adjacent view patterns that line up
800 f ((view -> A, p1), p2) = e1
801 f ((view -> B, p3), p4) = e2
805 <para> The current notion of when two view pattern expressions are "the
806 same" is very restricted: it is not even full syntactic equality.
807 However, it does include variables, literals, applications, and tuples;
808 e.g., two instances of <literal>view ("hi", "there")</literal> will be
809 collected. However, the current implementation does not compare up to
810 alpha-equivalence, so two instances of <literal>(x, view x ->
811 y)</literal> will not be coalesced.
821 <!-- ===================== n+k patterns =================== -->
823 <sect2 id="n-k-patterns">
824 <title>n+k patterns</title>
825 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
828 <literal>n+k</literal> pattern support is enabled by default. To disable
829 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
834 <!-- ===================== Recursive do-notation =================== -->
836 <sect2 id="recursive-do-notation">
837 <title>The recursive do-notation
841 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
842 that is, the variables bound in a do-expression are visible only in the textually following
843 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
844 group. It turns out that several applications can benefit from recursive bindings in
845 the do-notation. The <option>-XDoRec</option> flag provides the necessary syntactic support.
848 Here is a simple (albeit contrived) example:
850 {-# LANGUAGE DoRec #-}
851 justOnes = do { rec { xs <- Just (1:xs) }
852 ; return (map negate xs) }
854 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
857 The background and motivation for recursive do-notation is described in
858 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
859 by Levent Erkok, John Launchbury,
860 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
861 The theory behind monadic value recursion is explained further in Erkok's thesis
862 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.
863 However, note that GHC uses a different syntax than the one described in these documents.
867 <title>Details of recursive do-notation</title>
869 The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
870 the LANGUAGE pragma <option>DoRec</option>. It introduces the single new keyword "<literal>rec</literal>",
871 which wraps a mutually-recursive group of monadic statements,
872 producing a single statement.
874 <para>Similar to a <literal>let</literal>
875 statement, the variables bound in the <literal>rec</literal> are
876 visible throughout the <literal>rec</literal> group, and below it.
879 do { a <- getChar do { a <- getChar
880 ; let { r1 = f a r2 ; rec { r1 <- f a r2
881 ; r2 = g r1 } ; r2 <- g r1 }
882 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
884 In both cases, <literal>r1</literal> and <literal>r2</literal> are
885 available both throughout the <literal>let</literal> or <literal>rec</literal> block, and
886 in the statements that follow it. The difference is that <literal>let</literal> is non-monadic,
887 while <literal>rec</literal> is monadic. (In Haskell <literal>let</literal> is
888 really <literal>letrec</literal>, of course.)
891 The static and dynamic semantics of <literal>rec</literal> can be described as follows:
895 similar to let-bindings, the <literal>rec</literal> is broken into
896 minimal recursive groups, a process known as <emphasis>segmentation</emphasis>.
899 rec { a <- getChar ===> a <- getChar
900 ; b <- f a c rec { b <- f a c
901 ; c <- f b a ; c <- f b a }
902 ; putChar c } putChar c
904 The details of segmentation are described in Section 3.2 of
905 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>.
906 Segmentation improves polymorphism, reduces the size of the recursive "knot", and, as the paper
907 describes, also has a semantic effect (unless the monad satisfies the right-shrinking law).
910 Then each resulting <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal>.
911 For example, the <literal>rec</literal> group in the preceding example is desugared like this:
913 rec { b <- f a c ===> (b,c) <- mfix (\~(b,c) -> do { b <- f a c
914 ; c <- f b a } ; c <- f b a
917 In general, the statment <literal>rec <replaceable>ss</replaceable></literal>
918 is desugared to the statement
920 <replaceable>vs</replaceable> <- mfix (\~<replaceable>vs</replaceable> -> do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
922 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
924 The original <literal>rec</literal> typechecks exactly
925 when the above desugared version would do so. For example, this means that
926 the variables <replaceable>vs</replaceable> are all monomorphic in the statements
927 following the <literal>rec</literal>, because they are bound by a lambda.
930 The <literal>mfix</literal> function is defined in the <literal>MonadFix</literal>
931 class, in <literal>Control.Monad.Fix</literal>, thus:
933 class Monad m => MonadFix m where
934 mfix :: (a -> m a) -> m a
941 Here are some other important points in using the recursive-do notation:
944 It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
945 <literal>-fglasgow-exts</literal>.
949 If recursive bindings are required for a monad,
950 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
954 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
955 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
956 for Haskell's internal state monad (strict and lazy, respectively).
960 Like <literal>let</literal> and <literal>where</literal> bindings,
961 name shadowing is not allowed within a <literal>rec</literal>;
962 that is, all the names bound in a single <literal>rec</literal> must
963 be distinct (Section 3.3 of the paper).
966 It supports rebindable syntax (see <xref linkend="rebindable-syntax"/>).
972 <sect3 id="mdo-notation"> <title> Mdo-notation (deprecated) </title>
974 <para> GHC used to support the flag <option>-XRecursiveDo</option>,
975 which enabled the keyword <literal>mdo</literal>, precisely as described in
976 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
977 but this is now deprecated. Instead of <literal>mdo { Q; e }</literal>, write
978 <literal>do { rec Q; e }</literal>.
981 Historical note: The old implementation of the mdo-notation (and most
982 of the existing documents) used the name
983 <literal>MonadRec</literal> for the class and the corresponding library.
984 This name is not supported by GHC.
991 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
993 <sect2 id="parallel-list-comprehensions">
994 <title>Parallel List Comprehensions</title>
995 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
997 <indexterm><primary>parallel list comprehensions</primary>
1000 <para>Parallel list comprehensions are a natural extension to list
1001 comprehensions. List comprehensions can be thought of as a nice
1002 syntax for writing maps and filters. Parallel comprehensions
1003 extend this to include the zipWith family.</para>
1005 <para>A parallel list comprehension has multiple independent
1006 branches of qualifier lists, each separated by a `|' symbol. For
1007 example, the following zips together two lists:</para>
1010 [ (x, y) | x <- xs | y <- ys ]
1013 <para>The behavior of parallel list comprehensions follows that of
1014 zip, in that the resulting list will have the same length as the
1015 shortest branch.</para>
1017 <para>We can define parallel list comprehensions by translation to
1018 regular comprehensions. Here's the basic idea:</para>
1020 <para>Given a parallel comprehension of the form: </para>
1023 [ e | p1 <- e11, p2 <- e12, ...
1024 | q1 <- e21, q2 <- e22, ...
1029 <para>This will be translated to: </para>
1032 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1033 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1038 <para>where `zipN' is the appropriate zip for the given number of
1043 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1045 <sect2 id="generalised-list-comprehensions">
1046 <title>Generalised (SQL-Like) List Comprehensions</title>
1047 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1049 <indexterm><primary>extended list comprehensions</primary>
1051 <indexterm><primary>group</primary></indexterm>
1052 <indexterm><primary>sql</primary></indexterm>
1055 <para>Generalised list comprehensions are a further enhancement to the
1056 list comprehension syntactic sugar to allow operations such as sorting
1057 and grouping which are familiar from SQL. They are fully described in the
1058 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1059 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1060 except that the syntax we use differs slightly from the paper.</para>
1061 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1062 <para>Here is an example:
1064 employees = [ ("Simon", "MS", 80)
1065 , ("Erik", "MS", 100)
1066 , ("Phil", "Ed", 40)
1067 , ("Gordon", "Ed", 45)
1068 , ("Paul", "Yale", 60)]
1070 output = [ (the dept, sum salary)
1071 | (name, dept, salary) <- employees
1072 , then group by dept
1073 , then sortWith by (sum salary)
1076 In this example, the list <literal>output</literal> would take on
1080 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1083 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1084 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1085 function that is exported by <literal>GHC.Exts</literal>.)</para>
1087 <para>There are five new forms of comprehension qualifier,
1088 all introduced by the (existing) keyword <literal>then</literal>:
1096 This statement requires that <literal>f</literal> have the type <literal>
1097 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1098 motivating example, as this form is used to apply <literal>take 5</literal>.
1109 This form is similar to the previous one, but allows you to create a function
1110 which will be passed as the first argument to f. As a consequence f must have
1111 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1112 from the type, this function lets f "project out" some information
1113 from the elements of the list it is transforming.</para>
1115 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1116 is supplied with a function that lets it find out the <literal>sum salary</literal>
1117 for any item in the list comprehension it transforms.</para>
1125 then group by e using f
1128 <para>This is the most general of the grouping-type statements. In this form,
1129 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1130 As with the <literal>then f by e</literal> case above, the first argument
1131 is a function supplied to f by the compiler which lets it compute e on every
1132 element of the list being transformed. However, unlike the non-grouping case,
1133 f additionally partitions the list into a number of sublists: this means that
1134 at every point after this statement, binders occurring before it in the comprehension
1135 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1136 this, let's look at an example:</para>
1139 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1140 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1141 groupRuns f = groupBy (\x y -> f x == f y)
1143 output = [ (the x, y)
1144 | x <- ([1..3] ++ [1..2])
1146 , then group by x using groupRuns ]
1149 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1152 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1155 <para>Note that we have used the <literal>the</literal> function to change the type
1156 of x from a list to its original numeric type. The variable y, in contrast, is left
1157 unchanged from the list form introduced by the grouping.</para>
1167 <para>This form of grouping is essentially the same as the one described above. However,
1168 since no function to use for the grouping has been supplied it will fall back on the
1169 <literal>groupWith</literal> function defined in
1170 <ulink url="&libraryBaseLocation;/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1171 is the form of the group statement that we made use of in the opening example.</para>
1182 <para>With this form of the group statement, f is required to simply have the type
1183 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1184 comprehension so far directly. An example of this form is as follows:</para>
1190 , then group using inits]
1193 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1196 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1204 <!-- ===================== MONAD COMPREHENSIONS ===================== -->
1206 <sect2 id="monad-comprehensions">
1207 <title>Monad comprehensions</title>
1208 <indexterm><primary>monad comprehensions</primary></indexterm>
1211 Monad comprehesions generalise the list comprehension notation to work
1215 <para>Monad comprehensions support:</para>
1224 [ x + y | x <- Just 1, y <- Just 2 ]
1228 Bindings are translated with the <literal>(>>=)</literal> and
1229 <literal>return</literal> functions to the usual do-notation:
1245 [ x | x <- [1..10], x <= 5 ]
1249 Guards are translated with the <literal>guard</literal> function,
1250 which requires a <literal>MonadPlus</literal> instance:
1262 Transform statements (as with <literal>-XTransformListComp</literal>):
1266 [ x+y | x <- [1..10], y <- [1..x], then take 2 ]
1274 do (x,y) <- take 2 (do x <- [1..10]
1283 Group statements (as with <literal>-XTransformListComp</literal>):
1287 [ x | x <- [1,1,2,2,3], then group by x ]
1288 [ x | x <- [1,1,2,2,3], then group by x using GHC.Exts.groupWith ]
1289 [ x | x <- [1,1,2,2,3], then group using myGroup ]
1293 The basic <literal>then group by e</literal> statement is
1294 translated using the <literal>mgroupWith</literal> function, which
1295 requires a <literal>MonadGroup</literal> instance, defined in
1296 <ulink url="&libraryBaseLocation;/Control-Monad-Group.html"><literal>Control.Monad.Group</literal></ulink>:
1300 do x <- mgroupWith (do x <- [1,1,2,2,3]
1306 Note that the type of <literal>x</literal> is changed by the
1311 The grouping function can also be defined with the
1312 <literal>using</literal> keyword.
1318 Parallel statements (as with <literal>-XParallelListComp</literal>):
1322 [ (x+y) | x <- [1..10]
1328 Parallel statements are translated using the
1329 <literal>mzip</literal> function, which requires a
1330 <literal>MonadZip</literal> instance defined in
1331 <ulink url="&libraryBaseLocation;/Control-Monad-Zip.html"><literal>Control.Monad.Zip</literal></ulink>:
1335 do (x,y) <- mzip (do x <- [1..10]
1337 (do y <- [11..20]
1346 All these features are enabled by default if the
1347 <literal>MonadComprehensions</literal> extension is enabled. The types
1348 and more detailed examples on how to use comprehensions are explained
1349 in the previous chapters <xref
1350 linkend="generalised-list-comprehensions"/> and <xref
1351 linkend="parallel-list-comprehensions"/>. In general you just have
1352 to replace the type <literal>[a]</literal> with the type
1353 <literal>Monad m => m a</literal> for monad comprehensions.
1357 Note: Even though most of these examples are using the list monad,
1358 monad comprehensions work for any monad.
1359 The <literal>base</literal> package offers all necessary instances for
1360 lists, which make <literal>MonadComprehensions</literal> backward
1361 compatible to built-in, transform and parallel list comprehensions.
1366 <!-- ===================== REBINDABLE SYNTAX =================== -->
1368 <sect2 id="rebindable-syntax">
1369 <title>Rebindable syntax and the implicit Prelude import</title>
1371 <para><indexterm><primary>-XNoImplicitPrelude
1372 option</primary></indexterm> GHC normally imports
1373 <filename>Prelude.hi</filename> files for you. If you'd
1374 rather it didn't, then give it a
1375 <option>-XNoImplicitPrelude</option> option. The idea is
1376 that you can then import a Prelude of your own. (But don't
1377 call it <literal>Prelude</literal>; the Haskell module
1378 namespace is flat, and you must not conflict with any
1379 Prelude module.)</para>
1381 <para>Suppose you are importing a Prelude of your own
1382 in order to define your own numeric class
1383 hierarchy. It completely defeats that purpose if the
1384 literal "1" means "<literal>Prelude.fromInteger
1385 1</literal>", which is what the Haskell Report specifies.
1386 So the <option>-XRebindableSyntax</option>
1388 the following pieces of built-in syntax to refer to
1389 <emphasis>whatever is in scope</emphasis>, not the Prelude
1393 <para>An integer literal <literal>368</literal> means
1394 "<literal>fromInteger (368::Integer)</literal>", rather than
1395 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1398 <listitem><para>Fractional literals are handed in just the same way,
1399 except that the translation is
1400 <literal>fromRational (3.68::Rational)</literal>.
1403 <listitem><para>The equality test in an overloaded numeric pattern
1404 uses whatever <literal>(==)</literal> is in scope.
1407 <listitem><para>The subtraction operation, and the
1408 greater-than-or-equal test, in <literal>n+k</literal> patterns
1409 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1413 <para>Negation (e.g. "<literal>- (f x)</literal>")
1414 means "<literal>negate (f x)</literal>", both in numeric
1415 patterns, and expressions.
1419 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1420 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1424 <para>"Do" notation is translated using whatever
1425 functions <literal>(>>=)</literal>,
1426 <literal>(>>)</literal>, and <literal>fail</literal>,
1427 are in scope (not the Prelude
1428 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1429 comprehensions, are unaffected. </para></listitem>
1433 notation (see <xref linkend="arrow-notation"/>)
1434 uses whatever <literal>arr</literal>,
1435 <literal>(>>>)</literal>, <literal>first</literal>,
1436 <literal>app</literal>, <literal>(|||)</literal> and
1437 <literal>loop</literal> functions are in scope. But unlike the
1438 other constructs, the types of these functions must match the
1439 Prelude types very closely. Details are in flux; if you want
1443 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1446 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1447 even if that is a little unexpected. For example, the
1448 static semantics of the literal <literal>368</literal>
1449 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1450 <literal>fromInteger</literal> to have any of the types:
1452 fromInteger :: Integer -> Integer
1453 fromInteger :: forall a. Foo a => Integer -> a
1454 fromInteger :: Num a => a -> Integer
1455 fromInteger :: Integer -> Bool -> Bool
1459 <para>Be warned: this is an experimental facility, with
1460 fewer checks than usual. Use <literal>-dcore-lint</literal>
1461 to typecheck the desugared program. If Core Lint is happy
1462 you should be all right.</para>
1466 <sect2 id="postfix-operators">
1467 <title>Postfix operators</title>
1470 The <option>-XPostfixOperators</option> flag enables a small
1471 extension to the syntax of left operator sections, which allows you to
1472 define postfix operators. The extension is this: the left section
1476 is equivalent (from the point of view of both type checking and execution) to the expression
1480 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1481 The strict Haskell 98 interpretation is that the section is equivalent to
1485 That is, the operator must be a function of two arguments. GHC allows it to
1486 take only one argument, and that in turn allows you to write the function
1489 <para>The extension does not extend to the left-hand side of function
1490 definitions; you must define such a function in prefix form.</para>
1494 <sect2 id="tuple-sections">
1495 <title>Tuple sections</title>
1498 The <option>-XTupleSections</option> flag enables Python-style partially applied
1499 tuple constructors. For example, the following program
1503 is considered to be an alternative notation for the more unwieldy alternative
1507 You can omit any combination of arguments to the tuple, as in the following
1509 (, "I", , , "Love", , 1337)
1513 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1518 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1519 will also be available for them, like so
1523 Because there is no unboxed unit tuple, the following expression
1527 continues to stand for the unboxed singleton tuple data constructor.
1532 <sect2 id="disambiguate-fields">
1533 <title>Record field disambiguation</title>
1535 In record construction and record pattern matching
1536 it is entirely unambiguous which field is referred to, even if there are two different
1537 data types in scope with a common field name. For example:
1540 data S = MkS { x :: Int, y :: Bool }
1545 data T = MkT { x :: Int }
1547 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1548 ok2 n = MkT { x = n+1 } -- Unambiguous
1550 bad1 k = k { x = 3 } -- Ambiguous
1551 bad2 k = x k -- Ambiguous
1553 Even though there are two <literal>x</literal>'s in scope,
1554 it is clear that the <literal>x</literal> in the pattern in the
1555 definition of <literal>ok1</literal> can only mean the field
1556 <literal>x</literal> from type <literal>S</literal>. Similarly for
1557 the function <literal>ok2</literal>. However, in the record update
1558 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1559 it is not clear which of the two types is intended.
1562 Haskell 98 regards all four as ambiguous, but with the
1563 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1564 the former two. The rules are precisely the same as those for instance
1565 declarations in Haskell 98, where the method names on the left-hand side
1566 of the method bindings in an instance declaration refer unambiguously
1567 to the method of that class (provided they are in scope at all), even
1568 if there are other variables in scope with the same name.
1569 This reduces the clutter of qualified names when you import two
1570 records from different modules that use the same field name.
1576 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1581 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1586 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1587 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1588 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1591 import qualified M -- Note qualified
1593 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1595 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1596 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1597 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1598 is not. (In effect, it is qualified by the constructor.)
1605 <!-- ===================== Record puns =================== -->
1607 <sect2 id="record-puns">
1612 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1616 When using records, it is common to write a pattern that binds a
1617 variable with the same name as a record field, such as:
1620 data C = C {a :: Int}
1626 Record punning permits the variable name to be elided, so one can simply
1633 to mean the same pattern as above. That is, in a record pattern, the
1634 pattern <literal>a</literal> expands into the pattern <literal>a =
1635 a</literal> for the same name <literal>a</literal>.
1642 Record punning can also be used in an expression, writing, for example,
1648 let a = 1 in C {a = a}
1650 The expansion is purely syntactic, so the expanded right-hand side
1651 expression refers to the nearest enclosing variable that is spelled the
1652 same as the field name.
1656 Puns and other patterns can be mixed in the same record:
1658 data C = C {a :: Int, b :: Int}
1659 f (C {a, b = 4}) = a
1664 Puns can be used wherever record patterns occur (e.g. in
1665 <literal>let</literal> bindings or at the top-level).
1669 A pun on a qualified field name is expanded by stripping off the module qualifier.
1676 f (M.C {M.a = a}) = a
1678 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1679 is only in scope in qualified form.)
1687 <!-- ===================== Record wildcards =================== -->
1689 <sect2 id="record-wildcards">
1690 <title>Record wildcards
1694 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1695 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1699 For records with many fields, it can be tiresome to write out each field
1700 individually in a record pattern, as in
1702 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1703 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1708 Record wildcard syntax permits a "<literal>..</literal>" in a record
1709 pattern, where each elided field <literal>f</literal> is replaced by the
1710 pattern <literal>f = f</literal>. For example, the above pattern can be
1713 f (C {a = 1, ..}) = b + c + d
1721 Wildcards can be mixed with other patterns, including puns
1722 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1723 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1724 wherever record patterns occur, including in <literal>let</literal>
1725 bindings and at the top-level. For example, the top-level binding
1729 defines <literal>b</literal>, <literal>c</literal>, and
1730 <literal>d</literal>.
1734 Record wildcards can also be used in expressions, writing, for example,
1736 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1740 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1742 The expansion is purely syntactic, so the record wildcard
1743 expression refers to the nearest enclosing variables that are spelled
1744 the same as the omitted field names.
1748 The "<literal>..</literal>" expands to the missing
1749 <emphasis>in-scope</emphasis> record fields, where "in scope"
1750 includes both unqualified and qualified-only.
1751 Any fields that are not in scope are not filled in. For example
1754 data R = R { a,b,c :: Int }
1756 import qualified M( R(a,b) )
1759 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1760 omitting <literal>c</literal> since it is not in scope at all.
1767 <!-- ===================== Local fixity declarations =================== -->
1769 <sect2 id="local-fixity-declarations">
1770 <title>Local Fixity Declarations
1773 <para>A careful reading of the Haskell 98 Report reveals that fixity
1774 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1775 <literal>infixr</literal>) are permitted to appear inside local bindings
1776 such those introduced by <literal>let</literal> and
1777 <literal>where</literal>. However, the Haskell Report does not specify
1778 the semantics of such bindings very precisely.
1781 <para>In GHC, a fixity declaration may accompany a local binding:
1788 and the fixity declaration applies wherever the binding is in scope.
1789 For example, in a <literal>let</literal>, it applies in the right-hand
1790 sides of other <literal>let</literal>-bindings and the body of the
1791 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1792 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
1793 declarations of a <literal>let</literal> statement scope over other
1794 statements in the group, just as the bound name does.
1798 Moreover, a local fixity declaration *must* accompany a local binding of
1799 that name: it is not possible to revise the fixity of name bound
1802 let infixr 9 $ in ...
1805 Because local fixity declarations are technically Haskell 98, no flag is
1806 necessary to enable them.
1810 <sect2 id="package-imports">
1811 <title>Package-qualified imports</title>
1813 <para>With the <option>-XPackageImports</option> flag, GHC allows
1814 import declarations to be qualified by the package name that the
1815 module is intended to be imported from. For example:</para>
1818 import "network" Network.Socket
1821 <para>would import the module <literal>Network.Socket</literal> from
1822 the package <literal>network</literal> (any version). This may
1823 be used to disambiguate an import when the same module is
1824 available from multiple packages, or is present in both the
1825 current package being built and an external package.</para>
1827 <para>Note: you probably don't need to use this feature, it was
1828 added mainly so that we can build backwards-compatible versions of
1829 packages when APIs change. It can lead to fragile dependencies in
1830 the common case: modules occasionally move from one package to
1831 another, rendering any package-qualified imports broken.</para>
1834 <sect2 id="syntax-stolen">
1835 <title>Summary of stolen syntax</title>
1837 <para>Turning on an option that enables special syntax
1838 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1839 to compile, perhaps because it uses a variable name which has
1840 become a reserved word. This section lists the syntax that is
1841 "stolen" by language extensions.
1843 notation and nonterminal names from the Haskell 98 lexical syntax
1844 (see the Haskell 98 Report).
1845 We only list syntax changes here that might affect
1846 existing working programs (i.e. "stolen" syntax). Many of these
1847 extensions will also enable new context-free syntax, but in all
1848 cases programs written to use the new syntax would not be
1849 compilable without the option enabled.</para>
1851 <para>There are two classes of special
1856 <para>New reserved words and symbols: character sequences
1857 which are no longer available for use as identifiers in the
1861 <para>Other special syntax: sequences of characters that have
1862 a different meaning when this particular option is turned
1867 The following syntax is stolen:
1872 <literal>forall</literal>
1873 <indexterm><primary><literal>forall</literal></primary></indexterm>
1876 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1877 <option>-XScopedTypeVariables</option>,
1878 <option>-XLiberalTypeSynonyms</option>,
1879 <option>-XRank2Types</option>,
1880 <option>-XRankNTypes</option>,
1881 <option>-XPolymorphicComponents</option>,
1882 <option>-XExistentialQuantification</option>
1888 <literal>mdo</literal>
1889 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1892 Stolen by: <option>-XRecursiveDo</option>,
1898 <literal>foreign</literal>
1899 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1902 Stolen by: <option>-XForeignFunctionInterface</option>,
1908 <literal>rec</literal>,
1909 <literal>proc</literal>, <literal>-<</literal>,
1910 <literal>>-</literal>, <literal>-<<</literal>,
1911 <literal>>>-</literal>, and <literal>(|</literal>,
1912 <literal>|)</literal> brackets
1913 <indexterm><primary><literal>proc</literal></primary></indexterm>
1916 Stolen by: <option>-XArrows</option>,
1922 <literal>?<replaceable>varid</replaceable></literal>,
1923 <literal>%<replaceable>varid</replaceable></literal>
1924 <indexterm><primary>implicit parameters</primary></indexterm>
1927 Stolen by: <option>-XImplicitParams</option>,
1933 <literal>[|</literal>,
1934 <literal>[e|</literal>, <literal>[p|</literal>,
1935 <literal>[d|</literal>, <literal>[t|</literal>,
1936 <literal>$(</literal>,
1937 <literal>$<replaceable>varid</replaceable></literal>
1938 <indexterm><primary>Template Haskell</primary></indexterm>
1941 Stolen by: <option>-XTemplateHaskell</option>,
1947 <literal>[:<replaceable>varid</replaceable>|</literal>
1948 <indexterm><primary>quasi-quotation</primary></indexterm>
1951 Stolen by: <option>-XQuasiQuotes</option>,
1957 <replaceable>varid</replaceable>{<literal>#</literal>},
1958 <replaceable>char</replaceable><literal>#</literal>,
1959 <replaceable>string</replaceable><literal>#</literal>,
1960 <replaceable>integer</replaceable><literal>#</literal>,
1961 <replaceable>float</replaceable><literal>#</literal>,
1962 <replaceable>float</replaceable><literal>##</literal>,
1963 <literal>(#</literal>, <literal>#)</literal>,
1966 Stolen by: <option>-XMagicHash</option>,
1975 <!-- TYPE SYSTEM EXTENSIONS -->
1976 <sect1 id="data-type-extensions">
1977 <title>Extensions to data types and type synonyms</title>
1979 <sect2 id="nullary-types">
1980 <title>Data types with no constructors</title>
1982 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1983 a data type with no constructors. For example:</para>
1987 data T a -- T :: * -> *
1990 <para>Syntactically, the declaration lacks the "= constrs" part. The
1991 type can be parameterised over types of any kind, but if the kind is
1992 not <literal>*</literal> then an explicit kind annotation must be used
1993 (see <xref linkend="kinding"/>).</para>
1995 <para>Such data types have only one value, namely bottom.
1996 Nevertheless, they can be useful when defining "phantom types".</para>
1999 <sect2 id="datatype-contexts">
2000 <title>Data type contexts</title>
2002 <para>Haskell allows datatypes to be given contexts, e.g.</para>
2005 data Eq a => Set a = NilSet | ConsSet a (Set a)
2008 <para>give constructors with types:</para>
2012 ConsSet :: Eq a => a -> Set a -> Set a
2015 <para>In GHC this feature is an extension called
2016 <literal>DatatypeContexts</literal>, and on by default.</para>
2019 <sect2 id="infix-tycons">
2020 <title>Infix type constructors, classes, and type variables</title>
2023 GHC allows type constructors, classes, and type variables to be operators, and
2024 to be written infix, very much like expressions. More specifically:
2027 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
2028 The lexical syntax is the same as that for data constructors.
2031 Data type and type-synonym declarations can be written infix, parenthesised
2032 if you want further arguments. E.g.
2034 data a :*: b = Foo a b
2035 type a :+: b = Either a b
2036 class a :=: b where ...
2038 data (a :**: b) x = Baz a b x
2039 type (a :++: b) y = Either (a,b) y
2043 Types, and class constraints, can be written infix. For example
2046 f :: (a :=: b) => a -> b
2050 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
2051 The lexical syntax is the same as that for variable operators, excluding "(.)",
2052 "(!)", and "(*)". In a binding position, the operator must be
2053 parenthesised. For example:
2055 type T (+) = Int + Int
2059 liftA2 :: Arrow (~>)
2060 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
2066 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
2067 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
2070 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
2071 one cannot distinguish between the two in a fixity declaration; a fixity declaration
2072 sets the fixity for a data constructor and the corresponding type constructor. For example:
2076 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
2077 and similarly for <literal>:*:</literal>.
2078 <literal>Int `a` Bool</literal>.
2081 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
2088 <sect2 id="type-synonyms">
2089 <title>Liberalised type synonyms</title>
2092 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
2093 on individual synonym declarations.
2094 With the <option>-XLiberalTypeSynonyms</option> extension,
2095 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2096 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
2099 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2100 in a type synonym, thus:
2102 type Discard a = forall b. Show b => a -> b -> (a, String)
2107 g :: Discard Int -> (Int,String) -- A rank-2 type
2114 If you also use <option>-XUnboxedTuples</option>,
2115 you can write an unboxed tuple in a type synonym:
2117 type Pr = (# Int, Int #)
2125 You can apply a type synonym to a forall type:
2127 type Foo a = a -> a -> Bool
2129 f :: Foo (forall b. b->b)
2131 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2133 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2138 You can apply a type synonym to a partially applied type synonym:
2140 type Generic i o = forall x. i x -> o x
2143 foo :: Generic Id []
2145 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2147 foo :: forall x. x -> [x]
2155 GHC currently does kind checking before expanding synonyms (though even that
2159 After expanding type synonyms, GHC does validity checking on types, looking for
2160 the following mal-formedness which isn't detected simply by kind checking:
2163 Type constructor applied to a type involving for-alls.
2166 Unboxed tuple on left of an arrow.
2169 Partially-applied type synonym.
2173 this will be rejected:
2175 type Pr = (# Int, Int #)
2180 because GHC does not allow unboxed tuples on the left of a function arrow.
2185 <sect2 id="existential-quantification">
2186 <title>Existentially quantified data constructors
2190 The idea of using existential quantification in data type declarations
2191 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2192 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2193 London, 1991). It was later formalised by Laufer and Odersky
2194 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2195 TOPLAS, 16(5), pp1411-1430, 1994).
2196 It's been in Lennart
2197 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2198 proved very useful. Here's the idea. Consider the declaration:
2204 data Foo = forall a. MkFoo a (a -> Bool)
2211 The data type <literal>Foo</literal> has two constructors with types:
2217 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2224 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2225 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2226 For example, the following expression is fine:
2232 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2238 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2239 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2240 isUpper</function> packages a character with a compatible function. These
2241 two things are each of type <literal>Foo</literal> and can be put in a list.
2245 What can we do with a value of type <literal>Foo</literal>?. In particular,
2246 what happens when we pattern-match on <function>MkFoo</function>?
2252 f (MkFoo val fn) = ???
2258 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2259 are compatible, the only (useful) thing we can do with them is to
2260 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2267 f (MkFoo val fn) = fn val
2273 What this allows us to do is to package heterogeneous values
2274 together with a bunch of functions that manipulate them, and then treat
2275 that collection of packages in a uniform manner. You can express
2276 quite a bit of object-oriented-like programming this way.
2279 <sect3 id="existential">
2280 <title>Why existential?
2284 What has this to do with <emphasis>existential</emphasis> quantification?
2285 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2291 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2297 But Haskell programmers can safely think of the ordinary
2298 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2299 adding a new existential quantification construct.
2304 <sect3 id="existential-with-context">
2305 <title>Existentials and type classes</title>
2308 An easy extension is to allow
2309 arbitrary contexts before the constructor. For example:
2315 data Baz = forall a. Eq a => Baz1 a a
2316 | forall b. Show b => Baz2 b (b -> b)
2322 The two constructors have the types you'd expect:
2328 Baz1 :: forall a. Eq a => a -> a -> Baz
2329 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2335 But when pattern matching on <function>Baz1</function> the matched values can be compared
2336 for equality, and when pattern matching on <function>Baz2</function> the first matched
2337 value can be converted to a string (as well as applying the function to it).
2338 So this program is legal:
2345 f (Baz1 p q) | p == q = "Yes"
2347 f (Baz2 v fn) = show (fn v)
2353 Operationally, in a dictionary-passing implementation, the
2354 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2355 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2356 extract it on pattern matching.
2361 <sect3 id="existential-records">
2362 <title>Record Constructors</title>
2365 GHC allows existentials to be used with records syntax as well. For example:
2368 data Counter a = forall self. NewCounter
2370 , _inc :: self -> self
2371 , _display :: self -> IO ()
2375 Here <literal>tag</literal> is a public field, with a well-typed selector
2376 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2377 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2378 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2379 compile-time error. In other words, <emphasis>GHC defines a record selector function
2380 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2381 (This example used an underscore in the fields for which record selectors
2382 will not be defined, but that is only programming style; GHC ignores them.)
2386 To make use of these hidden fields, we need to create some helper functions:
2389 inc :: Counter a -> Counter a
2390 inc (NewCounter x i d t) = NewCounter
2391 { _this = i x, _inc = i, _display = d, tag = t }
2393 display :: Counter a -> IO ()
2394 display NewCounter{ _this = x, _display = d } = d x
2397 Now we can define counters with different underlying implementations:
2400 counterA :: Counter String
2401 counterA = NewCounter
2402 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2404 counterB :: Counter String
2405 counterB = NewCounter
2406 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2409 display (inc counterA) -- prints "1"
2410 display (inc (inc counterB)) -- prints "##"
2413 Record update syntax is supported for existentials (and GADTs):
2415 setTag :: Counter a -> a -> Counter a
2416 setTag obj t = obj{ tag = t }
2418 The rule for record update is this: <emphasis>
2419 the types of the updated fields may
2420 mention only the universally-quantified type variables
2421 of the data constructor. For GADTs, the field may mention only types
2422 that appear as a simple type-variable argument in the constructor's result
2423 type</emphasis>. For example:
2425 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2426 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2427 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2428 -- existentially quantified)
2430 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2431 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2432 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2433 -- type-variable argument in G1's result type)
2441 <title>Restrictions</title>
2444 There are several restrictions on the ways in which existentially-quantified
2445 constructors can be use.
2454 When pattern matching, each pattern match introduces a new,
2455 distinct, type for each existential type variable. These types cannot
2456 be unified with any other type, nor can they escape from the scope of
2457 the pattern match. For example, these fragments are incorrect:
2465 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2466 is the result of <function>f1</function>. One way to see why this is wrong is to
2467 ask what type <function>f1</function> has:
2471 f1 :: Foo -> a -- Weird!
2475 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2480 f1 :: forall a. Foo -> a -- Wrong!
2484 The original program is just plain wrong. Here's another sort of error
2488 f2 (Baz1 a b) (Baz1 p q) = a==q
2492 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2493 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2494 from the two <function>Baz1</function> constructors.
2502 You can't pattern-match on an existentially quantified
2503 constructor in a <literal>let</literal> or <literal>where</literal> group of
2504 bindings. So this is illegal:
2508 f3 x = a==b where { Baz1 a b = x }
2511 Instead, use a <literal>case</literal> expression:
2514 f3 x = case x of Baz1 a b -> a==b
2517 In general, you can only pattern-match
2518 on an existentially-quantified constructor in a <literal>case</literal> expression or
2519 in the patterns of a function definition.
2521 The reason for this restriction is really an implementation one.
2522 Type-checking binding groups is already a nightmare without
2523 existentials complicating the picture. Also an existential pattern
2524 binding at the top level of a module doesn't make sense, because it's
2525 not clear how to prevent the existentially-quantified type "escaping".
2526 So for now, there's a simple-to-state restriction. We'll see how
2534 You can't use existential quantification for <literal>newtype</literal>
2535 declarations. So this is illegal:
2539 newtype T = forall a. Ord a => MkT a
2543 Reason: a value of type <literal>T</literal> must be represented as a
2544 pair of a dictionary for <literal>Ord t</literal> and a value of type
2545 <literal>t</literal>. That contradicts the idea that
2546 <literal>newtype</literal> should have no concrete representation.
2547 You can get just the same efficiency and effect by using
2548 <literal>data</literal> instead of <literal>newtype</literal>. If
2549 there is no overloading involved, then there is more of a case for
2550 allowing an existentially-quantified <literal>newtype</literal>,
2551 because the <literal>data</literal> version does carry an
2552 implementation cost, but single-field existentially quantified
2553 constructors aren't much use. So the simple restriction (no
2554 existential stuff on <literal>newtype</literal>) stands, unless there
2555 are convincing reasons to change it.
2563 You can't use <literal>deriving</literal> to define instances of a
2564 data type with existentially quantified data constructors.
2566 Reason: in most cases it would not make sense. For example:;
2569 data T = forall a. MkT [a] deriving( Eq )
2572 To derive <literal>Eq</literal> in the standard way we would need to have equality
2573 between the single component of two <function>MkT</function> constructors:
2577 (MkT a) == (MkT b) = ???
2580 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2581 It's just about possible to imagine examples in which the derived instance
2582 would make sense, but it seems altogether simpler simply to prohibit such
2583 declarations. Define your own instances!
2594 <!-- ====================== Generalised algebraic data types ======================= -->
2596 <sect2 id="gadt-style">
2597 <title>Declaring data types with explicit constructor signatures</title>
2599 <para>When the <literal>GADTSyntax</literal> extension is enabled,
2600 GHC allows you to declare an algebraic data type by
2601 giving the type signatures of constructors explicitly. For example:
2605 Just :: a -> Maybe a
2607 The form is called a "GADT-style declaration"
2608 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2609 can only be declared using this form.</para>
2610 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2611 For example, these two declarations are equivalent:
2613 data Foo = forall a. MkFoo a (a -> Bool)
2614 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2617 <para>Any data type that can be declared in standard Haskell-98 syntax
2618 can also be declared using GADT-style syntax.
2619 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2620 they treat class constraints on the data constructors differently.
2621 Specifically, if the constructor is given a type-class context, that
2622 context is made available by pattern matching. For example:
2625 MkSet :: Eq a => [a] -> Set a
2627 makeSet :: Eq a => [a] -> Set a
2628 makeSet xs = MkSet (nub xs)
2630 insert :: a -> Set a -> Set a
2631 insert a (MkSet as) | a `elem` as = MkSet as
2632 | otherwise = MkSet (a:as)
2634 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2635 gives rise to a <literal>(Eq a)</literal>
2636 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2637 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2638 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2639 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2640 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2641 In the example, the equality dictionary is used to satisfy the equality constraint
2642 generated by the call to <literal>elem</literal>, so that the type of
2643 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2646 For example, one possible application is to reify dictionaries:
2648 data NumInst a where
2649 MkNumInst :: Num a => NumInst a
2651 intInst :: NumInst Int
2654 plus :: NumInst a -> a -> a -> a
2655 plus MkNumInst p q = p + q
2657 Here, a value of type <literal>NumInst a</literal> is equivalent
2658 to an explicit <literal>(Num a)</literal> dictionary.
2661 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2662 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2666 = Num a => MkNumInst (NumInst a)
2668 Notice that, unlike the situation when declaring an existential, there is
2669 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2670 data type's universally quantified type variable <literal>a</literal>.
2671 A constructor may have both universal and existential type variables: for example,
2672 the following two declarations are equivalent:
2675 = forall b. (Num a, Eq b) => MkT1 a b
2677 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2680 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2681 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2682 In Haskell 98 the definition
2684 data Eq a => Set' a = MkSet' [a]
2686 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2687 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2688 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2689 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2690 GHC's behaviour is much more useful, as well as much more intuitive.
2694 The rest of this section gives further details about GADT-style data
2699 The result type of each data constructor must begin with the type constructor being defined.
2700 If the result type of all constructors
2701 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2702 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2703 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2707 As with other type signatures, you can give a single signature for several data constructors.
2708 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2717 The type signature of
2718 each constructor is independent, and is implicitly universally quantified as usual.
2719 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2720 have no scope, and different constructors may have different universally-quantified type variables:
2722 data T a where -- The 'a' has no scope
2723 T1,T2 :: b -> T b -- Means forall b. b -> T b
2724 T3 :: T a -- Means forall a. T a
2729 A constructor signature may mention type class constraints, which can differ for
2730 different constructors. For example, this is fine:
2733 T1 :: Eq b => b -> b -> T b
2734 T2 :: (Show c, Ix c) => c -> [c] -> T c
2736 When patten matching, these constraints are made available to discharge constraints
2737 in the body of the match. For example:
2740 f (T1 x y) | x==y = "yes"
2744 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2745 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2746 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2750 Unlike a Haskell-98-style
2751 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2752 have no scope. Indeed, one can write a kind signature instead:
2754 data Set :: * -> * where ...
2756 or even a mixture of the two:
2758 data Bar a :: (* -> *) -> * where ...
2760 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2763 data Bar a (b :: * -> *) where ...
2769 You can use strictness annotations, in the obvious places
2770 in the constructor type:
2773 Lit :: !Int -> Term Int
2774 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2775 Pair :: Term a -> Term b -> Term (a,b)
2780 You can use a <literal>deriving</literal> clause on a GADT-style data type
2781 declaration. For example, these two declarations are equivalent
2783 data Maybe1 a where {
2784 Nothing1 :: Maybe1 a ;
2785 Just1 :: a -> Maybe1 a
2786 } deriving( Eq, Ord )
2788 data Maybe2 a = Nothing2 | Just2 a
2794 The type signature may have quantified type variables that do not appear
2798 MkFoo :: a -> (a->Bool) -> Foo
2801 Here the type variable <literal>a</literal> does not appear in the result type
2802 of either constructor.
2803 Although it is universally quantified in the type of the constructor, such
2804 a type variable is often called "existential".
2805 Indeed, the above declaration declares precisely the same type as
2806 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2808 The type may contain a class context too, of course:
2811 MkShowable :: Show a => a -> Showable
2816 You can use record syntax on a GADT-style data type declaration:
2820 Adult :: { name :: String, children :: [Person] } -> Person
2821 Child :: Show a => { name :: !String, funny :: a } -> Person
2823 As usual, for every constructor that has a field <literal>f</literal>, the type of
2824 field <literal>f</literal> must be the same (modulo alpha conversion).
2825 The <literal>Child</literal> constructor above shows that the signature
2826 may have a context, existentially-quantified variables, and strictness annotations,
2827 just as in the non-record case. (NB: the "type" that follows the double-colon
2828 is not really a type, because of the record syntax and strictness annotations.
2829 A "type" of this form can appear only in a constructor signature.)
2833 Record updates are allowed with GADT-style declarations,
2834 only fields that have the following property: the type of the field
2835 mentions no existential type variables.
2839 As in the case of existentials declared using the Haskell-98-like record syntax
2840 (<xref linkend="existential-records"/>),
2841 record-selector functions are generated only for those fields that have well-typed
2843 Here is the example of that section, in GADT-style syntax:
2845 data Counter a where
2846 NewCounter { _this :: self
2847 , _inc :: self -> self
2848 , _display :: self -> IO ()
2853 As before, only one selector function is generated here, that for <literal>tag</literal>.
2854 Nevertheless, you can still use all the field names in pattern matching and record construction.
2856 </itemizedlist></para>
2860 <title>Generalised Algebraic Data Types (GADTs)</title>
2862 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2863 by allowing constructors to have richer return types. Here is an example:
2866 Lit :: Int -> Term Int
2867 Succ :: Term Int -> Term Int
2868 IsZero :: Term Int -> Term Bool
2869 If :: Term Bool -> Term a -> Term a -> Term a
2870 Pair :: Term a -> Term b -> Term (a,b)
2872 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2873 case with ordinary data types. This generality allows us to
2874 write a well-typed <literal>eval</literal> function
2875 for these <literal>Terms</literal>:
2879 eval (Succ t) = 1 + eval t
2880 eval (IsZero t) = eval t == 0
2881 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2882 eval (Pair e1 e2) = (eval e1, eval e2)
2884 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2885 For example, in the right hand side of the equation
2890 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2891 A precise specification of the type rules is beyond what this user manual aspires to,
2892 but the design closely follows that described in
2894 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2895 unification-based type inference for GADTs</ulink>,
2897 The general principle is this: <emphasis>type refinement is only carried out
2898 based on user-supplied type annotations</emphasis>.
2899 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2900 and lots of obscure error messages will
2901 occur. However, the refinement is quite general. For example, if we had:
2903 eval :: Term a -> a -> a
2904 eval (Lit i) j = i+j
2906 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2907 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2908 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2911 These and many other examples are given in papers by Hongwei Xi, and
2912 Tim Sheard. There is a longer introduction
2913 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2915 <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
2916 may use different notation to that implemented in GHC.
2919 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2920 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2923 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2924 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2925 The result type of each constructor must begin with the type constructor being defined,
2926 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2927 For example, in the <literal>Term</literal> data
2928 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2929 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2934 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2935 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2936 whose result type is not just <literal>T a b</literal>.
2940 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2941 an ordinary data type.
2945 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2949 Lit { val :: Int } :: Term Int
2950 Succ { num :: Term Int } :: Term Int
2951 Pred { num :: Term Int } :: Term Int
2952 IsZero { arg :: Term Int } :: Term Bool
2953 Pair { arg1 :: Term a
2956 If { cnd :: Term Bool
2961 However, for GADTs there is the following additional constraint:
2962 every constructor that has a field <literal>f</literal> must have
2963 the same result type (modulo alpha conversion)
2964 Hence, in the above example, we cannot merge the <literal>num</literal>
2965 and <literal>arg</literal> fields above into a
2966 single name. Although their field types are both <literal>Term Int</literal>,
2967 their selector functions actually have different types:
2970 num :: Term Int -> Term Int
2971 arg :: Term Bool -> Term Int
2976 When pattern-matching against data constructors drawn from a GADT,
2977 for example in a <literal>case</literal> expression, the following rules apply:
2979 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2980 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2981 <listitem><para>The type of any free variable mentioned in any of
2982 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2984 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2985 way to ensure that a variable a rigid type is to give it a type signature.
2986 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2987 Simple unification-based type inference for GADTs
2988 </ulink>. The criteria implemented by GHC are given in the Appendix.
2998 <!-- ====================== End of Generalised algebraic data types ======================= -->
3000 <sect1 id="deriving">
3001 <title>Extensions to the "deriving" mechanism</title>
3003 <sect2 id="deriving-inferred">
3004 <title>Inferred context for deriving clauses</title>
3007 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
3010 data T0 f a = MkT0 a deriving( Eq )
3011 data T1 f a = MkT1 (f a) deriving( Eq )
3012 data T2 f a = MkT2 (f (f a)) deriving( Eq )
3014 The natural generated <literal>Eq</literal> code would result in these instance declarations:
3016 instance Eq a => Eq (T0 f a) where ...
3017 instance Eq (f a) => Eq (T1 f a) where ...
3018 instance Eq (f (f a)) => Eq (T2 f a) where ...
3020 The first of these is obviously fine. The second is still fine, although less obviously.
3021 The third is not Haskell 98, and risks losing termination of instances.
3024 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
3025 each constraint in the inferred instance context must consist only of type variables,
3026 with no repetitions.
3029 This rule is applied regardless of flags. If you want a more exotic context, you can write
3030 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
3034 <sect2 id="stand-alone-deriving">
3035 <title>Stand-alone deriving declarations</title>
3038 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
3040 data Foo a = Bar a | Baz String
3042 deriving instance Eq a => Eq (Foo a)
3044 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
3045 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
3046 Note the following points:
3049 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
3050 exactly as you would in an ordinary instance declaration.
3051 (In contrast, in a <literal>deriving</literal> clause
3052 attached to a data type declaration, the context is inferred.)
3056 A <literal>deriving instance</literal> declaration
3057 must obey the same rules concerning form and termination as ordinary instance declarations,
3058 controlled by the same flags; see <xref linkend="instance-decls"/>.
3062 Unlike a <literal>deriving</literal>
3063 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
3064 than the data type (assuming you also use
3065 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
3068 data Foo a = Bar a | Baz String
3070 deriving instance Eq a => Eq (Foo [a])
3071 deriving instance Eq a => Eq (Foo (Maybe a))
3073 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
3074 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
3078 Unlike a <literal>deriving</literal>
3079 declaration attached to a <literal>data</literal> declaration,
3080 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
3081 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
3082 your problem. (GHC will show you the offending code if it has a type error.)
3083 The merit of this is that you can derive instances for GADTs and other exotic
3084 data types, providing only that the boilerplate code does indeed typecheck. For example:
3090 deriving instance Show (T a)
3092 In this example, you cannot say <literal>... deriving( Show )</literal> on the
3093 data type declaration for <literal>T</literal>,
3094 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
3095 the instance declaration using stand-alone deriving.
3100 <para>The stand-alone syntax is generalised for newtypes in exactly the same
3101 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3104 newtype Foo a = MkFoo (State Int a)
3106 deriving instance MonadState Int Foo
3108 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3109 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3111 </itemizedlist></para>
3116 <sect2 id="deriving-typeable">
3117 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
3120 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3121 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3122 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3123 classes <literal>Eq</literal>, <literal>Ord</literal>,
3124 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3127 GHC extends this list with several more classes that may be automatically derived:
3129 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
3130 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
3131 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
3133 <para>An instance of <literal>Typeable</literal> can only be derived if the
3134 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3135 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3137 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3138 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3140 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3141 are used, and only <literal>Typeable1</literal> up to
3142 <literal>Typeable7</literal> are provided in the library.)
3143 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3144 class, whose kind suits that of the data type constructor, and
3145 then writing the data type instance by hand.
3149 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3150 the class <literal>Functor</literal>,
3151 defined in <literal>GHC.Base</literal>.
3154 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3155 the class <literal>Foldable</literal>,
3156 defined in <literal>Data.Foldable</literal>.
3159 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3160 the class <literal>Traversable</literal>,
3161 defined in <literal>Data.Traversable</literal>.
3164 In each case the appropriate class must be in scope before it
3165 can be mentioned in the <literal>deriving</literal> clause.
3169 <sect2 id="newtype-deriving">
3170 <title>Generalised derived instances for newtypes</title>
3173 When you define an abstract type using <literal>newtype</literal>, you may want
3174 the new type to inherit some instances from its representation. In
3175 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3176 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3177 other classes you have to write an explicit instance declaration. For
3178 example, if you define
3181 newtype Dollars = Dollars Int
3184 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3185 explicitly define an instance of <literal>Num</literal>:
3188 instance Num Dollars where
3189 Dollars a + Dollars b = Dollars (a+b)
3192 All the instance does is apply and remove the <literal>newtype</literal>
3193 constructor. It is particularly galling that, since the constructor
3194 doesn't appear at run-time, this instance declaration defines a
3195 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3196 dictionary, only slower!
3200 <sect3> <title> Generalising the deriving clause </title>
3202 GHC now permits such instances to be derived instead,
3203 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3206 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3209 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3210 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3211 derives an instance declaration of the form
3214 instance Num Int => Num Dollars
3217 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3221 We can also derive instances of constructor classes in a similar
3222 way. For example, suppose we have implemented state and failure monad
3223 transformers, such that
3226 instance Monad m => Monad (State s m)
3227 instance Monad m => Monad (Failure m)
3229 In Haskell 98, we can define a parsing monad by
3231 type Parser tok m a = State [tok] (Failure m) a
3234 which is automatically a monad thanks to the instance declarations
3235 above. With the extension, we can make the parser type abstract,
3236 without needing to write an instance of class <literal>Monad</literal>, via
3239 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3242 In this case the derived instance declaration is of the form
3244 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3247 Notice that, since <literal>Monad</literal> is a constructor class, the
3248 instance is a <emphasis>partial application</emphasis> of the new type, not the
3249 entire left hand side. We can imagine that the type declaration is
3250 "eta-converted" to generate the context of the instance
3255 We can even derive instances of multi-parameter classes, provided the
3256 newtype is the last class parameter. In this case, a ``partial
3257 application'' of the class appears in the <literal>deriving</literal>
3258 clause. For example, given the class
3261 class StateMonad s m | m -> s where ...
3262 instance Monad m => StateMonad s (State s m) where ...
3264 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3266 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3267 deriving (Monad, StateMonad [tok])
3270 The derived instance is obtained by completing the application of the
3271 class to the new type:
3274 instance StateMonad [tok] (State [tok] (Failure m)) =>
3275 StateMonad [tok] (Parser tok m)
3280 As a result of this extension, all derived instances in newtype
3281 declarations are treated uniformly (and implemented just by reusing
3282 the dictionary for the representation type), <emphasis>except</emphasis>
3283 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3284 the newtype and its representation.
3288 <sect3> <title> A more precise specification </title>
3290 Derived instance declarations are constructed as follows. Consider the
3291 declaration (after expansion of any type synonyms)
3294 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3300 The <literal>ci</literal> are partial applications of
3301 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3302 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3305 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3308 The type <literal>t</literal> is an arbitrary type.
3311 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3312 nor in the <literal>ci</literal>, and
3315 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3316 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3317 should not "look through" the type or its constructor. You can still
3318 derive these classes for a newtype, but it happens in the usual way, not
3319 via this new mechanism.
3322 Then, for each <literal>ci</literal>, the derived instance
3325 instance ci t => ci (T v1...vk)
3327 As an example which does <emphasis>not</emphasis> work, consider
3329 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3331 Here we cannot derive the instance
3333 instance Monad (State s m) => Monad (NonMonad m)
3336 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3337 and so cannot be "eta-converted" away. It is a good thing that this
3338 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3339 not, in fact, a monad --- for the same reason. Try defining
3340 <literal>>>=</literal> with the correct type: you won't be able to.
3344 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3345 important, since we can only derive instances for the last one. If the
3346 <literal>StateMonad</literal> class above were instead defined as
3349 class StateMonad m s | m -> s where ...
3352 then we would not have been able to derive an instance for the
3353 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3354 classes usually have one "main" parameter for which deriving new
3355 instances is most interesting.
3357 <para>Lastly, all of this applies only for classes other than
3358 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3359 and <literal>Data</literal>, for which the built-in derivation applies (section
3360 4.3.3. of the Haskell Report).
3361 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3362 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3363 the standard method is used or the one described here.)
3370 <!-- TYPE SYSTEM EXTENSIONS -->
3371 <sect1 id="type-class-extensions">
3372 <title>Class and instances declarations</title>
3374 <sect2 id="multi-param-type-classes">
3375 <title>Class declarations</title>
3378 This section, and the next one, documents GHC's type-class extensions.
3379 There's lots of background in the paper <ulink
3380 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3381 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3382 Jones, Erik Meijer).
3385 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3389 <title>Multi-parameter type classes</title>
3391 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3396 class Collection c a where
3397 union :: c a -> c a -> c a
3404 <sect3 id="superclass-rules">
3405 <title>The superclasses of a class declaration</title>
3408 In Haskell 98 the context of a class declaration (which introduces superclasses)
3409 must be simple; that is, each predicate must consist of a class applied to
3410 type variables. The flag <option>-XFlexibleContexts</option>
3411 (<xref linkend="flexible-contexts"/>)
3412 lifts this restriction,
3413 so that the only restriction on the context in a class declaration is
3414 that the class hierarchy must be acyclic. So these class declarations are OK:
3418 class Functor (m k) => FiniteMap m k where
3421 class (Monad m, Monad (t m)) => Transform t m where
3422 lift :: m a -> (t m) a
3428 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3429 of "acyclic" involves only the superclass relationships. For example,
3435 op :: D b => a -> b -> b
3438 class C a => D a where { ... }
3442 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3443 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3444 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3451 <sect3 id="class-method-types">
3452 <title>Class method types</title>
3455 Haskell 98 prohibits class method types to mention constraints on the
3456 class type variable, thus:
3459 fromList :: [a] -> s a
3460 elem :: Eq a => a -> s a -> Bool
3462 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3463 contains the constraint <literal>Eq a</literal>, constrains only the
3464 class type variable (in this case <literal>a</literal>).
3465 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3472 <sect2 id="functional-dependencies">
3473 <title>Functional dependencies
3476 <para> Functional dependencies are implemented as described by Mark Jones
3477 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3478 In Proceedings of the 9th European Symposium on Programming,
3479 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3483 Functional dependencies are introduced by a vertical bar in the syntax of a
3484 class declaration; e.g.
3486 class (Monad m) => MonadState s m | m -> s where ...
3488 class Foo a b c | a b -> c where ...
3490 There should be more documentation, but there isn't (yet). Yell if you need it.
3493 <sect3><title>Rules for functional dependencies </title>
3495 In a class declaration, all of the class type variables must be reachable (in the sense
3496 mentioned in <xref linkend="flexible-contexts"/>)
3497 from the free variables of each method type.
3501 class Coll s a where
3503 insert :: s -> a -> s
3506 is not OK, because the type of <literal>empty</literal> doesn't mention
3507 <literal>a</literal>. Functional dependencies can make the type variable
3510 class Coll s a | s -> a where
3512 insert :: s -> a -> s
3515 Alternatively <literal>Coll</literal> might be rewritten
3518 class Coll s a where
3520 insert :: s a -> a -> s a
3524 which makes the connection between the type of a collection of
3525 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3526 Occasionally this really doesn't work, in which case you can split the
3534 class CollE s => Coll s a where
3535 insert :: s -> a -> s
3542 <title>Background on functional dependencies</title>
3544 <para>The following description of the motivation and use of functional dependencies is taken
3545 from the Hugs user manual, reproduced here (with minor changes) by kind
3546 permission of Mark Jones.
3549 Consider the following class, intended as part of a
3550 library for collection types:
3552 class Collects e ce where
3554 insert :: e -> ce -> ce
3555 member :: e -> ce -> Bool
3557 The type variable e used here represents the element type, while ce is the type
3558 of the container itself. Within this framework, we might want to define
3559 instances of this class for lists or characteristic functions (both of which
3560 can be used to represent collections of any equality type), bit sets (which can
3561 be used to represent collections of characters), or hash tables (which can be
3562 used to represent any collection whose elements have a hash function). Omitting
3563 standard implementation details, this would lead to the following declarations:
3565 instance Eq e => Collects e [e] where ...
3566 instance Eq e => Collects e (e -> Bool) where ...
3567 instance Collects Char BitSet where ...
3568 instance (Hashable e, Collects a ce)
3569 => Collects e (Array Int ce) where ...
3571 All this looks quite promising; we have a class and a range of interesting
3572 implementations. Unfortunately, there are some serious problems with the class
3573 declaration. First, the empty function has an ambiguous type:
3575 empty :: Collects e ce => ce
3577 By "ambiguous" we mean that there is a type variable e that appears on the left
3578 of the <literal>=></literal> symbol, but not on the right. The problem with
3579 this is that, according to the theoretical foundations of Haskell overloading,
3580 we cannot guarantee a well-defined semantics for any term with an ambiguous
3584 We can sidestep this specific problem by removing the empty member from the
3585 class declaration. However, although the remaining members, insert and member,
3586 do not have ambiguous types, we still run into problems when we try to use
3587 them. For example, consider the following two functions:
3589 f x y = insert x . insert y
3592 for which GHC infers the following types:
3594 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3595 g :: (Collects Bool c, Collects Char c) => c -> c
3597 Notice that the type for f allows the two parameters x and y to be assigned
3598 different types, even though it attempts to insert each of the two values, one
3599 after the other, into the same collection. If we're trying to model collections
3600 that contain only one type of value, then this is clearly an inaccurate
3601 type. Worse still, the definition for g is accepted, without causing a type
3602 error. As a result, the error in this code will not be flagged at the point
3603 where it appears. Instead, it will show up only when we try to use g, which
3604 might even be in a different module.
3607 <sect4><title>An attempt to use constructor classes</title>
3610 Faced with the problems described above, some Haskell programmers might be
3611 tempted to use something like the following version of the class declaration:
3613 class Collects e c where
3615 insert :: e -> c e -> c e
3616 member :: e -> c e -> Bool
3618 The key difference here is that we abstract over the type constructor c that is
3619 used to form the collection type c e, and not over that collection type itself,
3620 represented by ce in the original class declaration. This avoids the immediate
3621 problems that we mentioned above: empty has type <literal>Collects e c => c
3622 e</literal>, which is not ambiguous.
3625 The function f from the previous section has a more accurate type:
3627 f :: (Collects e c) => e -> e -> c e -> c e
3629 The function g from the previous section is now rejected with a type error as
3630 we would hope because the type of f does not allow the two arguments to have
3632 This, then, is an example of a multiple parameter class that does actually work
3633 quite well in practice, without ambiguity problems.
3634 There is, however, a catch. This version of the Collects class is nowhere near
3635 as general as the original class seemed to be: only one of the four instances
3636 for <literal>Collects</literal>
3637 given above can be used with this version of Collects because only one of
3638 them---the instance for lists---has a collection type that can be written in
3639 the form c e, for some type constructor c, and element type e.
3643 <sect4><title>Adding functional dependencies</title>
3646 To get a more useful version of the Collects class, Hugs provides a mechanism
3647 that allows programmers to specify dependencies between the parameters of a
3648 multiple parameter class (For readers with an interest in theoretical
3649 foundations and previous work: The use of dependency information can be seen
3650 both as a generalization of the proposal for `parametric type classes' that was
3651 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3652 later framework for "improvement" of qualified types. The
3653 underlying ideas are also discussed in a more theoretical and abstract setting
3654 in a manuscript [implparam], where they are identified as one point in a
3655 general design space for systems of implicit parameterization.).
3657 To start with an abstract example, consider a declaration such as:
3659 class C a b where ...
3661 which tells us simply that C can be thought of as a binary relation on types
3662 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3663 included in the definition of classes to add information about dependencies
3664 between parameters, as in the following examples:
3666 class D a b | a -> b where ...
3667 class E a b | a -> b, b -> a where ...
3669 The notation <literal>a -> b</literal> used here between the | and where
3670 symbols --- not to be
3671 confused with a function type --- indicates that the a parameter uniquely
3672 determines the b parameter, and might be read as "a determines b." Thus D is
3673 not just a relation, but actually a (partial) function. Similarly, from the two
3674 dependencies that are included in the definition of E, we can see that E
3675 represents a (partial) one-one mapping between types.
3678 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3679 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3680 m>=0, meaning that the y parameters are uniquely determined by the x
3681 parameters. Spaces can be used as separators if more than one variable appears
3682 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3683 annotated with multiple dependencies using commas as separators, as in the
3684 definition of E above. Some dependencies that we can write in this notation are
3685 redundant, and will be rejected because they don't serve any useful
3686 purpose, and may instead indicate an error in the program. Examples of
3687 dependencies like this include <literal>a -> a </literal>,
3688 <literal>a -> a a </literal>,
3689 <literal>a -> </literal>, etc. There can also be
3690 some redundancy if multiple dependencies are given, as in
3691 <literal>a->b</literal>,
3692 <literal>b->c </literal>, <literal>a->c </literal>, and
3693 in which some subset implies the remaining dependencies. Examples like this are
3694 not treated as errors. Note that dependencies appear only in class
3695 declarations, and not in any other part of the language. In particular, the
3696 syntax for instance declarations, class constraints, and types is completely
3700 By including dependencies in a class declaration, we provide a mechanism for
3701 the programmer to specify each multiple parameter class more precisely. The
3702 compiler, on the other hand, is responsible for ensuring that the set of
3703 instances that are in scope at any given point in the program is consistent
3704 with any declared dependencies. For example, the following pair of instance
3705 declarations cannot appear together in the same scope because they violate the
3706 dependency for D, even though either one on its own would be acceptable:
3708 instance D Bool Int where ...
3709 instance D Bool Char where ...
3711 Note also that the following declaration is not allowed, even by itself:
3713 instance D [a] b where ...
3715 The problem here is that this instance would allow one particular choice of [a]
3716 to be associated with more than one choice for b, which contradicts the
3717 dependency specified in the definition of D. More generally, this means that,
3718 in any instance of the form:
3720 instance D t s where ...
3722 for some particular types t and s, the only variables that can appear in s are
3723 the ones that appear in t, and hence, if the type t is known, then s will be
3724 uniquely determined.
3727 The benefit of including dependency information is that it allows us to define
3728 more general multiple parameter classes, without ambiguity problems, and with
3729 the benefit of more accurate types. To illustrate this, we return to the
3730 collection class example, and annotate the original definition of <literal>Collects</literal>
3731 with a simple dependency:
3733 class Collects e ce | ce -> e where
3735 insert :: e -> ce -> ce
3736 member :: e -> ce -> Bool
3738 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3739 determined by the type of the collection ce. Note that both parameters of
3740 Collects are of kind *; there are no constructor classes here. Note too that
3741 all of the instances of Collects that we gave earlier can be used
3742 together with this new definition.
3745 What about the ambiguity problems that we encountered with the original
3746 definition? The empty function still has type Collects e ce => ce, but it is no
3747 longer necessary to regard that as an ambiguous type: Although the variable e
3748 does not appear on the right of the => symbol, the dependency for class
3749 Collects tells us that it is uniquely determined by ce, which does appear on
3750 the right of the => symbol. Hence the context in which empty is used can still
3751 give enough information to determine types for both ce and e, without
3752 ambiguity. More generally, we need only regard a type as ambiguous if it
3753 contains a variable on the left of the => that is not uniquely determined
3754 (either directly or indirectly) by the variables on the right.
3757 Dependencies also help to produce more accurate types for user defined
3758 functions, and hence to provide earlier detection of errors, and less cluttered
3759 types for programmers to work with. Recall the previous definition for a
3762 f x y = insert x y = insert x . insert y
3764 for which we originally obtained a type:
3766 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3768 Given the dependency information that we have for Collects, however, we can
3769 deduce that a and b must be equal because they both appear as the second
3770 parameter in a Collects constraint with the same first parameter c. Hence we
3771 can infer a shorter and more accurate type for f:
3773 f :: (Collects a c) => a -> a -> c -> c
3775 In a similar way, the earlier definition of g will now be flagged as a type error.
3778 Although we have given only a few examples here, it should be clear that the
3779 addition of dependency information can help to make multiple parameter classes
3780 more useful in practice, avoiding ambiguity problems, and allowing more general
3781 sets of instance declarations.
3787 <sect2 id="instance-decls">
3788 <title>Instance declarations</title>
3790 <para>An instance declaration has the form
3792 instance ( <replaceable>assertion</replaceable><subscript>1</subscript>, ..., <replaceable>assertion</replaceable><subscript>n</subscript>) => <replaceable>class</replaceable> <replaceable>type</replaceable><subscript>1</subscript> ... <replaceable>type</replaceable><subscript>m</subscript> where ...
3794 The part before the "<literal>=></literal>" is the
3795 <emphasis>context</emphasis>, while the part after the
3796 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3799 <sect3 id="flexible-instance-head">
3800 <title>Relaxed rules for the instance head</title>
3803 In Haskell 98 the head of an instance declaration
3804 must be of the form <literal>C (T a1 ... an)</literal>, where
3805 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3806 and the <literal>a1 ... an</literal> are distinct type variables.
3807 GHC relaxes these rules in two ways.
3811 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3812 declaration to mention arbitrary nested types.
3813 For example, this becomes a legal instance declaration
3815 instance C (Maybe Int) where ...
3817 See also the <link linkend="instance-overlap">rules on overlap</link>.
3820 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3821 synonyms. As always, using a type synonym is just shorthand for
3822 writing the RHS of the type synonym definition. For example:
3826 type Point = (Int,Int)
3827 instance C Point where ...
3828 instance C [Point] where ...
3832 is legal. However, if you added
3836 instance C (Int,Int) where ...
3840 as well, then the compiler will complain about the overlapping
3841 (actually, identical) instance declarations. As always, type synonyms
3842 must be fully applied. You cannot, for example, write:
3846 instance Monad P where ...
3854 <sect3 id="instance-rules">
3855 <title>Relaxed rules for instance contexts</title>
3857 <para>In Haskell 98, the assertions in the context of the instance declaration
3858 must be of the form <literal>C a</literal> where <literal>a</literal>
3859 is a type variable that occurs in the head.
3863 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3864 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3865 With this flag the context of the instance declaration can each consist of arbitrary
3866 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3870 The Paterson Conditions: for each assertion in the context
3872 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3873 <listitem><para>The assertion has fewer constructors and variables (taken together
3874 and counting repetitions) than the head</para></listitem>
3878 <listitem><para>The Coverage Condition. For each functional dependency,
3879 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3880 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3881 every type variable in
3882 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3883 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3884 substitution mapping each type variable in the class declaration to the
3885 corresponding type in the instance declaration.
3888 These restrictions ensure that context reduction terminates: each reduction
3889 step makes the problem smaller by at least one
3890 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3891 if you give the <option>-XUndecidableInstances</option>
3892 flag (<xref linkend="undecidable-instances"/>).
3893 You can find lots of background material about the reason for these
3894 restrictions in the paper <ulink
3895 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3896 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3899 For example, these are OK:
3901 instance C Int [a] -- Multiple parameters
3902 instance Eq (S [a]) -- Structured type in head
3904 -- Repeated type variable in head
3905 instance C4 a a => C4 [a] [a]
3906 instance Stateful (ST s) (MutVar s)
3908 -- Head can consist of type variables only
3910 instance (Eq a, Show b) => C2 a b
3912 -- Non-type variables in context
3913 instance Show (s a) => Show (Sized s a)
3914 instance C2 Int a => C3 Bool [a]
3915 instance C2 Int a => C3 [a] b
3919 -- Context assertion no smaller than head
3920 instance C a => C a where ...
3921 -- (C b b) has more more occurrences of b than the head
3922 instance C b b => Foo [b] where ...
3927 The same restrictions apply to instances generated by
3928 <literal>deriving</literal> clauses. Thus the following is accepted:
3930 data MinHeap h a = H a (h a)
3933 because the derived instance
3935 instance (Show a, Show (h a)) => Show (MinHeap h a)
3937 conforms to the above rules.
3941 A useful idiom permitted by the above rules is as follows.
3942 If one allows overlapping instance declarations then it's quite
3943 convenient to have a "default instance" declaration that applies if
3944 something more specific does not:
3952 <sect3 id="undecidable-instances">
3953 <title>Undecidable instances</title>
3956 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3957 For example, sometimes you might want to use the following to get the
3958 effect of a "class synonym":
3960 class (C1 a, C2 a, C3 a) => C a where { }
3962 instance (C1 a, C2 a, C3 a) => C a where { }
3964 This allows you to write shorter signatures:
3970 f :: (C1 a, C2 a, C3 a) => ...
3972 The restrictions on functional dependencies (<xref
3973 linkend="functional-dependencies"/>) are particularly troublesome.
3974 It is tempting to introduce type variables in the context that do not appear in
3975 the head, something that is excluded by the normal rules. For example:
3977 class HasConverter a b | a -> b where
3980 data Foo a = MkFoo a
3982 instance (HasConverter a b,Show b) => Show (Foo a) where
3983 show (MkFoo value) = show (convert value)
3985 This is dangerous territory, however. Here, for example, is a program that would make the
3990 instance F [a] [[a]]
3991 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3993 Similarly, it can be tempting to lift the coverage condition:
3995 class Mul a b c | a b -> c where
3996 (.*.) :: a -> b -> c
3998 instance Mul Int Int Int where (.*.) = (*)
3999 instance Mul Int Float Float where x .*. y = fromIntegral x * y
4000 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
4002 The third instance declaration does not obey the coverage condition;
4003 and indeed the (somewhat strange) definition:
4005 f = \ b x y -> if b then x .*. [y] else y
4007 makes instance inference go into a loop, because it requires the constraint
4008 <literal>(Mul a [b] b)</literal>.
4011 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
4012 the experimental flag <option>-XUndecidableInstances</option>
4013 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
4014 both the Paterson Conditions and the Coverage Condition
4015 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
4016 fixed-depth recursion stack. If you exceed the stack depth you get a
4017 sort of backtrace, and the opportunity to increase the stack depth
4018 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
4024 <sect3 id="instance-overlap">
4025 <title>Overlapping instances</title>
4027 In general, <emphasis>GHC requires that that it be unambiguous which instance
4029 should be used to resolve a type-class constraint</emphasis>. This behaviour
4030 can be modified by two flags: <option>-XOverlappingInstances</option>
4031 <indexterm><primary>-XOverlappingInstances
4032 </primary></indexterm>
4033 and <option>-XIncoherentInstances</option>
4034 <indexterm><primary>-XIncoherentInstances
4035 </primary></indexterm>, as this section discusses. Both these
4036 flags are dynamic flags, and can be set on a per-module basis, using
4037 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
4039 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
4040 it tries to match every instance declaration against the
4042 by instantiating the head of the instance declaration. For example, consider
4045 instance context1 => C Int a where ... -- (A)
4046 instance context2 => C a Bool where ... -- (B)
4047 instance context3 => C Int [a] where ... -- (C)
4048 instance context4 => C Int [Int] where ... -- (D)
4050 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
4051 but (C) and (D) do not. When matching, GHC takes
4052 no account of the context of the instance declaration
4053 (<literal>context1</literal> etc).
4054 GHC's default behaviour is that <emphasis>exactly one instance must match the
4055 constraint it is trying to resolve</emphasis>.
4056 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
4057 including both declarations (A) and (B), say); an error is only reported if a
4058 particular constraint matches more than one.
4062 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
4063 more than one instance to match, provided there is a most specific one. For
4064 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
4065 (C) and (D), but the last is more specific, and hence is chosen. If there is no
4066 most-specific match, the program is rejected.
4069 However, GHC is conservative about committing to an overlapping instance. For example:
4074 Suppose that from the RHS of <literal>f</literal> we get the constraint
4075 <literal>C Int [b]</literal>. But
4076 GHC does not commit to instance (C), because in a particular
4077 call of <literal>f</literal>, <literal>b</literal> might be instantiate
4078 to <literal>Int</literal>, in which case instance (D) would be more specific still.
4079 So GHC rejects the program.
4080 (If you add the flag <option>-XIncoherentInstances</option>,
4081 GHC will instead pick (C), without complaining about
4082 the problem of subsequent instantiations.)
4085 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
4086 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
4087 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
4088 it instead. In this case, GHC will refrain from
4089 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
4090 as before) but, rather than rejecting the program, it will infer the type
4092 f :: C Int [b] => [b] -> [b]
4094 That postpones the question of which instance to pick to the
4095 call site for <literal>f</literal>
4096 by which time more is known about the type <literal>b</literal>.
4097 You can write this type signature yourself if you use the
4098 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
4102 Exactly the same situation can arise in instance declarations themselves. Suppose we have
4106 instance Foo [b] where
4109 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
4110 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
4111 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
4112 declaration. The solution is to postpone the choice by adding the constraint to the context
4113 of the instance declaration, thus:
4115 instance C Int [b] => Foo [b] where
4118 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
4121 Warning: overlapping instances must be used with care. They
4122 can give rise to incoherence (ie different instance choices are made
4123 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
4125 {-# LANGUAGE OverlappingInstances #-}
4128 class MyShow a where
4129 myshow :: a -> String
4131 instance MyShow a => MyShow [a] where
4132 myshow xs = concatMap myshow xs
4134 showHelp :: MyShow a => [a] -> String
4135 showHelp xs = myshow xs
4137 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
4143 instance MyShow T where
4144 myshow x = "Used generic instance"
4146 instance MyShow [T] where
4147 myshow xs = "Used more specific instance"
4149 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
4151 In function <literal>showHelp</literal> GHC sees no overlapping
4152 instances, and so uses the <literal>MyShow [a]</literal> instance
4153 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
4154 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
4155 instance declaration in module <literal>Main</literal>. As a result,
4158 "Used more specific instance"
4159 "Used generic instance"
4161 (An alternative possible behaviour, not currently implemented,
4162 would be to reject module <literal>Help</literal>
4163 on the grounds that a later instance declaration might overlap the local one.)
4166 The willingness to be overlapped or incoherent is a property of
4167 the <emphasis>instance declaration</emphasis> itself, controlled by the
4168 presence or otherwise of the <option>-XOverlappingInstances</option>
4169 and <option>-XIncoherentInstances</option> flags when that module is
4170 being defined. Specifically, during the lookup process:
4173 If the constraint being looked up matches two instance declarations IA and IB,
4176 <listitem><para>IB is a substitution instance of IA (but not vice versa);
4177 that is, IB is strictly more specific than IA</para></listitem>
4178 <listitem><para>either IA or IB was compiled with <option>-XOverlappingInstances</option></para></listitem>
4180 then the less-specific instance IA is ignored.
4183 Suppose an instance declaration does not match the constraint being looked up, but
4184 does <emphasis>unify</emphasis> with it, so that it might match when the constraint is further
4185 instantiated. Usually GHC will regard this as a reason for not committing to
4186 some other constraint. But if the instance declaration was compiled with
4187 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4188 check for that declaration.
4191 These rules make it possible for a library author to design a library that relies on
4192 overlapping instances without the library client having to know.
4194 <para>The <option>-XIncoherentInstances</option> flag implies the
4195 <option>-XOverlappingInstances</option> flag, but not vice versa.
4203 <sect2 id="overloaded-strings">
4204 <title>Overloaded string literals
4208 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4209 string literal has type <literal>String</literal>, but with overloaded string
4210 literals enabled (with <literal>-XOverloadedStrings</literal>)
4211 a string literal has type <literal>(IsString a) => a</literal>.
4214 This means that the usual string syntax can be used, e.g., for packed strings
4215 and other variations of string like types. String literals behave very much
4216 like integer literals, i.e., they can be used in both expressions and patterns.
4217 If used in a pattern the literal with be replaced by an equality test, in the same
4218 way as an integer literal is.
4221 The class <literal>IsString</literal> is defined as:
4223 class IsString a where
4224 fromString :: String -> a
4226 The only predefined instance is the obvious one to make strings work as usual:
4228 instance IsString [Char] where
4231 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4232 it explicitly (for example, to give an instance declaration for it), you can import it
4233 from module <literal>GHC.Exts</literal>.
4236 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4240 Each type in a default declaration must be an
4241 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4245 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4246 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4247 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4248 <emphasis>or</emphasis> <literal>IsString</literal>.
4257 import GHC.Exts( IsString(..) )
4259 newtype MyString = MyString String deriving (Eq, Show)
4260 instance IsString MyString where
4261 fromString = MyString
4263 greet :: MyString -> MyString
4264 greet "hello" = "world"
4268 print $ greet "hello"
4269 print $ greet "fool"
4273 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4274 to work since it gets translated into an equality comparison.
4280 <sect1 id="type-families">
4281 <title>Type families</title>
4284 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4285 facilitate type-level
4286 programming. Type families are a generalisation of <firstterm>associated
4287 data types</firstterm>
4288 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4289 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4290 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4291 Symposium on Principles of Programming Languages (POPL'05)”, pages
4292 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4293 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4294 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4296 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4297 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4298 themselves are described in the paper “<ulink
4299 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4300 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4302 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4303 13th ACM SIGPLAN International Conference on Functional
4304 Programming”, ACM Press, pages 51-62, 2008. Type families
4305 essentially provide type-indexed data types and named functions on types,
4306 which are useful for generic programming and highly parameterised library
4307 interfaces as well as interfaces with enhanced static information, much like
4308 dependent types. They might also be regarded as an alternative to functional
4309 dependencies, but provide a more functional style of type-level programming
4310 than the relational style of functional dependencies.
4313 Indexed type families, or type families for short, are type constructors that
4314 represent sets of types. Set members are denoted by supplying the type family
4315 constructor with type parameters, which are called <firstterm>type
4316 indices</firstterm>. The
4317 difference between vanilla parametrised type constructors and family
4318 constructors is much like between parametrically polymorphic functions and
4319 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4320 behave the same at all type instances, whereas class methods can change their
4321 behaviour in dependence on the class type parameters. Similarly, vanilla type
4322 constructors imply the same data representation for all type instances, but
4323 family constructors can have varying representation types for varying type
4327 Indexed type families come in two flavours: <firstterm>data
4328 families</firstterm> and <firstterm>type synonym
4329 families</firstterm>. They are the indexed family variants of algebraic
4330 data types and type synonyms, respectively. The instances of data families
4331 can be data types and newtypes.
4334 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4335 Additional information on the use of type families in GHC is available on
4336 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4337 Haskell wiki page on type families</ulink>.
4340 <sect2 id="data-families">
4341 <title>Data families</title>
4344 Data families appear in two flavours: (1) they can be defined on the
4346 or (2) they can appear inside type classes (in which case they are known as
4347 associated types). The former is the more general variant, as it lacks the
4348 requirement for the type-indexes to coincide with the class
4349 parameters. However, the latter can lead to more clearly structured code and
4350 compiler warnings if some type instances were - possibly accidentally -
4351 omitted. In the following, we always discuss the general toplevel form first
4352 and then cover the additional constraints placed on associated types.
4355 <sect3 id="data-family-declarations">
4356 <title>Data family declarations</title>
4359 Indexed data families are introduced by a signature, such as
4361 data family GMap k :: * -> *
4363 The special <literal>family</literal> distinguishes family from standard
4364 data declarations. The result kind annotation is optional and, as
4365 usual, defaults to <literal>*</literal> if omitted. An example is
4369 Named arguments can also be given explicit kind signatures if needed.
4371 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4372 declarations] named arguments are entirely optional, so that we can
4373 declare <literal>Array</literal> alternatively with
4375 data family Array :: * -> *
4379 <sect4 id="assoc-data-family-decl">
4380 <title>Associated data family declarations</title>
4382 When a data family is declared as part of a type class, we drop
4383 the <literal>family</literal> special. The <literal>GMap</literal>
4384 declaration takes the following form
4386 class GMapKey k where
4387 data GMap k :: * -> *
4390 In contrast to toplevel declarations, named arguments must be used for
4391 all type parameters that are to be used as type-indexes. Moreover,
4392 the argument names must be class parameters. Each class parameter may
4393 only be used at most once per associated type, but some may be omitted
4394 and they may be in an order other than in the class head. Hence, the
4395 following contrived example is admissible:
4404 <sect3 id="data-instance-declarations">
4405 <title>Data instance declarations</title>
4408 Instance declarations of data and newtype families are very similar to
4409 standard data and newtype declarations. The only two differences are
4410 that the keyword <literal>data</literal> or <literal>newtype</literal>
4411 is followed by <literal>instance</literal> and that some or all of the
4412 type arguments can be non-variable types, but may not contain forall
4413 types or type synonym families. However, data families are generally
4414 allowed in type parameters, and type synonyms are allowed as long as
4415 they are fully applied and expand to a type that is itself admissible -
4416 exactly as this is required for occurrences of type synonyms in class
4417 instance parameters. For example, the <literal>Either</literal>
4418 instance for <literal>GMap</literal> is
4420 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4422 In this example, the declaration has only one variant. In general, it
4426 Data and newtype instance declarations are only permitted when an
4427 appropriate family declaration is in scope - just as a class instance declaratoin
4428 requires the class declaration to be visible. Moreover, each instance
4429 declaration has to conform to the kind determined by its family
4430 declaration. This implies that the number of parameters of an instance
4431 declaration matches the arity determined by the kind of the family.
4434 A data family instance declaration can use the full exprssiveness of
4435 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4437 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4438 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4439 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4442 data instance T Int = T1 Int | T2 Bool
4443 newtype instance T Char = TC Bool
4446 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4447 and indeed can define a GADT. For example:
4450 data instance G [a] b where
4451 G1 :: c -> G [Int] b
4455 <listitem><para> You can use a <literal>deriving</literal> clause on a
4456 <literal>data instance</literal> or <literal>newtype instance</literal>
4463 Even if type families are defined as toplevel declarations, functions
4464 that perform different computations for different family instances may still
4465 need to be defined as methods of type classes. In particular, the
4466 following is not possible:
4469 data instance T Int = A
4470 data instance T Char = B
4472 foo A = 1 -- WRONG: These two equations together...
4473 foo B = 2 -- ...will produce a type error.
4475 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4479 instance Foo Int where
4481 instance Foo Char where
4484 (Given the functionality provided by GADTs (Generalised Algebraic Data
4485 Types), it might seem as if a definition, such as the above, should be
4486 feasible. However, type families are - in contrast to GADTs - are
4487 <emphasis>open;</emphasis> i.e., new instances can always be added,
4489 modules. Supporting pattern matching across different data instances
4490 would require a form of extensible case construct.)
4493 <sect4 id="assoc-data-inst">
4494 <title>Associated data instances</title>
4496 When an associated data family instance is declared within a type
4497 class instance, we drop the <literal>instance</literal> keyword in the
4498 family instance. So, the <literal>Either</literal> instance
4499 for <literal>GMap</literal> becomes:
4501 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4502 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4505 The most important point about associated family instances is that the
4506 type indexes corresponding to class parameters must be identical to
4507 the type given in the instance head; here this is the first argument
4508 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4509 which coincides with the only class parameter. Any parameters to the
4510 family constructor that do not correspond to class parameters, need to
4511 be variables in every instance; here this is the
4512 variable <literal>v</literal>.
4515 Instances for an associated family can only appear as part of
4516 instances declarations of the class in which the family was declared -
4517 just as with the equations of the methods of a class. Also in
4518 correspondence to how methods are handled, declarations of associated
4519 types can be omitted in class instances. If an associated family
4520 instance is omitted, the corresponding instance type is not inhabited;
4521 i.e., only diverging expressions, such
4522 as <literal>undefined</literal>, can assume the type.
4526 <sect4 id="scoping-class-params">
4527 <title>Scoping of class parameters</title>
4529 In the case of multi-parameter type classes, the visibility of class
4530 parameters in the right-hand side of associated family instances
4531 depends <emphasis>solely</emphasis> on the parameters of the data
4532 family. As an example, consider the simple class declaration
4537 Only one of the two class parameters is a parameter to the data
4538 family. Hence, the following instance declaration is invalid:
4540 instance C [c] d where
4541 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4543 Here, the right-hand side of the data instance mentions the type
4544 variable <literal>d</literal> that does not occur in its left-hand
4545 side. We cannot admit such data instances as they would compromise
4550 <sect4 id="family-class-inst">
4551 <title>Type class instances of family instances</title>
4553 Type class instances of instances of data families can be defined as
4554 usual, and in particular data instance declarations can
4555 have <literal>deriving</literal> clauses. For example, we can write
4557 data GMap () v = GMapUnit (Maybe v)
4560 which implicitly defines an instance of the form
4562 instance Show v => Show (GMap () v) where ...
4566 Note that class instances are always for
4567 particular <emphasis>instances</emphasis> of a data family and never
4568 for an entire family as a whole. This is for essentially the same
4569 reasons that we cannot define a toplevel function that performs
4570 pattern matching on the data constructors
4571 of <emphasis>different</emphasis> instances of a single type family.
4572 It would require a form of extensible case construct.
4576 <sect4 id="data-family-overlap">
4577 <title>Overlap of data instances</title>
4579 The instance declarations of a data family used in a single program
4580 may not overlap at all, independent of whether they are associated or
4581 not. In contrast to type class instances, this is not only a matter
4582 of consistency, but one of type safety.
4588 <sect3 id="data-family-import-export">
4589 <title>Import and export</title>
4592 The association of data constructors with type families is more dynamic
4593 than that is the case with standard data and newtype declarations. In
4594 the standard case, the notation <literal>T(..)</literal> in an import or
4595 export list denotes the type constructor and all the data constructors
4596 introduced in its declaration. However, a family declaration never
4597 introduces any data constructors; instead, data constructors are
4598 introduced by family instances. As a result, which data constructors
4599 are associated with a type family depends on the currently visible
4600 instance declarations for that family. Consequently, an import or
4601 export item of the form <literal>T(..)</literal> denotes the family
4602 constructor and all currently visible data constructors - in the case of
4603 an export item, these may be either imported or defined in the current
4604 module. The treatment of import and export items that explicitly list
4605 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4609 <sect4 id="data-family-impexp-assoc">
4610 <title>Associated families</title>
4612 As expected, an import or export item of the
4613 form <literal>C(..)</literal> denotes all of the class' methods and
4614 associated types. However, when associated types are explicitly
4615 listed as subitems of a class, we need some new syntax, as uppercase
4616 identifiers as subitems are usually data constructors, not type
4617 constructors. To clarify that we denote types here, each associated
4618 type name needs to be prefixed by the keyword <literal>type</literal>.
4619 So for example, when explicitly listing the components of
4620 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4621 GMap, empty, lookup, insert)</literal>.
4625 <sect4 id="data-family-impexp-examples">
4626 <title>Examples</title>
4628 Assuming our running <literal>GMapKey</literal> class example, let us
4629 look at some export lists and their meaning:
4632 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4633 just the class name.</para>
4636 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4637 Exports the class, the associated type <literal>GMap</literal>
4639 functions <literal>empty</literal>, <literal>lookup</literal>,
4640 and <literal>insert</literal>. None of the data constructors is
4644 <para><literal>module GMap (GMapKey(..), GMap(..))
4645 where...</literal>: As before, but also exports all the data
4646 constructors <literal>GMapInt</literal>,
4647 <literal>GMapChar</literal>,
4648 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4649 and <literal>GMapUnit</literal>.</para>
4652 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4653 GMap(..)) where...</literal>: As before.</para>
4656 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4657 where...</literal>: As before.</para>
4662 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4663 both the class <literal>GMapKey</literal> as well as its associated
4664 type <literal>GMap</literal>. However, you cannot
4665 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4666 sub-component specifications cannot be nested. To
4667 specify <literal>GMap</literal>'s data constructors, you have to list
4672 <sect4 id="data-family-impexp-instances">
4673 <title>Instances</title>
4675 Family instances are implicitly exported, just like class instances.
4676 However, this applies only to the heads of instances, not to the data
4677 constructors an instance defines.
4685 <sect2 id="synonym-families">
4686 <title>Synonym families</title>
4689 Type families appear in two flavours: (1) they can be defined on the
4690 toplevel or (2) they can appear inside type classes (in which case they
4691 are known as associated type synonyms). The former is the more general
4692 variant, as it lacks the requirement for the type-indexes to coincide with
4693 the class parameters. However, the latter can lead to more clearly
4694 structured code and compiler warnings if some type instances were -
4695 possibly accidentally - omitted. In the following, we always discuss the
4696 general toplevel form first and then cover the additional constraints
4697 placed on associated types.
4700 <sect3 id="type-family-declarations">
4701 <title>Type family declarations</title>
4704 Indexed type families are introduced by a signature, such as
4706 type family Elem c :: *
4708 The special <literal>family</literal> distinguishes family from standard
4709 type declarations. The result kind annotation is optional and, as
4710 usual, defaults to <literal>*</literal> if omitted. An example is
4714 Parameters can also be given explicit kind signatures if needed. We
4715 call the number of parameters in a type family declaration, the family's
4716 arity, and all applications of a type family must be fully saturated
4717 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4718 and it implies that the kind of a type family is not sufficient to
4719 determine a family's arity, and hence in general, also insufficient to
4720 determine whether a type family application is well formed. As an
4721 example, consider the following declaration:
4723 type family F a b :: * -> * -- F's arity is 2,
4724 -- although its overall kind is * -> * -> * -> *
4726 Given this declaration the following are examples of well-formed and
4729 F Char [Int] -- OK! Kind: * -> *
4730 F Char [Int] Bool -- OK! Kind: *
4731 F IO Bool -- WRONG: kind mismatch in the first argument
4732 F Bool -- WRONG: unsaturated application
4736 <sect4 id="assoc-type-family-decl">
4737 <title>Associated type family declarations</title>
4739 When a type family is declared as part of a type class, we drop
4740 the <literal>family</literal> special. The <literal>Elem</literal>
4741 declaration takes the following form
4743 class Collects ce where
4747 The argument names of the type family must be class parameters. Each
4748 class parameter may only be used at most once per associated type, but
4749 some may be omitted and they may be in an order other than in the
4750 class head. Hence, the following contrived example is admissible:
4755 These rules are exactly as for associated data families.
4760 <sect3 id="type-instance-declarations">
4761 <title>Type instance declarations</title>
4763 Instance declarations of type families are very similar to standard type
4764 synonym declarations. The only two differences are that the
4765 keyword <literal>type</literal> is followed
4766 by <literal>instance</literal> and that some or all of the type
4767 arguments can be non-variable types, but may not contain forall types or
4768 type synonym families. However, data families are generally allowed, and
4769 type synonyms are allowed as long as they are fully applied and expand
4770 to a type that is admissible - these are the exact same requirements as
4771 for data instances. For example, the <literal>[e]</literal> instance
4772 for <literal>Elem</literal> is
4774 type instance Elem [e] = e
4778 Type family instance declarations are only legitimate when an
4779 appropriate family declaration is in scope - just like class instances
4780 require the class declaration to be visible. Moreover, each instance
4781 declaration has to conform to the kind determined by its family
4782 declaration, and the number of type parameters in an instance
4783 declaration must match the number of type parameters in the family
4784 declaration. Finally, the right-hand side of a type instance must be a
4785 monotype (i.e., it may not include foralls) and after the expansion of
4786 all saturated vanilla type synonyms, no synonyms, except family synonyms
4787 may remain. Here are some examples of admissible and illegal type
4790 type family F a :: *
4791 type instance F [Int] = Int -- OK!
4792 type instance F String = Char -- OK!
4793 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4794 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4795 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4797 type family G a b :: * -> *
4798 type instance G Int = (,) -- WRONG: must be two type parameters
4799 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4803 <sect4 id="assoc-type-instance">
4804 <title>Associated type instance declarations</title>
4806 When an associated family instance is declared within a type class
4807 instance, we drop the <literal>instance</literal> keyword in the family
4808 instance. So, the <literal>[e]</literal> instance
4809 for <literal>Elem</literal> becomes:
4811 instance (Eq (Elem [e])) => Collects ([e]) where
4815 The most important point about associated family instances is that the
4816 type indexes corresponding to class parameters must be identical to the
4817 type given in the instance head; here this is <literal>[e]</literal>,
4818 which coincides with the only class parameter.
4821 Instances for an associated family can only appear as part of instances
4822 declarations of the class in which the family was declared - just as
4823 with the equations of the methods of a class. Also in correspondence to
4824 how methods are handled, declarations of associated types can be omitted
4825 in class instances. If an associated family instance is omitted, the
4826 corresponding instance type is not inhabited; i.e., only diverging
4827 expressions, such as <literal>undefined</literal>, can assume the type.
4831 <sect4 id="type-family-overlap">
4832 <title>Overlap of type synonym instances</title>
4834 The instance declarations of a type family used in a single program
4835 may only overlap if the right-hand sides of the overlapping instances
4836 coincide for the overlapping types. More formally, two instance
4837 declarations overlap if there is a substitution that makes the
4838 left-hand sides of the instances syntactically the same. Whenever
4839 that is the case, the right-hand sides of the instances must also be
4840 syntactically equal under the same substitution. This condition is
4841 independent of whether the type family is associated or not, and it is
4842 not only a matter of consistency, but one of type safety.
4845 Here are two example to illustrate the condition under which overlap
4848 type instance F (a, Int) = [a]
4849 type instance F (Int, b) = [b] -- overlap permitted
4851 type instance G (a, Int) = [a]
4852 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4857 <sect4 id="type-family-decidability">
4858 <title>Decidability of type synonym instances</title>
4860 In order to guarantee that type inference in the presence of type
4861 families decidable, we need to place a number of additional
4862 restrictions on the formation of type instance declarations (c.f.,
4863 Definition 5 (Relaxed Conditions) of “<ulink
4864 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4865 Checking with Open Type Functions</ulink>”). Instance
4866 declarations have the general form
4868 type instance F t1 .. tn = t
4870 where we require that for every type family application <literal>(G s1
4871 .. sm)</literal> in <literal>t</literal>,
4874 <para><literal>s1 .. sm</literal> do not contain any type family
4875 constructors,</para>
4878 <para>the total number of symbols (data type constructors and type
4879 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4880 in <literal>t1 .. tn</literal>, and</para>
4883 <para>for every type
4884 variable <literal>a</literal>, <literal>a</literal> occurs
4885 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4886 .. tn</literal>.</para>
4889 These restrictions are easily verified and ensure termination of type
4890 inference. However, they are not sufficient to guarantee completeness
4891 of type inference in the presence of, so called, ''loopy equalities'',
4892 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4893 a type variable is underneath a family application and data
4894 constructor application - see the above mentioned paper for details.
4897 If the option <option>-XUndecidableInstances</option> is passed to the
4898 compiler, the above restrictions are not enforced and it is on the
4899 programmer to ensure termination of the normalisation of type families
4900 during type inference.
4905 <sect3 id-="equality-constraints">
4906 <title>Equality constraints</title>
4908 Type context can include equality constraints of the form <literal>t1 ~
4909 t2</literal>, which denote that the types <literal>t1</literal>
4910 and <literal>t2</literal> need to be the same. In the presence of type
4911 families, whether two types are equal cannot generally be decided
4912 locally. Hence, the contexts of function signatures may include
4913 equality constraints, as in the following example:
4915 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4917 where we require that the element type of <literal>c1</literal>
4918 and <literal>c2</literal> are the same. In general, the
4919 types <literal>t1</literal> and <literal>t2</literal> of an equality
4920 constraint may be arbitrary monotypes; i.e., they may not contain any
4921 quantifiers, independent of whether higher-rank types are otherwise
4925 Equality constraints can also appear in class and instance contexts.
4926 The former enable a simple translation of programs using functional
4927 dependencies into programs using family synonyms instead. The general
4928 idea is to rewrite a class declaration of the form
4930 class C a b | a -> b
4934 class (F a ~ b) => C a b where
4937 That is, we represent every functional dependency (FD) <literal>a1 .. an
4938 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4939 superclass context equality <literal>F a1 .. an ~ b</literal>,
4940 essentially giving a name to the functional dependency. In class
4941 instances, we define the type instances of FD families in accordance
4942 with the class head. Method signatures are not affected by that
4946 NB: Equalities in superclass contexts are not fully implemented in
4951 <sect3 id-="ty-fams-in-instances">
4952 <title>Type families and instance declarations</title>
4953 <para>Type families require us to extend the rules for
4954 the form of instance heads, which are given
4955 in <xref linkend="flexible-instance-head"/>.
4958 <listitem><para>Data type families may appear in an instance head</para></listitem>
4959 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4961 The reason for the latter restriction is that there is no way to check for. Consider
4964 type instance F Bool = Int
4971 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4972 The situation is especially bad because the type instance for <literal>F Bool</literal>
4973 might be in another module, or even in a module that is not yet written.
4980 <sect1 id="other-type-extensions">
4981 <title>Other type system extensions</title>
4983 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4985 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4986 is used, the keyword <literal>forall</literal>
4987 allows us to say exactly what this means. For example:
4995 g :: forall b. (b -> b)
4997 The two are treated identically.
5000 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5001 a type variable any more!
5006 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
5008 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
5009 that the type-class constraints in a type signature must have the
5010 form <emphasis>(class type-variable)</emphasis> or
5011 <emphasis>(class (type-variable type-variable ...))</emphasis>.
5012 With <option>-XFlexibleContexts</option>
5013 these type signatures are perfectly OK
5016 g :: Ord (T a ()) => ...
5018 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
5019 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
5020 (<xref linkend="instance-rules"/>).
5024 GHC imposes the following restrictions on the constraints in a type signature.
5028 forall tv1..tvn (c1, ...,cn) => type
5031 (Here, we write the "foralls" explicitly, although the Haskell source
5032 language omits them; in Haskell 98, all the free type variables of an
5033 explicit source-language type signature are universally quantified,
5034 except for the class type variables in a class declaration. However,
5035 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
5044 <emphasis>Each universally quantified type variable
5045 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
5047 A type variable <literal>a</literal> is "reachable" if it appears
5048 in the same constraint as either a type variable free in
5049 <literal>type</literal>, or another reachable type variable.
5050 A value with a type that does not obey
5051 this reachability restriction cannot be used without introducing
5052 ambiguity; that is why the type is rejected.
5053 Here, for example, is an illegal type:
5057 forall a. Eq a => Int
5061 When a value with this type was used, the constraint <literal>Eq tv</literal>
5062 would be introduced where <literal>tv</literal> is a fresh type variable, and
5063 (in the dictionary-translation implementation) the value would be
5064 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
5065 can never know which instance of <literal>Eq</literal> to use because we never
5066 get any more information about <literal>tv</literal>.
5070 that the reachability condition is weaker than saying that <literal>a</literal> is
5071 functionally dependent on a type variable free in
5072 <literal>type</literal> (see <xref
5073 linkend="functional-dependencies"/>). The reason for this is there
5074 might be a "hidden" dependency, in a superclass perhaps. So
5075 "reachable" is a conservative approximation to "functionally dependent".
5076 For example, consider:
5078 class C a b | a -> b where ...
5079 class C a b => D a b where ...
5080 f :: forall a b. D a b => a -> a
5082 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
5083 but that is not immediately apparent from <literal>f</literal>'s type.
5089 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
5090 universally quantified type variables <literal>tvi</literal></emphasis>.
5092 For example, this type is OK because <literal>C a b</literal> mentions the
5093 universally quantified type variable <literal>b</literal>:
5097 forall a. C a b => burble
5101 The next type is illegal because the constraint <literal>Eq b</literal> does not
5102 mention <literal>a</literal>:
5106 forall a. Eq b => burble
5110 The reason for this restriction is milder than the other one. The
5111 excluded types are never useful or necessary (because the offending
5112 context doesn't need to be witnessed at this point; it can be floated
5113 out). Furthermore, floating them out increases sharing. Lastly,
5114 excluding them is a conservative choice; it leaves a patch of
5115 territory free in case we need it later.
5126 <sect2 id="implicit-parameters">
5127 <title>Implicit parameters</title>
5129 <para> Implicit parameters are implemented as described in
5130 "Implicit parameters: dynamic scoping with static types",
5131 J Lewis, MB Shields, E Meijer, J Launchbury,
5132 27th ACM Symposium on Principles of Programming Languages (POPL'00),
5136 <para>(Most of the following, still rather incomplete, documentation is
5137 due to Jeff Lewis.)</para>
5139 <para>Implicit parameter support is enabled with the option
5140 <option>-XImplicitParams</option>.</para>
5143 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
5144 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
5145 context. In Haskell, all variables are statically bound. Dynamic
5146 binding of variables is a notion that goes back to Lisp, but was later
5147 discarded in more modern incarnations, such as Scheme. Dynamic binding
5148 can be very confusing in an untyped language, and unfortunately, typed
5149 languages, in particular Hindley-Milner typed languages like Haskell,
5150 only support static scoping of variables.
5153 However, by a simple extension to the type class system of Haskell, we
5154 can support dynamic binding. Basically, we express the use of a
5155 dynamically bound variable as a constraint on the type. These
5156 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
5157 function uses a dynamically-bound variable <literal>?x</literal>
5158 of type <literal>t'</literal>". For
5159 example, the following expresses the type of a sort function,
5160 implicitly parameterized by a comparison function named <literal>cmp</literal>.
5162 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5164 The dynamic binding constraints are just a new form of predicate in the type class system.
5167 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5168 where <literal>x</literal> is
5169 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5170 Use of this construct also introduces a new
5171 dynamic-binding constraint in the type of the expression.
5172 For example, the following definition
5173 shows how we can define an implicitly parameterized sort function in
5174 terms of an explicitly parameterized <literal>sortBy</literal> function:
5176 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5178 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5184 <title>Implicit-parameter type constraints</title>
5186 Dynamic binding constraints behave just like other type class
5187 constraints in that they are automatically propagated. Thus, when a
5188 function is used, its implicit parameters are inherited by the
5189 function that called it. For example, our <literal>sort</literal> function might be used
5190 to pick out the least value in a list:
5192 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5193 least xs = head (sort xs)
5195 Without lifting a finger, the <literal>?cmp</literal> parameter is
5196 propagated to become a parameter of <literal>least</literal> as well. With explicit
5197 parameters, the default is that parameters must always be explicit
5198 propagated. With implicit parameters, the default is to always
5202 An implicit-parameter type constraint differs from other type class constraints in the
5203 following way: All uses of a particular implicit parameter must have
5204 the same type. This means that the type of <literal>(?x, ?x)</literal>
5205 is <literal>(?x::a) => (a,a)</literal>, and not
5206 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5210 <para> You can't have an implicit parameter in the context of a class or instance
5211 declaration. For example, both these declarations are illegal:
5213 class (?x::Int) => C a where ...
5214 instance (?x::a) => Foo [a] where ...
5216 Reason: exactly which implicit parameter you pick up depends on exactly where
5217 you invoke a function. But the ``invocation'' of instance declarations is done
5218 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5219 Easiest thing is to outlaw the offending types.</para>
5221 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5223 f :: (?x :: [a]) => Int -> Int
5226 g :: (Read a, Show a) => String -> String
5229 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5230 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5231 quite unambiguous, and fixes the type <literal>a</literal>.
5236 <title>Implicit-parameter bindings</title>
5239 An implicit parameter is <emphasis>bound</emphasis> using the standard
5240 <literal>let</literal> or <literal>where</literal> binding forms.
5241 For example, we define the <literal>min</literal> function by binding
5242 <literal>cmp</literal>.
5245 min = let ?cmp = (<=) in least
5249 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5250 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5251 (including in a list comprehension, or do-notation, or pattern guards),
5252 or a <literal>where</literal> clause.
5253 Note the following points:
5256 An implicit-parameter binding group must be a
5257 collection of simple bindings to implicit-style variables (no
5258 function-style bindings, and no type signatures); these bindings are
5259 neither polymorphic or recursive.
5262 You may not mix implicit-parameter bindings with ordinary bindings in a
5263 single <literal>let</literal>
5264 expression; use two nested <literal>let</literal>s instead.
5265 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5269 You may put multiple implicit-parameter bindings in a
5270 single binding group; but they are <emphasis>not</emphasis> treated
5271 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5272 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5273 parameter. The bindings are not nested, and may be re-ordered without changing
5274 the meaning of the program.
5275 For example, consider:
5277 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5279 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5280 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5282 f :: (?x::Int) => Int -> Int
5290 <sect3><title>Implicit parameters and polymorphic recursion</title>
5293 Consider these two definitions:
5296 len1 xs = let ?acc = 0 in len_acc1 xs
5299 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5304 len2 xs = let ?acc = 0 in len_acc2 xs
5306 len_acc2 :: (?acc :: Int) => [a] -> Int
5308 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5310 The only difference between the two groups is that in the second group
5311 <literal>len_acc</literal> is given a type signature.
5312 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5313 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5314 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5315 has a type signature, the recursive call is made to the
5316 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5317 as an implicit parameter. So we get the following results in GHCi:
5324 Adding a type signature dramatically changes the result! This is a rather
5325 counter-intuitive phenomenon, worth watching out for.
5329 <sect3><title>Implicit parameters and monomorphism</title>
5331 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5332 Haskell Report) to implicit parameters. For example, consider:
5340 Since the binding for <literal>y</literal> falls under the Monomorphism
5341 Restriction it is not generalised, so the type of <literal>y</literal> is
5342 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5343 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5344 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5345 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5346 <literal>y</literal> in the body of the <literal>let</literal> will see the
5347 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5348 <literal>14</literal>.
5353 <!-- ======================= COMMENTED OUT ========================
5355 We intend to remove linear implicit parameters, so I'm at least removing
5356 them from the 6.6 user manual
5358 <sect2 id="linear-implicit-parameters">
5359 <title>Linear implicit parameters</title>
5361 Linear implicit parameters are an idea developed by Koen Claessen,
5362 Mark Shields, and Simon PJ. They address the long-standing
5363 problem that monads seem over-kill for certain sorts of problem, notably:
5366 <listitem> <para> distributing a supply of unique names </para> </listitem>
5367 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5368 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5372 Linear implicit parameters are just like ordinary implicit parameters,
5373 except that they are "linear"; that is, they cannot be copied, and
5374 must be explicitly "split" instead. Linear implicit parameters are
5375 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5376 (The '/' in the '%' suggests the split!)
5381 import GHC.Exts( Splittable )
5383 data NameSupply = ...
5385 splitNS :: NameSupply -> (NameSupply, NameSupply)
5386 newName :: NameSupply -> Name
5388 instance Splittable NameSupply where
5392 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5393 f env (Lam x e) = Lam x' (f env e)
5396 env' = extend env x x'
5397 ...more equations for f...
5399 Notice that the implicit parameter %ns is consumed
5401 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5402 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5406 So the translation done by the type checker makes
5407 the parameter explicit:
5409 f :: NameSupply -> Env -> Expr -> Expr
5410 f ns env (Lam x e) = Lam x' (f ns1 env e)
5412 (ns1,ns2) = splitNS ns
5414 env = extend env x x'
5416 Notice the call to 'split' introduced by the type checker.
5417 How did it know to use 'splitNS'? Because what it really did
5418 was to introduce a call to the overloaded function 'split',
5419 defined by the class <literal>Splittable</literal>:
5421 class Splittable a where
5424 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5425 split for name supplies. But we can simply write
5431 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5433 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5434 <literal>GHC.Exts</literal>.
5439 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5440 are entirely distinct implicit parameters: you
5441 can use them together and they won't interfere with each other. </para>
5444 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5446 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5447 in the context of a class or instance declaration. </para></listitem>
5451 <sect3><title>Warnings</title>
5454 The monomorphism restriction is even more important than usual.
5455 Consider the example above:
5457 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5458 f env (Lam x e) = Lam x' (f env e)
5461 env' = extend env x x'
5463 If we replaced the two occurrences of x' by (newName %ns), which is
5464 usually a harmless thing to do, we get:
5466 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5467 f env (Lam x e) = Lam (newName %ns) (f env e)
5469 env' = extend env x (newName %ns)
5471 But now the name supply is consumed in <emphasis>three</emphasis> places
5472 (the two calls to newName,and the recursive call to f), so
5473 the result is utterly different. Urk! We don't even have
5477 Well, this is an experimental change. With implicit
5478 parameters we have already lost beta reduction anyway, and
5479 (as John Launchbury puts it) we can't sensibly reason about
5480 Haskell programs without knowing their typing.
5485 <sect3><title>Recursive functions</title>
5486 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5489 foo :: %x::T => Int -> [Int]
5491 foo n = %x : foo (n-1)
5493 where T is some type in class Splittable.</para>
5495 Do you get a list of all the same T's or all different T's
5496 (assuming that split gives two distinct T's back)?
5498 If you supply the type signature, taking advantage of polymorphic
5499 recursion, you get what you'd probably expect. Here's the
5500 translated term, where the implicit param is made explicit:
5503 foo x n = let (x1,x2) = split x
5504 in x1 : foo x2 (n-1)
5506 But if you don't supply a type signature, GHC uses the Hindley
5507 Milner trick of using a single monomorphic instance of the function
5508 for the recursive calls. That is what makes Hindley Milner type inference
5509 work. So the translation becomes
5513 foom n = x : foom (n-1)
5517 Result: 'x' is not split, and you get a list of identical T's. So the
5518 semantics of the program depends on whether or not foo has a type signature.
5521 You may say that this is a good reason to dislike linear implicit parameters
5522 and you'd be right. That is why they are an experimental feature.
5528 ================ END OF Linear Implicit Parameters commented out -->
5530 <sect2 id="kinding">
5531 <title>Explicitly-kinded quantification</title>
5534 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5535 to give the kind explicitly as (machine-checked) documentation,
5536 just as it is nice to give a type signature for a function. On some occasions,
5537 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5538 John Hughes had to define the data type:
5540 data Set cxt a = Set [a]
5541 | Unused (cxt a -> ())
5543 The only use for the <literal>Unused</literal> constructor was to force the correct
5544 kind for the type variable <literal>cxt</literal>.
5547 GHC now instead allows you to specify the kind of a type variable directly, wherever
5548 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5551 This flag enables kind signatures in the following places:
5553 <listitem><para><literal>data</literal> declarations:
5555 data Set (cxt :: * -> *) a = Set [a]
5556 </screen></para></listitem>
5557 <listitem><para><literal>type</literal> declarations:
5559 type T (f :: * -> *) = f Int
5560 </screen></para></listitem>
5561 <listitem><para><literal>class</literal> declarations:
5563 class (Eq a) => C (f :: * -> *) a where ...
5564 </screen></para></listitem>
5565 <listitem><para><literal>forall</literal>'s in type signatures:
5567 f :: forall (cxt :: * -> *). Set cxt Int
5568 </screen></para></listitem>
5573 The parentheses are required. Some of the spaces are required too, to
5574 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5575 will get a parse error, because "<literal>::*->*</literal>" is a
5576 single lexeme in Haskell.
5580 As part of the same extension, you can put kind annotations in types
5583 f :: (Int :: *) -> Int
5584 g :: forall a. a -> (a :: *)
5588 atype ::= '(' ctype '::' kind ')
5590 The parentheses are required.
5595 <sect2 id="universal-quantification">
5596 <title>Arbitrary-rank polymorphism
5600 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5601 explicit universal quantification in
5603 For example, all the following types are legal:
5605 f1 :: forall a b. a -> b -> a
5606 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5608 f2 :: (forall a. a->a) -> Int -> Int
5609 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5611 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5613 f4 :: Int -> (forall a. a -> a)
5615 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5616 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5617 The <literal>forall</literal> makes explicit the universal quantification that
5618 is implicitly added by Haskell.
5621 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5622 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5623 shows, the polymorphic type on the left of the function arrow can be overloaded.
5626 The function <literal>f3</literal> has a rank-3 type;
5627 it has rank-2 types on the left of a function arrow.
5630 GHC has three flags to control higher-rank types:
5633 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5636 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5639 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5640 That is, you can nest <literal>forall</literal>s
5641 arbitrarily deep in function arrows.
5642 In particular, a forall-type (also called a "type scheme"),
5643 including an operational type class context, is legal:
5645 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5646 of a function arrow </para> </listitem>
5647 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5648 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5649 field type signatures.</para> </listitem>
5650 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5651 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5663 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5664 the types of the constructor arguments. Here are several examples:
5670 data T a = T1 (forall b. b -> b -> b) a
5672 data MonadT m = MkMonad { return :: forall a. a -> m a,
5673 bind :: forall a b. m a -> (a -> m b) -> m b
5676 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5682 The constructors have rank-2 types:
5688 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5689 MkMonad :: forall m. (forall a. a -> m a)
5690 -> (forall a b. m a -> (a -> m b) -> m b)
5692 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5698 Notice that you don't need to use a <literal>forall</literal> if there's an
5699 explicit context. For example in the first argument of the
5700 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5701 prefixed to the argument type. The implicit <literal>forall</literal>
5702 quantifies all type variables that are not already in scope, and are
5703 mentioned in the type quantified over.
5707 As for type signatures, implicit quantification happens for non-overloaded
5708 types too. So if you write this:
5711 data T a = MkT (Either a b) (b -> b)
5714 it's just as if you had written this:
5717 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5720 That is, since the type variable <literal>b</literal> isn't in scope, it's
5721 implicitly universally quantified. (Arguably, it would be better
5722 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5723 where that is what is wanted. Feedback welcomed.)
5727 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5728 the constructor to suitable values, just as usual. For example,
5739 a3 = MkSwizzle reverse
5742 a4 = let r x = Just x
5749 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5750 mkTs f x y = [T1 f x, T1 f y]
5756 The type of the argument can, as usual, be more general than the type
5757 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5758 does not need the <literal>Ord</literal> constraint.)
5762 When you use pattern matching, the bound variables may now have
5763 polymorphic types. For example:
5769 f :: T a -> a -> (a, Char)
5770 f (T1 w k) x = (w k x, w 'c' 'd')
5772 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5773 g (MkSwizzle s) xs f = s (map f (s xs))
5775 h :: MonadT m -> [m a] -> m [a]
5776 h m [] = return m []
5777 h m (x:xs) = bind m x $ \y ->
5778 bind m (h m xs) $ \ys ->
5785 In the function <function>h</function> we use the record selectors <literal>return</literal>
5786 and <literal>bind</literal> to extract the polymorphic bind and return functions
5787 from the <literal>MonadT</literal> data structure, rather than using pattern
5793 <title>Type inference</title>
5796 In general, type inference for arbitrary-rank types is undecidable.
5797 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5798 to get a decidable algorithm by requiring some help from the programmer.
5799 We do not yet have a formal specification of "some help" but the rule is this:
5802 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5803 provides an explicit polymorphic type for x, or GHC's type inference will assume
5804 that x's type has no foralls in it</emphasis>.
5807 What does it mean to "provide" an explicit type for x? You can do that by
5808 giving a type signature for x directly, using a pattern type signature
5809 (<xref linkend="scoped-type-variables"/>), thus:
5811 \ f :: (forall a. a->a) -> (f True, f 'c')
5813 Alternatively, you can give a type signature to the enclosing
5814 context, which GHC can "push down" to find the type for the variable:
5816 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5818 Here the type signature on the expression can be pushed inwards
5819 to give a type signature for f. Similarly, and more commonly,
5820 one can give a type signature for the function itself:
5822 h :: (forall a. a->a) -> (Bool,Char)
5823 h f = (f True, f 'c')
5825 You don't need to give a type signature if the lambda bound variable
5826 is a constructor argument. Here is an example we saw earlier:
5828 f :: T a -> a -> (a, Char)
5829 f (T1 w k) x = (w k x, w 'c' 'd')
5831 Here we do not need to give a type signature to <literal>w</literal>, because
5832 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5839 <sect3 id="implicit-quant">
5840 <title>Implicit quantification</title>
5843 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5844 user-written types, if and only if there is no explicit <literal>forall</literal>,
5845 GHC finds all the type variables mentioned in the type that are not already
5846 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5850 f :: forall a. a -> a
5857 h :: forall b. a -> b -> b
5863 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5866 f :: (a -> a) -> Int
5868 f :: forall a. (a -> a) -> Int
5870 f :: (forall a. a -> a) -> Int
5873 g :: (Ord a => a -> a) -> Int
5874 -- MEANS the illegal type
5875 g :: forall a. (Ord a => a -> a) -> Int
5877 g :: (forall a. Ord a => a -> a) -> Int
5879 The latter produces an illegal type, which you might think is silly,
5880 but at least the rule is simple. If you want the latter type, you
5881 can write your for-alls explicitly. Indeed, doing so is strongly advised
5888 <sect2 id="impredicative-polymorphism">
5889 <title>Impredicative polymorphism
5891 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5892 enabled with <option>-XImpredicativeTypes</option>.
5894 that you can call a polymorphic function at a polymorphic type, and
5895 parameterise data structures over polymorphic types. For example:
5897 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5898 f (Just g) = Just (g [3], g "hello")
5901 Notice here that the <literal>Maybe</literal> type is parameterised by the
5902 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5905 <para>The technical details of this extension are described in the paper
5906 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5907 type inference for higher-rank types and impredicativity</ulink>,
5908 which appeared at ICFP 2006.
5912 <sect2 id="scoped-type-variables">
5913 <title>Lexically scoped type variables
5917 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5918 which some type signatures are simply impossible to write. For example:
5920 f :: forall a. [a] -> [a]
5926 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5927 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5928 The type variables bound by a <literal>forall</literal> scope over
5929 the entire definition of the accompanying value declaration.
5930 In this example, the type variable <literal>a</literal> scopes over the whole
5931 definition of <literal>f</literal>, including over
5932 the type signature for <varname>ys</varname>.
5933 In Haskell 98 it is not possible to declare
5934 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5935 it becomes possible to do so.
5937 <para>Lexically-scoped type variables are enabled by
5938 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5940 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5941 variables work, compared to earlier releases. Read this section
5945 <title>Overview</title>
5947 <para>The design follows the following principles
5949 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5950 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5951 design.)</para></listitem>
5952 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5953 type variables. This means that every programmer-written type signature
5954 (including one that contains free scoped type variables) denotes a
5955 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5956 checker, and no inference is involved.</para></listitem>
5957 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5958 changing the program.</para></listitem>
5962 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5964 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5965 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5966 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5967 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5971 In Haskell, a programmer-written type signature is implicitly quantified over
5972 its free type variables (<ulink
5973 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5975 of the Haskell Report).
5976 Lexically scoped type variables affect this implicit quantification rules
5977 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5978 quantified. For example, if type variable <literal>a</literal> is in scope,
5981 (e :: a -> a) means (e :: a -> a)
5982 (e :: b -> b) means (e :: forall b. b->b)
5983 (e :: a -> b) means (e :: forall b. a->b)
5991 <sect3 id="decl-type-sigs">
5992 <title>Declaration type signatures</title>
5993 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5994 quantification (using <literal>forall</literal>) brings into scope the
5995 explicitly-quantified
5996 type variables, in the definition of the named function. For example:
5998 f :: forall a. [a] -> [a]
5999 f (x:xs) = xs ++ [ x :: a ]
6001 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
6002 the definition of "<literal>f</literal>".
6004 <para>This only happens if:
6006 <listitem><para> The quantification in <literal>f</literal>'s type
6007 signature is explicit. For example:
6010 g (x:xs) = xs ++ [ x :: a ]
6012 This program will be rejected, because "<literal>a</literal>" does not scope
6013 over the definition of "<literal>g</literal>", so "<literal>x::a</literal>"
6014 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
6015 quantification rules.
6017 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
6018 not a pattern binding.
6021 f1 :: forall a. [a] -> [a]
6022 f1 (x:xs) = xs ++ [ x :: a ] -- OK
6024 f2 :: forall a. [a] -> [a]
6025 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
6027 f3 :: forall a. [a] -> [a]
6028 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
6030 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
6031 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
6032 function binding, and <literal>f2</literal> binds a bare variable; in both cases
6033 the type signature brings <literal>a</literal> into scope.
6039 <sect3 id="exp-type-sigs">
6040 <title>Expression type signatures</title>
6042 <para>An expression type signature that has <emphasis>explicit</emphasis>
6043 quantification (using <literal>forall</literal>) brings into scope the
6044 explicitly-quantified
6045 type variables, in the annotated expression. For example:
6047 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
6049 Here, the type signature <literal>forall s. ST s Bool</literal> brings the
6050 type variable <literal>s</literal> into scope, in the annotated expression
6051 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
6056 <sect3 id="pattern-type-sigs">
6057 <title>Pattern type signatures</title>
6059 A type signature may occur in any pattern; this is a <emphasis>pattern type
6060 signature</emphasis>.
6063 -- f and g assume that 'a' is already in scope
6064 f = \(x::Int, y::a) -> x
6066 h ((x,y) :: (Int,Bool)) = (y,x)
6068 In the case where all the type variables in the pattern type signature are
6069 already in scope (i.e. bound by the enclosing context), matters are simple: the
6070 signature simply constrains the type of the pattern in the obvious way.
6073 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
6074 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
6075 that are already in scope. For example:
6077 f :: forall a. [a] -> (Int, [a])
6080 (ys::[a], n) = (reverse xs, length xs) -- OK
6081 zs::[a] = xs ++ ys -- OK
6083 Just (v::b) = ... -- Not OK; b is not in scope
6085 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
6086 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
6090 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
6091 type signature may mention a type variable that is not in scope; in this case,
6092 <emphasis>the signature brings that type variable into scope</emphasis>.
6093 This is particularly important for existential data constructors. For example:
6095 data T = forall a. MkT [a]
6098 k (MkT [t::a]) = MkT t3
6102 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
6103 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
6104 because it is bound by the pattern match. GHC's rule is that in this situation
6105 (and only then), a pattern type signature can mention a type variable that is
6106 not already in scope; the effect is to bring it into scope, standing for the
6107 existentially-bound type variable.
6110 When a pattern type signature binds a type variable in this way, GHC insists that the
6111 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
6112 This means that any user-written type signature always stands for a completely known type.
6115 If all this seems a little odd, we think so too. But we must have
6116 <emphasis>some</emphasis> way to bring such type variables into scope, else we
6117 could not name existentially-bound type variables in subsequent type signatures.
6120 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
6121 signature is allowed to mention a lexical variable that is not already in
6123 For example, both <literal>f</literal> and <literal>g</literal> would be
6124 illegal if <literal>a</literal> was not already in scope.
6130 <!-- ==================== Commented out part about result type signatures
6132 <sect3 id="result-type-sigs">
6133 <title>Result type signatures</title>
6136 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
6139 {- f assumes that 'a' is already in scope -}
6140 f x y :: [a] = [x,y,x]
6142 g = \ x :: [Int] -> [3,4]
6144 h :: forall a. [a] -> a
6148 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
6149 the result of the function. Similarly, the body of the lambda in the RHS of
6150 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
6151 alternative in <literal>h</literal> is <literal>a</literal>.
6153 <para> A result type signature never brings new type variables into scope.</para>
6155 There are a couple of syntactic wrinkles. First, notice that all three
6156 examples would parse quite differently with parentheses:
6158 {- f assumes that 'a' is already in scope -}
6159 f x (y :: [a]) = [x,y,x]
6161 g = \ (x :: [Int]) -> [3,4]
6163 h :: forall a. [a] -> a
6167 Now the signature is on the <emphasis>pattern</emphasis>; and
6168 <literal>h</literal> would certainly be ill-typed (since the pattern
6169 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6171 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6172 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6173 token or a parenthesised type of some sort). To see why,
6174 consider how one would parse this:
6183 <sect3 id="cls-inst-scoped-tyvars">
6184 <title>Class and instance declarations</title>
6187 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6188 scope over the methods defined in the <literal>where</literal> part. For example:
6206 <sect2 id="typing-binds">
6207 <title>Generalised typing of mutually recursive bindings</title>
6210 The Haskell Report specifies that a group of bindings (at top level, or in a
6211 <literal>let</literal> or <literal>where</literal>) should be sorted into
6212 strongly-connected components, and then type-checked in dependency order
6213 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6214 Report, Section 4.5.1</ulink>).
6215 As each group is type-checked, any binders of the group that
6217 an explicit type signature are put in the type environment with the specified
6219 and all others are monomorphic until the group is generalised
6220 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6223 <para>Following a suggestion of Mark Jones, in his paper
6224 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6226 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6228 <emphasis>the dependency analysis ignores references to variables that have an explicit
6229 type signature</emphasis>.
6230 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6231 typecheck. For example, consider:
6233 f :: Eq a => a -> Bool
6234 f x = (x == x) || g True || g "Yes"
6236 g y = (y <= y) || f True
6238 This is rejected by Haskell 98, but under Jones's scheme the definition for
6239 <literal>g</literal> is typechecked first, separately from that for
6240 <literal>f</literal>,
6241 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6242 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6243 type is generalised, to get
6245 g :: Ord a => a -> Bool
6247 Now, the definition for <literal>f</literal> is typechecked, with this type for
6248 <literal>g</literal> in the type environment.
6252 The same refined dependency analysis also allows the type signatures of
6253 mutually-recursive functions to have different contexts, something that is illegal in
6254 Haskell 98 (Section 4.5.2, last sentence). With
6255 <option>-XRelaxedPolyRec</option>
6256 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6257 type signatures; in practice this means that only variables bound by the same
6258 pattern binding must have the same context. For example, this is fine:
6260 f :: Eq a => a -> Bool
6261 f x = (x == x) || g True
6263 g :: Ord a => a -> Bool
6264 g y = (y <= y) || f True
6269 <sect2 id="mono-local-binds">
6270 <title>Monomorphic local bindings</title>
6272 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6273 The rationale is described in the paper
6274 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6277 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6278 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6279 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6280 If you supply a type signature, then the flag has no effect.
6285 <!-- ==================== End of type system extensions ================= -->
6287 <!-- ====================== TEMPLATE HASKELL ======================= -->
6289 <sect1 id="template-haskell">
6290 <title>Template Haskell</title>
6292 <para>Template Haskell allows you to do compile-time meta-programming in
6295 the main technical innovations is discussed in "<ulink
6296 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6297 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6300 There is a Wiki page about
6301 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6302 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6306 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6307 Haskell library reference material</ulink>
6308 (look for module <literal>Language.Haskell.TH</literal>).
6309 Many changes to the original design are described in
6310 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6311 Notes on Template Haskell version 2</ulink>.
6312 Not all of these changes are in GHC, however.
6315 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6316 as a worked example to help get you started.
6320 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6321 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6326 <title>Syntax</title>
6328 <para> Template Haskell has the following new syntactic
6329 constructions. You need to use the flag
6330 <option>-XTemplateHaskell</option>
6331 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6332 </indexterm>to switch these syntactic extensions on
6333 (<option>-XTemplateHaskell</option> is no longer implied by
6334 <option>-fglasgow-exts</option>).</para>
6338 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6339 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6340 There must be no space between the "$" and the identifier or parenthesis. This use
6341 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6342 of "." as an infix operator. If you want the infix operator, put spaces around it.
6344 <para> A splice can occur in place of
6346 <listitem><para> an expression; the spliced expression must
6347 have type <literal>Q Exp</literal></para></listitem>
6348 <listitem><para> an type; the spliced expression must
6349 have type <literal>Q Typ</literal></para></listitem>
6350 <listitem><para> a list of top-level declarations; the spliced expression
6351 must have type <literal>Q [Dec]</literal></para></listitem>
6353 Note that pattern splices are not supported.
6354 Inside a splice you can can only call functions defined in imported modules,
6355 not functions defined elsewhere in the same module.</para></listitem>
6358 A expression quotation is written in Oxford brackets, thus:
6360 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6361 where the "..." is an expression;
6362 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6363 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6364 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6365 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6366 the quotation has type <literal>Q Type</literal>.</para></listitem>
6367 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6368 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6369 </itemizedlist></para></listitem>
6372 A quasi-quotation can appear in either a pattern context or an
6373 expression context and is also written in Oxford brackets:
6375 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6376 where the "..." is an arbitrary string; a full description of the
6377 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6378 </itemizedlist></para></listitem>
6381 A name can be quoted with either one or two prefix single quotes:
6383 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6384 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6385 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6387 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6388 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6391 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6392 may also be given as an argument to the <literal>reify</literal> function.
6396 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6397 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6404 $(deriveStuff 'f) -- Uses the $(...) notation
6408 deriveStuff 'g -- Omits the $(...)
6412 This abbreviation makes top-level declaration slices quieter and less intimidating.
6417 (Compared to the original paper, there are many differences of detail.
6418 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6419 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6420 Pattern splices and quotations are not implemented.)
6424 <sect2> <title> Using Template Haskell </title>
6428 The data types and monadic constructor functions for Template Haskell are in the library
6429 <literal>Language.Haskell.THSyntax</literal>.
6433 You can only run a function at compile time if it is imported from another module. That is,
6434 you can't define a function in a module, and call it from within a splice in the same module.
6435 (It would make sense to do so, but it's hard to implement.)
6439 You can only run a function at compile time if it is imported
6440 from another module <emphasis>that is not part of a mutually-recursive group of modules
6441 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6442 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6443 splice is to be run.</para>
6445 For example, when compiling module A,
6446 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6447 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6451 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6454 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6455 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6456 compiles and runs a program, and then looks at the result. So it's important that
6457 the program it compiles produces results whose representations are identical to
6458 those of the compiler itself.
6462 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6463 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6468 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6469 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6470 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6477 -- Import our template "pr"
6478 import Printf ( pr )
6480 -- The splice operator $ takes the Haskell source code
6481 -- generated at compile time by "pr" and splices it into
6482 -- the argument of "putStrLn".
6483 main = putStrLn ( $(pr "Hello") )
6489 -- Skeletal printf from the paper.
6490 -- It needs to be in a separate module to the one where
6491 -- you intend to use it.
6493 -- Import some Template Haskell syntax
6494 import Language.Haskell.TH
6496 -- Describe a format string
6497 data Format = D | S | L String
6499 -- Parse a format string. This is left largely to you
6500 -- as we are here interested in building our first ever
6501 -- Template Haskell program and not in building printf.
6502 parse :: String -> [Format]
6505 -- Generate Haskell source code from a parsed representation
6506 -- of the format string. This code will be spliced into
6507 -- the module which calls "pr", at compile time.
6508 gen :: [Format] -> Q Exp
6509 gen [D] = [| \n -> show n |]
6510 gen [S] = [| \s -> s |]
6511 gen [L s] = stringE s
6513 -- Here we generate the Haskell code for the splice
6514 -- from an input format string.
6515 pr :: String -> Q Exp
6516 pr s = gen (parse s)
6519 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6522 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6525 <para>Run "main.exe" and here is your output:</para>
6535 <title>Using Template Haskell with Profiling</title>
6536 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6538 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6539 interpreter to run the splice expressions. The bytecode interpreter
6540 runs the compiled expression on top of the same runtime on which GHC
6541 itself is running; this means that the compiled code referred to by
6542 the interpreted expression must be compatible with this runtime, and
6543 in particular this means that object code that is compiled for
6544 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6545 expression, because profiled object code is only compatible with the
6546 profiling version of the runtime.</para>
6548 <para>This causes difficulties if you have a multi-module program
6549 containing Template Haskell code and you need to compile it for
6550 profiling, because GHC cannot load the profiled object code and use it
6551 when executing the splices. Fortunately GHC provides a workaround.
6552 The basic idea is to compile the program twice:</para>
6556 <para>Compile the program or library first the normal way, without
6557 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6560 <para>Then compile it again with <option>-prof</option>, and
6561 additionally use <option>-osuf
6562 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6563 to name the object files differently (you can choose any suffix
6564 that isn't the normal object suffix here). GHC will automatically
6565 load the object files built in the first step when executing splice
6566 expressions. If you omit the <option>-osuf</option> flag when
6567 building with <option>-prof</option> and Template Haskell is used,
6568 GHC will emit an error message. </para>
6573 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6574 <para>Quasi-quotation allows patterns and expressions to be written using
6575 programmer-defined concrete syntax; the motivation behind the extension and
6576 several examples are documented in
6577 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6578 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6579 2007). The example below shows how to write a quasiquoter for a simple
6580 expression language.</para>
6582 Here are the salient features
6585 A quasi-quote has the form
6586 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6589 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6590 quoter; it cannot be an arbitrary expression.
6593 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6594 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6595 those overlap with Template Haskell quotations.
6598 There must be no spaces in the token
6599 <literal>[<replaceable>quoter</replaceable>|</literal>.
6602 The quoted <replaceable>string</replaceable>
6603 can be arbitrary, and may contain newlines.
6609 A quasiquote may appear in place of
6611 <listitem><para>An expression</para></listitem>
6612 <listitem><para>A pattern</para></listitem>
6613 <listitem><para>A type</para></listitem>
6614 <listitem><para>A top-level declaration</para></listitem>
6616 (Only the first two are described in the paper.)
6620 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6621 which is defined thus:
6623 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6624 quotePat :: String -> Q Pat,
6625 quoteType :: String -> Q Type,
6626 quoteDec :: String -> Q [Dec] }
6628 That is, a quoter is a tuple of four parsers, one for each of the contexts
6629 in which a quasi-quote can occur.
6632 A quasi-quote is expanded by applying the appropriate parser to the string
6633 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6634 type, declaration) determines which of the parsers is called.
6639 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6640 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6641 The example makes use of an antiquoted
6642 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6643 (this syntax for anti-quotation was defined by the parser's
6644 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6645 integer value argument of the constructor <literal>IntExpr</literal> when
6646 pattern matching. Please see the referenced paper for further details regarding
6647 anti-quotation as well as the description of a technique that uses SYB to
6648 leverage a single parser of type <literal>String -> a</literal> to generate both
6649 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6650 pattern parser that returns a value of type <literal>Q Pat</literal>.
6654 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6655 the example, <literal>expr</literal> cannot be defined
6656 in <literal>Main.hs</literal> where it is used, but must be imported.
6660 {- ------------- file Main.hs --------------- -}
6666 main = do { print $ eval [expr|1 + 2|]
6668 { [expr|'int:n|] -> print n
6674 {- ------------- file Expr.hs --------------- -}
6677 import qualified Language.Haskell.TH as TH
6678 import Language.Haskell.TH.Quote
6680 data Expr = IntExpr Integer
6681 | AntiIntExpr String
6682 | BinopExpr BinOp Expr Expr
6684 deriving(Show, Typeable, Data)
6690 deriving(Show, Typeable, Data)
6692 eval :: Expr -> Integer
6693 eval (IntExpr n) = n
6694 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6701 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6703 -- Parse an Expr, returning its representation as
6704 -- either a Q Exp or a Q Pat. See the referenced paper
6705 -- for how to use SYB to do this by writing a single
6706 -- parser of type String -> Expr instead of two
6707 -- separate parsers.
6709 parseExprExp :: String -> Q Exp
6712 parseExprPat :: String -> Q Pat
6716 <para>Now run the compiler:
6718 $ ghc --make -XQuasiQuotes Main.hs -o main
6722 <para>Run "main" and here is your output:
6733 <!-- ===================== Arrow notation =================== -->
6735 <sect1 id="arrow-notation">
6736 <title>Arrow notation
6739 <para>Arrows are a generalization of monads introduced by John Hughes.
6740 For more details, see
6745 “Generalising Monads to Arrows”,
6746 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6747 pp67–111, May 2000.
6748 The paper that introduced arrows: a friendly introduction, motivated with
6749 programming examples.
6755 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6756 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6757 Introduced the notation described here.
6763 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6764 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6771 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6772 John Hughes, in <citetitle>5th International Summer School on
6773 Advanced Functional Programming</citetitle>,
6774 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6776 This paper includes another introduction to the notation,
6777 with practical examples.
6783 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6784 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6785 A terse enumeration of the formal rules used
6786 (extracted from comments in the source code).
6792 The arrows web page at
6793 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6798 With the <option>-XArrows</option> flag, GHC supports the arrow
6799 notation described in the second of these papers,
6800 translating it using combinators from the
6801 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6803 What follows is a brief introduction to the notation;
6804 it won't make much sense unless you've read Hughes's paper.
6807 <para>The extension adds a new kind of expression for defining arrows:
6809 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6810 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6812 where <literal>proc</literal> is a new keyword.
6813 The variables of the pattern are bound in the body of the
6814 <literal>proc</literal>-expression,
6815 which is a new sort of thing called a <firstterm>command</firstterm>.
6816 The syntax of commands is as follows:
6818 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6819 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6820 | <replaceable>cmd</replaceable><superscript>0</superscript>
6822 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6823 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6824 infix operators as for expressions, and
6826 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6827 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6828 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6829 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6830 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6831 | <replaceable>fcmd</replaceable>
6833 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6834 | ( <replaceable>cmd</replaceable> )
6835 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6837 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6838 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6839 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6840 | <replaceable>cmd</replaceable>
6842 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6843 except that the bodies are commands instead of expressions.
6847 Commands produce values, but (like monadic computations)
6848 may yield more than one value,
6849 or none, and may do other things as well.
6850 For the most part, familiarity with monadic notation is a good guide to
6852 However the values of expressions, even monadic ones,
6853 are determined by the values of the variables they contain;
6854 this is not necessarily the case for commands.
6858 A simple example of the new notation is the expression
6860 proc x -> f -< x+1
6862 We call this a <firstterm>procedure</firstterm> or
6863 <firstterm>arrow abstraction</firstterm>.
6864 As with a lambda expression, the variable <literal>x</literal>
6865 is a new variable bound within the <literal>proc</literal>-expression.
6866 It refers to the input to the arrow.
6867 In the above example, <literal>-<</literal> is not an identifier but an
6868 new reserved symbol used for building commands from an expression of arrow
6869 type and an expression to be fed as input to that arrow.
6870 (The weird look will make more sense later.)
6871 It may be read as analogue of application for arrows.
6872 The above example is equivalent to the Haskell expression
6874 arr (\ x -> x+1) >>> f
6876 That would make no sense if the expression to the left of
6877 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6878 More generally, the expression to the left of <literal>-<</literal>
6879 may not involve any <firstterm>local variable</firstterm>,
6880 i.e. a variable bound in the current arrow abstraction.
6881 For such a situation there is a variant <literal>-<<</literal>, as in
6883 proc x -> f x -<< x+1
6885 which is equivalent to
6887 arr (\ x -> (f x, x+1)) >>> app
6889 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6891 Such an arrow is equivalent to a monad, so if you're using this form
6892 you may find a monadic formulation more convenient.
6896 <title>do-notation for commands</title>
6899 Another form of command is a form of <literal>do</literal>-notation.
6900 For example, you can write
6909 You can read this much like ordinary <literal>do</literal>-notation,
6910 but with commands in place of monadic expressions.
6911 The first line sends the value of <literal>x+1</literal> as an input to
6912 the arrow <literal>f</literal>, and matches its output against
6913 <literal>y</literal>.
6914 In the next line, the output is discarded.
6915 The arrow <function>returnA</function> is defined in the
6916 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6917 module as <literal>arr id</literal>.
6918 The above example is treated as an abbreviation for
6920 arr (\ x -> (x, x)) >>>
6921 first (arr (\ x -> x+1) >>> f) >>>
6922 arr (\ (y, x) -> (y, (x, y))) >>>
6923 first (arr (\ y -> 2*y) >>> g) >>>
6925 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6926 first (arr (\ (x, z) -> x*z) >>> h) >>>
6927 arr (\ (t, z) -> t+z) >>>
6930 Note that variables not used later in the composition are projected out.
6931 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6933 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6934 module, this reduces to
6936 arr (\ x -> (x+1, x)) >>>
6938 arr (\ (y, x) -> (2*y, (x, y))) >>>
6940 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6942 arr (\ (t, z) -> t+z)
6944 which is what you might have written by hand.
6945 With arrow notation, GHC keeps track of all those tuples of variables for you.
6949 Note that although the above translation suggests that
6950 <literal>let</literal>-bound variables like <literal>z</literal> must be
6951 monomorphic, the actual translation produces Core,
6952 so polymorphic variables are allowed.
6956 It's also possible to have mutually recursive bindings,
6957 using the new <literal>rec</literal> keyword, as in the following example:
6959 counter :: ArrowCircuit a => a Bool Int
6960 counter = proc reset -> do
6961 rec output <- returnA -< if reset then 0 else next
6962 next <- delay 0 -< output+1
6963 returnA -< output
6965 The translation of such forms uses the <function>loop</function> combinator,
6966 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6972 <title>Conditional commands</title>
6975 In the previous example, we used a conditional expression to construct the
6977 Sometimes we want to conditionally execute different commands, as in
6984 which is translated to
6986 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6987 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6989 Since the translation uses <function>|||</function>,
6990 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6994 There are also <literal>case</literal> commands, like
7000 y <- h -< (x1, x2)
7004 The syntax is the same as for <literal>case</literal> expressions,
7005 except that the bodies of the alternatives are commands rather than expressions.
7006 The translation is similar to that of <literal>if</literal> commands.
7012 <title>Defining your own control structures</title>
7015 As we're seen, arrow notation provides constructs,
7016 modelled on those for expressions,
7017 for sequencing, value recursion and conditionals.
7018 But suitable combinators,
7019 which you can define in ordinary Haskell,
7020 may also be used to build new commands out of existing ones.
7021 The basic idea is that a command defines an arrow from environments to values.
7022 These environments assign values to the free local variables of the command.
7023 Thus combinators that produce arrows from arrows
7024 may also be used to build commands from commands.
7025 For example, the <literal>ArrowChoice</literal> class includes a combinator
7027 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
7029 so we can use it to build commands:
7031 expr' = proc x -> do
7034 symbol Plus -< ()
7035 y <- term -< ()
7038 symbol Minus -< ()
7039 y <- term -< ()
7042 (The <literal>do</literal> on the first line is needed to prevent the first
7043 <literal><+> ...</literal> from being interpreted as part of the
7044 expression on the previous line.)
7045 This is equivalent to
7047 expr' = (proc x -> returnA -< x)
7048 <+> (proc x -> do
7049 symbol Plus -< ()
7050 y <- term -< ()
7052 <+> (proc x -> do
7053 symbol Minus -< ()
7054 y <- term -< ()
7057 It is essential that this operator be polymorphic in <literal>e</literal>
7058 (representing the environment input to the command
7059 and thence to its subcommands)
7060 and satisfy the corresponding naturality property
7062 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
7064 at least for strict <literal>k</literal>.
7065 (This should be automatic if you're not using <function>seq</function>.)
7066 This ensures that environments seen by the subcommands are environments
7067 of the whole command,
7068 and also allows the translation to safely trim these environments.
7069 The operator must also not use any variable defined within the current
7074 We could define our own operator
7076 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
7077 untilA body cond = proc x ->
7078 b <- cond -< x
7079 if b then returnA -< ()
7082 untilA body cond -< x
7084 and use it in the same way.
7085 Of course this infix syntax only makes sense for binary operators;
7086 there is also a more general syntax involving special brackets:
7090 (|untilA (increment -< x+y) (within 0.5 -< x)|)
7097 <title>Primitive constructs</title>
7100 Some operators will need to pass additional inputs to their subcommands.
7101 For example, in an arrow type supporting exceptions,
7102 the operator that attaches an exception handler will wish to pass the
7103 exception that occurred to the handler.
7104 Such an operator might have a type
7106 handleA :: ... => a e c -> a (e,Ex) c -> a e c
7108 where <literal>Ex</literal> is the type of exceptions handled.
7109 You could then use this with arrow notation by writing a command
7111 body `handleA` \ ex -> handler
7113 so that if an exception is raised in the command <literal>body</literal>,
7114 the variable <literal>ex</literal> is bound to the value of the exception
7115 and the command <literal>handler</literal>,
7116 which typically refers to <literal>ex</literal>, is entered.
7117 Though the syntax here looks like a functional lambda,
7118 we are talking about commands, and something different is going on.
7119 The input to the arrow represented by a command consists of values for
7120 the free local variables in the command, plus a stack of anonymous values.
7121 In all the prior examples, this stack was empty.
7122 In the second argument to <function>handleA</function>,
7123 this stack consists of one value, the value of the exception.
7124 The command form of lambda merely gives this value a name.
7129 the values on the stack are paired to the right of the environment.
7130 So operators like <function>handleA</function> that pass
7131 extra inputs to their subcommands can be designed for use with the notation
7132 by pairing the values with the environment in this way.
7133 More precisely, the type of each argument of the operator (and its result)
7134 should have the form
7136 a (...(e,t1), ... tn) t
7138 where <replaceable>e</replaceable> is a polymorphic variable
7139 (representing the environment)
7140 and <replaceable>ti</replaceable> are the types of the values on the stack,
7141 with <replaceable>t1</replaceable> being the <quote>top</quote>.
7142 The polymorphic variable <replaceable>e</replaceable> must not occur in
7143 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
7144 <replaceable>t</replaceable>.
7145 However the arrows involved need not be the same.
7146 Here are some more examples of suitable operators:
7148 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
7149 runReader :: ... => a e c -> a' (e,State) c
7150 runState :: ... => a e c -> a' (e,State) (c,State)
7152 We can supply the extra input required by commands built with the last two
7153 by applying them to ordinary expressions, as in
7157 (|runReader (do { ... })|) s
7159 which adds <literal>s</literal> to the stack of inputs to the command
7160 built using <function>runReader</function>.
7164 The command versions of lambda abstraction and application are analogous to
7165 the expression versions.
7166 In particular, the beta and eta rules describe equivalences of commands.
7167 These three features (operators, lambda abstraction and application)
7168 are the core of the notation; everything else can be built using them,
7169 though the results would be somewhat clumsy.
7170 For example, we could simulate <literal>do</literal>-notation by defining
7172 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7173 u `bind` f = returnA &&& u >>> f
7175 bind_ :: Arrow a => a e b -> a e c -> a e c
7176 u `bind_` f = u `bind` (arr fst >>> f)
7178 We could simulate <literal>if</literal> by defining
7180 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7181 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7188 <title>Differences with the paper</title>
7193 <para>Instead of a single form of arrow application (arrow tail) with two
7194 translations, the implementation provides two forms
7195 <quote><literal>-<</literal></quote> (first-order)
7196 and <quote><literal>-<<</literal></quote> (higher-order).
7201 <para>User-defined operators are flagged with banana brackets instead of
7202 a new <literal>form</literal> keyword.
7211 <title>Portability</title>
7214 Although only GHC implements arrow notation directly,
7215 there is also a preprocessor
7217 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7218 that translates arrow notation into Haskell 98
7219 for use with other Haskell systems.
7220 You would still want to check arrow programs with GHC;
7221 tracing type errors in the preprocessor output is not easy.
7222 Modules intended for both GHC and the preprocessor must observe some
7223 additional restrictions:
7228 The module must import
7229 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7235 The preprocessor cannot cope with other Haskell extensions.
7236 These would have to go in separate modules.
7242 Because the preprocessor targets Haskell (rather than Core),
7243 <literal>let</literal>-bound variables are monomorphic.
7254 <!-- ==================== BANG PATTERNS ================= -->
7256 <sect1 id="bang-patterns">
7257 <title>Bang patterns
7258 <indexterm><primary>Bang patterns</primary></indexterm>
7260 <para>GHC supports an extension of pattern matching called <emphasis>bang
7261 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7262 Bang patterns are under consideration for Haskell Prime.
7264 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7265 prime feature description</ulink> contains more discussion and examples
7266 than the material below.
7269 The key change is the addition of a new rule to the
7270 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7271 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7272 against a value <replaceable>v</replaceable> behaves as follows:
7274 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7275 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7279 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7282 <sect2 id="bang-patterns-informal">
7283 <title>Informal description of bang patterns
7286 The main idea is to add a single new production to the syntax of patterns:
7290 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7291 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7296 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7297 whereas without the bang it would be lazy.
7298 Bang patterns can be nested of course:
7302 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7303 <literal>y</literal>.
7304 A bang only really has an effect if it precedes a variable or wild-card pattern:
7309 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7310 putting a bang before a pattern that
7311 forces evaluation anyway does nothing.
7314 There is one (apparent) exception to this general rule that a bang only
7315 makes a difference when it precedes a variable or wild-card: a bang at the
7316 top level of a <literal>let</literal> or <literal>where</literal>
7317 binding makes the binding strict, regardless of the pattern.
7318 (We say "apparent" exception because the Right Way to think of it is that the bang
7319 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7320 is part of the syntax of the <emphasis>binding</emphasis>,
7321 creating a "bang-pattern binding".)
7326 is a bang-pattern binding. Operationally, it behaves just like a case expression:
7328 case e of [x,y] -> b
7330 Like a case expression, a bang-pattern binding must be non-recursive, and
7333 However, <emphasis>nested</emphasis> bangs in a pattern binding behave uniformly with all other forms of
7334 pattern matching. For example
7336 let (!x,[y]) = e in b
7338 is equivalent to this:
7340 let { t = case e of (x,[y]) -> x `seq` (x,y)
7345 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7346 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7347 evaluation of <literal>x</literal>.
7350 Bang patterns work in <literal>case</literal> expressions too, of course:
7352 g5 x = let y = f x in body
7353 g6 x = case f x of { y -> body }
7354 g7 x = case f x of { !y -> body }
7356 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7357 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7358 result, and then evaluates <literal>body</literal>.
7363 <sect2 id="bang-patterns-sem">
7364 <title>Syntax and semantics
7368 We add a single new production to the syntax of patterns:
7372 There is one problem with syntactic ambiguity. Consider:
7376 Is this a definition of the infix function "<literal>(!)</literal>",
7377 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7378 ambiguity in favour of the latter. If you want to define
7379 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7384 The semantics of Haskell pattern matching is described in <ulink
7385 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7386 Section 3.17.2</ulink> of the Haskell Report. To this description add
7387 one extra item 10, saying:
7388 <itemizedlist><listitem><para>Matching
7389 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7390 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7391 <listitem><para>otherwise, <literal>pat</literal> is matched against
7392 <literal>v</literal></para></listitem>
7394 </para></listitem></itemizedlist>
7395 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7396 Section 3.17.3</ulink>, add a new case (t):
7398 case v of { !pat -> e; _ -> e' }
7399 = v `seq` case v of { pat -> e; _ -> e' }
7402 That leaves let expressions, whose translation is given in
7403 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7405 of the Haskell Report.
7406 In the translation box, first apply
7407 the following transformation: for each pattern <literal>pi</literal> that is of
7408 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7409 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7410 have a bang at the top, apply the rules in the existing box.
7412 <para>The effect of the let rule is to force complete matching of the pattern
7413 <literal>qi</literal> before evaluation of the body is begun. The bang is
7414 retained in the translated form in case <literal>qi</literal> is a variable,
7422 The let-binding can be recursive. However, it is much more common for
7423 the let-binding to be non-recursive, in which case the following law holds:
7424 <literal>(let !p = rhs in body)</literal>
7426 <literal>(case rhs of !p -> body)</literal>
7429 A pattern with a bang at the outermost level is not allowed at the top level of
7435 <!-- ==================== ASSERTIONS ================= -->
7437 <sect1 id="assertions">
7439 <indexterm><primary>Assertions</primary></indexterm>
7443 If you want to make use of assertions in your standard Haskell code, you
7444 could define a function like the following:
7450 assert :: Bool -> a -> a
7451 assert False x = error "assertion failed!"
7458 which works, but gives you back a less than useful error message --
7459 an assertion failed, but which and where?
7463 One way out is to define an extended <function>assert</function> function which also
7464 takes a descriptive string to include in the error message and
7465 perhaps combine this with the use of a pre-processor which inserts
7466 the source location where <function>assert</function> was used.
7470 Ghc offers a helping hand here, doing all of this for you. For every
7471 use of <function>assert</function> in the user's source:
7477 kelvinToC :: Double -> Double
7478 kelvinToC k = assert (k >= 0.0) (k+273.15)
7484 Ghc will rewrite this to also include the source location where the
7491 assert pred val ==> assertError "Main.hs|15" pred val
7497 The rewrite is only performed by the compiler when it spots
7498 applications of <function>Control.Exception.assert</function>, so you
7499 can still define and use your own versions of
7500 <function>assert</function>, should you so wish. If not, import
7501 <literal>Control.Exception</literal> to make use
7502 <function>assert</function> in your code.
7506 GHC ignores assertions when optimisation is turned on with the
7507 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7508 <literal>assert pred e</literal> will be rewritten to
7509 <literal>e</literal>. You can also disable assertions using the
7510 <option>-fignore-asserts</option>
7511 option<indexterm><primary><option>-fignore-asserts</option></primary>
7512 </indexterm>.</para>
7515 Assertion failures can be caught, see the documentation for the
7516 <literal>Control.Exception</literal> library for the details.
7522 <!-- =============================== PRAGMAS =========================== -->
7524 <sect1 id="pragmas">
7525 <title>Pragmas</title>
7527 <indexterm><primary>pragma</primary></indexterm>
7529 <para>GHC supports several pragmas, or instructions to the
7530 compiler placed in the source code. Pragmas don't normally affect
7531 the meaning of the program, but they might affect the efficiency
7532 of the generated code.</para>
7534 <para>Pragmas all take the form
7536 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7538 where <replaceable>word</replaceable> indicates the type of
7539 pragma, and is followed optionally by information specific to that
7540 type of pragma. Case is ignored in
7541 <replaceable>word</replaceable>. The various values for
7542 <replaceable>word</replaceable> that GHC understands are described
7543 in the following sections; any pragma encountered with an
7544 unrecognised <replaceable>word</replaceable> is
7545 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7546 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7548 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7552 pragma must precede the <literal>module</literal> keyword in the file.
7555 There can be as many file-header pragmas as you please, and they can be
7556 preceded or followed by comments.
7559 File-header pragmas are read once only, before
7560 pre-processing the file (e.g. with cpp).
7563 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7564 <literal>{-# OPTIONS_GHC #-}</literal>, and
7565 <literal>{-# INCLUDE #-}</literal>.
7570 <sect2 id="language-pragma">
7571 <title>LANGUAGE pragma</title>
7573 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7574 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7576 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7578 It is the intention that all Haskell compilers support the
7579 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7580 all extensions are supported by all compilers, of
7581 course. The <literal>LANGUAGE</literal> pragma should be used instead
7582 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7584 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7586 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7588 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7590 <para>Every language extension can also be turned into a command-line flag
7591 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7592 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7595 <para>A list of all supported language extensions can be obtained by invoking
7596 <literal>ghc --supported-extensions</literal> (see <xref linkend="modes"/>).</para>
7598 <para>Any extension from the <literal>Extension</literal> type defined in
7600 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7601 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7605 <sect2 id="options-pragma">
7606 <title>OPTIONS_GHC pragma</title>
7607 <indexterm><primary>OPTIONS_GHC</primary>
7609 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7612 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7613 additional options that are given to the compiler when compiling
7614 this source file. See <xref linkend="source-file-options"/> for
7617 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7618 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7621 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7623 <sect2 id="include-pragma">
7624 <title>INCLUDE pragma</title>
7626 <para>The <literal>INCLUDE</literal> used to be necessary for
7627 specifying header files to be included when using the FFI and
7628 compiling via C. It is no longer required for GHC, but is
7629 accepted (and ignored) for compatibility with other
7633 <sect2 id="warning-deprecated-pragma">
7634 <title>WARNING and DEPRECATED pragmas</title>
7635 <indexterm><primary>WARNING</primary></indexterm>
7636 <indexterm><primary>DEPRECATED</primary></indexterm>
7638 <para>The WARNING pragma allows you to attach an arbitrary warning
7639 to a particular function, class, or type.
7640 A DEPRECATED pragma lets you specify that
7641 a particular function, class, or type is deprecated.
7642 There are two ways of using these pragmas.
7646 <para>You can work on an entire module thus:</para>
7648 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7653 module Wibble {-# WARNING "This is an unstable interface." #-} where
7656 <para>When you compile any module that import
7657 <literal>Wibble</literal>, GHC will print the specified
7662 <para>You can attach a warning to a function, class, type, or data constructor, with the
7663 following top-level declarations:</para>
7665 {-# DEPRECATED f, C, T "Don't use these" #-}
7666 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7668 <para>When you compile any module that imports and uses any
7669 of the specified entities, GHC will print the specified
7671 <para> You can only attach to entities declared at top level in the module
7672 being compiled, and you can only use unqualified names in the list of
7673 entities. A capitalised name, such as <literal>T</literal>
7674 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7675 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7676 both are in scope. If both are in scope, there is currently no way to
7677 specify one without the other (c.f. fixities
7678 <xref linkend="infix-tycons"/>).</para>
7681 Warnings and deprecations are not reported for
7682 (a) uses within the defining module, and
7683 (b) uses in an export list.
7684 The latter reduces spurious complaints within a library
7685 in which one module gathers together and re-exports
7686 the exports of several others.
7688 <para>You can suppress the warnings with the flag
7689 <option>-fno-warn-warnings-deprecations</option>.</para>
7692 <sect2 id="inline-noinline-pragma">
7693 <title>INLINE and NOINLINE pragmas</title>
7695 <para>These pragmas control the inlining of function
7698 <sect3 id="inline-pragma">
7699 <title>INLINE pragma</title>
7700 <indexterm><primary>INLINE</primary></indexterm>
7702 <para>GHC (with <option>-O</option>, as always) tries to
7703 inline (or “unfold”) functions/values that are
7704 “small enough,” thus avoiding the call overhead
7705 and possibly exposing other more-wonderful optimisations.
7706 Normally, if GHC decides a function is “too
7707 expensive” to inline, it will not do so, nor will it
7708 export that unfolding for other modules to use.</para>
7710 <para>The sledgehammer you can bring to bear is the
7711 <literal>INLINE</literal><indexterm><primary>INLINE
7712 pragma</primary></indexterm> pragma, used thusly:</para>
7715 key_function :: Int -> String -> (Bool, Double)
7716 {-# INLINE key_function #-}
7719 <para>The major effect of an <literal>INLINE</literal> pragma
7720 is to declare a function's “cost” to be very low.
7721 The normal unfolding machinery will then be very keen to
7722 inline it. However, an <literal>INLINE</literal> pragma for a
7723 function "<literal>f</literal>" has a number of other effects:
7726 While GHC is keen to inline the function, it does not do so
7727 blindly. For example, if you write
7731 there really isn't any point in inlining <literal>key_function</literal> to get
7733 map (\x -> <replaceable>body</replaceable>) xs
7735 In general, GHC only inlines the function if there is some reason (no matter
7736 how slight) to supose that it is useful to do so.
7740 Moreover, GHC will only inline the function if it is <emphasis>fully applied</emphasis>,
7741 where "fully applied"
7742 means applied to as many arguments as appear (syntactically)
7743 on the LHS of the function
7744 definition. For example:
7746 comp1 :: (b -> c) -> (a -> b) -> a -> c
7747 {-# INLINE comp1 #-}
7748 comp1 f g = \x -> f (g x)
7750 comp2 :: (b -> c) -> (a -> b) -> a -> c
7751 {-# INLINE comp2 #-}
7752 comp2 f g x = f (g x)
7754 The two functions <literal>comp1</literal> and <literal>comp2</literal> have the
7755 same semantics, but <literal>comp1</literal> will be inlined when applied
7756 to <emphasis>two</emphasis> arguments, while <literal>comp2</literal> requires
7757 <emphasis>three</emphasis>. This might make a big difference if you say
7759 map (not `comp1` not) xs
7761 which will optimise better than the corresponding use of `comp2`.
7765 It is useful for GHC to optimise the definition of an
7766 INLINE function <literal>f</literal> just like any other non-INLINE function,
7767 in case the non-inlined version of <literal>f</literal> is
7768 ultimately called. But we don't want to inline
7769 the <emphasis>optimised</emphasis> version
7770 of <literal>f</literal>;
7771 a major reason for INLINE pragmas is to expose functions
7772 in <literal>f</literal>'s RHS that have
7773 rewrite rules, and it's no good if those functions have been optimised
7777 So <emphasis>GHC guarantees to inline precisely the code that you wrote</emphasis>, no more
7778 and no less. It does this by capturing a copy of the definition of the function to use
7779 for inlining (we call this the "inline-RHS"), which it leaves untouched,
7780 while optimising the ordinarly RHS as usual. For externally-visible functions
7781 the inline-RHS (not the optimised RHS) is recorded in the interface file.
7784 An INLINE function is not worker/wrappered by strictness analysis.
7785 It's going to be inlined wholesale instead.
7789 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7790 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7791 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7792 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7793 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7794 when there is no choice even an INLINE function can be selected, in which case
7795 the INLINE pragma is ignored.
7796 For example, for a self-recursive function, the loop breaker can only be the function
7797 itself, so an INLINE pragma is always ignored.</para>
7799 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7800 function can be put anywhere its type signature could be
7803 <para><literal>INLINE</literal> pragmas are a particularly
7805 <literal>then</literal>/<literal>return</literal> (or
7806 <literal>bind</literal>/<literal>unit</literal>) functions in
7807 a monad. For example, in GHC's own
7808 <literal>UniqueSupply</literal> monad code, we have:</para>
7811 {-# INLINE thenUs #-}
7812 {-# INLINE returnUs #-}
7815 <para>See also the <literal>NOINLINE</literal> (<xref linkend="inlinable-pragma"/>)
7816 and <literal>INLINABLE</literal> (<xref linkend="noinline-pragma"/>)
7819 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7820 so if you want your code to be HBC-compatible you'll have to surround
7821 the pragma with C pre-processor directives
7822 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7826 <sect3 id="inlinable-pragma">
7827 <title>INLINABLE pragma</title>
7829 <para>An <literal>{-# INLINABLE f #-}</literal> pragma on a
7830 function <literal>f</literal> has the following behaviour:
7833 While <literal>INLINE</literal> says "please inline me", the <literal>INLINABLE</literal>
7834 says "feel free to inline me; use your
7835 discretion". In other words the choice is left to GHC, which uses the same
7836 rules as for pragma-free functions. Unlike <literal>INLINE</literal>, that decision is made at
7837 the <emphasis>call site</emphasis>, and
7838 will therefore be affected by the inlining threshold, optimisation level etc.
7841 Like <literal>INLINE</literal>, the <literal>INLINABLE</literal> pragma retains a
7842 copy of the original RHS for
7843 inlining purposes, and persists it in the interface file, regardless of
7844 the size of the RHS.
7848 One way to use <literal>INLINABLE</literal> is in conjunction with
7849 the special function <literal>inline</literal> (<xref linkend="special-ids"/>).
7850 The call <literal>inline f</literal> tries very hard to inline <literal>f</literal>.
7851 To make sure that <literal>f</literal> can be inlined,
7852 it is a good idea to mark the definition
7853 of <literal>f</literal> as <literal>INLINABLE</literal>,
7854 so that GHC guarantees to expose an unfolding regardless of how big it is.
7855 Moreover, by annotating <literal>f</literal> as <literal>INLINABLE</literal>,
7856 you ensure that <literal>f</literal>'s original RHS is inlined, rather than
7857 whatever random optimised version of <literal>f</literal> GHC's optimiser
7862 The <literal>INLINABLE</literal> pragma also works with <literal>SPECIALISE</literal>:
7863 if you mark function <literal>f</literal> as <literal>INLINABLE</literal>, then
7864 you can subsequently <literal>SPECIALISE</literal> in another module
7865 (see <xref linkend="specialize-pragma"/>).</para></listitem>
7868 Unlike <literal>INLINE</literal>, it is OK to use
7869 an <literal>INLINABLE</literal> pragma on a recursive function.
7870 The principal reason do to so to allow later use of <literal>SPECIALISE</literal>
7877 <sect3 id="noinline-pragma">
7878 <title>NOINLINE pragma</title>
7880 <indexterm><primary>NOINLINE</primary></indexterm>
7881 <indexterm><primary>NOTINLINE</primary></indexterm>
7883 <para>The <literal>NOINLINE</literal> pragma does exactly what
7884 you'd expect: it stops the named function from being inlined
7885 by the compiler. You shouldn't ever need to do this, unless
7886 you're very cautious about code size.</para>
7888 <para><literal>NOTINLINE</literal> is a synonym for
7889 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7890 specified by Haskell 98 as the standard way to disable
7891 inlining, so it should be used if you want your code to be
7895 <sect3 id="conlike-pragma">
7896 <title>CONLIKE modifier</title>
7897 <indexterm><primary>CONLIKE</primary></indexterm>
7898 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7899 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7903 <sect3 id="phase-control">
7904 <title>Phase control</title>
7906 <para> Sometimes you want to control exactly when in GHC's
7907 pipeline the INLINE pragma is switched on. Inlining happens
7908 only during runs of the <emphasis>simplifier</emphasis>. Each
7909 run of the simplifier has a different <emphasis>phase
7910 number</emphasis>; the phase number decreases towards zero.
7911 If you use <option>-dverbose-core2core</option> you'll see the
7912 sequence of phase numbers for successive runs of the
7913 simplifier. In an INLINE pragma you can optionally specify a
7917 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7918 <literal>f</literal>
7919 until phase <literal>k</literal>, but from phase
7920 <literal>k</literal> onwards be very keen to inline it.
7923 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7924 <literal>f</literal>
7925 until phase <literal>k</literal>, but from phase
7926 <literal>k</literal> onwards do not inline it.
7929 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7930 <literal>f</literal>
7931 until phase <literal>k</literal>, but from phase
7932 <literal>k</literal> onwards be willing to inline it (as if
7933 there was no pragma).
7936 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7937 <literal>f</literal>
7938 until phase <literal>k</literal>, but from phase
7939 <literal>k</literal> onwards do not inline it.
7942 The same information is summarised here:
7944 -- Before phase 2 Phase 2 and later
7945 {-# INLINE [2] f #-} -- No Yes
7946 {-# INLINE [~2] f #-} -- Yes No
7947 {-# NOINLINE [2] f #-} -- No Maybe
7948 {-# NOINLINE [~2] f #-} -- Maybe No
7950 {-# INLINE f #-} -- Yes Yes
7951 {-# NOINLINE f #-} -- No No
7953 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7954 function body is small, or it is applied to interesting-looking arguments etc).
7955 Another way to understand the semantics is this:
7957 <listitem><para>For both INLINE and NOINLINE, the phase number says
7958 when inlining is allowed at all.</para></listitem>
7959 <listitem><para>The INLINE pragma has the additional effect of making the
7960 function body look small, so that when inlining is allowed it is very likely to
7965 <para>The same phase-numbering control is available for RULES
7966 (<xref linkend="rewrite-rules"/>).</para>
7970 <sect2 id="annotation-pragmas">
7971 <title>ANN pragmas</title>
7973 <para>GHC offers the ability to annotate various code constructs with additional
7974 data by using three pragmas. This data can then be inspected at a later date by
7975 using GHC-as-a-library.</para>
7977 <sect3 id="ann-pragma">
7978 <title>Annotating values</title>
7980 <indexterm><primary>ANN</primary></indexterm>
7982 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7983 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7984 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7985 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7986 you would do this:</para>
7989 {-# ANN foo (Just "Hello") #-}
7994 A number of restrictions apply to use of annotations:
7996 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7997 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7998 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7999 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
8000 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
8002 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
8003 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
8006 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
8007 please give the GHC team a shout</ulink>.
8010 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
8011 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
8014 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
8019 <sect3 id="typeann-pragma">
8020 <title>Annotating types</title>
8022 <indexterm><primary>ANN type</primary></indexterm>
8023 <indexterm><primary>ANN</primary></indexterm>
8025 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
8028 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
8033 <sect3 id="modann-pragma">
8034 <title>Annotating modules</title>
8036 <indexterm><primary>ANN module</primary></indexterm>
8037 <indexterm><primary>ANN</primary></indexterm>
8039 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
8042 {-# ANN module (Just "A `Maybe String' annotation") #-}
8047 <sect2 id="line-pragma">
8048 <title>LINE pragma</title>
8050 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
8051 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
8052 <para>This pragma is similar to C's <literal>#line</literal>
8053 pragma, and is mainly for use in automatically generated Haskell
8054 code. It lets you specify the line number and filename of the
8055 original code; for example</para>
8057 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
8059 <para>if you'd generated the current file from something called
8060 <filename>Foo.vhs</filename> and this line corresponds to line
8061 42 in the original. GHC will adjust its error messages to refer
8062 to the line/file named in the <literal>LINE</literal>
8067 <title>RULES pragma</title>
8069 <para>The RULES pragma lets you specify rewrite rules. It is
8070 described in <xref linkend="rewrite-rules"/>.</para>
8073 <sect2 id="specialize-pragma">
8074 <title>SPECIALIZE pragma</title>
8076 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
8077 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
8078 <indexterm><primary>overloading, death to</primary></indexterm>
8080 <para>(UK spelling also accepted.) For key overloaded
8081 functions, you can create extra versions (NB: more code space)
8082 specialised to particular types. Thus, if you have an
8083 overloaded function:</para>
8086 hammeredLookup :: Ord key => [(key, value)] -> key -> value
8089 <para>If it is heavily used on lists with
8090 <literal>Widget</literal> keys, you could specialise it as
8094 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
8097 <para>A <literal>SPECIALIZE</literal> pragma for a function can
8098 be put anywhere its type signature could be put.</para>
8100 <para>A <literal>SPECIALIZE</literal> has the effect of generating
8101 (a) a specialised version of the function and (b) a rewrite rule
8102 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
8103 un-specialised function into a call to the specialised one.</para>
8105 <para>The type in a SPECIALIZE pragma can be any type that is less
8106 polymorphic than the type of the original function. In concrete terms,
8107 if the original function is <literal>f</literal> then the pragma
8109 {-# SPECIALIZE f :: <type> #-}
8111 is valid if and only if the definition
8113 f_spec :: <type>
8116 is valid. Here are some examples (where we only give the type signature
8117 for the original function, not its code):
8119 f :: Eq a => a -> b -> b
8120 {-# SPECIALISE f :: Int -> b -> b #-}
8122 g :: (Eq a, Ix b) => a -> b -> b
8123 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
8125 h :: Eq a => a -> a -> a
8126 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
8128 The last of these examples will generate a
8129 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
8130 well. If you use this kind of specialisation, let us know how well it works.
8133 <sect3 id="specialize-inline">
8134 <title>SPECIALIZE INLINE</title>
8136 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
8137 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
8138 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
8139 The <literal>INLINE</literal> pragma affects the specialised version of the
8140 function (only), and applies even if the function is recursive. The motivating
8143 -- A GADT for arrays with type-indexed representation
8145 ArrInt :: !Int -> ByteArray# -> Arr Int
8146 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
8148 (!:) :: Arr e -> Int -> e
8149 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
8150 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
8151 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
8152 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
8154 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
8155 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
8156 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
8157 the specialised function will be inlined. It has two calls to
8158 <literal>(!:)</literal>,
8159 both at type <literal>Int</literal>. Both these calls fire the first
8160 specialisation, whose body is also inlined. The result is a type-based
8161 unrolling of the indexing function.</para>
8162 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
8163 on an ordinarily-recursive function.</para>
8166 <sect3><title>SPECIALIZE for imported functions</title>
8169 Generally, you can only give a <literal>SPECIALIZE</literal> pragma
8170 for a function defined in the same module.
8171 However if a function <literal>f</literal> is given an <literal>INLINABLE</literal>
8172 pragma at its definition site, then it can subequently be specialised by
8173 importing modules (see <xref linkend="inlinable-pragma"/>).
8176 module Map( lookup, blah blah ) where
8177 lookup :: Ord key => [(key,a)] -> key -> Maybe a
8179 {-# INLINABLE lookup #-}
8182 import Map( lookup )
8184 data T = T1 | T2 deriving( Eq, Ord )
8185 {-# SPECIALISE lookup :: [(T,a)] -> T -> Maybe a
8187 Here, <literal>lookup</literal> is declared <literal>INLINABLE</literal>, but
8188 it cannot be specialised for type <literal>T</literal> at its definition site,
8189 because that type does not exist yet. Instead a client module can define <literal>T</literal>
8190 and then specialise <literal>lookup</literal> at that type.
8193 Moreover, every module that imports <literal>Client</literal> (or imports a module
8194 that imports <literal>Client</literal>, transitively) will "see", and make use of,
8195 the specialised version of <literal>lookup</literal>. You don't need to put
8196 a <literal>SPECIALIZE</literal> pragma in every module.
8199 Moreover you often don't even need the <literal>SPECIALIZE</literal> pragma in the
8200 first place. When compiling a module M,
8201 GHC's optimiser (with -O) automatically considers each top-level
8202 overloaded function declared in M, and specialises it
8203 for the different types at which it is called in M. The optimiser
8204 <emphasis>also</emphasis> considers each <emphasis>imported</emphasis>
8205 <literal>INLINABLE</literal> overloaded function, and specialises it
8206 for the different types at which it is called in M.
8207 So in our example, it would be enough for <literal>lookup</literal> to
8208 be called at type <literal>T</literal>:
8211 import Map( lookup )
8213 data T = T1 | T2 deriving( Eq, Ord )
8215 findT1 :: [(T,a)] -> Maybe a
8216 findT1 m = lookup m T1 -- A call of lookup at type T
8218 However, sometimes there are no such calls, in which case the
8219 pragma can be useful.
8223 <sect3><title>Obselete SPECIALIZE syntax</title>
8225 <para>Note: In earlier versions of GHC, it was possible to provide your own
8226 specialised function for a given type:
8229 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
8232 This feature has been removed, as it is now subsumed by the
8233 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
8238 <sect2 id="specialize-instance-pragma">
8239 <title>SPECIALIZE instance pragma
8243 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
8244 <indexterm><primary>overloading, death to</primary></indexterm>
8245 Same idea, except for instance declarations. For example:
8248 instance (Eq a) => Eq (Foo a) where {
8249 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
8253 The pragma must occur inside the <literal>where</literal> part
8254 of the instance declaration.
8257 Compatible with HBC, by the way, except perhaps in the placement
8263 <sect2 id="unpack-pragma">
8264 <title>UNPACK pragma</title>
8266 <indexterm><primary>UNPACK</primary></indexterm>
8268 <para>The <literal>UNPACK</literal> indicates to the compiler
8269 that it should unpack the contents of a constructor field into
8270 the constructor itself, removing a level of indirection. For
8274 data T = T {-# UNPACK #-} !Float
8275 {-# UNPACK #-} !Float
8278 <para>will create a constructor <literal>T</literal> containing
8279 two unboxed floats. This may not always be an optimisation: if
8280 the <function>T</function> constructor is scrutinised and the
8281 floats passed to a non-strict function for example, they will
8282 have to be reboxed (this is done automatically by the
8285 <para>Unpacking constructor fields should only be used in
8286 conjunction with <option>-O</option>, in order to expose
8287 unfoldings to the compiler so the reboxing can be removed as
8288 often as possible. For example:</para>
8292 f (T f1 f2) = f1 + f2
8295 <para>The compiler will avoid reboxing <function>f1</function>
8296 and <function>f2</function> by inlining <function>+</function>
8297 on floats, but only when <option>-O</option> is on.</para>
8299 <para>Any single-constructor data is eligible for unpacking; for
8303 data T = T {-# UNPACK #-} !(Int,Int)
8306 <para>will store the two <literal>Int</literal>s directly in the
8307 <function>T</function> constructor, by flattening the pair.
8308 Multi-level unpacking is also supported:
8311 data T = T {-# UNPACK #-} !S
8312 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8315 will store two unboxed <literal>Int#</literal>s
8316 directly in the <function>T</function> constructor. The
8317 unpacker can see through newtypes, too.</para>
8319 <para>See also the <option>-funbox-strict-fields</option> flag,
8320 which essentially has the effect of adding
8321 <literal>{-# UNPACK #-}</literal> to every strict
8322 constructor field.</para>
8325 <sect2 id="source-pragma">
8326 <title>SOURCE pragma</title>
8328 <indexterm><primary>SOURCE</primary></indexterm>
8329 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8330 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8336 <!-- ======================= REWRITE RULES ======================== -->
8338 <sect1 id="rewrite-rules">
8339 <title>Rewrite rules
8341 <indexterm><primary>RULES pragma</primary></indexterm>
8342 <indexterm><primary>pragma, RULES</primary></indexterm>
8343 <indexterm><primary>rewrite rules</primary></indexterm></title>
8346 The programmer can specify rewrite rules as part of the source program
8352 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8357 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8358 If you need more information, then <option>-ddump-rule-firings</option> shows you
8359 each individual rule firing and <option>-ddump-rule-rewrites</option> also shows what the code looks like before and after the rewrite.
8363 <title>Syntax</title>
8366 From a syntactic point of view:
8372 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8373 may be generated by the layout rule).
8379 The layout rule applies in a pragma.
8380 Currently no new indentation level
8381 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8382 you must lay out the starting in the same column as the enclosing definitions.
8385 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8386 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8389 Furthermore, the closing <literal>#-}</literal>
8390 should start in a column to the right of the opening <literal>{-#</literal>.
8396 Each rule has a name, enclosed in double quotes. The name itself has
8397 no significance at all. It is only used when reporting how many times the rule fired.
8403 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8404 immediately after the name of the rule. Thus:
8407 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8410 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8411 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8420 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8421 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8422 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8423 by spaces, just like in a type <literal>forall</literal>.
8429 A pattern variable may optionally have a type signature.
8430 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8431 For example, here is the <literal>foldr/build</literal> rule:
8434 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8435 foldr k z (build g) = g k z
8438 Since <function>g</function> has a polymorphic type, it must have a type signature.
8445 The left hand side of a rule must consist of a top-level variable applied
8446 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8449 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8450 "wrong2" forall f. f True = True
8453 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8460 A rule does not need to be in the same module as (any of) the
8461 variables it mentions, though of course they need to be in scope.
8467 All rules are implicitly exported from the module, and are therefore
8468 in force in any module that imports the module that defined the rule, directly
8469 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8470 in force when compiling A.) The situation is very similar to that for instance
8478 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8479 any other flag settings. Furthermore, inside a RULE, the language extension
8480 <option>-XScopedTypeVariables</option> is automatically enabled; see
8481 <xref linkend="scoped-type-variables"/>.
8487 Like other pragmas, RULE pragmas are always checked for scope errors, and
8488 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8489 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8490 if the <option>-fenable-rewrite-rules</option> flag is
8491 on (see <xref linkend="rule-semantics"/>).
8500 <sect2 id="rule-semantics">
8501 <title>Semantics</title>
8504 From a semantic point of view:
8509 Rules are enabled (that is, used during optimisation)
8510 by the <option>-fenable-rewrite-rules</option> flag.
8511 This flag is implied by <option>-O</option>, and may be switched
8512 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8513 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8514 may not do what you expect, though, because without <option>-O</option> GHC
8515 ignores all optimisation information in interface files;
8516 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8517 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8518 has no effect on parsing or typechecking.
8524 Rules are regarded as left-to-right rewrite rules.
8525 When GHC finds an expression that is a substitution instance of the LHS
8526 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8527 By "a substitution instance" we mean that the LHS can be made equal to the
8528 expression by substituting for the pattern variables.
8535 GHC makes absolutely no attempt to verify that the LHS and RHS
8536 of a rule have the same meaning. That is undecidable in general, and
8537 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8544 GHC makes no attempt to make sure that the rules are confluent or
8545 terminating. For example:
8548 "loop" forall x y. f x y = f y x
8551 This rule will cause the compiler to go into an infinite loop.
8558 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8564 GHC currently uses a very simple, syntactic, matching algorithm
8565 for matching a rule LHS with an expression. It seeks a substitution
8566 which makes the LHS and expression syntactically equal modulo alpha
8567 conversion. The pattern (rule), but not the expression, is eta-expanded if
8568 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8569 But not beta conversion (that's called higher-order matching).
8573 Matching is carried out on GHC's intermediate language, which includes
8574 type abstractions and applications. So a rule only matches if the
8575 types match too. See <xref linkend="rule-spec"/> below.
8581 GHC keeps trying to apply the rules as it optimises the program.
8582 For example, consider:
8591 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8592 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8593 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8594 not be substituted, and the rule would not fire.
8604 <sect2 id="conlike">
8605 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8608 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8609 results. Consider this (artificial) example
8615 {-# RULES "f" f True = False #-}
8617 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8622 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8624 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8625 would have been a better chance that <literal>f</literal>'s RULE might fire.
8628 The way to get predictable behaviour is to use a NOINLINE
8629 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8630 that it is not inlined until its RULEs have had a chance to fire.
8633 GHC is very cautious about duplicating work. For example, consider
8635 f k z xs = let xs = build g
8636 in ...(foldr k z xs)...sum xs...
8637 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8639 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8640 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8641 duplicated if the rule fired.
8644 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8645 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8646 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8648 {-# INLINE[1] CONLIKE f #-}
8649 f x = <replaceable>blah</replaceable>
8651 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8652 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8653 should be considered cheap enough to duplicate, if such a duplication would make rule
8654 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8655 have such a property.)
8656 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8657 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8658 not going to be inlined before the rule has a chance to fire.
8663 <title>List fusion</title>
8666 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8667 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8668 intermediate list should be eliminated entirely.
8672 The following are good producers:
8684 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8690 Explicit lists (e.g. <literal>[True, False]</literal>)
8696 The cons constructor (e.g <literal>3:4:[]</literal>)
8702 <function>++</function>
8708 <function>map</function>
8714 <function>take</function>, <function>filter</function>
8720 <function>iterate</function>, <function>repeat</function>
8726 <function>zip</function>, <function>zipWith</function>
8735 The following are good consumers:
8747 <function>array</function> (on its second argument)
8753 <function>++</function> (on its first argument)
8759 <function>foldr</function>
8765 <function>map</function>
8771 <function>take</function>, <function>filter</function>
8777 <function>concat</function>
8783 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8789 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8790 will fuse with one but not the other)
8796 <function>partition</function>
8802 <function>head</function>
8808 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8814 <function>sequence_</function>
8820 <function>msum</function>
8826 <function>sortBy</function>
8835 So, for example, the following should generate no intermediate lists:
8838 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8844 This list could readily be extended; if there are Prelude functions that you use
8845 a lot which are not included, please tell us.
8849 If you want to write your own good consumers or producers, look at the
8850 Prelude definitions of the above functions to see how to do so.
8855 <sect2 id="rule-spec">
8856 <title>Specialisation
8860 Rewrite rules can be used to get the same effect as a feature
8861 present in earlier versions of GHC.
8862 For example, suppose that:
8865 genericLookup :: Ord a => Table a b -> a -> b
8866 intLookup :: Table Int b -> Int -> b
8869 where <function>intLookup</function> is an implementation of
8870 <function>genericLookup</function> that works very fast for
8871 keys of type <literal>Int</literal>. You might wish
8872 to tell GHC to use <function>intLookup</function> instead of
8873 <function>genericLookup</function> whenever the latter was called with
8874 type <literal>Table Int b -> Int -> b</literal>.
8875 It used to be possible to write
8878 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8881 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8884 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8887 This slightly odd-looking rule instructs GHC to replace
8888 <function>genericLookup</function> by <function>intLookup</function>
8889 <emphasis>whenever the types match</emphasis>.
8890 What is more, this rule does not need to be in the same
8891 file as <function>genericLookup</function>, unlike the
8892 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8893 have an original definition available to specialise).
8896 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8897 <function>intLookup</function> really behaves as a specialised version
8898 of <function>genericLookup</function>!!!</para>
8900 <para>An example in which using <literal>RULES</literal> for
8901 specialisation will Win Big:
8904 toDouble :: Real a => a -> Double
8905 toDouble = fromRational . toRational
8907 {-# RULES "toDouble/Int" toDouble = i2d #-}
8908 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8911 The <function>i2d</function> function is virtually one machine
8912 instruction; the default conversion—via an intermediate
8913 <literal>Rational</literal>—is obscenely expensive by
8919 <sect2 id="controlling-rules">
8920 <title>Controlling what's going on in rewrite rules</title>
8928 Use <option>-ddump-rules</option> to see the rules that are defined
8929 <emphasis>in this module</emphasis>.
8930 This includes rules generated by the specialisation pass, but excludes
8931 rules imported from other modules.
8937 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8938 If you add <option>-dppr-debug</option> you get a more detailed listing.
8944 Use <option>-ddump-rule-firings</option> or <option>-ddump-rule-rewrites</option>
8945 to see in great detail what rules are being fired.
8946 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8952 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8955 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8956 {-# INLINE build #-}
8960 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8961 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8962 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8963 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8970 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8971 see how to write rules that will do fusion and yet give an efficient
8972 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8982 <sect2 id="core-pragma">
8983 <title>CORE pragma</title>
8985 <indexterm><primary>CORE pragma</primary></indexterm>
8986 <indexterm><primary>pragma, CORE</primary></indexterm>
8987 <indexterm><primary>core, annotation</primary></indexterm>
8990 The external core format supports <quote>Note</quote> annotations;
8991 the <literal>CORE</literal> pragma gives a way to specify what these
8992 should be in your Haskell source code. Syntactically, core
8993 annotations are attached to expressions and take a Haskell string
8994 literal as an argument. The following function definition shows an
8998 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
9001 Semantically, this is equivalent to:
9009 However, when external core is generated (via
9010 <option>-fext-core</option>), there will be Notes attached to the
9011 expressions <function>show</function> and <varname>x</varname>.
9012 The core function declaration for <function>f</function> is:
9016 f :: %forall a . GHCziShow.ZCTShow a ->
9017 a -> GHCziBase.ZMZN GHCziBase.Char =
9018 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
9020 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
9022 (tpl1::GHCziBase.Int ->
9024 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
9026 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
9027 (tpl3::GHCziBase.ZMZN a ->
9028 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
9036 Here, we can see that the function <function>show</function> (which
9037 has been expanded out to a case expression over the Show dictionary)
9038 has a <literal>%note</literal> attached to it, as does the
9039 expression <varname>eta</varname> (which used to be called
9040 <varname>x</varname>).
9047 <sect1 id="special-ids">
9048 <title>Special built-in functions</title>
9049 <para>GHC has a few built-in functions with special behaviour. These
9050 are now described in the module <ulink
9051 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
9052 in the library documentation.
9056 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Ainline"><literal>inline</literal></ulink>
9057 allows control over inlining on a per-call-site basis.
9060 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Alazy"><literal>lazy</literal></ulink>
9061 restrains the strictness analyser.
9064 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3AunsafeCoerce%23"><literal>lazy</literal></ulink>
9065 allows you to fool the type checker.
9072 <sect1 id="generic-classes">
9073 <title>Generic classes</title>
9076 The ideas behind this extension are described in detail in "Derivable type classes",
9077 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
9078 An example will give the idea:
9082 import Data.Generics
9086 fromBin :: [Int] -> (a, [Int])
9088 toBin {| Unit |} Unit = []
9089 toBin {| a :+: b |} (Inl x) = 0 : toBin x
9090 toBin {| a :+: b |} (Inr y) = 1 : toBin y
9091 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
9093 fromBin {| Unit |} bs = (Unit, bs)
9094 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
9095 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
9096 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
9097 (y,bs'') = fromBin bs'
9100 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
9101 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
9102 which are defined thus in the library module <literal>Data.Generics</literal>:
9106 data a :+: b = Inl a | Inr b
9107 data a :*: b = a :*: b
9110 Now you can make a data type into an instance of Bin like this:
9112 instance (Bin a, Bin b) => Bin (a,b)
9113 instance Bin a => Bin [a]
9115 That is, just leave off the "where" clause. Of course, you can put in the
9116 where clause and over-ride whichever methods you please.
9120 <title> Using generics </title>
9121 <para>To use generics you need to</para>
9125 Use the flags <option>-XGenerics</option> (to enable the
9126 extra syntax and generate extra per-data-type code),
9127 and <option>-package syb</option> (to make the
9128 <literal>Data.Generics</literal> module available.
9132 <para>Import the module <literal>Data.Generics</literal> from the
9133 <literal>syb</literal> package. This import brings into
9134 scope the data types <literal>Unit</literal>,
9135 <literal>:*:</literal>, and <literal>:+:</literal>. (You
9136 don't need this import if you don't mention these types
9137 explicitly; for example, if you are simply giving instance
9138 declarations.)</para>
9143 <sect2> <title> Changes wrt the paper </title>
9145 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
9146 can be written infix (indeed, you can now use
9147 any operator starting in a colon as an infix type constructor). Also note that
9148 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
9149 Finally, note that the syntax of the type patterns in the class declaration
9150 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
9151 alone would ambiguous when they appear on right hand sides (an extension we
9152 anticipate wanting).
9156 <sect2> <title>Terminology and restrictions</title>
9158 Terminology. A "generic default method" in a class declaration
9159 is one that is defined using type patterns as above.
9160 A "polymorphic default method" is a default method defined as in Haskell 98.
9161 A "generic class declaration" is a class declaration with at least one
9162 generic default method.
9170 Alas, we do not yet implement the stuff about constructor names and
9177 A generic class can have only one parameter; you can't have a generic
9178 multi-parameter class.
9184 A default method must be defined entirely using type patterns, or entirely
9185 without. So this is illegal:
9188 op :: a -> (a, Bool)
9189 op {| Unit |} Unit = (Unit, True)
9192 However it is perfectly OK for some methods of a generic class to have
9193 generic default methods and others to have polymorphic default methods.
9199 The type variable(s) in the type pattern for a generic method declaration
9200 scope over the right hand side. So this is legal (note the use of the type variable ``p'' in a type signature on the right hand side:
9204 op {| p :*: q |} (x :*: y) = op (x :: p)
9212 The type patterns in a generic default method must take one of the forms:
9218 where "a" and "b" are type variables. Furthermore, all the type patterns for
9219 a single type constructor (<literal>:*:</literal>, say) must be identical; they
9220 must use the same type variables. So this is illegal:
9224 op {| a :+: b |} (Inl x) = True
9225 op {| p :+: q |} (Inr y) = False
9227 The type patterns must be identical, even in equations for different methods of the class.
9228 So this too is illegal:
9232 op1 {| a :*: b |} (x :*: y) = True
9235 op2 {| p :*: q |} (x :*: y) = False
9237 (The reason for this restriction is that we gather all the equations for a particular type constructor
9238 into a single generic instance declaration.)
9244 A generic method declaration must give a case for each of the three type constructors.
9250 The type for a generic method can be built only from:
9252 <listitem> <para> Function arrows </para> </listitem>
9253 <listitem> <para> Type variables </para> </listitem>
9254 <listitem> <para> Tuples </para> </listitem>
9255 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
9257 Here are some example type signatures for generic methods:
9260 op2 :: Bool -> (a,Bool)
9261 op3 :: [Int] -> a -> a
9264 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
9268 This restriction is an implementation restriction: we just haven't got around to
9269 implementing the necessary bidirectional maps over arbitrary type constructors.
9270 It would be relatively easy to add specific type constructors, such as Maybe and list,
9271 to the ones that are allowed.</para>
9276 In an instance declaration for a generic class, the idea is that the compiler
9277 will fill in the methods for you, based on the generic templates. However it can only
9282 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
9287 No constructor of the instance type has unboxed fields.
9291 (Of course, these things can only arise if you are already using GHC extensions.)
9292 However, you can still give an instance declarations for types which break these rules,
9293 provided you give explicit code to override any generic default methods.
9301 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9302 what the compiler does with generic declarations.
9307 <sect2> <title> Another example </title>
9309 Just to finish with, here's another example I rather like:
9313 nCons {| Unit |} _ = 1
9314 nCons {| a :*: b |} _ = 1
9315 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9318 tag {| Unit |} _ = 1
9319 tag {| a :*: b |} _ = 1
9320 tag {| a :+: b |} (Inl x) = tag x
9321 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9327 <sect1 id="monomorphism">
9328 <title>Control over monomorphism</title>
9330 <para>GHC supports two flags that control the way in which generalisation is
9331 carried out at let and where bindings.
9335 <title>Switching off the dreaded Monomorphism Restriction</title>
9336 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9338 <para>Haskell's monomorphism restriction (see
9339 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9341 of the Haskell Report)
9342 can be completely switched off by
9343 <option>-XNoMonomorphismRestriction</option>.
9348 <title>Monomorphic pattern bindings</title>
9349 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9350 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9352 <para> As an experimental change, we are exploring the possibility of
9353 making pattern bindings monomorphic; that is, not generalised at all.
9354 A pattern binding is a binding whose LHS has no function arguments,
9355 and is not a simple variable. For example:
9357 f x = x -- Not a pattern binding
9358 f = \x -> x -- Not a pattern binding
9359 f :: Int -> Int = \x -> x -- Not a pattern binding
9361 (g,h) = e -- A pattern binding
9362 (f) = e -- A pattern binding
9363 [x] = e -- A pattern binding
9365 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9366 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
9375 ;;; Local Variables: ***
9376 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
9377 ;;; ispell-local-dictionary: "british" ***
projects / ghc-hetmet.git / blob