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 <!-- ===================== REBINDABLE SYNTAX =================== -->
1206 <sect2 id="rebindable-syntax">
1207 <title>Rebindable syntax and the implicit Prelude import</title>
1209 <para><indexterm><primary>-XNoImplicitPrelude
1210 option</primary></indexterm> GHC normally imports
1211 <filename>Prelude.hi</filename> files for you. If you'd
1212 rather it didn't, then give it a
1213 <option>-XNoImplicitPrelude</option> option. The idea is
1214 that you can then import a Prelude of your own. (But don't
1215 call it <literal>Prelude</literal>; the Haskell module
1216 namespace is flat, and you must not conflict with any
1217 Prelude module.)</para>
1219 <para>Suppose you are importing a Prelude of your own
1220 in order to define your own numeric class
1221 hierarchy. It completely defeats that purpose if the
1222 literal "1" means "<literal>Prelude.fromInteger
1223 1</literal>", which is what the Haskell Report specifies.
1224 So the <option>-XRebindableSyntax</option>
1226 the following pieces of built-in syntax to refer to
1227 <emphasis>whatever is in scope</emphasis>, not the Prelude
1231 <para>An integer literal <literal>368</literal> means
1232 "<literal>fromInteger (368::Integer)</literal>", rather than
1233 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1236 <listitem><para>Fractional literals are handed in just the same way,
1237 except that the translation is
1238 <literal>fromRational (3.68::Rational)</literal>.
1241 <listitem><para>The equality test in an overloaded numeric pattern
1242 uses whatever <literal>(==)</literal> is in scope.
1245 <listitem><para>The subtraction operation, and the
1246 greater-than-or-equal test, in <literal>n+k</literal> patterns
1247 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1251 <para>Negation (e.g. "<literal>- (f x)</literal>")
1252 means "<literal>negate (f x)</literal>", both in numeric
1253 patterns, and expressions.
1257 <para>Conditionals (e.g. "<literal>if</literal> e1 <literal>then</literal> e2 <literal>else</literal> e3")
1258 means "<literal>ifThenElse</literal> e1 e2 e3". However <literal>case</literal> expressions are unaffected.
1262 <para>"Do" notation is translated using whatever
1263 functions <literal>(>>=)</literal>,
1264 <literal>(>>)</literal>, and <literal>fail</literal>,
1265 are in scope (not the Prelude
1266 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1267 comprehensions, are unaffected. </para></listitem>
1271 notation (see <xref linkend="arrow-notation"/>)
1272 uses whatever <literal>arr</literal>,
1273 <literal>(>>>)</literal>, <literal>first</literal>,
1274 <literal>app</literal>, <literal>(|||)</literal> and
1275 <literal>loop</literal> functions are in scope. But unlike the
1276 other constructs, the types of these functions must match the
1277 Prelude types very closely. Details are in flux; if you want
1281 <option>-XRebindableSyntax</option> implies <option>-XNoImplicitPrelude</option>.
1284 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1285 even if that is a little unexpected. For example, the
1286 static semantics of the literal <literal>368</literal>
1287 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1288 <literal>fromInteger</literal> to have any of the types:
1290 fromInteger :: Integer -> Integer
1291 fromInteger :: forall a. Foo a => Integer -> a
1292 fromInteger :: Num a => a -> Integer
1293 fromInteger :: Integer -> Bool -> Bool
1297 <para>Be warned: this is an experimental facility, with
1298 fewer checks than usual. Use <literal>-dcore-lint</literal>
1299 to typecheck the desugared program. If Core Lint is happy
1300 you should be all right.</para>
1304 <sect2 id="postfix-operators">
1305 <title>Postfix operators</title>
1308 The <option>-XPostfixOperators</option> flag enables a small
1309 extension to the syntax of left operator sections, which allows you to
1310 define postfix operators. The extension is this: the left section
1314 is equivalent (from the point of view of both type checking and execution) to the expression
1318 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1319 The strict Haskell 98 interpretation is that the section is equivalent to
1323 That is, the operator must be a function of two arguments. GHC allows it to
1324 take only one argument, and that in turn allows you to write the function
1327 <para>The extension does not extend to the left-hand side of function
1328 definitions; you must define such a function in prefix form.</para>
1332 <sect2 id="tuple-sections">
1333 <title>Tuple sections</title>
1336 The <option>-XTupleSections</option> flag enables Python-style partially applied
1337 tuple constructors. For example, the following program
1341 is considered to be an alternative notation for the more unwieldy alternative
1345 You can omit any combination of arguments to the tuple, as in the following
1347 (, "I", , , "Love", , 1337)
1351 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1356 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1357 will also be available for them, like so
1361 Because there is no unboxed unit tuple, the following expression
1365 continues to stand for the unboxed singleton tuple data constructor.
1370 <sect2 id="disambiguate-fields">
1371 <title>Record field disambiguation</title>
1373 In record construction and record pattern matching
1374 it is entirely unambiguous which field is referred to, even if there are two different
1375 data types in scope with a common field name. For example:
1378 data S = MkS { x :: Int, y :: Bool }
1383 data T = MkT { x :: Int }
1385 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1386 ok2 n = MkT { x = n+1 } -- Unambiguous
1388 bad1 k = k { x = 3 } -- Ambiguous
1389 bad2 k = x k -- Ambiguous
1391 Even though there are two <literal>x</literal>'s in scope,
1392 it is clear that the <literal>x</literal> in the pattern in the
1393 definition of <literal>ok1</literal> can only mean the field
1394 <literal>x</literal> from type <literal>S</literal>. Similarly for
1395 the function <literal>ok2</literal>. However, in the record update
1396 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1397 it is not clear which of the two types is intended.
1400 Haskell 98 regards all four as ambiguous, but with the
1401 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1402 the former two. The rules are precisely the same as those for instance
1403 declarations in Haskell 98, where the method names on the left-hand side
1404 of the method bindings in an instance declaration refer unambiguously
1405 to the method of that class (provided they are in scope at all), even
1406 if there are other variables in scope with the same name.
1407 This reduces the clutter of qualified names when you import two
1408 records from different modules that use the same field name.
1414 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1419 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1424 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1425 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1426 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1429 import qualified M -- Note qualified
1431 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1433 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1434 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1435 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1436 is not. (In effect, it is qualified by the constructor.)
1443 <!-- ===================== Record puns =================== -->
1445 <sect2 id="record-puns">
1450 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1454 When using records, it is common to write a pattern that binds a
1455 variable with the same name as a record field, such as:
1458 data C = C {a :: Int}
1464 Record punning permits the variable name to be elided, so one can simply
1471 to mean the same pattern as above. That is, in a record pattern, the
1472 pattern <literal>a</literal> expands into the pattern <literal>a =
1473 a</literal> for the same name <literal>a</literal>.
1480 Record punning can also be used in an expression, writing, for example,
1486 let a = 1 in C {a = a}
1488 The expansion is purely syntactic, so the expanded right-hand side
1489 expression refers to the nearest enclosing variable that is spelled the
1490 same as the field name.
1494 Puns and other patterns can be mixed in the same record:
1496 data C = C {a :: Int, b :: Int}
1497 f (C {a, b = 4}) = a
1502 Puns can be used wherever record patterns occur (e.g. in
1503 <literal>let</literal> bindings or at the top-level).
1507 A pun on a qualified field name is expanded by stripping off the module qualifier.
1514 f (M.C {M.a = a}) = a
1516 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1517 is only in scope in qualified form.)
1525 <!-- ===================== Record wildcards =================== -->
1527 <sect2 id="record-wildcards">
1528 <title>Record wildcards
1532 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1533 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1537 For records with many fields, it can be tiresome to write out each field
1538 individually in a record pattern, as in
1540 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1541 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1546 Record wildcard syntax permits a "<literal>..</literal>" in a record
1547 pattern, where each elided field <literal>f</literal> is replaced by the
1548 pattern <literal>f = f</literal>. For example, the above pattern can be
1551 f (C {a = 1, ..}) = b + c + d
1559 Wildcards can be mixed with other patterns, including puns
1560 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1561 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1562 wherever record patterns occur, including in <literal>let</literal>
1563 bindings and at the top-level. For example, the top-level binding
1567 defines <literal>b</literal>, <literal>c</literal>, and
1568 <literal>d</literal>.
1572 Record wildcards can also be used in expressions, writing, for example,
1574 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1578 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1580 The expansion is purely syntactic, so the record wildcard
1581 expression refers to the nearest enclosing variables that are spelled
1582 the same as the omitted field names.
1586 The "<literal>..</literal>" expands to the missing
1587 <emphasis>in-scope</emphasis> record fields, where "in scope"
1588 includes both unqualified and qualified-only.
1589 Any fields that are not in scope are not filled in. For example
1592 data R = R { a,b,c :: Int }
1594 import qualified M( R(a,b) )
1597 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1598 omitting <literal>c</literal> since it is not in scope at all.
1605 <!-- ===================== Local fixity declarations =================== -->
1607 <sect2 id="local-fixity-declarations">
1608 <title>Local Fixity Declarations
1611 <para>A careful reading of the Haskell 98 Report reveals that fixity
1612 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1613 <literal>infixr</literal>) are permitted to appear inside local bindings
1614 such those introduced by <literal>let</literal> and
1615 <literal>where</literal>. However, the Haskell Report does not specify
1616 the semantics of such bindings very precisely.
1619 <para>In GHC, a fixity declaration may accompany a local binding:
1626 and the fixity declaration applies wherever the binding is in scope.
1627 For example, in a <literal>let</literal>, it applies in the right-hand
1628 sides of other <literal>let</literal>-bindings and the body of the
1629 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1630 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
1631 declarations of a <literal>let</literal> statement scope over other
1632 statements in the group, just as the bound name does.
1636 Moreover, a local fixity declaration *must* accompany a local binding of
1637 that name: it is not possible to revise the fixity of name bound
1640 let infixr 9 $ in ...
1643 Because local fixity declarations are technically Haskell 98, no flag is
1644 necessary to enable them.
1648 <sect2 id="package-imports">
1649 <title>Package-qualified imports</title>
1651 <para>With the <option>-XPackageImports</option> flag, GHC allows
1652 import declarations to be qualified by the package name that the
1653 module is intended to be imported from. For example:</para>
1656 import "network" Network.Socket
1659 <para>would import the module <literal>Network.Socket</literal> from
1660 the package <literal>network</literal> (any version). This may
1661 be used to disambiguate an import when the same module is
1662 available from multiple packages, or is present in both the
1663 current package being built and an external package.</para>
1665 <para>Note: you probably don't need to use this feature, it was
1666 added mainly so that we can build backwards-compatible versions of
1667 packages when APIs change. It can lead to fragile dependencies in
1668 the common case: modules occasionally move from one package to
1669 another, rendering any package-qualified imports broken.</para>
1672 <sect2 id="syntax-stolen">
1673 <title>Summary of stolen syntax</title>
1675 <para>Turning on an option that enables special syntax
1676 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1677 to compile, perhaps because it uses a variable name which has
1678 become a reserved word. This section lists the syntax that is
1679 "stolen" by language extensions.
1681 notation and nonterminal names from the Haskell 98 lexical syntax
1682 (see the Haskell 98 Report).
1683 We only list syntax changes here that might affect
1684 existing working programs (i.e. "stolen" syntax). Many of these
1685 extensions will also enable new context-free syntax, but in all
1686 cases programs written to use the new syntax would not be
1687 compilable without the option enabled.</para>
1689 <para>There are two classes of special
1694 <para>New reserved words and symbols: character sequences
1695 which are no longer available for use as identifiers in the
1699 <para>Other special syntax: sequences of characters that have
1700 a different meaning when this particular option is turned
1705 The following syntax is stolen:
1710 <literal>forall</literal>
1711 <indexterm><primary><literal>forall</literal></primary></indexterm>
1714 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1715 <option>-XScopedTypeVariables</option>,
1716 <option>-XLiberalTypeSynonyms</option>,
1717 <option>-XRank2Types</option>,
1718 <option>-XRankNTypes</option>,
1719 <option>-XPolymorphicComponents</option>,
1720 <option>-XExistentialQuantification</option>
1726 <literal>mdo</literal>
1727 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1730 Stolen by: <option>-XRecursiveDo</option>,
1736 <literal>foreign</literal>
1737 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1740 Stolen by: <option>-XForeignFunctionInterface</option>,
1746 <literal>rec</literal>,
1747 <literal>proc</literal>, <literal>-<</literal>,
1748 <literal>>-</literal>, <literal>-<<</literal>,
1749 <literal>>>-</literal>, and <literal>(|</literal>,
1750 <literal>|)</literal> brackets
1751 <indexterm><primary><literal>proc</literal></primary></indexterm>
1754 Stolen by: <option>-XArrows</option>,
1760 <literal>?<replaceable>varid</replaceable></literal>,
1761 <literal>%<replaceable>varid</replaceable></literal>
1762 <indexterm><primary>implicit parameters</primary></indexterm>
1765 Stolen by: <option>-XImplicitParams</option>,
1771 <literal>[|</literal>,
1772 <literal>[e|</literal>, <literal>[p|</literal>,
1773 <literal>[d|</literal>, <literal>[t|</literal>,
1774 <literal>$(</literal>,
1775 <literal>$<replaceable>varid</replaceable></literal>
1776 <indexterm><primary>Template Haskell</primary></indexterm>
1779 Stolen by: <option>-XTemplateHaskell</option>,
1785 <literal>[:<replaceable>varid</replaceable>|</literal>
1786 <indexterm><primary>quasi-quotation</primary></indexterm>
1789 Stolen by: <option>-XQuasiQuotes</option>,
1795 <replaceable>varid</replaceable>{<literal>#</literal>},
1796 <replaceable>char</replaceable><literal>#</literal>,
1797 <replaceable>string</replaceable><literal>#</literal>,
1798 <replaceable>integer</replaceable><literal>#</literal>,
1799 <replaceable>float</replaceable><literal>#</literal>,
1800 <replaceable>float</replaceable><literal>##</literal>,
1801 <literal>(#</literal>, <literal>#)</literal>,
1804 Stolen by: <option>-XMagicHash</option>,
1813 <!-- TYPE SYSTEM EXTENSIONS -->
1814 <sect1 id="data-type-extensions">
1815 <title>Extensions to data types and type synonyms</title>
1817 <sect2 id="nullary-types">
1818 <title>Data types with no constructors</title>
1820 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1821 a data type with no constructors. For example:</para>
1825 data T a -- T :: * -> *
1828 <para>Syntactically, the declaration lacks the "= constrs" part. The
1829 type can be parameterised over types of any kind, but if the kind is
1830 not <literal>*</literal> then an explicit kind annotation must be used
1831 (see <xref linkend="kinding"/>).</para>
1833 <para>Such data types have only one value, namely bottom.
1834 Nevertheless, they can be useful when defining "phantom types".</para>
1837 <sect2 id="datatype-contexts">
1838 <title>Data type contexts</title>
1840 <para>Haskell allows datatypes to be given contexts, e.g.</para>
1843 data Eq a => Set a = NilSet | ConsSet a (Set a)
1846 <para>give constructors with types:</para>
1850 ConsSet :: Eq a => a -> Set a -> Set a
1853 <para>In GHC this feature is an extension called
1854 <literal>DatatypeContexts</literal>, and on by default.</para>
1857 <sect2 id="infix-tycons">
1858 <title>Infix type constructors, classes, and type variables</title>
1861 GHC allows type constructors, classes, and type variables to be operators, and
1862 to be written infix, very much like expressions. More specifically:
1865 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1866 The lexical syntax is the same as that for data constructors.
1869 Data type and type-synonym declarations can be written infix, parenthesised
1870 if you want further arguments. E.g.
1872 data a :*: b = Foo a b
1873 type a :+: b = Either a b
1874 class a :=: b where ...
1876 data (a :**: b) x = Baz a b x
1877 type (a :++: b) y = Either (a,b) y
1881 Types, and class constraints, can be written infix. For example
1884 f :: (a :=: b) => a -> b
1888 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1889 The lexical syntax is the same as that for variable operators, excluding "(.)",
1890 "(!)", and "(*)". In a binding position, the operator must be
1891 parenthesised. For example:
1893 type T (+) = Int + Int
1897 liftA2 :: Arrow (~>)
1898 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1904 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1905 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1908 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1909 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1910 sets the fixity for a data constructor and the corresponding type constructor. For example:
1914 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1915 and similarly for <literal>:*:</literal>.
1916 <literal>Int `a` Bool</literal>.
1919 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1926 <sect2 id="type-synonyms">
1927 <title>Liberalised type synonyms</title>
1930 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1931 on individual synonym declarations.
1932 With the <option>-XLiberalTypeSynonyms</option> extension,
1933 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1934 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1937 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1938 in a type synonym, thus:
1940 type Discard a = forall b. Show b => a -> b -> (a, String)
1945 g :: Discard Int -> (Int,String) -- A rank-2 type
1952 If you also use <option>-XUnboxedTuples</option>,
1953 you can write an unboxed tuple in a type synonym:
1955 type Pr = (# Int, Int #)
1963 You can apply a type synonym to a forall type:
1965 type Foo a = a -> a -> Bool
1967 f :: Foo (forall b. b->b)
1969 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1971 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1976 You can apply a type synonym to a partially applied type synonym:
1978 type Generic i o = forall x. i x -> o x
1981 foo :: Generic Id []
1983 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1985 foo :: forall x. x -> [x]
1993 GHC currently does kind checking before expanding synonyms (though even that
1997 After expanding type synonyms, GHC does validity checking on types, looking for
1998 the following mal-formedness which isn't detected simply by kind checking:
2001 Type constructor applied to a type involving for-alls.
2004 Unboxed tuple on left of an arrow.
2007 Partially-applied type synonym.
2011 this will be rejected:
2013 type Pr = (# Int, Int #)
2018 because GHC does not allow unboxed tuples on the left of a function arrow.
2023 <sect2 id="existential-quantification">
2024 <title>Existentially quantified data constructors
2028 The idea of using existential quantification in data type declarations
2029 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2030 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2031 London, 1991). It was later formalised by Laufer and Odersky
2032 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2033 TOPLAS, 16(5), pp1411-1430, 1994).
2034 It's been in Lennart
2035 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2036 proved very useful. Here's the idea. Consider the declaration:
2042 data Foo = forall a. MkFoo a (a -> Bool)
2049 The data type <literal>Foo</literal> has two constructors with types:
2055 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2062 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2063 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2064 For example, the following expression is fine:
2070 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2076 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2077 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2078 isUpper</function> packages a character with a compatible function. These
2079 two things are each of type <literal>Foo</literal> and can be put in a list.
2083 What can we do with a value of type <literal>Foo</literal>?. In particular,
2084 what happens when we pattern-match on <function>MkFoo</function>?
2090 f (MkFoo val fn) = ???
2096 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2097 are compatible, the only (useful) thing we can do with them is to
2098 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2105 f (MkFoo val fn) = fn val
2111 What this allows us to do is to package heterogeneous values
2112 together with a bunch of functions that manipulate them, and then treat
2113 that collection of packages in a uniform manner. You can express
2114 quite a bit of object-oriented-like programming this way.
2117 <sect3 id="existential">
2118 <title>Why existential?
2122 What has this to do with <emphasis>existential</emphasis> quantification?
2123 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2129 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2135 But Haskell programmers can safely think of the ordinary
2136 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2137 adding a new existential quantification construct.
2142 <sect3 id="existential-with-context">
2143 <title>Existentials and type classes</title>
2146 An easy extension is to allow
2147 arbitrary contexts before the constructor. For example:
2153 data Baz = forall a. Eq a => Baz1 a a
2154 | forall b. Show b => Baz2 b (b -> b)
2160 The two constructors have the types you'd expect:
2166 Baz1 :: forall a. Eq a => a -> a -> Baz
2167 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2173 But when pattern matching on <function>Baz1</function> the matched values can be compared
2174 for equality, and when pattern matching on <function>Baz2</function> the first matched
2175 value can be converted to a string (as well as applying the function to it).
2176 So this program is legal:
2183 f (Baz1 p q) | p == q = "Yes"
2185 f (Baz2 v fn) = show (fn v)
2191 Operationally, in a dictionary-passing implementation, the
2192 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2193 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2194 extract it on pattern matching.
2199 <sect3 id="existential-records">
2200 <title>Record Constructors</title>
2203 GHC allows existentials to be used with records syntax as well. For example:
2206 data Counter a = forall self. NewCounter
2208 , _inc :: self -> self
2209 , _display :: self -> IO ()
2213 Here <literal>tag</literal> is a public field, with a well-typed selector
2214 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2215 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2216 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2217 compile-time error. In other words, <emphasis>GHC defines a record selector function
2218 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2219 (This example used an underscore in the fields for which record selectors
2220 will not be defined, but that is only programming style; GHC ignores them.)
2224 To make use of these hidden fields, we need to create some helper functions:
2227 inc :: Counter a -> Counter a
2228 inc (NewCounter x i d t) = NewCounter
2229 { _this = i x, _inc = i, _display = d, tag = t }
2231 display :: Counter a -> IO ()
2232 display NewCounter{ _this = x, _display = d } = d x
2235 Now we can define counters with different underlying implementations:
2238 counterA :: Counter String
2239 counterA = NewCounter
2240 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2242 counterB :: Counter String
2243 counterB = NewCounter
2244 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2247 display (inc counterA) -- prints "1"
2248 display (inc (inc counterB)) -- prints "##"
2251 Record update syntax is supported for existentials (and GADTs):
2253 setTag :: Counter a -> a -> Counter a
2254 setTag obj t = obj{ tag = t }
2256 The rule for record update is this: <emphasis>
2257 the types of the updated fields may
2258 mention only the universally-quantified type variables
2259 of the data constructor. For GADTs, the field may mention only types
2260 that appear as a simple type-variable argument in the constructor's result
2261 type</emphasis>. For example:
2263 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2264 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2265 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2266 -- existentially quantified)
2268 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2269 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2270 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2271 -- type-variable argument in G1's result type)
2279 <title>Restrictions</title>
2282 There are several restrictions on the ways in which existentially-quantified
2283 constructors can be use.
2292 When pattern matching, each pattern match introduces a new,
2293 distinct, type for each existential type variable. These types cannot
2294 be unified with any other type, nor can they escape from the scope of
2295 the pattern match. For example, these fragments are incorrect:
2303 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2304 is the result of <function>f1</function>. One way to see why this is wrong is to
2305 ask what type <function>f1</function> has:
2309 f1 :: Foo -> a -- Weird!
2313 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2318 f1 :: forall a. Foo -> a -- Wrong!
2322 The original program is just plain wrong. Here's another sort of error
2326 f2 (Baz1 a b) (Baz1 p q) = a==q
2330 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2331 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2332 from the two <function>Baz1</function> constructors.
2340 You can't pattern-match on an existentially quantified
2341 constructor in a <literal>let</literal> or <literal>where</literal> group of
2342 bindings. So this is illegal:
2346 f3 x = a==b where { Baz1 a b = x }
2349 Instead, use a <literal>case</literal> expression:
2352 f3 x = case x of Baz1 a b -> a==b
2355 In general, you can only pattern-match
2356 on an existentially-quantified constructor in a <literal>case</literal> expression or
2357 in the patterns of a function definition.
2359 The reason for this restriction is really an implementation one.
2360 Type-checking binding groups is already a nightmare without
2361 existentials complicating the picture. Also an existential pattern
2362 binding at the top level of a module doesn't make sense, because it's
2363 not clear how to prevent the existentially-quantified type "escaping".
2364 So for now, there's a simple-to-state restriction. We'll see how
2372 You can't use existential quantification for <literal>newtype</literal>
2373 declarations. So this is illegal:
2377 newtype T = forall a. Ord a => MkT a
2381 Reason: a value of type <literal>T</literal> must be represented as a
2382 pair of a dictionary for <literal>Ord t</literal> and a value of type
2383 <literal>t</literal>. That contradicts the idea that
2384 <literal>newtype</literal> should have no concrete representation.
2385 You can get just the same efficiency and effect by using
2386 <literal>data</literal> instead of <literal>newtype</literal>. If
2387 there is no overloading involved, then there is more of a case for
2388 allowing an existentially-quantified <literal>newtype</literal>,
2389 because the <literal>data</literal> version does carry an
2390 implementation cost, but single-field existentially quantified
2391 constructors aren't much use. So the simple restriction (no
2392 existential stuff on <literal>newtype</literal>) stands, unless there
2393 are convincing reasons to change it.
2401 You can't use <literal>deriving</literal> to define instances of a
2402 data type with existentially quantified data constructors.
2404 Reason: in most cases it would not make sense. For example:;
2407 data T = forall a. MkT [a] deriving( Eq )
2410 To derive <literal>Eq</literal> in the standard way we would need to have equality
2411 between the single component of two <function>MkT</function> constructors:
2415 (MkT a) == (MkT b) = ???
2418 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2419 It's just about possible to imagine examples in which the derived instance
2420 would make sense, but it seems altogether simpler simply to prohibit such
2421 declarations. Define your own instances!
2432 <!-- ====================== Generalised algebraic data types ======================= -->
2434 <sect2 id="gadt-style">
2435 <title>Declaring data types with explicit constructor signatures</title>
2437 <para>When the <literal>GADTSyntax</literal> extension is enabled,
2438 GHC allows you to declare an algebraic data type by
2439 giving the type signatures of constructors explicitly. For example:
2443 Just :: a -> Maybe a
2445 The form is called a "GADT-style declaration"
2446 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2447 can only be declared using this form.</para>
2448 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2449 For example, these two declarations are equivalent:
2451 data Foo = forall a. MkFoo a (a -> Bool)
2452 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2455 <para>Any data type that can be declared in standard Haskell-98 syntax
2456 can also be declared using GADT-style syntax.
2457 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2458 they treat class constraints on the data constructors differently.
2459 Specifically, if the constructor is given a type-class context, that
2460 context is made available by pattern matching. For example:
2463 MkSet :: Eq a => [a] -> Set a
2465 makeSet :: Eq a => [a] -> Set a
2466 makeSet xs = MkSet (nub xs)
2468 insert :: a -> Set a -> Set a
2469 insert a (MkSet as) | a `elem` as = MkSet as
2470 | otherwise = MkSet (a:as)
2472 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2473 gives rise to a <literal>(Eq a)</literal>
2474 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2475 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2476 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2477 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2478 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2479 In the example, the equality dictionary is used to satisfy the equality constraint
2480 generated by the call to <literal>elem</literal>, so that the type of
2481 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2484 For example, one possible application is to reify dictionaries:
2486 data NumInst a where
2487 MkNumInst :: Num a => NumInst a
2489 intInst :: NumInst Int
2492 plus :: NumInst a -> a -> a -> a
2493 plus MkNumInst p q = p + q
2495 Here, a value of type <literal>NumInst a</literal> is equivalent
2496 to an explicit <literal>(Num a)</literal> dictionary.
2499 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2500 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2504 = Num a => MkNumInst (NumInst a)
2506 Notice that, unlike the situation when declaring an existential, there is
2507 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2508 data type's universally quantified type variable <literal>a</literal>.
2509 A constructor may have both universal and existential type variables: for example,
2510 the following two declarations are equivalent:
2513 = forall b. (Num a, Eq b) => MkT1 a b
2515 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2518 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2519 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2520 In Haskell 98 the definition
2522 data Eq a => Set' a = MkSet' [a]
2524 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2525 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2526 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2527 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2528 GHC's behaviour is much more useful, as well as much more intuitive.
2532 The rest of this section gives further details about GADT-style data
2537 The result type of each data constructor must begin with the type constructor being defined.
2538 If the result type of all constructors
2539 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2540 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2541 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2545 As with other type signatures, you can give a single signature for several data constructors.
2546 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2555 The type signature of
2556 each constructor is independent, and is implicitly universally quantified as usual.
2557 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2558 have no scope, and different constructors may have different universally-quantified type variables:
2560 data T a where -- The 'a' has no scope
2561 T1,T2 :: b -> T b -- Means forall b. b -> T b
2562 T3 :: T a -- Means forall a. T a
2567 A constructor signature may mention type class constraints, which can differ for
2568 different constructors. For example, this is fine:
2571 T1 :: Eq b => b -> b -> T b
2572 T2 :: (Show c, Ix c) => c -> [c] -> T c
2574 When patten matching, these constraints are made available to discharge constraints
2575 in the body of the match. For example:
2578 f (T1 x y) | x==y = "yes"
2582 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2583 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2584 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2588 Unlike a Haskell-98-style
2589 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2590 have no scope. Indeed, one can write a kind signature instead:
2592 data Set :: * -> * where ...
2594 or even a mixture of the two:
2596 data Bar a :: (* -> *) -> * where ...
2598 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2601 data Bar a (b :: * -> *) where ...
2607 You can use strictness annotations, in the obvious places
2608 in the constructor type:
2611 Lit :: !Int -> Term Int
2612 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2613 Pair :: Term a -> Term b -> Term (a,b)
2618 You can use a <literal>deriving</literal> clause on a GADT-style data type
2619 declaration. For example, these two declarations are equivalent
2621 data Maybe1 a where {
2622 Nothing1 :: Maybe1 a ;
2623 Just1 :: a -> Maybe1 a
2624 } deriving( Eq, Ord )
2626 data Maybe2 a = Nothing2 | Just2 a
2632 The type signature may have quantified type variables that do not appear
2636 MkFoo :: a -> (a->Bool) -> Foo
2639 Here the type variable <literal>a</literal> does not appear in the result type
2640 of either constructor.
2641 Although it is universally quantified in the type of the constructor, such
2642 a type variable is often called "existential".
2643 Indeed, the above declaration declares precisely the same type as
2644 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2646 The type may contain a class context too, of course:
2649 MkShowable :: Show a => a -> Showable
2654 You can use record syntax on a GADT-style data type declaration:
2658 Adult :: { name :: String, children :: [Person] } -> Person
2659 Child :: Show a => { name :: !String, funny :: a } -> Person
2661 As usual, for every constructor that has a field <literal>f</literal>, the type of
2662 field <literal>f</literal> must be the same (modulo alpha conversion).
2663 The <literal>Child</literal> constructor above shows that the signature
2664 may have a context, existentially-quantified variables, and strictness annotations,
2665 just as in the non-record case. (NB: the "type" that follows the double-colon
2666 is not really a type, because of the record syntax and strictness annotations.
2667 A "type" of this form can appear only in a constructor signature.)
2671 Record updates are allowed with GADT-style declarations,
2672 only fields that have the following property: the type of the field
2673 mentions no existential type variables.
2677 As in the case of existentials declared using the Haskell-98-like record syntax
2678 (<xref linkend="existential-records"/>),
2679 record-selector functions are generated only for those fields that have well-typed
2681 Here is the example of that section, in GADT-style syntax:
2683 data Counter a where
2684 NewCounter { _this :: self
2685 , _inc :: self -> self
2686 , _display :: self -> IO ()
2691 As before, only one selector function is generated here, that for <literal>tag</literal>.
2692 Nevertheless, you can still use all the field names in pattern matching and record construction.
2694 </itemizedlist></para>
2698 <title>Generalised Algebraic Data Types (GADTs)</title>
2700 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2701 by allowing constructors to have richer return types. Here is an example:
2704 Lit :: Int -> Term Int
2705 Succ :: Term Int -> Term Int
2706 IsZero :: Term Int -> Term Bool
2707 If :: Term Bool -> Term a -> Term a -> Term a
2708 Pair :: Term a -> Term b -> Term (a,b)
2710 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2711 case with ordinary data types. This generality allows us to
2712 write a well-typed <literal>eval</literal> function
2713 for these <literal>Terms</literal>:
2717 eval (Succ t) = 1 + eval t
2718 eval (IsZero t) = eval t == 0
2719 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2720 eval (Pair e1 e2) = (eval e1, eval e2)
2722 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2723 For example, in the right hand side of the equation
2728 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2729 A precise specification of the type rules is beyond what this user manual aspires to,
2730 but the design closely follows that described in
2732 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2733 unification-based type inference for GADTs</ulink>,
2735 The general principle is this: <emphasis>type refinement is only carried out
2736 based on user-supplied type annotations</emphasis>.
2737 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2738 and lots of obscure error messages will
2739 occur. However, the refinement is quite general. For example, if we had:
2741 eval :: Term a -> a -> a
2742 eval (Lit i) j = i+j
2744 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2745 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2746 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2749 These and many other examples are given in papers by Hongwei Xi, and
2750 Tim Sheard. There is a longer introduction
2751 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2753 <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
2754 may use different notation to that implemented in GHC.
2757 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2758 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2761 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2762 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2763 The result type of each constructor must begin with the type constructor being defined,
2764 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2765 For example, in the <literal>Term</literal> data
2766 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2767 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2772 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2773 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2774 whose result type is not just <literal>T a b</literal>.
2778 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2779 an ordinary data type.
2783 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2787 Lit { val :: Int } :: Term Int
2788 Succ { num :: Term Int } :: Term Int
2789 Pred { num :: Term Int } :: Term Int
2790 IsZero { arg :: Term Int } :: Term Bool
2791 Pair { arg1 :: Term a
2794 If { cnd :: Term Bool
2799 However, for GADTs there is the following additional constraint:
2800 every constructor that has a field <literal>f</literal> must have
2801 the same result type (modulo alpha conversion)
2802 Hence, in the above example, we cannot merge the <literal>num</literal>
2803 and <literal>arg</literal> fields above into a
2804 single name. Although their field types are both <literal>Term Int</literal>,
2805 their selector functions actually have different types:
2808 num :: Term Int -> Term Int
2809 arg :: Term Bool -> Term Int
2814 When pattern-matching against data constructors drawn from a GADT,
2815 for example in a <literal>case</literal> expression, the following rules apply:
2817 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2818 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2819 <listitem><para>The type of any free variable mentioned in any of
2820 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2822 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2823 way to ensure that a variable a rigid type is to give it a type signature.
2824 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2825 Simple unification-based type inference for GADTs
2826 </ulink>. The criteria implemented by GHC are given in the Appendix.
2836 <!-- ====================== End of Generalised algebraic data types ======================= -->
2838 <sect1 id="deriving">
2839 <title>Extensions to the "deriving" mechanism</title>
2841 <sect2 id="deriving-inferred">
2842 <title>Inferred context for deriving clauses</title>
2845 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2848 data T0 f a = MkT0 a deriving( Eq )
2849 data T1 f a = MkT1 (f a) deriving( Eq )
2850 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2852 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2854 instance Eq a => Eq (T0 f a) where ...
2855 instance Eq (f a) => Eq (T1 f a) where ...
2856 instance Eq (f (f a)) => Eq (T2 f a) where ...
2858 The first of these is obviously fine. The second is still fine, although less obviously.
2859 The third is not Haskell 98, and risks losing termination of instances.
2862 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2863 each constraint in the inferred instance context must consist only of type variables,
2864 with no repetitions.
2867 This rule is applied regardless of flags. If you want a more exotic context, you can write
2868 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2872 <sect2 id="stand-alone-deriving">
2873 <title>Stand-alone deriving declarations</title>
2876 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2878 data Foo a = Bar a | Baz String
2880 deriving instance Eq a => Eq (Foo a)
2882 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2883 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2884 Note the following points:
2887 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2888 exactly as you would in an ordinary instance declaration.
2889 (In contrast, in a <literal>deriving</literal> clause
2890 attached to a data type declaration, the context is inferred.)
2894 A <literal>deriving instance</literal> declaration
2895 must obey the same rules concerning form and termination as ordinary instance declarations,
2896 controlled by the same flags; see <xref linkend="instance-decls"/>.
2900 Unlike a <literal>deriving</literal>
2901 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2902 than the data type (assuming you also use
2903 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2906 data Foo a = Bar a | Baz String
2908 deriving instance Eq a => Eq (Foo [a])
2909 deriving instance Eq a => Eq (Foo (Maybe a))
2911 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2912 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2916 Unlike a <literal>deriving</literal>
2917 declaration attached to a <literal>data</literal> declaration,
2918 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2919 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2920 your problem. (GHC will show you the offending code if it has a type error.)
2921 The merit of this is that you can derive instances for GADTs and other exotic
2922 data types, providing only that the boilerplate code does indeed typecheck. For example:
2928 deriving instance Show (T a)
2930 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2931 data type declaration for <literal>T</literal>,
2932 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2933 the instance declaration using stand-alone deriving.
2938 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2939 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2942 newtype Foo a = MkFoo (State Int a)
2944 deriving instance MonadState Int Foo
2946 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2947 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2949 </itemizedlist></para>
2954 <sect2 id="deriving-typeable">
2955 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2958 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2959 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2960 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2961 classes <literal>Eq</literal>, <literal>Ord</literal>,
2962 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2965 GHC extends this list with several more classes that may be automatically derived:
2967 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2968 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2969 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2971 <para>An instance of <literal>Typeable</literal> can only be derived if the
2972 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2973 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2975 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2976 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2978 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2979 are used, and only <literal>Typeable1</literal> up to
2980 <literal>Typeable7</literal> are provided in the library.)
2981 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2982 class, whose kind suits that of the data type constructor, and
2983 then writing the data type instance by hand.
2987 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2988 the class <literal>Functor</literal>,
2989 defined in <literal>GHC.Base</literal>.
2992 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2993 the class <literal>Foldable</literal>,
2994 defined in <literal>Data.Foldable</literal>.
2997 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2998 the class <literal>Traversable</literal>,
2999 defined in <literal>Data.Traversable</literal>.
3002 In each case the appropriate class must be in scope before it
3003 can be mentioned in the <literal>deriving</literal> clause.
3007 <sect2 id="newtype-deriving">
3008 <title>Generalised derived instances for newtypes</title>
3011 When you define an abstract type using <literal>newtype</literal>, you may want
3012 the new type to inherit some instances from its representation. In
3013 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3014 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3015 other classes you have to write an explicit instance declaration. For
3016 example, if you define
3019 newtype Dollars = Dollars Int
3022 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3023 explicitly define an instance of <literal>Num</literal>:
3026 instance Num Dollars where
3027 Dollars a + Dollars b = Dollars (a+b)
3030 All the instance does is apply and remove the <literal>newtype</literal>
3031 constructor. It is particularly galling that, since the constructor
3032 doesn't appear at run-time, this instance declaration defines a
3033 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3034 dictionary, only slower!
3038 <sect3> <title> Generalising the deriving clause </title>
3040 GHC now permits such instances to be derived instead,
3041 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3044 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3047 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3048 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3049 derives an instance declaration of the form
3052 instance Num Int => Num Dollars
3055 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3059 We can also derive instances of constructor classes in a similar
3060 way. For example, suppose we have implemented state and failure monad
3061 transformers, such that
3064 instance Monad m => Monad (State s m)
3065 instance Monad m => Monad (Failure m)
3067 In Haskell 98, we can define a parsing monad by
3069 type Parser tok m a = State [tok] (Failure m) a
3072 which is automatically a monad thanks to the instance declarations
3073 above. With the extension, we can make the parser type abstract,
3074 without needing to write an instance of class <literal>Monad</literal>, via
3077 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3080 In this case the derived instance declaration is of the form
3082 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3085 Notice that, since <literal>Monad</literal> is a constructor class, the
3086 instance is a <emphasis>partial application</emphasis> of the new type, not the
3087 entire left hand side. We can imagine that the type declaration is
3088 "eta-converted" to generate the context of the instance
3093 We can even derive instances of multi-parameter classes, provided the
3094 newtype is the last class parameter. In this case, a ``partial
3095 application'' of the class appears in the <literal>deriving</literal>
3096 clause. For example, given the class
3099 class StateMonad s m | m -> s where ...
3100 instance Monad m => StateMonad s (State s m) where ...
3102 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3104 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3105 deriving (Monad, StateMonad [tok])
3108 The derived instance is obtained by completing the application of the
3109 class to the new type:
3112 instance StateMonad [tok] (State [tok] (Failure m)) =>
3113 StateMonad [tok] (Parser tok m)
3118 As a result of this extension, all derived instances in newtype
3119 declarations are treated uniformly (and implemented just by reusing
3120 the dictionary for the representation type), <emphasis>except</emphasis>
3121 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3122 the newtype and its representation.
3126 <sect3> <title> A more precise specification </title>
3128 Derived instance declarations are constructed as follows. Consider the
3129 declaration (after expansion of any type synonyms)
3132 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3138 The <literal>ci</literal> are partial applications of
3139 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3140 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3143 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3146 The type <literal>t</literal> is an arbitrary type.
3149 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3150 nor in the <literal>ci</literal>, and
3153 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3154 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3155 should not "look through" the type or its constructor. You can still
3156 derive these classes for a newtype, but it happens in the usual way, not
3157 via this new mechanism.
3160 Then, for each <literal>ci</literal>, the derived instance
3163 instance ci t => ci (T v1...vk)
3165 As an example which does <emphasis>not</emphasis> work, consider
3167 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3169 Here we cannot derive the instance
3171 instance Monad (State s m) => Monad (NonMonad m)
3174 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3175 and so cannot be "eta-converted" away. It is a good thing that this
3176 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3177 not, in fact, a monad --- for the same reason. Try defining
3178 <literal>>>=</literal> with the correct type: you won't be able to.
3182 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3183 important, since we can only derive instances for the last one. If the
3184 <literal>StateMonad</literal> class above were instead defined as
3187 class StateMonad m s | m -> s where ...
3190 then we would not have been able to derive an instance for the
3191 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3192 classes usually have one "main" parameter for which deriving new
3193 instances is most interesting.
3195 <para>Lastly, all of this applies only for classes other than
3196 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3197 and <literal>Data</literal>, for which the built-in derivation applies (section
3198 4.3.3. of the Haskell Report).
3199 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3200 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3201 the standard method is used or the one described here.)
3208 <!-- TYPE SYSTEM EXTENSIONS -->
3209 <sect1 id="type-class-extensions">
3210 <title>Class and instances declarations</title>
3212 <sect2 id="multi-param-type-classes">
3213 <title>Class declarations</title>
3216 This section, and the next one, documents GHC's type-class extensions.
3217 There's lots of background in the paper <ulink
3218 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3219 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3220 Jones, Erik Meijer).
3223 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3227 <title>Multi-parameter type classes</title>
3229 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3234 class Collection c a where
3235 union :: c a -> c a -> c a
3242 <sect3 id="superclass-rules">
3243 <title>The superclasses of a class declaration</title>
3246 In Haskell 98 the context of a class declaration (which introduces superclasses)
3247 must be simple; that is, each predicate must consist of a class applied to
3248 type variables. The flag <option>-XFlexibleContexts</option>
3249 (<xref linkend="flexible-contexts"/>)
3250 lifts this restriction,
3251 so that the only restriction on the context in a class declaration is
3252 that the class hierarchy must be acyclic. So these class declarations are OK:
3256 class Functor (m k) => FiniteMap m k where
3259 class (Monad m, Monad (t m)) => Transform t m where
3260 lift :: m a -> (t m) a
3266 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3267 of "acyclic" involves only the superclass relationships. For example,
3273 op :: D b => a -> b -> b
3276 class C a => D a where { ... }
3280 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3281 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3282 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3289 <sect3 id="class-method-types">
3290 <title>Class method types</title>
3293 Haskell 98 prohibits class method types to mention constraints on the
3294 class type variable, thus:
3297 fromList :: [a] -> s a
3298 elem :: Eq a => a -> s a -> Bool
3300 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3301 contains the constraint <literal>Eq a</literal>, constrains only the
3302 class type variable (in this case <literal>a</literal>).
3303 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3310 <sect2 id="functional-dependencies">
3311 <title>Functional dependencies
3314 <para> Functional dependencies are implemented as described by Mark Jones
3315 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3316 In Proceedings of the 9th European Symposium on Programming,
3317 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3321 Functional dependencies are introduced by a vertical bar in the syntax of a
3322 class declaration; e.g.
3324 class (Monad m) => MonadState s m | m -> s where ...
3326 class Foo a b c | a b -> c where ...
3328 There should be more documentation, but there isn't (yet). Yell if you need it.
3331 <sect3><title>Rules for functional dependencies </title>
3333 In a class declaration, all of the class type variables must be reachable (in the sense
3334 mentioned in <xref linkend="flexible-contexts"/>)
3335 from the free variables of each method type.
3339 class Coll s a where
3341 insert :: s -> a -> s
3344 is not OK, because the type of <literal>empty</literal> doesn't mention
3345 <literal>a</literal>. Functional dependencies can make the type variable
3348 class Coll s a | s -> a where
3350 insert :: s -> a -> s
3353 Alternatively <literal>Coll</literal> might be rewritten
3356 class Coll s a where
3358 insert :: s a -> a -> s a
3362 which makes the connection between the type of a collection of
3363 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3364 Occasionally this really doesn't work, in which case you can split the
3372 class CollE s => Coll s a where
3373 insert :: s -> a -> s
3380 <title>Background on functional dependencies</title>
3382 <para>The following description of the motivation and use of functional dependencies is taken
3383 from the Hugs user manual, reproduced here (with minor changes) by kind
3384 permission of Mark Jones.
3387 Consider the following class, intended as part of a
3388 library for collection types:
3390 class Collects e ce where
3392 insert :: e -> ce -> ce
3393 member :: e -> ce -> Bool
3395 The type variable e used here represents the element type, while ce is the type
3396 of the container itself. Within this framework, we might want to define
3397 instances of this class for lists or characteristic functions (both of which
3398 can be used to represent collections of any equality type), bit sets (which can
3399 be used to represent collections of characters), or hash tables (which can be
3400 used to represent any collection whose elements have a hash function). Omitting
3401 standard implementation details, this would lead to the following declarations:
3403 instance Eq e => Collects e [e] where ...
3404 instance Eq e => Collects e (e -> Bool) where ...
3405 instance Collects Char BitSet where ...
3406 instance (Hashable e, Collects a ce)
3407 => Collects e (Array Int ce) where ...
3409 All this looks quite promising; we have a class and a range of interesting
3410 implementations. Unfortunately, there are some serious problems with the class
3411 declaration. First, the empty function has an ambiguous type:
3413 empty :: Collects e ce => ce
3415 By "ambiguous" we mean that there is a type variable e that appears on the left
3416 of the <literal>=></literal> symbol, but not on the right. The problem with
3417 this is that, according to the theoretical foundations of Haskell overloading,
3418 we cannot guarantee a well-defined semantics for any term with an ambiguous
3422 We can sidestep this specific problem by removing the empty member from the
3423 class declaration. However, although the remaining members, insert and member,
3424 do not have ambiguous types, we still run into problems when we try to use
3425 them. For example, consider the following two functions:
3427 f x y = insert x . insert y
3430 for which GHC infers the following types:
3432 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3433 g :: (Collects Bool c, Collects Char c) => c -> c
3435 Notice that the type for f allows the two parameters x and y to be assigned
3436 different types, even though it attempts to insert each of the two values, one
3437 after the other, into the same collection. If we're trying to model collections
3438 that contain only one type of value, then this is clearly an inaccurate
3439 type. Worse still, the definition for g is accepted, without causing a type
3440 error. As a result, the error in this code will not be flagged at the point
3441 where it appears. Instead, it will show up only when we try to use g, which
3442 might even be in a different module.
3445 <sect4><title>An attempt to use constructor classes</title>
3448 Faced with the problems described above, some Haskell programmers might be
3449 tempted to use something like the following version of the class declaration:
3451 class Collects e c where
3453 insert :: e -> c e -> c e
3454 member :: e -> c e -> Bool
3456 The key difference here is that we abstract over the type constructor c that is
3457 used to form the collection type c e, and not over that collection type itself,
3458 represented by ce in the original class declaration. This avoids the immediate
3459 problems that we mentioned above: empty has type <literal>Collects e c => c
3460 e</literal>, which is not ambiguous.
3463 The function f from the previous section has a more accurate type:
3465 f :: (Collects e c) => e -> e -> c e -> c e
3467 The function g from the previous section is now rejected with a type error as
3468 we would hope because the type of f does not allow the two arguments to have
3470 This, then, is an example of a multiple parameter class that does actually work
3471 quite well in practice, without ambiguity problems.
3472 There is, however, a catch. This version of the Collects class is nowhere near
3473 as general as the original class seemed to be: only one of the four instances
3474 for <literal>Collects</literal>
3475 given above can be used with this version of Collects because only one of
3476 them---the instance for lists---has a collection type that can be written in
3477 the form c e, for some type constructor c, and element type e.
3481 <sect4><title>Adding functional dependencies</title>
3484 To get a more useful version of the Collects class, Hugs provides a mechanism
3485 that allows programmers to specify dependencies between the parameters of a
3486 multiple parameter class (For readers with an interest in theoretical
3487 foundations and previous work: The use of dependency information can be seen
3488 both as a generalization of the proposal for `parametric type classes' that was
3489 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3490 later framework for "improvement" of qualified types. The
3491 underlying ideas are also discussed in a more theoretical and abstract setting
3492 in a manuscript [implparam], where they are identified as one point in a
3493 general design space for systems of implicit parameterization.).
3495 To start with an abstract example, consider a declaration such as:
3497 class C a b where ...
3499 which tells us simply that C can be thought of as a binary relation on types
3500 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3501 included in the definition of classes to add information about dependencies
3502 between parameters, as in the following examples:
3504 class D a b | a -> b where ...
3505 class E a b | a -> b, b -> a where ...
3507 The notation <literal>a -> b</literal> used here between the | and where
3508 symbols --- not to be
3509 confused with a function type --- indicates that the a parameter uniquely
3510 determines the b parameter, and might be read as "a determines b." Thus D is
3511 not just a relation, but actually a (partial) function. Similarly, from the two
3512 dependencies that are included in the definition of E, we can see that E
3513 represents a (partial) one-one mapping between types.
3516 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3517 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3518 m>=0, meaning that the y parameters are uniquely determined by the x
3519 parameters. Spaces can be used as separators if more than one variable appears
3520 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3521 annotated with multiple dependencies using commas as separators, as in the
3522 definition of E above. Some dependencies that we can write in this notation are
3523 redundant, and will be rejected because they don't serve any useful
3524 purpose, and may instead indicate an error in the program. Examples of
3525 dependencies like this include <literal>a -> a </literal>,
3526 <literal>a -> a a </literal>,
3527 <literal>a -> </literal>, etc. There can also be
3528 some redundancy if multiple dependencies are given, as in
3529 <literal>a->b</literal>,
3530 <literal>b->c </literal>, <literal>a->c </literal>, and
3531 in which some subset implies the remaining dependencies. Examples like this are
3532 not treated as errors. Note that dependencies appear only in class
3533 declarations, and not in any other part of the language. In particular, the
3534 syntax for instance declarations, class constraints, and types is completely
3538 By including dependencies in a class declaration, we provide a mechanism for
3539 the programmer to specify each multiple parameter class more precisely. The
3540 compiler, on the other hand, is responsible for ensuring that the set of
3541 instances that are in scope at any given point in the program is consistent
3542 with any declared dependencies. For example, the following pair of instance
3543 declarations cannot appear together in the same scope because they violate the
3544 dependency for D, even though either one on its own would be acceptable:
3546 instance D Bool Int where ...
3547 instance D Bool Char where ...
3549 Note also that the following declaration is not allowed, even by itself:
3551 instance D [a] b where ...
3553 The problem here is that this instance would allow one particular choice of [a]
3554 to be associated with more than one choice for b, which contradicts the
3555 dependency specified in the definition of D. More generally, this means that,
3556 in any instance of the form:
3558 instance D t s where ...
3560 for some particular types t and s, the only variables that can appear in s are
3561 the ones that appear in t, and hence, if the type t is known, then s will be
3562 uniquely determined.
3565 The benefit of including dependency information is that it allows us to define
3566 more general multiple parameter classes, without ambiguity problems, and with
3567 the benefit of more accurate types. To illustrate this, we return to the
3568 collection class example, and annotate the original definition of <literal>Collects</literal>
3569 with a simple dependency:
3571 class Collects e ce | ce -> e where
3573 insert :: e -> ce -> ce
3574 member :: e -> ce -> Bool
3576 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3577 determined by the type of the collection ce. Note that both parameters of
3578 Collects are of kind *; there are no constructor classes here. Note too that
3579 all of the instances of Collects that we gave earlier can be used
3580 together with this new definition.
3583 What about the ambiguity problems that we encountered with the original
3584 definition? The empty function still has type Collects e ce => ce, but it is no
3585 longer necessary to regard that as an ambiguous type: Although the variable e
3586 does not appear on the right of the => symbol, the dependency for class
3587 Collects tells us that it is uniquely determined by ce, which does appear on
3588 the right of the => symbol. Hence the context in which empty is used can still
3589 give enough information to determine types for both ce and e, without
3590 ambiguity. More generally, we need only regard a type as ambiguous if it
3591 contains a variable on the left of the => that is not uniquely determined
3592 (either directly or indirectly) by the variables on the right.
3595 Dependencies also help to produce more accurate types for user defined
3596 functions, and hence to provide earlier detection of errors, and less cluttered
3597 types for programmers to work with. Recall the previous definition for a
3600 f x y = insert x y = insert x . insert y
3602 for which we originally obtained a type:
3604 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3606 Given the dependency information that we have for Collects, however, we can
3607 deduce that a and b must be equal because they both appear as the second
3608 parameter in a Collects constraint with the same first parameter c. Hence we
3609 can infer a shorter and more accurate type for f:
3611 f :: (Collects a c) => a -> a -> c -> c
3613 In a similar way, the earlier definition of g will now be flagged as a type error.
3616 Although we have given only a few examples here, it should be clear that the
3617 addition of dependency information can help to make multiple parameter classes
3618 more useful in practice, avoiding ambiguity problems, and allowing more general
3619 sets of instance declarations.
3625 <sect2 id="instance-decls">
3626 <title>Instance declarations</title>
3628 <para>An instance declaration has the form
3630 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 ...
3632 The part before the "<literal>=></literal>" is the
3633 <emphasis>context</emphasis>, while the part after the
3634 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3637 <sect3 id="flexible-instance-head">
3638 <title>Relaxed rules for the instance head</title>
3641 In Haskell 98 the head of an instance declaration
3642 must be of the form <literal>C (T a1 ... an)</literal>, where
3643 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3644 and the <literal>a1 ... an</literal> are distinct type variables.
3645 GHC relaxes these rules in two ways.
3649 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3650 declaration to mention arbitrary nested types.
3651 For example, this becomes a legal instance declaration
3653 instance C (Maybe Int) where ...
3655 See also the <link linkend="instance-overlap">rules on overlap</link>.
3658 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3659 synonyms. As always, using a type synonym is just shorthand for
3660 writing the RHS of the type synonym definition. For example:
3664 type Point = (Int,Int)
3665 instance C Point where ...
3666 instance C [Point] where ...
3670 is legal. However, if you added
3674 instance C (Int,Int) where ...
3678 as well, then the compiler will complain about the overlapping
3679 (actually, identical) instance declarations. As always, type synonyms
3680 must be fully applied. You cannot, for example, write:
3684 instance Monad P where ...
3692 <sect3 id="instance-rules">
3693 <title>Relaxed rules for instance contexts</title>
3695 <para>In Haskell 98, the assertions in the context of the instance declaration
3696 must be of the form <literal>C a</literal> where <literal>a</literal>
3697 is a type variable that occurs in the head.
3701 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3702 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3703 With this flag the context of the instance declaration can each consist of arbitrary
3704 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3708 The Paterson Conditions: for each assertion in the context
3710 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3711 <listitem><para>The assertion has fewer constructors and variables (taken together
3712 and counting repetitions) than the head</para></listitem>
3716 <listitem><para>The Coverage Condition. For each functional dependency,
3717 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3718 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3719 every type variable in
3720 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3721 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3722 substitution mapping each type variable in the class declaration to the
3723 corresponding type in the instance declaration.
3726 These restrictions ensure that context reduction terminates: each reduction
3727 step makes the problem smaller by at least one
3728 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3729 if you give the <option>-XUndecidableInstances</option>
3730 flag (<xref linkend="undecidable-instances"/>).
3731 You can find lots of background material about the reason for these
3732 restrictions in the paper <ulink
3733 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3734 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3737 For example, these are OK:
3739 instance C Int [a] -- Multiple parameters
3740 instance Eq (S [a]) -- Structured type in head
3742 -- Repeated type variable in head
3743 instance C4 a a => C4 [a] [a]
3744 instance Stateful (ST s) (MutVar s)
3746 -- Head can consist of type variables only
3748 instance (Eq a, Show b) => C2 a b
3750 -- Non-type variables in context
3751 instance Show (s a) => Show (Sized s a)
3752 instance C2 Int a => C3 Bool [a]
3753 instance C2 Int a => C3 [a] b
3757 -- Context assertion no smaller than head
3758 instance C a => C a where ...
3759 -- (C b b) has more more occurrences of b than the head
3760 instance C b b => Foo [b] where ...
3765 The same restrictions apply to instances generated by
3766 <literal>deriving</literal> clauses. Thus the following is accepted:
3768 data MinHeap h a = H a (h a)
3771 because the derived instance
3773 instance (Show a, Show (h a)) => Show (MinHeap h a)
3775 conforms to the above rules.
3779 A useful idiom permitted by the above rules is as follows.
3780 If one allows overlapping instance declarations then it's quite
3781 convenient to have a "default instance" declaration that applies if
3782 something more specific does not:
3790 <sect3 id="undecidable-instances">
3791 <title>Undecidable instances</title>
3794 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3795 For example, sometimes you might want to use the following to get the
3796 effect of a "class synonym":
3798 class (C1 a, C2 a, C3 a) => C a where { }
3800 instance (C1 a, C2 a, C3 a) => C a where { }
3802 This allows you to write shorter signatures:
3808 f :: (C1 a, C2 a, C3 a) => ...
3810 The restrictions on functional dependencies (<xref
3811 linkend="functional-dependencies"/>) are particularly troublesome.
3812 It is tempting to introduce type variables in the context that do not appear in
3813 the head, something that is excluded by the normal rules. For example:
3815 class HasConverter a b | a -> b where
3818 data Foo a = MkFoo a
3820 instance (HasConverter a b,Show b) => Show (Foo a) where
3821 show (MkFoo value) = show (convert value)
3823 This is dangerous territory, however. Here, for example, is a program that would make the
3828 instance F [a] [[a]]
3829 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3831 Similarly, it can be tempting to lift the coverage condition:
3833 class Mul a b c | a b -> c where
3834 (.*.) :: a -> b -> c
3836 instance Mul Int Int Int where (.*.) = (*)
3837 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3838 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3840 The third instance declaration does not obey the coverage condition;
3841 and indeed the (somewhat strange) definition:
3843 f = \ b x y -> if b then x .*. [y] else y
3845 makes instance inference go into a loop, because it requires the constraint
3846 <literal>(Mul a [b] b)</literal>.
3849 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3850 the experimental flag <option>-XUndecidableInstances</option>
3851 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3852 both the Paterson Conditions and the Coverage Condition
3853 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3854 fixed-depth recursion stack. If you exceed the stack depth you get a
3855 sort of backtrace, and the opportunity to increase the stack depth
3856 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3862 <sect3 id="instance-overlap">
3863 <title>Overlapping instances</title>
3865 In general, <emphasis>GHC requires that that it be unambiguous which instance
3867 should be used to resolve a type-class constraint</emphasis>. This behaviour
3868 can be modified by two flags: <option>-XOverlappingInstances</option>
3869 <indexterm><primary>-XOverlappingInstances
3870 </primary></indexterm>
3871 and <option>-XIncoherentInstances</option>
3872 <indexterm><primary>-XIncoherentInstances
3873 </primary></indexterm>, as this section discusses. Both these
3874 flags are dynamic flags, and can be set on a per-module basis, using
3875 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3877 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3878 it tries to match every instance declaration against the
3880 by instantiating the head of the instance declaration. For example, consider
3883 instance context1 => C Int a where ... -- (A)
3884 instance context2 => C a Bool where ... -- (B)
3885 instance context3 => C Int [a] where ... -- (C)
3886 instance context4 => C Int [Int] where ... -- (D)
3888 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3889 but (C) and (D) do not. When matching, GHC takes
3890 no account of the context of the instance declaration
3891 (<literal>context1</literal> etc).
3892 GHC's default behaviour is that <emphasis>exactly one instance must match the
3893 constraint it is trying to resolve</emphasis>.
3894 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3895 including both declarations (A) and (B), say); an error is only reported if a
3896 particular constraint matches more than one.
3900 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3901 more than one instance to match, provided there is a most specific one. For
3902 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3903 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3904 most-specific match, the program is rejected.
3907 However, GHC is conservative about committing to an overlapping instance. For example:
3912 Suppose that from the RHS of <literal>f</literal> we get the constraint
3913 <literal>C Int [b]</literal>. But
3914 GHC does not commit to instance (C), because in a particular
3915 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3916 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3917 So GHC rejects the program.
3918 (If you add the flag <option>-XIncoherentInstances</option>,
3919 GHC will instead pick (C), without complaining about
3920 the problem of subsequent instantiations.)
3923 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3924 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3925 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3926 it instead. In this case, GHC will refrain from
3927 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3928 as before) but, rather than rejecting the program, it will infer the type
3930 f :: C Int [b] => [b] -> [b]
3932 That postpones the question of which instance to pick to the
3933 call site for <literal>f</literal>
3934 by which time more is known about the type <literal>b</literal>.
3935 You can write this type signature yourself if you use the
3936 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3940 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3944 instance Foo [b] where
3947 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3948 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3949 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3950 declaration. The solution is to postpone the choice by adding the constraint to the context
3951 of the instance declaration, thus:
3953 instance C Int [b] => Foo [b] where
3956 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3959 Warning: overlapping instances must be used with care. They
3960 can give rise to incoherence (ie different instance choices are made
3961 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
3963 {-# LANGUAGE OverlappingInstances #-}
3966 class MyShow a where
3967 myshow :: a -> String
3969 instance MyShow a => MyShow [a] where
3970 myshow xs = concatMap myshow xs
3972 showHelp :: MyShow a => [a] -> String
3973 showHelp xs = myshow xs
3975 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
3981 instance MyShow T where
3982 myshow x = "Used generic instance"
3984 instance MyShow [T] where
3985 myshow xs = "Used more specific instance"
3987 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
3989 In function <literal>showHelp</literal> GHC sees no overlapping
3990 instances, and so uses the <literal>MyShow [a]</literal> instance
3991 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
3992 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
3993 instance declaration in module <literal>Main</literal>. As a result,
3996 "Used more specific instance"
3997 "Used generic instance"
3999 (An alternative possible behaviour, not currently implemented,
4000 would be to reject module <literal>Help</literal>
4001 on the grounds that a later instance declaration might overlap the local one.)
4004 The willingness to be overlapped or incoherent is a property of
4005 the <emphasis>instance declaration</emphasis> itself, controlled by the
4006 presence or otherwise of the <option>-XOverlappingInstances</option>
4007 and <option>-XIncoherentInstances</option> flags when that module is
4008 being defined. Specifically, during the lookup process:
4011 If the constraint being looked up matches two instance declarations IA and IB,
4014 <listitem><para>IB is a substitution instance of IA (but not vice versa);
4015 that is, IB is strictly more specific than IA</para></listitem>
4016 <listitem><para>either IA or IB was compiled with <option>-XOverlappingInstances</option></para></listitem>
4018 then the less-specific instance IA is ignored.
4021 Suppose an instance declaration does not match the constraint being looked up, but
4022 does <emphasis>unify</emphasis> with it, so that it might match when the constraint is further
4023 instantiated. Usually GHC will regard this as a reason for not committing to
4024 some other constraint. But if the instance declaration was compiled with
4025 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4026 check for that declaration.
4029 These rules make it possible for a library author to design a library that relies on
4030 overlapping instances without the library client having to know.
4032 <para>The <option>-XIncoherentInstances</option> flag implies the
4033 <option>-XOverlappingInstances</option> flag, but not vice versa.
4041 <sect2 id="overloaded-strings">
4042 <title>Overloaded string literals
4046 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4047 string literal has type <literal>String</literal>, but with overloaded string
4048 literals enabled (with <literal>-XOverloadedStrings</literal>)
4049 a string literal has type <literal>(IsString a) => a</literal>.
4052 This means that the usual string syntax can be used, e.g., for packed strings
4053 and other variations of string like types. String literals behave very much
4054 like integer literals, i.e., they can be used in both expressions and patterns.
4055 If used in a pattern the literal with be replaced by an equality test, in the same
4056 way as an integer literal is.
4059 The class <literal>IsString</literal> is defined as:
4061 class IsString a where
4062 fromString :: String -> a
4064 The only predefined instance is the obvious one to make strings work as usual:
4066 instance IsString [Char] where
4069 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4070 it explicitly (for example, to give an instance declaration for it), you can import it
4071 from module <literal>GHC.Exts</literal>.
4074 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4078 Each type in a default declaration must be an
4079 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4083 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4084 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4085 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4086 <emphasis>or</emphasis> <literal>IsString</literal>.
4095 import GHC.Exts( IsString(..) )
4097 newtype MyString = MyString String deriving (Eq, Show)
4098 instance IsString MyString where
4099 fromString = MyString
4101 greet :: MyString -> MyString
4102 greet "hello" = "world"
4106 print $ greet "hello"
4107 print $ greet "fool"
4111 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4112 to work since it gets translated into an equality comparison.
4118 <sect1 id="type-families">
4119 <title>Type families</title>
4122 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4123 facilitate type-level
4124 programming. Type families are a generalisation of <firstterm>associated
4125 data types</firstterm>
4126 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4127 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4128 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4129 Symposium on Principles of Programming Languages (POPL'05)”, pages
4130 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4131 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4132 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4134 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4135 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4136 themselves are described in the paper “<ulink
4137 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4138 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4140 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4141 13th ACM SIGPLAN International Conference on Functional
4142 Programming”, ACM Press, pages 51-62, 2008. Type families
4143 essentially provide type-indexed data types and named functions on types,
4144 which are useful for generic programming and highly parameterised library
4145 interfaces as well as interfaces with enhanced static information, much like
4146 dependent types. They might also be regarded as an alternative to functional
4147 dependencies, but provide a more functional style of type-level programming
4148 than the relational style of functional dependencies.
4151 Indexed type families, or type families for short, are type constructors that
4152 represent sets of types. Set members are denoted by supplying the type family
4153 constructor with type parameters, which are called <firstterm>type
4154 indices</firstterm>. The
4155 difference between vanilla parametrised type constructors and family
4156 constructors is much like between parametrically polymorphic functions and
4157 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4158 behave the same at all type instances, whereas class methods can change their
4159 behaviour in dependence on the class type parameters. Similarly, vanilla type
4160 constructors imply the same data representation for all type instances, but
4161 family constructors can have varying representation types for varying type
4165 Indexed type families come in two flavours: <firstterm>data
4166 families</firstterm> and <firstterm>type synonym
4167 families</firstterm>. They are the indexed family variants of algebraic
4168 data types and type synonyms, respectively. The instances of data families
4169 can be data types and newtypes.
4172 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4173 Additional information on the use of type families in GHC is available on
4174 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4175 Haskell wiki page on type families</ulink>.
4178 <sect2 id="data-families">
4179 <title>Data families</title>
4182 Data families appear in two flavours: (1) they can be defined on the
4184 or (2) they can appear inside type classes (in which case they are known as
4185 associated types). The former is the more general variant, as it lacks the
4186 requirement for the type-indexes to coincide with the class
4187 parameters. However, the latter can lead to more clearly structured code and
4188 compiler warnings if some type instances were - possibly accidentally -
4189 omitted. In the following, we always discuss the general toplevel form first
4190 and then cover the additional constraints placed on associated types.
4193 <sect3 id="data-family-declarations">
4194 <title>Data family declarations</title>
4197 Indexed data families are introduced by a signature, such as
4199 data family GMap k :: * -> *
4201 The special <literal>family</literal> distinguishes family from standard
4202 data declarations. The result kind annotation is optional and, as
4203 usual, defaults to <literal>*</literal> if omitted. An example is
4207 Named arguments can also be given explicit kind signatures if needed.
4209 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4210 declarations] named arguments are entirely optional, so that we can
4211 declare <literal>Array</literal> alternatively with
4213 data family Array :: * -> *
4217 <sect4 id="assoc-data-family-decl">
4218 <title>Associated data family declarations</title>
4220 When a data family is declared as part of a type class, we drop
4221 the <literal>family</literal> special. The <literal>GMap</literal>
4222 declaration takes the following form
4224 class GMapKey k where
4225 data GMap k :: * -> *
4228 In contrast to toplevel declarations, named arguments must be used for
4229 all type parameters that are to be used as type-indexes. Moreover,
4230 the argument names must be class parameters. Each class parameter may
4231 only be used at most once per associated type, but some may be omitted
4232 and they may be in an order other than in the class head. Hence, the
4233 following contrived example is admissible:
4242 <sect3 id="data-instance-declarations">
4243 <title>Data instance declarations</title>
4246 Instance declarations of data and newtype families are very similar to
4247 standard data and newtype declarations. The only two differences are
4248 that the keyword <literal>data</literal> or <literal>newtype</literal>
4249 is followed by <literal>instance</literal> and that some or all of the
4250 type arguments can be non-variable types, but may not contain forall
4251 types or type synonym families. However, data families are generally
4252 allowed in type parameters, and type synonyms are allowed as long as
4253 they are fully applied and expand to a type that is itself admissible -
4254 exactly as this is required for occurrences of type synonyms in class
4255 instance parameters. For example, the <literal>Either</literal>
4256 instance for <literal>GMap</literal> is
4258 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4260 In this example, the declaration has only one variant. In general, it
4264 Data and newtype instance declarations are only permitted when an
4265 appropriate family declaration is in scope - just as a class instance declaratoin
4266 requires the class declaration to be visible. Moreover, each instance
4267 declaration has to conform to the kind determined by its family
4268 declaration. This implies that the number of parameters of an instance
4269 declaration matches the arity determined by the kind of the family.
4272 A data family instance declaration can use the full exprssiveness of
4273 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4275 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4276 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4277 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4280 data instance T Int = T1 Int | T2 Bool
4281 newtype instance T Char = TC Bool
4284 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4285 and indeed can define a GADT. For example:
4288 data instance G [a] b where
4289 G1 :: c -> G [Int] b
4293 <listitem><para> You can use a <literal>deriving</literal> clause on a
4294 <literal>data instance</literal> or <literal>newtype instance</literal>
4301 Even if type families are defined as toplevel declarations, functions
4302 that perform different computations for different family instances may still
4303 need to be defined as methods of type classes. In particular, the
4304 following is not possible:
4307 data instance T Int = A
4308 data instance T Char = B
4310 foo A = 1 -- WRONG: These two equations together...
4311 foo B = 2 -- ...will produce a type error.
4313 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4317 instance Foo Int where
4319 instance Foo Char where
4322 (Given the functionality provided by GADTs (Generalised Algebraic Data
4323 Types), it might seem as if a definition, such as the above, should be
4324 feasible. However, type families are - in contrast to GADTs - are
4325 <emphasis>open;</emphasis> i.e., new instances can always be added,
4327 modules. Supporting pattern matching across different data instances
4328 would require a form of extensible case construct.)
4331 <sect4 id="assoc-data-inst">
4332 <title>Associated data instances</title>
4334 When an associated data family instance is declared within a type
4335 class instance, we drop the <literal>instance</literal> keyword in the
4336 family instance. So, the <literal>Either</literal> instance
4337 for <literal>GMap</literal> becomes:
4339 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4340 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4343 The most important point about associated family instances is that the
4344 type indexes corresponding to class parameters must be identical to
4345 the type given in the instance head; here this is the first argument
4346 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4347 which coincides with the only class parameter. Any parameters to the
4348 family constructor that do not correspond to class parameters, need to
4349 be variables in every instance; here this is the
4350 variable <literal>v</literal>.
4353 Instances for an associated family can only appear as part of
4354 instances declarations of the class in which the family was declared -
4355 just as with the equations of the methods of a class. Also in
4356 correspondence to how methods are handled, declarations of associated
4357 types can be omitted in class instances. If an associated family
4358 instance is omitted, the corresponding instance type is not inhabited;
4359 i.e., only diverging expressions, such
4360 as <literal>undefined</literal>, can assume the type.
4364 <sect4 id="scoping-class-params">
4365 <title>Scoping of class parameters</title>
4367 In the case of multi-parameter type classes, the visibility of class
4368 parameters in the right-hand side of associated family instances
4369 depends <emphasis>solely</emphasis> on the parameters of the data
4370 family. As an example, consider the simple class declaration
4375 Only one of the two class parameters is a parameter to the data
4376 family. Hence, the following instance declaration is invalid:
4378 instance C [c] d where
4379 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4381 Here, the right-hand side of the data instance mentions the type
4382 variable <literal>d</literal> that does not occur in its left-hand
4383 side. We cannot admit such data instances as they would compromise
4388 <sect4 id="family-class-inst">
4389 <title>Type class instances of family instances</title>
4391 Type class instances of instances of data families can be defined as
4392 usual, and in particular data instance declarations can
4393 have <literal>deriving</literal> clauses. For example, we can write
4395 data GMap () v = GMapUnit (Maybe v)
4398 which implicitly defines an instance of the form
4400 instance Show v => Show (GMap () v) where ...
4404 Note that class instances are always for
4405 particular <emphasis>instances</emphasis> of a data family and never
4406 for an entire family as a whole. This is for essentially the same
4407 reasons that we cannot define a toplevel function that performs
4408 pattern matching on the data constructors
4409 of <emphasis>different</emphasis> instances of a single type family.
4410 It would require a form of extensible case construct.
4414 <sect4 id="data-family-overlap">
4415 <title>Overlap of data instances</title>
4417 The instance declarations of a data family used in a single program
4418 may not overlap at all, independent of whether they are associated or
4419 not. In contrast to type class instances, this is not only a matter
4420 of consistency, but one of type safety.
4426 <sect3 id="data-family-import-export">
4427 <title>Import and export</title>
4430 The association of data constructors with type families is more dynamic
4431 than that is the case with standard data and newtype declarations. In
4432 the standard case, the notation <literal>T(..)</literal> in an import or
4433 export list denotes the type constructor and all the data constructors
4434 introduced in its declaration. However, a family declaration never
4435 introduces any data constructors; instead, data constructors are
4436 introduced by family instances. As a result, which data constructors
4437 are associated with a type family depends on the currently visible
4438 instance declarations for that family. Consequently, an import or
4439 export item of the form <literal>T(..)</literal> denotes the family
4440 constructor and all currently visible data constructors - in the case of
4441 an export item, these may be either imported or defined in the current
4442 module. The treatment of import and export items that explicitly list
4443 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4447 <sect4 id="data-family-impexp-assoc">
4448 <title>Associated families</title>
4450 As expected, an import or export item of the
4451 form <literal>C(..)</literal> denotes all of the class' methods and
4452 associated types. However, when associated types are explicitly
4453 listed as subitems of a class, we need some new syntax, as uppercase
4454 identifiers as subitems are usually data constructors, not type
4455 constructors. To clarify that we denote types here, each associated
4456 type name needs to be prefixed by the keyword <literal>type</literal>.
4457 So for example, when explicitly listing the components of
4458 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4459 GMap, empty, lookup, insert)</literal>.
4463 <sect4 id="data-family-impexp-examples">
4464 <title>Examples</title>
4466 Assuming our running <literal>GMapKey</literal> class example, let us
4467 look at some export lists and their meaning:
4470 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4471 just the class name.</para>
4474 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4475 Exports the class, the associated type <literal>GMap</literal>
4477 functions <literal>empty</literal>, <literal>lookup</literal>,
4478 and <literal>insert</literal>. None of the data constructors is
4482 <para><literal>module GMap (GMapKey(..), GMap(..))
4483 where...</literal>: As before, but also exports all the data
4484 constructors <literal>GMapInt</literal>,
4485 <literal>GMapChar</literal>,
4486 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4487 and <literal>GMapUnit</literal>.</para>
4490 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4491 GMap(..)) where...</literal>: As before.</para>
4494 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4495 where...</literal>: As before.</para>
4500 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4501 both the class <literal>GMapKey</literal> as well as its associated
4502 type <literal>GMap</literal>. However, you cannot
4503 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4504 sub-component specifications cannot be nested. To
4505 specify <literal>GMap</literal>'s data constructors, you have to list
4510 <sect4 id="data-family-impexp-instances">
4511 <title>Instances</title>
4513 Family instances are implicitly exported, just like class instances.
4514 However, this applies only to the heads of instances, not to the data
4515 constructors an instance defines.
4523 <sect2 id="synonym-families">
4524 <title>Synonym families</title>
4527 Type families appear in two flavours: (1) they can be defined on the
4528 toplevel or (2) they can appear inside type classes (in which case they
4529 are known as associated type synonyms). The former is the more general
4530 variant, as it lacks the requirement for the type-indexes to coincide with
4531 the class parameters. However, the latter can lead to more clearly
4532 structured code and compiler warnings if some type instances were -
4533 possibly accidentally - omitted. In the following, we always discuss the
4534 general toplevel form first and then cover the additional constraints
4535 placed on associated types.
4538 <sect3 id="type-family-declarations">
4539 <title>Type family declarations</title>
4542 Indexed type families are introduced by a signature, such as
4544 type family Elem c :: *
4546 The special <literal>family</literal> distinguishes family from standard
4547 type declarations. The result kind annotation is optional and, as
4548 usual, defaults to <literal>*</literal> if omitted. An example is
4552 Parameters can also be given explicit kind signatures if needed. We
4553 call the number of parameters in a type family declaration, the family's
4554 arity, and all applications of a type family must be fully saturated
4555 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4556 and it implies that the kind of a type family is not sufficient to
4557 determine a family's arity, and hence in general, also insufficient to
4558 determine whether a type family application is well formed. As an
4559 example, consider the following declaration:
4561 type family F a b :: * -> * -- F's arity is 2,
4562 -- although its overall kind is * -> * -> * -> *
4564 Given this declaration the following are examples of well-formed and
4567 F Char [Int] -- OK! Kind: * -> *
4568 F Char [Int] Bool -- OK! Kind: *
4569 F IO Bool -- WRONG: kind mismatch in the first argument
4570 F Bool -- WRONG: unsaturated application
4574 <sect4 id="assoc-type-family-decl">
4575 <title>Associated type family declarations</title>
4577 When a type family is declared as part of a type class, we drop
4578 the <literal>family</literal> special. The <literal>Elem</literal>
4579 declaration takes the following form
4581 class Collects ce where
4585 The argument names of the type family must be class parameters. Each
4586 class parameter may only be used at most once per associated type, but
4587 some may be omitted and they may be in an order other than in the
4588 class head. Hence, the following contrived example is admissible:
4593 These rules are exactly as for associated data families.
4598 <sect3 id="type-instance-declarations">
4599 <title>Type instance declarations</title>
4601 Instance declarations of type families are very similar to standard type
4602 synonym declarations. The only two differences are that the
4603 keyword <literal>type</literal> is followed
4604 by <literal>instance</literal> and that some or all of the type
4605 arguments can be non-variable types, but may not contain forall types or
4606 type synonym families. However, data families are generally allowed, and
4607 type synonyms are allowed as long as they are fully applied and expand
4608 to a type that is admissible - these are the exact same requirements as
4609 for data instances. For example, the <literal>[e]</literal> instance
4610 for <literal>Elem</literal> is
4612 type instance Elem [e] = e
4616 Type family instance declarations are only legitimate when an
4617 appropriate family declaration is in scope - just like class instances
4618 require the class declaration to be visible. Moreover, each instance
4619 declaration has to conform to the kind determined by its family
4620 declaration, and the number of type parameters in an instance
4621 declaration must match the number of type parameters in the family
4622 declaration. Finally, the right-hand side of a type instance must be a
4623 monotype (i.e., it may not include foralls) and after the expansion of
4624 all saturated vanilla type synonyms, no synonyms, except family synonyms
4625 may remain. Here are some examples of admissible and illegal type
4628 type family F a :: *
4629 type instance F [Int] = Int -- OK!
4630 type instance F String = Char -- OK!
4631 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4632 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4633 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4635 type family G a b :: * -> *
4636 type instance G Int = (,) -- WRONG: must be two type parameters
4637 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4641 <sect4 id="assoc-type-instance">
4642 <title>Associated type instance declarations</title>
4644 When an associated family instance is declared within a type class
4645 instance, we drop the <literal>instance</literal> keyword in the family
4646 instance. So, the <literal>[e]</literal> instance
4647 for <literal>Elem</literal> becomes:
4649 instance (Eq (Elem [e])) => Collects ([e]) where
4653 The most important point about associated family instances is that the
4654 type indexes corresponding to class parameters must be identical to the
4655 type given in the instance head; here this is <literal>[e]</literal>,
4656 which coincides with the only class parameter.
4659 Instances for an associated family can only appear as part of instances
4660 declarations of the class in which the family was declared - just as
4661 with the equations of the methods of a class. Also in correspondence to
4662 how methods are handled, declarations of associated types can be omitted
4663 in class instances. If an associated family instance is omitted, the
4664 corresponding instance type is not inhabited; i.e., only diverging
4665 expressions, such as <literal>undefined</literal>, can assume the type.
4669 <sect4 id="type-family-overlap">
4670 <title>Overlap of type synonym instances</title>
4672 The instance declarations of a type family used in a single program
4673 may only overlap if the right-hand sides of the overlapping instances
4674 coincide for the overlapping types. More formally, two instance
4675 declarations overlap if there is a substitution that makes the
4676 left-hand sides of the instances syntactically the same. Whenever
4677 that is the case, the right-hand sides of the instances must also be
4678 syntactically equal under the same substitution. This condition is
4679 independent of whether the type family is associated or not, and it is
4680 not only a matter of consistency, but one of type safety.
4683 Here are two example to illustrate the condition under which overlap
4686 type instance F (a, Int) = [a]
4687 type instance F (Int, b) = [b] -- overlap permitted
4689 type instance G (a, Int) = [a]
4690 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4695 <sect4 id="type-family-decidability">
4696 <title>Decidability of type synonym instances</title>
4698 In order to guarantee that type inference in the presence of type
4699 families decidable, we need to place a number of additional
4700 restrictions on the formation of type instance declarations (c.f.,
4701 Definition 5 (Relaxed Conditions) of “<ulink
4702 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4703 Checking with Open Type Functions</ulink>”). Instance
4704 declarations have the general form
4706 type instance F t1 .. tn = t
4708 where we require that for every type family application <literal>(G s1
4709 .. sm)</literal> in <literal>t</literal>,
4712 <para><literal>s1 .. sm</literal> do not contain any type family
4713 constructors,</para>
4716 <para>the total number of symbols (data type constructors and type
4717 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4718 in <literal>t1 .. tn</literal>, and</para>
4721 <para>for every type
4722 variable <literal>a</literal>, <literal>a</literal> occurs
4723 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4724 .. tn</literal>.</para>
4727 These restrictions are easily verified and ensure termination of type
4728 inference. However, they are not sufficient to guarantee completeness
4729 of type inference in the presence of, so called, ''loopy equalities'',
4730 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4731 a type variable is underneath a family application and data
4732 constructor application - see the above mentioned paper for details.
4735 If the option <option>-XUndecidableInstances</option> is passed to the
4736 compiler, the above restrictions are not enforced and it is on the
4737 programmer to ensure termination of the normalisation of type families
4738 during type inference.
4743 <sect3 id-="equality-constraints">
4744 <title>Equality constraints</title>
4746 Type context can include equality constraints of the form <literal>t1 ~
4747 t2</literal>, which denote that the types <literal>t1</literal>
4748 and <literal>t2</literal> need to be the same. In the presence of type
4749 families, whether two types are equal cannot generally be decided
4750 locally. Hence, the contexts of function signatures may include
4751 equality constraints, as in the following example:
4753 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4755 where we require that the element type of <literal>c1</literal>
4756 and <literal>c2</literal> are the same. In general, the
4757 types <literal>t1</literal> and <literal>t2</literal> of an equality
4758 constraint may be arbitrary monotypes; i.e., they may not contain any
4759 quantifiers, independent of whether higher-rank types are otherwise
4763 Equality constraints can also appear in class and instance contexts.
4764 The former enable a simple translation of programs using functional
4765 dependencies into programs using family synonyms instead. The general
4766 idea is to rewrite a class declaration of the form
4768 class C a b | a -> b
4772 class (F a ~ b) => C a b where
4775 That is, we represent every functional dependency (FD) <literal>a1 .. an
4776 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4777 superclass context equality <literal>F a1 .. an ~ b</literal>,
4778 essentially giving a name to the functional dependency. In class
4779 instances, we define the type instances of FD families in accordance
4780 with the class head. Method signatures are not affected by that
4784 NB: Equalities in superclass contexts are not fully implemented in
4789 <sect3 id-="ty-fams-in-instances">
4790 <title>Type families and instance declarations</title>
4791 <para>Type families require us to extend the rules for
4792 the form of instance heads, which are given
4793 in <xref linkend="flexible-instance-head"/>.
4796 <listitem><para>Data type families may appear in an instance head</para></listitem>
4797 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4799 The reason for the latter restriction is that there is no way to check for. Consider
4802 type instance F Bool = Int
4809 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4810 The situation is especially bad because the type instance for <literal>F Bool</literal>
4811 might be in another module, or even in a module that is not yet written.
4818 <sect1 id="other-type-extensions">
4819 <title>Other type system extensions</title>
4821 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4823 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4824 is used, the keyword <literal>forall</literal>
4825 allows us to say exactly what this means. For example:
4833 g :: forall b. (b -> b)
4835 The two are treated identically.
4838 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4839 a type variable any more!
4844 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4846 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4847 that the type-class constraints in a type signature must have the
4848 form <emphasis>(class type-variable)</emphasis> or
4849 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4850 With <option>-XFlexibleContexts</option>
4851 these type signatures are perfectly OK
4854 g :: Ord (T a ()) => ...
4856 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4857 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4858 (<xref linkend="instance-rules"/>).
4862 GHC imposes the following restrictions on the constraints in a type signature.
4866 forall tv1..tvn (c1, ...,cn) => type
4869 (Here, we write the "foralls" explicitly, although the Haskell source
4870 language omits them; in Haskell 98, all the free type variables of an
4871 explicit source-language type signature are universally quantified,
4872 except for the class type variables in a class declaration. However,
4873 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4882 <emphasis>Each universally quantified type variable
4883 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4885 A type variable <literal>a</literal> is "reachable" if it appears
4886 in the same constraint as either a type variable free in
4887 <literal>type</literal>, or another reachable type variable.
4888 A value with a type that does not obey
4889 this reachability restriction cannot be used without introducing
4890 ambiguity; that is why the type is rejected.
4891 Here, for example, is an illegal type:
4895 forall a. Eq a => Int
4899 When a value with this type was used, the constraint <literal>Eq tv</literal>
4900 would be introduced where <literal>tv</literal> is a fresh type variable, and
4901 (in the dictionary-translation implementation) the value would be
4902 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4903 can never know which instance of <literal>Eq</literal> to use because we never
4904 get any more information about <literal>tv</literal>.
4908 that the reachability condition is weaker than saying that <literal>a</literal> is
4909 functionally dependent on a type variable free in
4910 <literal>type</literal> (see <xref
4911 linkend="functional-dependencies"/>). The reason for this is there
4912 might be a "hidden" dependency, in a superclass perhaps. So
4913 "reachable" is a conservative approximation to "functionally dependent".
4914 For example, consider:
4916 class C a b | a -> b where ...
4917 class C a b => D a b where ...
4918 f :: forall a b. D a b => a -> a
4920 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4921 but that is not immediately apparent from <literal>f</literal>'s type.
4927 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4928 universally quantified type variables <literal>tvi</literal></emphasis>.
4930 For example, this type is OK because <literal>C a b</literal> mentions the
4931 universally quantified type variable <literal>b</literal>:
4935 forall a. C a b => burble
4939 The next type is illegal because the constraint <literal>Eq b</literal> does not
4940 mention <literal>a</literal>:
4944 forall a. Eq b => burble
4948 The reason for this restriction is milder than the other one. The
4949 excluded types are never useful or necessary (because the offending
4950 context doesn't need to be witnessed at this point; it can be floated
4951 out). Furthermore, floating them out increases sharing. Lastly,
4952 excluding them is a conservative choice; it leaves a patch of
4953 territory free in case we need it later.
4964 <sect2 id="implicit-parameters">
4965 <title>Implicit parameters</title>
4967 <para> Implicit parameters are implemented as described in
4968 "Implicit parameters: dynamic scoping with static types",
4969 J Lewis, MB Shields, E Meijer, J Launchbury,
4970 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4974 <para>(Most of the following, still rather incomplete, documentation is
4975 due to Jeff Lewis.)</para>
4977 <para>Implicit parameter support is enabled with the option
4978 <option>-XImplicitParams</option>.</para>
4981 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4982 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4983 context. In Haskell, all variables are statically bound. Dynamic
4984 binding of variables is a notion that goes back to Lisp, but was later
4985 discarded in more modern incarnations, such as Scheme. Dynamic binding
4986 can be very confusing in an untyped language, and unfortunately, typed
4987 languages, in particular Hindley-Milner typed languages like Haskell,
4988 only support static scoping of variables.
4991 However, by a simple extension to the type class system of Haskell, we
4992 can support dynamic binding. Basically, we express the use of a
4993 dynamically bound variable as a constraint on the type. These
4994 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4995 function uses a dynamically-bound variable <literal>?x</literal>
4996 of type <literal>t'</literal>". For
4997 example, the following expresses the type of a sort function,
4998 implicitly parameterized by a comparison function named <literal>cmp</literal>.
5000 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5002 The dynamic binding constraints are just a new form of predicate in the type class system.
5005 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5006 where <literal>x</literal> is
5007 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5008 Use of this construct also introduces a new
5009 dynamic-binding constraint in the type of the expression.
5010 For example, the following definition
5011 shows how we can define an implicitly parameterized sort function in
5012 terms of an explicitly parameterized <literal>sortBy</literal> function:
5014 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5016 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5022 <title>Implicit-parameter type constraints</title>
5024 Dynamic binding constraints behave just like other type class
5025 constraints in that they are automatically propagated. Thus, when a
5026 function is used, its implicit parameters are inherited by the
5027 function that called it. For example, our <literal>sort</literal> function might be used
5028 to pick out the least value in a list:
5030 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5031 least xs = head (sort xs)
5033 Without lifting a finger, the <literal>?cmp</literal> parameter is
5034 propagated to become a parameter of <literal>least</literal> as well. With explicit
5035 parameters, the default is that parameters must always be explicit
5036 propagated. With implicit parameters, the default is to always
5040 An implicit-parameter type constraint differs from other type class constraints in the
5041 following way: All uses of a particular implicit parameter must have
5042 the same type. This means that the type of <literal>(?x, ?x)</literal>
5043 is <literal>(?x::a) => (a,a)</literal>, and not
5044 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5048 <para> You can't have an implicit parameter in the context of a class or instance
5049 declaration. For example, both these declarations are illegal:
5051 class (?x::Int) => C a where ...
5052 instance (?x::a) => Foo [a] where ...
5054 Reason: exactly which implicit parameter you pick up depends on exactly where
5055 you invoke a function. But the ``invocation'' of instance declarations is done
5056 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5057 Easiest thing is to outlaw the offending types.</para>
5059 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5061 f :: (?x :: [a]) => Int -> Int
5064 g :: (Read a, Show a) => String -> String
5067 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5068 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5069 quite unambiguous, and fixes the type <literal>a</literal>.
5074 <title>Implicit-parameter bindings</title>
5077 An implicit parameter is <emphasis>bound</emphasis> using the standard
5078 <literal>let</literal> or <literal>where</literal> binding forms.
5079 For example, we define the <literal>min</literal> function by binding
5080 <literal>cmp</literal>.
5083 min = let ?cmp = (<=) in least
5087 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5088 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5089 (including in a list comprehension, or do-notation, or pattern guards),
5090 or a <literal>where</literal> clause.
5091 Note the following points:
5094 An implicit-parameter binding group must be a
5095 collection of simple bindings to implicit-style variables (no
5096 function-style bindings, and no type signatures); these bindings are
5097 neither polymorphic or recursive.
5100 You may not mix implicit-parameter bindings with ordinary bindings in a
5101 single <literal>let</literal>
5102 expression; use two nested <literal>let</literal>s instead.
5103 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5107 You may put multiple implicit-parameter bindings in a
5108 single binding group; but they are <emphasis>not</emphasis> treated
5109 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5110 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5111 parameter. The bindings are not nested, and may be re-ordered without changing
5112 the meaning of the program.
5113 For example, consider:
5115 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5117 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5118 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5120 f :: (?x::Int) => Int -> Int
5128 <sect3><title>Implicit parameters and polymorphic recursion</title>
5131 Consider these two definitions:
5134 len1 xs = let ?acc = 0 in len_acc1 xs
5137 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5142 len2 xs = let ?acc = 0 in len_acc2 xs
5144 len_acc2 :: (?acc :: Int) => [a] -> Int
5146 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5148 The only difference between the two groups is that in the second group
5149 <literal>len_acc</literal> is given a type signature.
5150 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5151 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5152 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5153 has a type signature, the recursive call is made to the
5154 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5155 as an implicit parameter. So we get the following results in GHCi:
5162 Adding a type signature dramatically changes the result! This is a rather
5163 counter-intuitive phenomenon, worth watching out for.
5167 <sect3><title>Implicit parameters and monomorphism</title>
5169 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5170 Haskell Report) to implicit parameters. For example, consider:
5178 Since the binding for <literal>y</literal> falls under the Monomorphism
5179 Restriction it is not generalised, so the type of <literal>y</literal> is
5180 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5181 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5182 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5183 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5184 <literal>y</literal> in the body of the <literal>let</literal> will see the
5185 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5186 <literal>14</literal>.
5191 <!-- ======================= COMMENTED OUT ========================
5193 We intend to remove linear implicit parameters, so I'm at least removing
5194 them from the 6.6 user manual
5196 <sect2 id="linear-implicit-parameters">
5197 <title>Linear implicit parameters</title>
5199 Linear implicit parameters are an idea developed by Koen Claessen,
5200 Mark Shields, and Simon PJ. They address the long-standing
5201 problem that monads seem over-kill for certain sorts of problem, notably:
5204 <listitem> <para> distributing a supply of unique names </para> </listitem>
5205 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5206 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5210 Linear implicit parameters are just like ordinary implicit parameters,
5211 except that they are "linear"; that is, they cannot be copied, and
5212 must be explicitly "split" instead. Linear implicit parameters are
5213 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5214 (The '/' in the '%' suggests the split!)
5219 import GHC.Exts( Splittable )
5221 data NameSupply = ...
5223 splitNS :: NameSupply -> (NameSupply, NameSupply)
5224 newName :: NameSupply -> Name
5226 instance Splittable NameSupply where
5230 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5231 f env (Lam x e) = Lam x' (f env e)
5234 env' = extend env x x'
5235 ...more equations for f...
5237 Notice that the implicit parameter %ns is consumed
5239 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5240 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5244 So the translation done by the type checker makes
5245 the parameter explicit:
5247 f :: NameSupply -> Env -> Expr -> Expr
5248 f ns env (Lam x e) = Lam x' (f ns1 env e)
5250 (ns1,ns2) = splitNS ns
5252 env = extend env x x'
5254 Notice the call to 'split' introduced by the type checker.
5255 How did it know to use 'splitNS'? Because what it really did
5256 was to introduce a call to the overloaded function 'split',
5257 defined by the class <literal>Splittable</literal>:
5259 class Splittable a where
5262 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5263 split for name supplies. But we can simply write
5269 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5271 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5272 <literal>GHC.Exts</literal>.
5277 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5278 are entirely distinct implicit parameters: you
5279 can use them together and they won't interfere with each other. </para>
5282 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5284 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5285 in the context of a class or instance declaration. </para></listitem>
5289 <sect3><title>Warnings</title>
5292 The monomorphism restriction is even more important than usual.
5293 Consider the example above:
5295 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5296 f env (Lam x e) = Lam x' (f env e)
5299 env' = extend env x x'
5301 If we replaced the two occurrences of x' by (newName %ns), which is
5302 usually a harmless thing to do, we get:
5304 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5305 f env (Lam x e) = Lam (newName %ns) (f env e)
5307 env' = extend env x (newName %ns)
5309 But now the name supply is consumed in <emphasis>three</emphasis> places
5310 (the two calls to newName,and the recursive call to f), so
5311 the result is utterly different. Urk! We don't even have
5315 Well, this is an experimental change. With implicit
5316 parameters we have already lost beta reduction anyway, and
5317 (as John Launchbury puts it) we can't sensibly reason about
5318 Haskell programs without knowing their typing.
5323 <sect3><title>Recursive functions</title>
5324 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5327 foo :: %x::T => Int -> [Int]
5329 foo n = %x : foo (n-1)
5331 where T is some type in class Splittable.</para>
5333 Do you get a list of all the same T's or all different T's
5334 (assuming that split gives two distinct T's back)?
5336 If you supply the type signature, taking advantage of polymorphic
5337 recursion, you get what you'd probably expect. Here's the
5338 translated term, where the implicit param is made explicit:
5341 foo x n = let (x1,x2) = split x
5342 in x1 : foo x2 (n-1)
5344 But if you don't supply a type signature, GHC uses the Hindley
5345 Milner trick of using a single monomorphic instance of the function
5346 for the recursive calls. That is what makes Hindley Milner type inference
5347 work. So the translation becomes
5351 foom n = x : foom (n-1)
5355 Result: 'x' is not split, and you get a list of identical T's. So the
5356 semantics of the program depends on whether or not foo has a type signature.
5359 You may say that this is a good reason to dislike linear implicit parameters
5360 and you'd be right. That is why they are an experimental feature.
5366 ================ END OF Linear Implicit Parameters commented out -->
5368 <sect2 id="kinding">
5369 <title>Explicitly-kinded quantification</title>
5372 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5373 to give the kind explicitly as (machine-checked) documentation,
5374 just as it is nice to give a type signature for a function. On some occasions,
5375 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5376 John Hughes had to define the data type:
5378 data Set cxt a = Set [a]
5379 | Unused (cxt a -> ())
5381 The only use for the <literal>Unused</literal> constructor was to force the correct
5382 kind for the type variable <literal>cxt</literal>.
5385 GHC now instead allows you to specify the kind of a type variable directly, wherever
5386 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5389 This flag enables kind signatures in the following places:
5391 <listitem><para><literal>data</literal> declarations:
5393 data Set (cxt :: * -> *) a = Set [a]
5394 </screen></para></listitem>
5395 <listitem><para><literal>type</literal> declarations:
5397 type T (f :: * -> *) = f Int
5398 </screen></para></listitem>
5399 <listitem><para><literal>class</literal> declarations:
5401 class (Eq a) => C (f :: * -> *) a where ...
5402 </screen></para></listitem>
5403 <listitem><para><literal>forall</literal>'s in type signatures:
5405 f :: forall (cxt :: * -> *). Set cxt Int
5406 </screen></para></listitem>
5411 The parentheses are required. Some of the spaces are required too, to
5412 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5413 will get a parse error, because "<literal>::*->*</literal>" is a
5414 single lexeme in Haskell.
5418 As part of the same extension, you can put kind annotations in types
5421 f :: (Int :: *) -> Int
5422 g :: forall a. a -> (a :: *)
5426 atype ::= '(' ctype '::' kind ')
5428 The parentheses are required.
5433 <sect2 id="universal-quantification">
5434 <title>Arbitrary-rank polymorphism
5438 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5439 explicit universal quantification in
5441 For example, all the following types are legal:
5443 f1 :: forall a b. a -> b -> a
5444 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5446 f2 :: (forall a. a->a) -> Int -> Int
5447 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5449 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5451 f4 :: Int -> (forall a. a -> a)
5453 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5454 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5455 The <literal>forall</literal> makes explicit the universal quantification that
5456 is implicitly added by Haskell.
5459 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5460 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5461 shows, the polymorphic type on the left of the function arrow can be overloaded.
5464 The function <literal>f3</literal> has a rank-3 type;
5465 it has rank-2 types on the left of a function arrow.
5468 GHC has three flags to control higher-rank types:
5471 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5474 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5477 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5478 That is, you can nest <literal>forall</literal>s
5479 arbitrarily deep in function arrows.
5480 In particular, a forall-type (also called a "type scheme"),
5481 including an operational type class context, is legal:
5483 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5484 of a function arrow </para> </listitem>
5485 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5486 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5487 field type signatures.</para> </listitem>
5488 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5489 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5501 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5502 the types of the constructor arguments. Here are several examples:
5508 data T a = T1 (forall b. b -> b -> b) a
5510 data MonadT m = MkMonad { return :: forall a. a -> m a,
5511 bind :: forall a b. m a -> (a -> m b) -> m b
5514 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5520 The constructors have rank-2 types:
5526 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5527 MkMonad :: forall m. (forall a. a -> m a)
5528 -> (forall a b. m a -> (a -> m b) -> m b)
5530 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5536 Notice that you don't need to use a <literal>forall</literal> if there's an
5537 explicit context. For example in the first argument of the
5538 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5539 prefixed to the argument type. The implicit <literal>forall</literal>
5540 quantifies all type variables that are not already in scope, and are
5541 mentioned in the type quantified over.
5545 As for type signatures, implicit quantification happens for non-overloaded
5546 types too. So if you write this:
5549 data T a = MkT (Either a b) (b -> b)
5552 it's just as if you had written this:
5555 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5558 That is, since the type variable <literal>b</literal> isn't in scope, it's
5559 implicitly universally quantified. (Arguably, it would be better
5560 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5561 where that is what is wanted. Feedback welcomed.)
5565 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5566 the constructor to suitable values, just as usual. For example,
5577 a3 = MkSwizzle reverse
5580 a4 = let r x = Just x
5587 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5588 mkTs f x y = [T1 f x, T1 f y]
5594 The type of the argument can, as usual, be more general than the type
5595 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5596 does not need the <literal>Ord</literal> constraint.)
5600 When you use pattern matching, the bound variables may now have
5601 polymorphic types. For example:
5607 f :: T a -> a -> (a, Char)
5608 f (T1 w k) x = (w k x, w 'c' 'd')
5610 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5611 g (MkSwizzle s) xs f = s (map f (s xs))
5613 h :: MonadT m -> [m a] -> m [a]
5614 h m [] = return m []
5615 h m (x:xs) = bind m x $ \y ->
5616 bind m (h m xs) $ \ys ->
5623 In the function <function>h</function> we use the record selectors <literal>return</literal>
5624 and <literal>bind</literal> to extract the polymorphic bind and return functions
5625 from the <literal>MonadT</literal> data structure, rather than using pattern
5631 <title>Type inference</title>
5634 In general, type inference for arbitrary-rank types is undecidable.
5635 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5636 to get a decidable algorithm by requiring some help from the programmer.
5637 We do not yet have a formal specification of "some help" but the rule is this:
5640 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5641 provides an explicit polymorphic type for x, or GHC's type inference will assume
5642 that x's type has no foralls in it</emphasis>.
5645 What does it mean to "provide" an explicit type for x? You can do that by
5646 giving a type signature for x directly, using a pattern type signature
5647 (<xref linkend="scoped-type-variables"/>), thus:
5649 \ f :: (forall a. a->a) -> (f True, f 'c')
5651 Alternatively, you can give a type signature to the enclosing
5652 context, which GHC can "push down" to find the type for the variable:
5654 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5656 Here the type signature on the expression can be pushed inwards
5657 to give a type signature for f. Similarly, and more commonly,
5658 one can give a type signature for the function itself:
5660 h :: (forall a. a->a) -> (Bool,Char)
5661 h f = (f True, f 'c')
5663 You don't need to give a type signature if the lambda bound variable
5664 is a constructor argument. Here is an example we saw earlier:
5666 f :: T a -> a -> (a, Char)
5667 f (T1 w k) x = (w k x, w 'c' 'd')
5669 Here we do not need to give a type signature to <literal>w</literal>, because
5670 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5677 <sect3 id="implicit-quant">
5678 <title>Implicit quantification</title>
5681 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5682 user-written types, if and only if there is no explicit <literal>forall</literal>,
5683 GHC finds all the type variables mentioned in the type that are not already
5684 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5688 f :: forall a. a -> a
5695 h :: forall b. a -> b -> b
5701 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5704 f :: (a -> a) -> Int
5706 f :: forall a. (a -> a) -> Int
5708 f :: (forall a. a -> a) -> Int
5711 g :: (Ord a => a -> a) -> Int
5712 -- MEANS the illegal type
5713 g :: forall a. (Ord a => a -> a) -> Int
5715 g :: (forall a. Ord a => a -> a) -> Int
5717 The latter produces an illegal type, which you might think is silly,
5718 but at least the rule is simple. If you want the latter type, you
5719 can write your for-alls explicitly. Indeed, doing so is strongly advised
5726 <sect2 id="impredicative-polymorphism">
5727 <title>Impredicative polymorphism
5729 <para><emphasis>NOTE: the impredicative-polymorphism feature is deprecated in GHC 6.12, and
5730 will be removed or replaced in GHC 6.14.</emphasis></para>
5732 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5733 enabled with <option>-XImpredicativeTypes</option>.
5735 that you can call a polymorphic function at a polymorphic type, and
5736 parameterise data structures over polymorphic types. For example:
5738 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5739 f (Just g) = Just (g [3], g "hello")
5742 Notice here that the <literal>Maybe</literal> type is parameterised by the
5743 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5746 <para>The technical details of this extension are described in the paper
5747 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5748 type inference for higher-rank types and impredicativity</ulink>,
5749 which appeared at ICFP 2006.
5753 <sect2 id="scoped-type-variables">
5754 <title>Lexically scoped type variables
5758 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5759 which some type signatures are simply impossible to write. For example:
5761 f :: forall a. [a] -> [a]
5767 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5768 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5769 The type variables bound by a <literal>forall</literal> scope over
5770 the entire definition of the accompanying value declaration.
5771 In this example, the type variable <literal>a</literal> scopes over the whole
5772 definition of <literal>f</literal>, including over
5773 the type signature for <varname>ys</varname>.
5774 In Haskell 98 it is not possible to declare
5775 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5776 it becomes possible to do so.
5778 <para>Lexically-scoped type variables are enabled by
5779 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5781 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5782 variables work, compared to earlier releases. Read this section
5786 <title>Overview</title>
5788 <para>The design follows the following principles
5790 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5791 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5792 design.)</para></listitem>
5793 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5794 type variables. This means that every programmer-written type signature
5795 (including one that contains free scoped type variables) denotes a
5796 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5797 checker, and no inference is involved.</para></listitem>
5798 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5799 changing the program.</para></listitem>
5803 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5805 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5806 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5807 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5808 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5812 In Haskell, a programmer-written type signature is implicitly quantified over
5813 its free type variables (<ulink
5814 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5816 of the Haskell Report).
5817 Lexically scoped type variables affect this implicit quantification rules
5818 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5819 quantified. For example, if type variable <literal>a</literal> is in scope,
5822 (e :: a -> a) means (e :: a -> a)
5823 (e :: b -> b) means (e :: forall b. b->b)
5824 (e :: a -> b) means (e :: forall b. a->b)
5832 <sect3 id="decl-type-sigs">
5833 <title>Declaration type signatures</title>
5834 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5835 quantification (using <literal>forall</literal>) brings into scope the
5836 explicitly-quantified
5837 type variables, in the definition of the named function. For example:
5839 f :: forall a. [a] -> [a]
5840 f (x:xs) = xs ++ [ x :: a ]
5842 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5843 the definition of "<literal>f</literal>".
5845 <para>This only happens if:
5847 <listitem><para> The quantification in <literal>f</literal>'s type
5848 signature is explicit. For example:
5851 g (x:xs) = xs ++ [ x :: a ]
5853 This program will be rejected, because "<literal>a</literal>" does not scope
5854 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5855 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5856 quantification rules.
5858 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5859 not a pattern binding.
5862 f1 :: forall a. [a] -> [a]
5863 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5865 f2 :: forall a. [a] -> [a]
5866 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5868 f3 :: forall a. [a] -> [a]
5869 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5871 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5872 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5873 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5874 the type signature brings <literal>a</literal> into scope.
5880 <sect3 id="exp-type-sigs">
5881 <title>Expression type signatures</title>
5883 <para>An expression type signature that has <emphasis>explicit</emphasis>
5884 quantification (using <literal>forall</literal>) brings into scope the
5885 explicitly-quantified
5886 type variables, in the annotated expression. For example:
5888 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5890 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5891 type variable <literal>s</literal> into scope, in the annotated expression
5892 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5897 <sect3 id="pattern-type-sigs">
5898 <title>Pattern type signatures</title>
5900 A type signature may occur in any pattern; this is a <emphasis>pattern type
5901 signature</emphasis>.
5904 -- f and g assume that 'a' is already in scope
5905 f = \(x::Int, y::a) -> x
5907 h ((x,y) :: (Int,Bool)) = (y,x)
5909 In the case where all the type variables in the pattern type signature are
5910 already in scope (i.e. bound by the enclosing context), matters are simple: the
5911 signature simply constrains the type of the pattern in the obvious way.
5914 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5915 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5916 that are already in scope. For example:
5918 f :: forall a. [a] -> (Int, [a])
5921 (ys::[a], n) = (reverse xs, length xs) -- OK
5922 zs::[a] = xs ++ ys -- OK
5924 Just (v::b) = ... -- Not OK; b is not in scope
5926 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5927 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5931 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5932 type signature may mention a type variable that is not in scope; in this case,
5933 <emphasis>the signature brings that type variable into scope</emphasis>.
5934 This is particularly important for existential data constructors. For example:
5936 data T = forall a. MkT [a]
5939 k (MkT [t::a]) = MkT t3
5943 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5944 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5945 because it is bound by the pattern match. GHC's rule is that in this situation
5946 (and only then), a pattern type signature can mention a type variable that is
5947 not already in scope; the effect is to bring it into scope, standing for the
5948 existentially-bound type variable.
5951 When a pattern type signature binds a type variable in this way, GHC insists that the
5952 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5953 This means that any user-written type signature always stands for a completely known type.
5956 If all this seems a little odd, we think so too. But we must have
5957 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5958 could not name existentially-bound type variables in subsequent type signatures.
5961 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5962 signature is allowed to mention a lexical variable that is not already in
5964 For example, both <literal>f</literal> and <literal>g</literal> would be
5965 illegal if <literal>a</literal> was not already in scope.
5971 <!-- ==================== Commented out part about result type signatures
5973 <sect3 id="result-type-sigs">
5974 <title>Result type signatures</title>
5977 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5980 {- f assumes that 'a' is already in scope -}
5981 f x y :: [a] = [x,y,x]
5983 g = \ x :: [Int] -> [3,4]
5985 h :: forall a. [a] -> a
5989 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5990 the result of the function. Similarly, the body of the lambda in the RHS of
5991 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5992 alternative in <literal>h</literal> is <literal>a</literal>.
5994 <para> A result type signature never brings new type variables into scope.</para>
5996 There are a couple of syntactic wrinkles. First, notice that all three
5997 examples would parse quite differently with parentheses:
5999 {- f assumes that 'a' is already in scope -}
6000 f x (y :: [a]) = [x,y,x]
6002 g = \ (x :: [Int]) -> [3,4]
6004 h :: forall a. [a] -> a
6008 Now the signature is on the <emphasis>pattern</emphasis>; and
6009 <literal>h</literal> would certainly be ill-typed (since the pattern
6010 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6012 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6013 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6014 token or a parenthesised type of some sort). To see why,
6015 consider how one would parse this:
6024 <sect3 id="cls-inst-scoped-tyvars">
6025 <title>Class and instance declarations</title>
6028 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6029 scope over the methods defined in the <literal>where</literal> part. For example:
6047 <sect2 id="typing-binds">
6048 <title>Generalised typing of mutually recursive bindings</title>
6051 The Haskell Report specifies that a group of bindings (at top level, or in a
6052 <literal>let</literal> or <literal>where</literal>) should be sorted into
6053 strongly-connected components, and then type-checked in dependency order
6054 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6055 Report, Section 4.5.1</ulink>).
6056 As each group is type-checked, any binders of the group that
6058 an explicit type signature are put in the type environment with the specified
6060 and all others are monomorphic until the group is generalised
6061 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6064 <para>Following a suggestion of Mark Jones, in his paper
6065 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6067 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6069 <emphasis>the dependency analysis ignores references to variables that have an explicit
6070 type signature</emphasis>.
6071 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6072 typecheck. For example, consider:
6074 f :: Eq a => a -> Bool
6075 f x = (x == x) || g True || g "Yes"
6077 g y = (y <= y) || f True
6079 This is rejected by Haskell 98, but under Jones's scheme the definition for
6080 <literal>g</literal> is typechecked first, separately from that for
6081 <literal>f</literal>,
6082 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6083 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6084 type is generalised, to get
6086 g :: Ord a => a -> Bool
6088 Now, the definition for <literal>f</literal> is typechecked, with this type for
6089 <literal>g</literal> in the type environment.
6093 The same refined dependency analysis also allows the type signatures of
6094 mutually-recursive functions to have different contexts, something that is illegal in
6095 Haskell 98 (Section 4.5.2, last sentence). With
6096 <option>-XRelaxedPolyRec</option>
6097 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6098 type signatures; in practice this means that only variables bound by the same
6099 pattern binding must have the same context. For example, this is fine:
6101 f :: Eq a => a -> Bool
6102 f x = (x == x) || g True
6104 g :: Ord a => a -> Bool
6105 g y = (y <= y) || f True
6110 <sect2 id="mono-local-binds">
6111 <title>Monomorphic local bindings</title>
6113 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6114 The rationale is described in the paper
6115 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6118 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6119 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6120 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6121 If you supply a type signature, then the flag has no effect.
6126 <!-- ==================== End of type system extensions ================= -->
6128 <!-- ====================== TEMPLATE HASKELL ======================= -->
6130 <sect1 id="template-haskell">
6131 <title>Template Haskell</title>
6133 <para>Template Haskell allows you to do compile-time meta-programming in
6136 the main technical innovations is discussed in "<ulink
6137 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6138 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6141 There is a Wiki page about
6142 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6143 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6147 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6148 Haskell library reference material</ulink>
6149 (look for module <literal>Language.Haskell.TH</literal>).
6150 Many changes to the original design are described in
6151 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6152 Notes on Template Haskell version 2</ulink>.
6153 Not all of these changes are in GHC, however.
6156 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6157 as a worked example to help get you started.
6161 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6162 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6167 <title>Syntax</title>
6169 <para> Template Haskell has the following new syntactic
6170 constructions. You need to use the flag
6171 <option>-XTemplateHaskell</option>
6172 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6173 </indexterm>to switch these syntactic extensions on
6174 (<option>-XTemplateHaskell</option> is no longer implied by
6175 <option>-fglasgow-exts</option>).</para>
6179 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6180 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6181 There must be no space between the "$" and the identifier or parenthesis. This use
6182 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6183 of "." as an infix operator. If you want the infix operator, put spaces around it.
6185 <para> A splice can occur in place of
6187 <listitem><para> an expression; the spliced expression must
6188 have type <literal>Q Exp</literal></para></listitem>
6189 <listitem><para> an type; the spliced expression must
6190 have type <literal>Q Typ</literal></para></listitem>
6191 <listitem><para> a list of top-level declarations; the spliced expression
6192 must have type <literal>Q [Dec]</literal></para></listitem>
6194 Note that pattern splices are not supported.
6195 Inside a splice you can can only call functions defined in imported modules,
6196 not functions defined elsewhere in the same module.</para></listitem>
6199 A expression quotation is written in Oxford brackets, thus:
6201 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6202 where the "..." is an expression;
6203 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6204 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6205 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6206 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6207 the quotation has type <literal>Q Type</literal>.</para></listitem>
6208 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6209 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6210 </itemizedlist></para></listitem>
6213 A quasi-quotation can appear in either a pattern context or an
6214 expression context and is also written in Oxford brackets:
6216 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6217 where the "..." is an arbitrary string; a full description of the
6218 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6219 </itemizedlist></para></listitem>
6222 A name can be quoted with either one or two prefix single quotes:
6224 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6225 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6226 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6228 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6229 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6232 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6233 may also be given as an argument to the <literal>reify</literal> function.
6237 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6238 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6245 $(deriveStuff 'f) -- Uses the $(...) notation
6249 deriveStuff 'g -- Omits the $(...)
6253 This abbreviation makes top-level declaration slices quieter and less intimidating.
6258 (Compared to the original paper, there are many differences of detail.
6259 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6260 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6261 Pattern splices and quotations are not implemented.)
6265 <sect2> <title> Using Template Haskell </title>
6269 The data types and monadic constructor functions for Template Haskell are in the library
6270 <literal>Language.Haskell.THSyntax</literal>.
6274 You can only run a function at compile time if it is imported from another module. That is,
6275 you can't define a function in a module, and call it from within a splice in the same module.
6276 (It would make sense to do so, but it's hard to implement.)
6280 You can only run a function at compile time if it is imported
6281 from another module <emphasis>that is not part of a mutually-recursive group of modules
6282 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6283 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6284 splice is to be run.</para>
6286 For example, when compiling module A,
6287 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6288 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6292 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6295 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6296 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6297 compiles and runs a program, and then looks at the result. So it's important that
6298 the program it compiles produces results whose representations are identical to
6299 those of the compiler itself.
6303 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6304 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6309 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6310 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6311 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6318 -- Import our template "pr"
6319 import Printf ( pr )
6321 -- The splice operator $ takes the Haskell source code
6322 -- generated at compile time by "pr" and splices it into
6323 -- the argument of "putStrLn".
6324 main = putStrLn ( $(pr "Hello") )
6330 -- Skeletal printf from the paper.
6331 -- It needs to be in a separate module to the one where
6332 -- you intend to use it.
6334 -- Import some Template Haskell syntax
6335 import Language.Haskell.TH
6337 -- Describe a format string
6338 data Format = D | S | L String
6340 -- Parse a format string. This is left largely to you
6341 -- as we are here interested in building our first ever
6342 -- Template Haskell program and not in building printf.
6343 parse :: String -> [Format]
6346 -- Generate Haskell source code from a parsed representation
6347 -- of the format string. This code will be spliced into
6348 -- the module which calls "pr", at compile time.
6349 gen :: [Format] -> Q Exp
6350 gen [D] = [| \n -> show n |]
6351 gen [S] = [| \s -> s |]
6352 gen [L s] = stringE s
6354 -- Here we generate the Haskell code for the splice
6355 -- from an input format string.
6356 pr :: String -> Q Exp
6357 pr s = gen (parse s)
6360 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6363 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6366 <para>Run "main.exe" and here is your output:</para>
6376 <title>Using Template Haskell with Profiling</title>
6377 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6379 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6380 interpreter to run the splice expressions. The bytecode interpreter
6381 runs the compiled expression on top of the same runtime on which GHC
6382 itself is running; this means that the compiled code referred to by
6383 the interpreted expression must be compatible with this runtime, and
6384 in particular this means that object code that is compiled for
6385 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6386 expression, because profiled object code is only compatible with the
6387 profiling version of the runtime.</para>
6389 <para>This causes difficulties if you have a multi-module program
6390 containing Template Haskell code and you need to compile it for
6391 profiling, because GHC cannot load the profiled object code and use it
6392 when executing the splices. Fortunately GHC provides a workaround.
6393 The basic idea is to compile the program twice:</para>
6397 <para>Compile the program or library first the normal way, without
6398 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6401 <para>Then compile it again with <option>-prof</option>, and
6402 additionally use <option>-osuf
6403 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6404 to name the object files differently (you can choose any suffix
6405 that isn't the normal object suffix here). GHC will automatically
6406 load the object files built in the first step when executing splice
6407 expressions. If you omit the <option>-osuf</option> flag when
6408 building with <option>-prof</option> and Template Haskell is used,
6409 GHC will emit an error message. </para>
6414 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6415 <para>Quasi-quotation allows patterns and expressions to be written using
6416 programmer-defined concrete syntax; the motivation behind the extension and
6417 several examples are documented in
6418 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6419 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6420 2007). The example below shows how to write a quasiquoter for a simple
6421 expression language.</para>
6423 Here are the salient features
6426 A quasi-quote has the form
6427 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6430 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6431 quoter; it cannot be an arbitrary expression.
6434 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6435 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6436 those overlap with Template Haskell quotations.
6439 There must be no spaces in the token
6440 <literal>[<replaceable>quoter</replaceable>|</literal>.
6443 The quoted <replaceable>string</replaceable>
6444 can be arbitrary, and may contain newlines.
6450 A quasiquote may appear in place of
6452 <listitem><para>An expression</para></listitem>
6453 <listitem><para>A pattern</para></listitem>
6454 <listitem><para>A type</para></listitem>
6455 <listitem><para>A top-level declaration</para></listitem>
6457 (Only the first two are described in the paper.)
6461 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6462 which is defined thus:
6464 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6465 quotePat :: String -> Q Pat,
6466 quoteType :: String -> Q Type,
6467 quoteDec :: String -> Q [Dec] }
6469 That is, a quoter is a tuple of four parsers, one for each of the contexts
6470 in which a quasi-quote can occur.
6473 A quasi-quote is expanded by applying the appropriate parser to the string
6474 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6475 type, declaration) determines which of the parsers is called.
6480 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6481 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6482 The example makes use of an antiquoted
6483 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6484 (this syntax for anti-quotation was defined by the parser's
6485 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6486 integer value argument of the constructor <literal>IntExpr</literal> when
6487 pattern matching. Please see the referenced paper for further details regarding
6488 anti-quotation as well as the description of a technique that uses SYB to
6489 leverage a single parser of type <literal>String -> a</literal> to generate both
6490 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6491 pattern parser that returns a value of type <literal>Q Pat</literal>.
6495 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6496 the example, <literal>expr</literal> cannot be defined
6497 in <literal>Main.hs</literal> where it is used, but must be imported.
6501 {- ------------- file Main.hs --------------- -}
6507 main = do { print $ eval [expr|1 + 2|]
6509 { [expr|'int:n|] -> print n
6515 {- ------------- file Expr.hs --------------- -}
6518 import qualified Language.Haskell.TH as TH
6519 import Language.Haskell.TH.Quote
6521 data Expr = IntExpr Integer
6522 | AntiIntExpr String
6523 | BinopExpr BinOp Expr Expr
6525 deriving(Show, Typeable, Data)
6531 deriving(Show, Typeable, Data)
6533 eval :: Expr -> Integer
6534 eval (IntExpr n) = n
6535 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6542 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6544 -- Parse an Expr, returning its representation as
6545 -- either a Q Exp or a Q Pat. See the referenced paper
6546 -- for how to use SYB to do this by writing a single
6547 -- parser of type String -> Expr instead of two
6548 -- separate parsers.
6550 parseExprExp :: String -> Q Exp
6553 parseExprPat :: String -> Q Pat
6557 <para>Now run the compiler:
6559 $ ghc --make -XQuasiQuotes Main.hs -o main
6563 <para>Run "main" and here is your output:
6574 <!-- ===================== Arrow notation =================== -->
6576 <sect1 id="arrow-notation">
6577 <title>Arrow notation
6580 <para>Arrows are a generalization of monads introduced by John Hughes.
6581 For more details, see
6586 “Generalising Monads to Arrows”,
6587 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6588 pp67–111, May 2000.
6589 The paper that introduced arrows: a friendly introduction, motivated with
6590 programming examples.
6596 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6597 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6598 Introduced the notation described here.
6604 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6605 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6612 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6613 John Hughes, in <citetitle>5th International Summer School on
6614 Advanced Functional Programming</citetitle>,
6615 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6617 This paper includes another introduction to the notation,
6618 with practical examples.
6624 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6625 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6626 A terse enumeration of the formal rules used
6627 (extracted from comments in the source code).
6633 The arrows web page at
6634 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6639 With the <option>-XArrows</option> flag, GHC supports the arrow
6640 notation described in the second of these papers,
6641 translating it using combinators from the
6642 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6644 What follows is a brief introduction to the notation;
6645 it won't make much sense unless you've read Hughes's paper.
6648 <para>The extension adds a new kind of expression for defining arrows:
6650 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6651 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6653 where <literal>proc</literal> is a new keyword.
6654 The variables of the pattern are bound in the body of the
6655 <literal>proc</literal>-expression,
6656 which is a new sort of thing called a <firstterm>command</firstterm>.
6657 The syntax of commands is as follows:
6659 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6660 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6661 | <replaceable>cmd</replaceable><superscript>0</superscript>
6663 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6664 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6665 infix operators as for expressions, and
6667 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6668 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6669 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6670 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6671 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6672 | <replaceable>fcmd</replaceable>
6674 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6675 | ( <replaceable>cmd</replaceable> )
6676 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6678 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6679 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6680 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6681 | <replaceable>cmd</replaceable>
6683 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6684 except that the bodies are commands instead of expressions.
6688 Commands produce values, but (like monadic computations)
6689 may yield more than one value,
6690 or none, and may do other things as well.
6691 For the most part, familiarity with monadic notation is a good guide to
6693 However the values of expressions, even monadic ones,
6694 are determined by the values of the variables they contain;
6695 this is not necessarily the case for commands.
6699 A simple example of the new notation is the expression
6701 proc x -> f -< x+1
6703 We call this a <firstterm>procedure</firstterm> or
6704 <firstterm>arrow abstraction</firstterm>.
6705 As with a lambda expression, the variable <literal>x</literal>
6706 is a new variable bound within the <literal>proc</literal>-expression.
6707 It refers to the input to the arrow.
6708 In the above example, <literal>-<</literal> is not an identifier but an
6709 new reserved symbol used for building commands from an expression of arrow
6710 type and an expression to be fed as input to that arrow.
6711 (The weird look will make more sense later.)
6712 It may be read as analogue of application for arrows.
6713 The above example is equivalent to the Haskell expression
6715 arr (\ x -> x+1) >>> f
6717 That would make no sense if the expression to the left of
6718 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6719 More generally, the expression to the left of <literal>-<</literal>
6720 may not involve any <firstterm>local variable</firstterm>,
6721 i.e. a variable bound in the current arrow abstraction.
6722 For such a situation there is a variant <literal>-<<</literal>, as in
6724 proc x -> f x -<< x+1
6726 which is equivalent to
6728 arr (\ x -> (f x, x+1)) >>> app
6730 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6732 Such an arrow is equivalent to a monad, so if you're using this form
6733 you may find a monadic formulation more convenient.
6737 <title>do-notation for commands</title>
6740 Another form of command is a form of <literal>do</literal>-notation.
6741 For example, you can write
6750 You can read this much like ordinary <literal>do</literal>-notation,
6751 but with commands in place of monadic expressions.
6752 The first line sends the value of <literal>x+1</literal> as an input to
6753 the arrow <literal>f</literal>, and matches its output against
6754 <literal>y</literal>.
6755 In the next line, the output is discarded.
6756 The arrow <function>returnA</function> is defined in the
6757 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6758 module as <literal>arr id</literal>.
6759 The above example is treated as an abbreviation for
6761 arr (\ x -> (x, x)) >>>
6762 first (arr (\ x -> x+1) >>> f) >>>
6763 arr (\ (y, x) -> (y, (x, y))) >>>
6764 first (arr (\ y -> 2*y) >>> g) >>>
6766 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6767 first (arr (\ (x, z) -> x*z) >>> h) >>>
6768 arr (\ (t, z) -> t+z) >>>
6771 Note that variables not used later in the composition are projected out.
6772 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6774 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6775 module, this reduces to
6777 arr (\ x -> (x+1, x)) >>>
6779 arr (\ (y, x) -> (2*y, (x, y))) >>>
6781 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6783 arr (\ (t, z) -> t+z)
6785 which is what you might have written by hand.
6786 With arrow notation, GHC keeps track of all those tuples of variables for you.
6790 Note that although the above translation suggests that
6791 <literal>let</literal>-bound variables like <literal>z</literal> must be
6792 monomorphic, the actual translation produces Core,
6793 so polymorphic variables are allowed.
6797 It's also possible to have mutually recursive bindings,
6798 using the new <literal>rec</literal> keyword, as in the following example:
6800 counter :: ArrowCircuit a => a Bool Int
6801 counter = proc reset -> do
6802 rec output <- returnA -< if reset then 0 else next
6803 next <- delay 0 -< output+1
6804 returnA -< output
6806 The translation of such forms uses the <function>loop</function> combinator,
6807 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6813 <title>Conditional commands</title>
6816 In the previous example, we used a conditional expression to construct the
6818 Sometimes we want to conditionally execute different commands, as in
6825 which is translated to
6827 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6828 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6830 Since the translation uses <function>|||</function>,
6831 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6835 There are also <literal>case</literal> commands, like
6841 y <- h -< (x1, x2)
6845 The syntax is the same as for <literal>case</literal> expressions,
6846 except that the bodies of the alternatives are commands rather than expressions.
6847 The translation is similar to that of <literal>if</literal> commands.
6853 <title>Defining your own control structures</title>
6856 As we're seen, arrow notation provides constructs,
6857 modelled on those for expressions,
6858 for sequencing, value recursion and conditionals.
6859 But suitable combinators,
6860 which you can define in ordinary Haskell,
6861 may also be used to build new commands out of existing ones.
6862 The basic idea is that a command defines an arrow from environments to values.
6863 These environments assign values to the free local variables of the command.
6864 Thus combinators that produce arrows from arrows
6865 may also be used to build commands from commands.
6866 For example, the <literal>ArrowChoice</literal> class includes a combinator
6868 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6870 so we can use it to build commands:
6872 expr' = proc x -> do
6875 symbol Plus -< ()
6876 y <- term -< ()
6879 symbol Minus -< ()
6880 y <- term -< ()
6883 (The <literal>do</literal> on the first line is needed to prevent the first
6884 <literal><+> ...</literal> from being interpreted as part of the
6885 expression on the previous line.)
6886 This is equivalent to
6888 expr' = (proc x -> returnA -< x)
6889 <+> (proc x -> do
6890 symbol Plus -< ()
6891 y <- term -< ()
6893 <+> (proc x -> do
6894 symbol Minus -< ()
6895 y <- term -< ()
6898 It is essential that this operator be polymorphic in <literal>e</literal>
6899 (representing the environment input to the command
6900 and thence to its subcommands)
6901 and satisfy the corresponding naturality property
6903 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6905 at least for strict <literal>k</literal>.
6906 (This should be automatic if you're not using <function>seq</function>.)
6907 This ensures that environments seen by the subcommands are environments
6908 of the whole command,
6909 and also allows the translation to safely trim these environments.
6910 The operator must also not use any variable defined within the current
6915 We could define our own operator
6917 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6918 untilA body cond = proc x ->
6919 b <- cond -< x
6920 if b then returnA -< ()
6923 untilA body cond -< x
6925 and use it in the same way.
6926 Of course this infix syntax only makes sense for binary operators;
6927 there is also a more general syntax involving special brackets:
6931 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6938 <title>Primitive constructs</title>
6941 Some operators will need to pass additional inputs to their subcommands.
6942 For example, in an arrow type supporting exceptions,
6943 the operator that attaches an exception handler will wish to pass the
6944 exception that occurred to the handler.
6945 Such an operator might have a type
6947 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6949 where <literal>Ex</literal> is the type of exceptions handled.
6950 You could then use this with arrow notation by writing a command
6952 body `handleA` \ ex -> handler
6954 so that if an exception is raised in the command <literal>body</literal>,
6955 the variable <literal>ex</literal> is bound to the value of the exception
6956 and the command <literal>handler</literal>,
6957 which typically refers to <literal>ex</literal>, is entered.
6958 Though the syntax here looks like a functional lambda,
6959 we are talking about commands, and something different is going on.
6960 The input to the arrow represented by a command consists of values for
6961 the free local variables in the command, plus a stack of anonymous values.
6962 In all the prior examples, this stack was empty.
6963 In the second argument to <function>handleA</function>,
6964 this stack consists of one value, the value of the exception.
6965 The command form of lambda merely gives this value a name.
6970 the values on the stack are paired to the right of the environment.
6971 So operators like <function>handleA</function> that pass
6972 extra inputs to their subcommands can be designed for use with the notation
6973 by pairing the values with the environment in this way.
6974 More precisely, the type of each argument of the operator (and its result)
6975 should have the form
6977 a (...(e,t1), ... tn) t
6979 where <replaceable>e</replaceable> is a polymorphic variable
6980 (representing the environment)
6981 and <replaceable>ti</replaceable> are the types of the values on the stack,
6982 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6983 The polymorphic variable <replaceable>e</replaceable> must not occur in
6984 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6985 <replaceable>t</replaceable>.
6986 However the arrows involved need not be the same.
6987 Here are some more examples of suitable operators:
6989 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6990 runReader :: ... => a e c -> a' (e,State) c
6991 runState :: ... => a e c -> a' (e,State) (c,State)
6993 We can supply the extra input required by commands built with the last two
6994 by applying them to ordinary expressions, as in
6998 (|runReader (do { ... })|) s
7000 which adds <literal>s</literal> to the stack of inputs to the command
7001 built using <function>runReader</function>.
7005 The command versions of lambda abstraction and application are analogous to
7006 the expression versions.
7007 In particular, the beta and eta rules describe equivalences of commands.
7008 These three features (operators, lambda abstraction and application)
7009 are the core of the notation; everything else can be built using them,
7010 though the results would be somewhat clumsy.
7011 For example, we could simulate <literal>do</literal>-notation by defining
7013 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7014 u `bind` f = returnA &&& u >>> f
7016 bind_ :: Arrow a => a e b -> a e c -> a e c
7017 u `bind_` f = u `bind` (arr fst >>> f)
7019 We could simulate <literal>if</literal> by defining
7021 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7022 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7029 <title>Differences with the paper</title>
7034 <para>Instead of a single form of arrow application (arrow tail) with two
7035 translations, the implementation provides two forms
7036 <quote><literal>-<</literal></quote> (first-order)
7037 and <quote><literal>-<<</literal></quote> (higher-order).
7042 <para>User-defined operators are flagged with banana brackets instead of
7043 a new <literal>form</literal> keyword.
7052 <title>Portability</title>
7055 Although only GHC implements arrow notation directly,
7056 there is also a preprocessor
7058 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7059 that translates arrow notation into Haskell 98
7060 for use with other Haskell systems.
7061 You would still want to check arrow programs with GHC;
7062 tracing type errors in the preprocessor output is not easy.
7063 Modules intended for both GHC and the preprocessor must observe some
7064 additional restrictions:
7069 The module must import
7070 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7076 The preprocessor cannot cope with other Haskell extensions.
7077 These would have to go in separate modules.
7083 Because the preprocessor targets Haskell (rather than Core),
7084 <literal>let</literal>-bound variables are monomorphic.
7095 <!-- ==================== BANG PATTERNS ================= -->
7097 <sect1 id="bang-patterns">
7098 <title>Bang patterns
7099 <indexterm><primary>Bang patterns</primary></indexterm>
7101 <para>GHC supports an extension of pattern matching called <emphasis>bang
7102 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7103 Bang patterns are under consideration for Haskell Prime.
7105 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7106 prime feature description</ulink> contains more discussion and examples
7107 than the material below.
7110 The key change is the addition of a new rule to the
7111 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7112 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7113 against a value <replaceable>v</replaceable> behaves as follows:
7115 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7116 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7120 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7123 <sect2 id="bang-patterns-informal">
7124 <title>Informal description of bang patterns
7127 The main idea is to add a single new production to the syntax of patterns:
7131 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7132 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7137 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7138 whereas without the bang it would be lazy.
7139 Bang patterns can be nested of course:
7143 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7144 <literal>y</literal>.
7145 A bang only really has an effect if it precedes a variable or wild-card pattern:
7150 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7151 putting a bang before a pattern that
7152 forces evaluation anyway does nothing.
7155 There is one (apparent) exception to this general rule that a bang only
7156 makes a difference when it precedes a variable or wild-card: a bang at the
7157 top level of a <literal>let</literal> or <literal>where</literal>
7158 binding makes the binding strict, regardless of the pattern.
7159 (We say "apparent" exception because the Right Way to think of it is that the bang
7160 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7161 is part of the syntax of the <emphasis>binding</emphasis>,
7162 creating a "bang-pattern binding".)
7167 is a bang-pattern binding. Operationally, it behaves just like a case expression:
7169 case e of [x,y] -> b
7171 Like a case expression, a bang-pattern binding must be non-recursive, and
7174 However, <emphasis>nested</emphasis> bangs in a pattern binding behave uniformly with all other forms of
7175 pattern matching. For example
7177 let (!x,[y]) = e in b
7179 is equivalent to this:
7181 let { t = case e of (x,[y]) -> x `seq` (x,y)
7186 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7187 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7188 evaluation of <literal>x</literal>.
7191 Bang patterns work in <literal>case</literal> expressions too, of course:
7193 g5 x = let y = f x in body
7194 g6 x = case f x of { y -> body }
7195 g7 x = case f x of { !y -> body }
7197 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7198 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7199 result, and then evaluates <literal>body</literal>.
7204 <sect2 id="bang-patterns-sem">
7205 <title>Syntax and semantics
7209 We add a single new production to the syntax of patterns:
7213 There is one problem with syntactic ambiguity. Consider:
7217 Is this a definition of the infix function "<literal>(!)</literal>",
7218 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7219 ambiguity in favour of the latter. If you want to define
7220 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7225 The semantics of Haskell pattern matching is described in <ulink
7226 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7227 Section 3.17.2</ulink> of the Haskell Report. To this description add
7228 one extra item 10, saying:
7229 <itemizedlist><listitem><para>Matching
7230 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7231 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7232 <listitem><para>otherwise, <literal>pat</literal> is matched against
7233 <literal>v</literal></para></listitem>
7235 </para></listitem></itemizedlist>
7236 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7237 Section 3.17.3</ulink>, add a new case (t):
7239 case v of { !pat -> e; _ -> e' }
7240 = v `seq` case v of { pat -> e; _ -> e' }
7243 That leaves let expressions, whose translation is given in
7244 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7246 of the Haskell Report.
7247 In the translation box, first apply
7248 the following transformation: for each pattern <literal>pi</literal> that is of
7249 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7250 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7251 have a bang at the top, apply the rules in the existing box.
7253 <para>The effect of the let rule is to force complete matching of the pattern
7254 <literal>qi</literal> before evaluation of the body is begun. The bang is
7255 retained in the translated form in case <literal>qi</literal> is a variable,
7263 The let-binding can be recursive. However, it is much more common for
7264 the let-binding to be non-recursive, in which case the following law holds:
7265 <literal>(let !p = rhs in body)</literal>
7267 <literal>(case rhs of !p -> body)</literal>
7270 A pattern with a bang at the outermost level is not allowed at the top level of
7276 <!-- ==================== ASSERTIONS ================= -->
7278 <sect1 id="assertions">
7280 <indexterm><primary>Assertions</primary></indexterm>
7284 If you want to make use of assertions in your standard Haskell code, you
7285 could define a function like the following:
7291 assert :: Bool -> a -> a
7292 assert False x = error "assertion failed!"
7299 which works, but gives you back a less than useful error message --
7300 an assertion failed, but which and where?
7304 One way out is to define an extended <function>assert</function> function which also
7305 takes a descriptive string to include in the error message and
7306 perhaps combine this with the use of a pre-processor which inserts
7307 the source location where <function>assert</function> was used.
7311 Ghc offers a helping hand here, doing all of this for you. For every
7312 use of <function>assert</function> in the user's source:
7318 kelvinToC :: Double -> Double
7319 kelvinToC k = assert (k >= 0.0) (k+273.15)
7325 Ghc will rewrite this to also include the source location where the
7332 assert pred val ==> assertError "Main.hs|15" pred val
7338 The rewrite is only performed by the compiler when it spots
7339 applications of <function>Control.Exception.assert</function>, so you
7340 can still define and use your own versions of
7341 <function>assert</function>, should you so wish. If not, import
7342 <literal>Control.Exception</literal> to make use
7343 <function>assert</function> in your code.
7347 GHC ignores assertions when optimisation is turned on with the
7348 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7349 <literal>assert pred e</literal> will be rewritten to
7350 <literal>e</literal>. You can also disable assertions using the
7351 <option>-fignore-asserts</option>
7352 option<indexterm><primary><option>-fignore-asserts</option></primary>
7353 </indexterm>.</para>
7356 Assertion failures can be caught, see the documentation for the
7357 <literal>Control.Exception</literal> library for the details.
7363 <!-- =============================== PRAGMAS =========================== -->
7365 <sect1 id="pragmas">
7366 <title>Pragmas</title>
7368 <indexterm><primary>pragma</primary></indexterm>
7370 <para>GHC supports several pragmas, or instructions to the
7371 compiler placed in the source code. Pragmas don't normally affect
7372 the meaning of the program, but they might affect the efficiency
7373 of the generated code.</para>
7375 <para>Pragmas all take the form
7377 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7379 where <replaceable>word</replaceable> indicates the type of
7380 pragma, and is followed optionally by information specific to that
7381 type of pragma. Case is ignored in
7382 <replaceable>word</replaceable>. The various values for
7383 <replaceable>word</replaceable> that GHC understands are described
7384 in the following sections; any pragma encountered with an
7385 unrecognised <replaceable>word</replaceable> is
7386 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7387 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7389 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7393 pragma must precede the <literal>module</literal> keyword in the file.
7396 There can be as many file-header pragmas as you please, and they can be
7397 preceded or followed by comments.
7400 File-header pragmas are read once only, before
7401 pre-processing the file (e.g. with cpp).
7404 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7405 <literal>{-# OPTIONS_GHC #-}</literal>, and
7406 <literal>{-# INCLUDE #-}</literal>.
7411 <sect2 id="language-pragma">
7412 <title>LANGUAGE pragma</title>
7414 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7415 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7417 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7419 It is the intention that all Haskell compilers support the
7420 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7421 all extensions are supported by all compilers, of
7422 course. The <literal>LANGUAGE</literal> pragma should be used instead
7423 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7425 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7427 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7429 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7431 <para>Every language extension can also be turned into a command-line flag
7432 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7433 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7436 <para>A list of all supported language extensions can be obtained by invoking
7437 <literal>ghc --supported-extensions</literal> (see <xref linkend="modes"/>).</para>
7439 <para>Any extension from the <literal>Extension</literal> type defined in
7441 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7442 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7446 <sect2 id="options-pragma">
7447 <title>OPTIONS_GHC pragma</title>
7448 <indexterm><primary>OPTIONS_GHC</primary>
7450 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7453 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7454 additional options that are given to the compiler when compiling
7455 this source file. See <xref linkend="source-file-options"/> for
7458 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7459 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7462 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7464 <sect2 id="include-pragma">
7465 <title>INCLUDE pragma</title>
7467 <para>The <literal>INCLUDE</literal> used to be necessary for
7468 specifying header files to be included when using the FFI and
7469 compiling via C. It is no longer required for GHC, but is
7470 accepted (and ignored) for compatibility with other
7474 <sect2 id="warning-deprecated-pragma">
7475 <title>WARNING and DEPRECATED pragmas</title>
7476 <indexterm><primary>WARNING</primary></indexterm>
7477 <indexterm><primary>DEPRECATED</primary></indexterm>
7479 <para>The WARNING pragma allows you to attach an arbitrary warning
7480 to a particular function, class, or type.
7481 A DEPRECATED pragma lets you specify that
7482 a particular function, class, or type is deprecated.
7483 There are two ways of using these pragmas.
7487 <para>You can work on an entire module thus:</para>
7489 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7494 module Wibble {-# WARNING "This is an unstable interface." #-} where
7497 <para>When you compile any module that import
7498 <literal>Wibble</literal>, GHC will print the specified
7503 <para>You can attach a warning to a function, class, type, or data constructor, with the
7504 following top-level declarations:</para>
7506 {-# DEPRECATED f, C, T "Don't use these" #-}
7507 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7509 <para>When you compile any module that imports and uses any
7510 of the specified entities, GHC will print the specified
7512 <para> You can only attach to entities declared at top level in the module
7513 being compiled, and you can only use unqualified names in the list of
7514 entities. A capitalised name, such as <literal>T</literal>
7515 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7516 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7517 both are in scope. If both are in scope, there is currently no way to
7518 specify one without the other (c.f. fixities
7519 <xref linkend="infix-tycons"/>).</para>
7522 Warnings and deprecations are not reported for
7523 (a) uses within the defining module, and
7524 (b) uses in an export list.
7525 The latter reduces spurious complaints within a library
7526 in which one module gathers together and re-exports
7527 the exports of several others.
7529 <para>You can suppress the warnings with the flag
7530 <option>-fno-warn-warnings-deprecations</option>.</para>
7533 <sect2 id="inline-noinline-pragma">
7534 <title>INLINE and NOINLINE pragmas</title>
7536 <para>These pragmas control the inlining of function
7539 <sect3 id="inline-pragma">
7540 <title>INLINE pragma</title>
7541 <indexterm><primary>INLINE</primary></indexterm>
7543 <para>GHC (with <option>-O</option>, as always) tries to
7544 inline (or “unfold”) functions/values that are
7545 “small enough,” thus avoiding the call overhead
7546 and possibly exposing other more-wonderful optimisations.
7547 Normally, if GHC decides a function is “too
7548 expensive” to inline, it will not do so, nor will it
7549 export that unfolding for other modules to use.</para>
7551 <para>The sledgehammer you can bring to bear is the
7552 <literal>INLINE</literal><indexterm><primary>INLINE
7553 pragma</primary></indexterm> pragma, used thusly:</para>
7556 key_function :: Int -> String -> (Bool, Double)
7557 {-# INLINE key_function #-}
7560 <para>The major effect of an <literal>INLINE</literal> pragma
7561 is to declare a function's “cost” to be very low.
7562 The normal unfolding machinery will then be very keen to
7563 inline it. However, an <literal>INLINE</literal> pragma for a
7564 function "<literal>f</literal>" has a number of other effects:
7567 While GHC is keen to inline the function, it does not do so
7568 blindly. For example, if you write
7572 there really isn't any point in inlining <literal>key_function</literal> to get
7574 map (\x -> <replaceable>body</replaceable>) xs
7576 In general, GHC only inlines the function if there is some reason (no matter
7577 how slight) to supose that it is useful to do so.
7581 Moreover, GHC will only inline the function if it is <emphasis>fully applied</emphasis>,
7582 where "fully applied"
7583 means applied to as many arguments as appear (syntactically)
7584 on the LHS of the function
7585 definition. For example:
7587 comp1 :: (b -> c) -> (a -> b) -> a -> c
7588 {-# INLINE comp1 #-}
7589 comp1 f g = \x -> f (g x)
7591 comp2 :: (b -> c) -> (a -> b) -> a -> c
7592 {-# INLINE comp2 #-}
7593 comp2 f g x = f (g x)
7595 The two functions <literal>comp1</literal> and <literal>comp2</literal> have the
7596 same semantics, but <literal>comp1</literal> will be inlined when applied
7597 to <emphasis>two</emphasis> arguments, while <literal>comp2</literal> requires
7598 <emphasis>three</emphasis>. This might make a big difference if you say
7600 map (not `comp1` not) xs
7602 which will optimise better than the corresponding use of `comp2`.
7606 It is useful for GHC to optimise the definition of an
7607 INLINE function <literal>f</literal> just like any other non-INLINE function,
7608 in case the non-inlined version of <literal>f</literal> is
7609 ultimately called. But we don't want to inline
7610 the <emphasis>optimised</emphasis> version
7611 of <literal>f</literal>;
7612 a major reason for INLINE pragmas is to expose functions
7613 in <literal>f</literal>'s RHS that have
7614 rewrite rules, and it's no good if those functions have been optimised
7618 So <emphasis>GHC guarantees to inline precisely the code that you wrote</emphasis>, no more
7619 and no less. It does this by capturing a copy of the definition of the function to use
7620 for inlining (we call this the "inline-RHS"), which it leaves untouched,
7621 while optimising the ordinarly RHS as usual. For externally-visible functions
7622 the inline-RHS (not the optimised RHS) is recorded in the interface file.
7625 An INLINE function is not worker/wrappered by strictness analysis.
7626 It's going to be inlined wholesale instead.
7630 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7631 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7632 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7633 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7634 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7635 when there is no choice even an INLINE function can be selected, in which case
7636 the INLINE pragma is ignored.
7637 For example, for a self-recursive function, the loop breaker can only be the function
7638 itself, so an INLINE pragma is always ignored.</para>
7640 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7641 function can be put anywhere its type signature could be
7644 <para><literal>INLINE</literal> pragmas are a particularly
7646 <literal>then</literal>/<literal>return</literal> (or
7647 <literal>bind</literal>/<literal>unit</literal>) functions in
7648 a monad. For example, in GHC's own
7649 <literal>UniqueSupply</literal> monad code, we have:</para>
7652 {-# INLINE thenUs #-}
7653 {-# INLINE returnUs #-}
7656 <para>See also the <literal>NOINLINE</literal> (<xref linkend="inlinable-pragma"/>)
7657 and <literal>INLINABLE</literal> (<xref linkend="noinline-pragma"/>)
7660 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7661 so if you want your code to be HBC-compatible you'll have to surround
7662 the pragma with C pre-processor directives
7663 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7667 <sect3 id="inlinable-pragma">
7668 <title>INLINABLE pragma</title>
7670 <para>An <literal>{-# INLINABLE f #-}</literal> pragma on a
7671 function <literal>f</literal> has the following behaviour:
7674 While <literal>INLINE</literal> says "please inline me", the <literal>INLINABLE</literal>
7675 says "feel free to inline me; use your
7676 discretion". In other words the choice is left to GHC, which uses the same
7677 rules as for pragma-free functions. Unlike <literal>INLINE</literal>, that decision is made at
7678 the <emphasis>call site</emphasis>, and
7679 will therefore be affected by the inlining threshold, optimisation level etc.
7682 Like <literal>INLINE</literal>, the <literal>INLINABLE</literal> pragma retains a
7683 copy of the original RHS for
7684 inlining purposes, and persists it in the interface file, regardless of
7685 the size of the RHS.
7689 One way to use <literal>INLINABLE</literal> is in conjunction with
7690 the special function <literal>inline</literal> (<xref linkend="special-ids"/>).
7691 The call <literal>inline f</literal> tries very hard to inline <literal>f</literal>.
7692 To make sure that <literal>f</literal> can be inlined,
7693 it is a good idea to mark the definition
7694 of <literal>f</literal> as <literal>INLINABLE</literal>,
7695 so that GHC guarantees to expose an unfolding regardless of how big it is.
7696 Moreover, by annotating <literal>f</literal> as <literal>INLINABLE</literal>,
7697 you ensure that <literal>f</literal>'s original RHS is inlined, rather than
7698 whatever random optimised version of <literal>f</literal> GHC's optimiser
7703 The <literal>INLINABLE</literal> pragma also works with <literal>SPECIALISE</literal>:
7704 if you mark function <literal>f</literal> as <literal>INLINABLE</literal>, then
7705 you can subsequently <literal>SPECIALISE</literal> in another module
7706 (see <xref linkend="specialize-pragma"/>).</para></listitem>
7709 Unlike <literal>INLINE</literal>, it is OK to use
7710 an <literal>INLINABLE</literal> pragma on a recursive function.
7711 The principal reason do to so to allow later use of <literal>SPECIALISE</literal>
7718 <sect3 id="noinline-pragma">
7719 <title>NOINLINE pragma</title>
7721 <indexterm><primary>NOINLINE</primary></indexterm>
7722 <indexterm><primary>NOTINLINE</primary></indexterm>
7724 <para>The <literal>NOINLINE</literal> pragma does exactly what
7725 you'd expect: it stops the named function from being inlined
7726 by the compiler. You shouldn't ever need to do this, unless
7727 you're very cautious about code size.</para>
7729 <para><literal>NOTINLINE</literal> is a synonym for
7730 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7731 specified by Haskell 98 as the standard way to disable
7732 inlining, so it should be used if you want your code to be
7736 <sect3 id="conlike-pragma">
7737 <title>CONLIKE modifier</title>
7738 <indexterm><primary>CONLIKE</primary></indexterm>
7739 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7740 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7744 <sect3 id="phase-control">
7745 <title>Phase control</title>
7747 <para> Sometimes you want to control exactly when in GHC's
7748 pipeline the INLINE pragma is switched on. Inlining happens
7749 only during runs of the <emphasis>simplifier</emphasis>. Each
7750 run of the simplifier has a different <emphasis>phase
7751 number</emphasis>; the phase number decreases towards zero.
7752 If you use <option>-dverbose-core2core</option> you'll see the
7753 sequence of phase numbers for successive runs of the
7754 simplifier. In an INLINE pragma you can optionally specify a
7758 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7759 <literal>f</literal>
7760 until phase <literal>k</literal>, but from phase
7761 <literal>k</literal> onwards be very keen to inline it.
7764 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7765 <literal>f</literal>
7766 until phase <literal>k</literal>, but from phase
7767 <literal>k</literal> onwards do not inline it.
7770 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7771 <literal>f</literal>
7772 until phase <literal>k</literal>, but from phase
7773 <literal>k</literal> onwards be willing to inline it (as if
7774 there was no pragma).
7777 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7778 <literal>f</literal>
7779 until phase <literal>k</literal>, but from phase
7780 <literal>k</literal> onwards do not inline it.
7783 The same information is summarised here:
7785 -- Before phase 2 Phase 2 and later
7786 {-# INLINE [2] f #-} -- No Yes
7787 {-# INLINE [~2] f #-} -- Yes No
7788 {-# NOINLINE [2] f #-} -- No Maybe
7789 {-# NOINLINE [~2] f #-} -- Maybe No
7791 {-# INLINE f #-} -- Yes Yes
7792 {-# NOINLINE f #-} -- No No
7794 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7795 function body is small, or it is applied to interesting-looking arguments etc).
7796 Another way to understand the semantics is this:
7798 <listitem><para>For both INLINE and NOINLINE, the phase number says
7799 when inlining is allowed at all.</para></listitem>
7800 <listitem><para>The INLINE pragma has the additional effect of making the
7801 function body look small, so that when inlining is allowed it is very likely to
7806 <para>The same phase-numbering control is available for RULES
7807 (<xref linkend="rewrite-rules"/>).</para>
7811 <sect2 id="annotation-pragmas">
7812 <title>ANN pragmas</title>
7814 <para>GHC offers the ability to annotate various code constructs with additional
7815 data by using three pragmas. This data can then be inspected at a later date by
7816 using GHC-as-a-library.</para>
7818 <sect3 id="ann-pragma">
7819 <title>Annotating values</title>
7821 <indexterm><primary>ANN</primary></indexterm>
7823 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7824 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7825 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7826 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7827 you would do this:</para>
7830 {-# ANN foo (Just "Hello") #-}
7835 A number of restrictions apply to use of annotations:
7837 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7838 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7839 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7840 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7841 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7843 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7844 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7847 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7848 please give the GHC team a shout</ulink>.
7851 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7852 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7855 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7860 <sect3 id="typeann-pragma">
7861 <title>Annotating types</title>
7863 <indexterm><primary>ANN type</primary></indexterm>
7864 <indexterm><primary>ANN</primary></indexterm>
7866 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7869 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7874 <sect3 id="modann-pragma">
7875 <title>Annotating modules</title>
7877 <indexterm><primary>ANN module</primary></indexterm>
7878 <indexterm><primary>ANN</primary></indexterm>
7880 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7883 {-# ANN module (Just "A `Maybe String' annotation") #-}
7888 <sect2 id="line-pragma">
7889 <title>LINE pragma</title>
7891 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7892 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7893 <para>This pragma is similar to C's <literal>#line</literal>
7894 pragma, and is mainly for use in automatically generated Haskell
7895 code. It lets you specify the line number and filename of the
7896 original code; for example</para>
7898 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7900 <para>if you'd generated the current file from something called
7901 <filename>Foo.vhs</filename> and this line corresponds to line
7902 42 in the original. GHC will adjust its error messages to refer
7903 to the line/file named in the <literal>LINE</literal>
7908 <title>RULES pragma</title>
7910 <para>The RULES pragma lets you specify rewrite rules. It is
7911 described in <xref linkend="rewrite-rules"/>.</para>
7914 <sect2 id="specialize-pragma">
7915 <title>SPECIALIZE pragma</title>
7917 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7918 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7919 <indexterm><primary>overloading, death to</primary></indexterm>
7921 <para>(UK spelling also accepted.) For key overloaded
7922 functions, you can create extra versions (NB: more code space)
7923 specialised to particular types. Thus, if you have an
7924 overloaded function:</para>
7927 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7930 <para>If it is heavily used on lists with
7931 <literal>Widget</literal> keys, you could specialise it as
7935 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7938 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7939 be put anywhere its type signature could be put.</para>
7941 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7942 (a) a specialised version of the function and (b) a rewrite rule
7943 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7944 un-specialised function into a call to the specialised one.</para>
7946 <para>The type in a SPECIALIZE pragma can be any type that is less
7947 polymorphic than the type of the original function. In concrete terms,
7948 if the original function is <literal>f</literal> then the pragma
7950 {-# SPECIALIZE f :: <type> #-}
7952 is valid if and only if the definition
7954 f_spec :: <type>
7957 is valid. Here are some examples (where we only give the type signature
7958 for the original function, not its code):
7960 f :: Eq a => a -> b -> b
7961 {-# SPECIALISE f :: Int -> b -> b #-}
7963 g :: (Eq a, Ix b) => a -> b -> b
7964 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7966 h :: Eq a => a -> a -> a
7967 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7969 The last of these examples will generate a
7970 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7971 well. If you use this kind of specialisation, let us know how well it works.
7974 <sect3 id="specialize-inline">
7975 <title>SPECIALIZE INLINE</title>
7977 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7978 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7979 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7980 The <literal>INLINE</literal> pragma affects the specialised version of the
7981 function (only), and applies even if the function is recursive. The motivating
7984 -- A GADT for arrays with type-indexed representation
7986 ArrInt :: !Int -> ByteArray# -> Arr Int
7987 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7989 (!:) :: Arr e -> Int -> e
7990 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7991 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7992 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7993 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7995 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7996 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7997 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7998 the specialised function will be inlined. It has two calls to
7999 <literal>(!:)</literal>,
8000 both at type <literal>Int</literal>. Both these calls fire the first
8001 specialisation, whose body is also inlined. The result is a type-based
8002 unrolling of the indexing function.</para>
8003 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
8004 on an ordinarily-recursive function.</para>
8007 <sect3><title>SPECIALIZE for imported functions</title>
8010 Generally, you can only give a <literal>SPECIALIZE</literal> pragma
8011 for a function defined in the same module.
8012 However if a function <literal>f</literal> is given an <literal>INLINABLE</literal>
8013 pragma at its definition site, then it can subequently be specialised by
8014 importing modules (see <xref linkend="inlinable-pragma"/>).
8017 module Map( lookup, blah blah ) where
8018 lookup :: Ord key => [(key,a)] -> key -> Maybe a
8020 {-# INLINABLE lookup #-}
8023 import Map( lookup )
8025 data T = T1 | T2 deriving( Eq, Ord )
8026 {-# SPECIALISE lookup :: [(T,a)] -> T -> Maybe a
8028 Here, <literal>lookup</literal> is declared <literal>INLINABLE</literal>, but
8029 it cannot be specialised for type <literal>T</literal> at its definition site,
8030 because that type does not exist yet. Instead a client module can define <literal>T</literal>
8031 and then specialise <literal>lookup</literal> at that type.
8034 Moreover, every module that imports <literal>Client</literal> (or imports a module
8035 that imports <literal>Client</literal>, transitively) will "see", and make use of,
8036 the specialised version of <literal>lookup</literal>. You don't need to put
8037 a <literal>SPECIALIZE</literal> pragma in every module.
8040 Moreover you often don't even need the <literal>SPECIALIZE</literal> pragma in the
8041 first place. When compiling a module M,
8042 GHC's optimiser (with -O) automatically considers each top-level
8043 overloaded function declared in M, and specialises it
8044 for the different types at which it is called in M. The optimiser
8045 <emphasis>also</emphasis> considers each <emphasis>imported</emphasis>
8046 <literal>INLINABLE</literal> overloaded function, and specialises it
8047 for the different types at which it is called in M.
8048 So in our example, it would be enough for <literal>lookup</literal> to
8049 be called at type <literal>T</literal>:
8052 import Map( lookup )
8054 data T = T1 | T2 deriving( Eq, Ord )
8056 findT1 :: [(T,a)] -> Maybe a
8057 findT1 m = lookup m T1 -- A call of lookup at type T
8059 However, sometimes there are no such calls, in which case the
8060 pragma can be useful.
8064 <sect3><title>Obselete SPECIALIZE syntax</title>
8066 <para>Note: In earlier versions of GHC, it was possible to provide your own
8067 specialised function for a given type:
8070 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
8073 This feature has been removed, as it is now subsumed by the
8074 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
8079 <sect2 id="specialize-instance-pragma">
8080 <title>SPECIALIZE instance pragma
8084 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
8085 <indexterm><primary>overloading, death to</primary></indexterm>
8086 Same idea, except for instance declarations. For example:
8089 instance (Eq a) => Eq (Foo a) where {
8090 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
8094 The pragma must occur inside the <literal>where</literal> part
8095 of the instance declaration.
8098 Compatible with HBC, by the way, except perhaps in the placement
8104 <sect2 id="unpack-pragma">
8105 <title>UNPACK pragma</title>
8107 <indexterm><primary>UNPACK</primary></indexterm>
8109 <para>The <literal>UNPACK</literal> indicates to the compiler
8110 that it should unpack the contents of a constructor field into
8111 the constructor itself, removing a level of indirection. For
8115 data T = T {-# UNPACK #-} !Float
8116 {-# UNPACK #-} !Float
8119 <para>will create a constructor <literal>T</literal> containing
8120 two unboxed floats. This may not always be an optimisation: if
8121 the <function>T</function> constructor is scrutinised and the
8122 floats passed to a non-strict function for example, they will
8123 have to be reboxed (this is done automatically by the
8126 <para>Unpacking constructor fields should only be used in
8127 conjunction with <option>-O</option>, in order to expose
8128 unfoldings to the compiler so the reboxing can be removed as
8129 often as possible. For example:</para>
8133 f (T f1 f2) = f1 + f2
8136 <para>The compiler will avoid reboxing <function>f1</function>
8137 and <function>f2</function> by inlining <function>+</function>
8138 on floats, but only when <option>-O</option> is on.</para>
8140 <para>Any single-constructor data is eligible for unpacking; for
8144 data T = T {-# UNPACK #-} !(Int,Int)
8147 <para>will store the two <literal>Int</literal>s directly in the
8148 <function>T</function> constructor, by flattening the pair.
8149 Multi-level unpacking is also supported:
8152 data T = T {-# UNPACK #-} !S
8153 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8156 will store two unboxed <literal>Int#</literal>s
8157 directly in the <function>T</function> constructor. The
8158 unpacker can see through newtypes, too.</para>
8160 <para>See also the <option>-funbox-strict-fields</option> flag,
8161 which essentially has the effect of adding
8162 <literal>{-# UNPACK #-}</literal> to every strict
8163 constructor field.</para>
8166 <sect2 id="source-pragma">
8167 <title>SOURCE pragma</title>
8169 <indexterm><primary>SOURCE</primary></indexterm>
8170 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8171 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8177 <!-- ======================= REWRITE RULES ======================== -->
8179 <sect1 id="rewrite-rules">
8180 <title>Rewrite rules
8182 <indexterm><primary>RULES pragma</primary></indexterm>
8183 <indexterm><primary>pragma, RULES</primary></indexterm>
8184 <indexterm><primary>rewrite rules</primary></indexterm></title>
8187 The programmer can specify rewrite rules as part of the source program
8193 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8198 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8199 If you need more information, then <option>-ddump-rule-firings</option> shows you
8200 each individual rule firing and <option>-ddump-rule-rewrites</option> also shows what the code looks like before and after the rewrite.
8204 <title>Syntax</title>
8207 From a syntactic point of view:
8213 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8214 may be generated by the layout rule).
8220 The layout rule applies in a pragma.
8221 Currently no new indentation level
8222 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8223 you must lay out the starting in the same column as the enclosing definitions.
8226 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8227 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8230 Furthermore, the closing <literal>#-}</literal>
8231 should start in a column to the right of the opening <literal>{-#</literal>.
8237 Each rule has a name, enclosed in double quotes. The name itself has
8238 no significance at all. It is only used when reporting how many times the rule fired.
8244 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8245 immediately after the name of the rule. Thus:
8248 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8251 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8252 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8261 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8262 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8263 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8264 by spaces, just like in a type <literal>forall</literal>.
8270 A pattern variable may optionally have a type signature.
8271 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8272 For example, here is the <literal>foldr/build</literal> rule:
8275 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8276 foldr k z (build g) = g k z
8279 Since <function>g</function> has a polymorphic type, it must have a type signature.
8286 The left hand side of a rule must consist of a top-level variable applied
8287 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8290 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8291 "wrong2" forall f. f True = True
8294 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8301 A rule does not need to be in the same module as (any of) the
8302 variables it mentions, though of course they need to be in scope.
8308 All rules are implicitly exported from the module, and are therefore
8309 in force in any module that imports the module that defined the rule, directly
8310 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8311 in force when compiling A.) The situation is very similar to that for instance
8319 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8320 any other flag settings. Furthermore, inside a RULE, the language extension
8321 <option>-XScopedTypeVariables</option> is automatically enabled; see
8322 <xref linkend="scoped-type-variables"/>.
8328 Like other pragmas, RULE pragmas are always checked for scope errors, and
8329 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8330 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8331 if the <option>-fenable-rewrite-rules</option> flag is
8332 on (see <xref linkend="rule-semantics"/>).
8341 <sect2 id="rule-semantics">
8342 <title>Semantics</title>
8345 From a semantic point of view:
8350 Rules are enabled (that is, used during optimisation)
8351 by the <option>-fenable-rewrite-rules</option> flag.
8352 This flag is implied by <option>-O</option>, and may be switched
8353 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8354 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8355 may not do what you expect, though, because without <option>-O</option> GHC
8356 ignores all optimisation information in interface files;
8357 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8358 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8359 has no effect on parsing or typechecking.
8365 Rules are regarded as left-to-right rewrite rules.
8366 When GHC finds an expression that is a substitution instance of the LHS
8367 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8368 By "a substitution instance" we mean that the LHS can be made equal to the
8369 expression by substituting for the pattern variables.
8376 GHC makes absolutely no attempt to verify that the LHS and RHS
8377 of a rule have the same meaning. That is undecidable in general, and
8378 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8385 GHC makes no attempt to make sure that the rules are confluent or
8386 terminating. For example:
8389 "loop" forall x y. f x y = f y x
8392 This rule will cause the compiler to go into an infinite loop.
8399 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8405 GHC currently uses a very simple, syntactic, matching algorithm
8406 for matching a rule LHS with an expression. It seeks a substitution
8407 which makes the LHS and expression syntactically equal modulo alpha
8408 conversion. The pattern (rule), but not the expression, is eta-expanded if
8409 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8410 But not beta conversion (that's called higher-order matching).
8414 Matching is carried out on GHC's intermediate language, which includes
8415 type abstractions and applications. So a rule only matches if the
8416 types match too. See <xref linkend="rule-spec"/> below.
8422 GHC keeps trying to apply the rules as it optimises the program.
8423 For example, consider:
8432 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8433 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8434 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8435 not be substituted, and the rule would not fire.
8445 <sect2 id="conlike">
8446 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8449 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8450 results. Consider this (artificial) example
8456 {-# RULES "f" f True = False #-}
8458 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8463 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8465 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8466 would have been a better chance that <literal>f</literal>'s RULE might fire.
8469 The way to get predictable behaviour is to use a NOINLINE
8470 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8471 that it is not inlined until its RULEs have had a chance to fire.
8474 GHC is very cautious about duplicating work. For example, consider
8476 f k z xs = let xs = build g
8477 in ...(foldr k z xs)...sum xs...
8478 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8480 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8481 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8482 duplicated if the rule fired.
8485 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8486 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8487 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8489 {-# INLINE[1] CONLIKE f #-}
8490 f x = <replaceable>blah</replaceable>
8492 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8493 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8494 should be considered cheap enough to duplicate, if such a duplication would make rule
8495 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8496 have such a property.)
8497 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8498 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8499 not going to be inlined before the rule has a chance to fire.
8504 <title>List fusion</title>
8507 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8508 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8509 intermediate list should be eliminated entirely.
8513 The following are good producers:
8525 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8531 Explicit lists (e.g. <literal>[True, False]</literal>)
8537 The cons constructor (e.g <literal>3:4:[]</literal>)
8543 <function>++</function>
8549 <function>map</function>
8555 <function>take</function>, <function>filter</function>
8561 <function>iterate</function>, <function>repeat</function>
8567 <function>zip</function>, <function>zipWith</function>
8576 The following are good consumers:
8588 <function>array</function> (on its second argument)
8594 <function>++</function> (on its first argument)
8600 <function>foldr</function>
8606 <function>map</function>
8612 <function>take</function>, <function>filter</function>
8618 <function>concat</function>
8624 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8630 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8631 will fuse with one but not the other)
8637 <function>partition</function>
8643 <function>head</function>
8649 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8655 <function>sequence_</function>
8661 <function>msum</function>
8667 <function>sortBy</function>
8676 So, for example, the following should generate no intermediate lists:
8679 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8685 This list could readily be extended; if there are Prelude functions that you use
8686 a lot which are not included, please tell us.
8690 If you want to write your own good consumers or producers, look at the
8691 Prelude definitions of the above functions to see how to do so.
8696 <sect2 id="rule-spec">
8697 <title>Specialisation
8701 Rewrite rules can be used to get the same effect as a feature
8702 present in earlier versions of GHC.
8703 For example, suppose that:
8706 genericLookup :: Ord a => Table a b -> a -> b
8707 intLookup :: Table Int b -> Int -> b
8710 where <function>intLookup</function> is an implementation of
8711 <function>genericLookup</function> that works very fast for
8712 keys of type <literal>Int</literal>. You might wish
8713 to tell GHC to use <function>intLookup</function> instead of
8714 <function>genericLookup</function> whenever the latter was called with
8715 type <literal>Table Int b -> Int -> b</literal>.
8716 It used to be possible to write
8719 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8722 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8725 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8728 This slightly odd-looking rule instructs GHC to replace
8729 <function>genericLookup</function> by <function>intLookup</function>
8730 <emphasis>whenever the types match</emphasis>.
8731 What is more, this rule does not need to be in the same
8732 file as <function>genericLookup</function>, unlike the
8733 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8734 have an original definition available to specialise).
8737 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8738 <function>intLookup</function> really behaves as a specialised version
8739 of <function>genericLookup</function>!!!</para>
8741 <para>An example in which using <literal>RULES</literal> for
8742 specialisation will Win Big:
8745 toDouble :: Real a => a -> Double
8746 toDouble = fromRational . toRational
8748 {-# RULES "toDouble/Int" toDouble = i2d #-}
8749 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8752 The <function>i2d</function> function is virtually one machine
8753 instruction; the default conversion—via an intermediate
8754 <literal>Rational</literal>—is obscenely expensive by
8760 <sect2 id="controlling-rules">
8761 <title>Controlling what's going on in rewrite rules</title>
8769 Use <option>-ddump-rules</option> to see the rules that are defined
8770 <emphasis>in this module</emphasis>.
8771 This includes rules generated by the specialisation pass, but excludes
8772 rules imported from other modules.
8778 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8779 If you add <option>-dppr-debug</option> you get a more detailed listing.
8785 Use <option>-ddump-rule-firings</option> or <option>-ddump-rule-rewrites</option>
8786 to see in great detail what rules are being fired.
8787 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8793 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8796 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8797 {-# INLINE build #-}
8801 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8802 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8803 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8804 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8811 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8812 see how to write rules that will do fusion and yet give an efficient
8813 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8823 <sect2 id="core-pragma">
8824 <title>CORE pragma</title>
8826 <indexterm><primary>CORE pragma</primary></indexterm>
8827 <indexterm><primary>pragma, CORE</primary></indexterm>
8828 <indexterm><primary>core, annotation</primary></indexterm>
8831 The external core format supports <quote>Note</quote> annotations;
8832 the <literal>CORE</literal> pragma gives a way to specify what these
8833 should be in your Haskell source code. Syntactically, core
8834 annotations are attached to expressions and take a Haskell string
8835 literal as an argument. The following function definition shows an
8839 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8842 Semantically, this is equivalent to:
8850 However, when external core is generated (via
8851 <option>-fext-core</option>), there will be Notes attached to the
8852 expressions <function>show</function> and <varname>x</varname>.
8853 The core function declaration for <function>f</function> is:
8857 f :: %forall a . GHCziShow.ZCTShow a ->
8858 a -> GHCziBase.ZMZN GHCziBase.Char =
8859 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8861 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8863 (tpl1::GHCziBase.Int ->
8865 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8867 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8868 (tpl3::GHCziBase.ZMZN a ->
8869 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8877 Here, we can see that the function <function>show</function> (which
8878 has been expanded out to a case expression over the Show dictionary)
8879 has a <literal>%note</literal> attached to it, as does the
8880 expression <varname>eta</varname> (which used to be called
8881 <varname>x</varname>).
8888 <sect1 id="special-ids">
8889 <title>Special built-in functions</title>
8890 <para>GHC has a few built-in functions with special behaviour. These
8891 are now described in the module <ulink
8892 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8893 in the library documentation.
8897 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Ainline"><literal>inline</literal></ulink>
8898 allows control over inlining on a per-call-site basis.
8901 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Alazy"><literal>lazy</literal></ulink>
8902 restrains the strictness analyser.
8905 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3AunsafeCoerce%23"><literal>lazy</literal></ulink>
8906 allows you to fool the type checker.
8913 <sect1 id="generic-classes">
8914 <title>Generic classes</title>
8917 The ideas behind this extension are described in detail in "Derivable type classes",
8918 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8919 An example will give the idea:
8927 fromBin :: [Int] -> (a, [Int])
8929 toBin {| Unit |} Unit = []
8930 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8931 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8932 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8934 fromBin {| Unit |} bs = (Unit, bs)
8935 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8936 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8937 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8938 (y,bs'') = fromBin bs'
8941 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8942 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8943 which are defined thus in the library module <literal>Generics</literal>:
8947 data a :+: b = Inl a | Inr b
8948 data a :*: b = a :*: b
8951 Now you can make a data type into an instance of Bin like this:
8953 instance (Bin a, Bin b) => Bin (a,b)
8954 instance Bin a => Bin [a]
8956 That is, just leave off the "where" clause. Of course, you can put in the
8957 where clause and over-ride whichever methods you please.
8961 <title> Using generics </title>
8962 <para>To use generics you need to</para>
8965 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8966 <option>-XGenerics</option> (to generate extra per-data-type code),
8967 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8971 <para>Import the module <literal>Generics</literal> from the
8972 <literal>lang</literal> package. This import brings into
8973 scope the data types <literal>Unit</literal>,
8974 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8975 don't need this import if you don't mention these types
8976 explicitly; for example, if you are simply giving instance
8977 declarations.)</para>
8982 <sect2> <title> Changes wrt the paper </title>
8984 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8985 can be written infix (indeed, you can now use
8986 any operator starting in a colon as an infix type constructor). Also note that
8987 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8988 Finally, note that the syntax of the type patterns in the class declaration
8989 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8990 alone would ambiguous when they appear on right hand sides (an extension we
8991 anticipate wanting).
8995 <sect2> <title>Terminology and restrictions</title>
8997 Terminology. A "generic default method" in a class declaration
8998 is one that is defined using type patterns as above.
8999 A "polymorphic default method" is a default method defined as in Haskell 98.
9000 A "generic class declaration" is a class declaration with at least one
9001 generic default method.
9009 Alas, we do not yet implement the stuff about constructor names and
9016 A generic class can have only one parameter; you can't have a generic
9017 multi-parameter class.
9023 A default method must be defined entirely using type patterns, or entirely
9024 without. So this is illegal:
9027 op :: a -> (a, Bool)
9028 op {| Unit |} Unit = (Unit, True)
9031 However it is perfectly OK for some methods of a generic class to have
9032 generic default methods and others to have polymorphic default methods.
9038 The type variable(s) in the type pattern for a generic method declaration
9039 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:
9043 op {| p :*: q |} (x :*: y) = op (x :: p)
9051 The type patterns in a generic default method must take one of the forms:
9057 where "a" and "b" are type variables. Furthermore, all the type patterns for
9058 a single type constructor (<literal>:*:</literal>, say) must be identical; they
9059 must use the same type variables. So this is illegal:
9063 op {| a :+: b |} (Inl x) = True
9064 op {| p :+: q |} (Inr y) = False
9066 The type patterns must be identical, even in equations for different methods of the class.
9067 So this too is illegal:
9071 op1 {| a :*: b |} (x :*: y) = True
9074 op2 {| p :*: q |} (x :*: y) = False
9076 (The reason for this restriction is that we gather all the equations for a particular type constructor
9077 into a single generic instance declaration.)
9083 A generic method declaration must give a case for each of the three type constructors.
9089 The type for a generic method can be built only from:
9091 <listitem> <para> Function arrows </para> </listitem>
9092 <listitem> <para> Type variables </para> </listitem>
9093 <listitem> <para> Tuples </para> </listitem>
9094 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
9096 Here are some example type signatures for generic methods:
9099 op2 :: Bool -> (a,Bool)
9100 op3 :: [Int] -> a -> a
9103 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
9107 This restriction is an implementation restriction: we just haven't got around to
9108 implementing the necessary bidirectional maps over arbitrary type constructors.
9109 It would be relatively easy to add specific type constructors, such as Maybe and list,
9110 to the ones that are allowed.</para>
9115 In an instance declaration for a generic class, the idea is that the compiler
9116 will fill in the methods for you, based on the generic templates. However it can only
9121 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
9126 No constructor of the instance type has unboxed fields.
9130 (Of course, these things can only arise if you are already using GHC extensions.)
9131 However, you can still give an instance declarations for types which break these rules,
9132 provided you give explicit code to override any generic default methods.
9140 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9141 what the compiler does with generic declarations.
9146 <sect2> <title> Another example </title>
9148 Just to finish with, here's another example I rather like:
9152 nCons {| Unit |} _ = 1
9153 nCons {| a :*: b |} _ = 1
9154 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9157 tag {| Unit |} _ = 1
9158 tag {| a :*: b |} _ = 1
9159 tag {| a :+: b |} (Inl x) = tag x
9160 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9166 <sect1 id="monomorphism">
9167 <title>Control over monomorphism</title>
9169 <para>GHC supports two flags that control the way in which generalisation is
9170 carried out at let and where bindings.
9174 <title>Switching off the dreaded Monomorphism Restriction</title>
9175 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9177 <para>Haskell's monomorphism restriction (see
9178 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9180 of the Haskell Report)
9181 can be completely switched off by
9182 <option>-XNoMonomorphismRestriction</option>.
9187 <title>Monomorphic pattern bindings</title>
9188 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9189 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9191 <para> As an experimental change, we are exploring the possibility of
9192 making pattern bindings monomorphic; that is, not generalised at all.
9193 A pattern binding is a binding whose LHS has no function arguments,
9194 and is not a simple variable. For example:
9196 f x = x -- Not a pattern binding
9197 f = \x -> x -- Not a pattern binding
9198 f :: Int -> Int = \x -> x -- Not a pattern binding
9200 (g,h) = e -- A pattern binding
9201 (f) = e -- A pattern binding
9202 [x] = e -- A pattern binding
9204 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9205 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
9214 ;;; Local Variables: ***
9215 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
9216 ;;; ispell-local-dictionary: "british" ***
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