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>GHC allows you to declare an algebraic data type by
2438 giving the type signatures of constructors explicitly. For example:
2442 Just :: a -> Maybe a
2444 The form is called a "GADT-style declaration"
2445 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2446 can only be declared using this form.</para>
2447 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2448 For example, these two declarations are equivalent:
2450 data Foo = forall a. MkFoo a (a -> Bool)
2451 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2454 <para>Any data type that can be declared in standard Haskell-98 syntax
2455 can also be declared using GADT-style syntax.
2456 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2457 they treat class constraints on the data constructors differently.
2458 Specifically, if the constructor is given a type-class context, that
2459 context is made available by pattern matching. For example:
2462 MkSet :: Eq a => [a] -> Set a
2464 makeSet :: Eq a => [a] -> Set a
2465 makeSet xs = MkSet (nub xs)
2467 insert :: a -> Set a -> Set a
2468 insert a (MkSet as) | a `elem` as = MkSet as
2469 | otherwise = MkSet (a:as)
2471 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2472 gives rise to a <literal>(Eq a)</literal>
2473 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2474 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2475 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2476 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2477 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2478 In the example, the equality dictionary is used to satisfy the equality constraint
2479 generated by the call to <literal>elem</literal>, so that the type of
2480 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2483 For example, one possible application is to reify dictionaries:
2485 data NumInst a where
2486 MkNumInst :: Num a => NumInst a
2488 intInst :: NumInst Int
2491 plus :: NumInst a -> a -> a -> a
2492 plus MkNumInst p q = p + q
2494 Here, a value of type <literal>NumInst a</literal> is equivalent
2495 to an explicit <literal>(Num a)</literal> dictionary.
2498 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2499 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2503 = Num a => MkNumInst (NumInst a)
2505 Notice that, unlike the situation when declaring an existential, there is
2506 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2507 data type's universally quantified type variable <literal>a</literal>.
2508 A constructor may have both universal and existential type variables: for example,
2509 the following two declarations are equivalent:
2512 = forall b. (Num a, Eq b) => MkT1 a b
2514 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2517 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2518 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2519 In Haskell 98 the definition
2521 data Eq a => Set' a = MkSet' [a]
2523 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2524 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2525 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2526 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2527 GHC's behaviour is much more useful, as well as much more intuitive.
2531 The rest of this section gives further details about GADT-style data
2536 The result type of each data constructor must begin with the type constructor being defined.
2537 If the result type of all constructors
2538 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2539 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2540 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2544 As with other type signatures, you can give a single signature for several data constructors.
2545 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2554 The type signature of
2555 each constructor is independent, and is implicitly universally quantified as usual.
2556 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2557 have no scope, and different constructors may have different universally-quantified type variables:
2559 data T a where -- The 'a' has no scope
2560 T1,T2 :: b -> T b -- Means forall b. b -> T b
2561 T3 :: T a -- Means forall a. T a
2566 A constructor signature may mention type class constraints, which can differ for
2567 different constructors. For example, this is fine:
2570 T1 :: Eq b => b -> b -> T b
2571 T2 :: (Show c, Ix c) => c -> [c] -> T c
2573 When patten matching, these constraints are made available to discharge constraints
2574 in the body of the match. For example:
2577 f (T1 x y) | x==y = "yes"
2581 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2582 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2583 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2587 Unlike a Haskell-98-style
2588 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2589 have no scope. Indeed, one can write a kind signature instead:
2591 data Set :: * -> * where ...
2593 or even a mixture of the two:
2595 data Bar a :: (* -> *) -> * where ...
2597 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2600 data Bar a (b :: * -> *) where ...
2606 You can use strictness annotations, in the obvious places
2607 in the constructor type:
2610 Lit :: !Int -> Term Int
2611 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2612 Pair :: Term a -> Term b -> Term (a,b)
2617 You can use a <literal>deriving</literal> clause on a GADT-style data type
2618 declaration. For example, these two declarations are equivalent
2620 data Maybe1 a where {
2621 Nothing1 :: Maybe1 a ;
2622 Just1 :: a -> Maybe1 a
2623 } deriving( Eq, Ord )
2625 data Maybe2 a = Nothing2 | Just2 a
2631 The type signature may have quantified type variables that do not appear
2635 MkFoo :: a -> (a->Bool) -> Foo
2638 Here the type variable <literal>a</literal> does not appear in the result type
2639 of either constructor.
2640 Although it is universally quantified in the type of the constructor, such
2641 a type variable is often called "existential".
2642 Indeed, the above declaration declares precisely the same type as
2643 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2645 The type may contain a class context too, of course:
2648 MkShowable :: Show a => a -> Showable
2653 You can use record syntax on a GADT-style data type declaration:
2657 Adult :: { name :: String, children :: [Person] } -> Person
2658 Child :: Show a => { name :: !String, funny :: a } -> Person
2660 As usual, for every constructor that has a field <literal>f</literal>, the type of
2661 field <literal>f</literal> must be the same (modulo alpha conversion).
2662 The <literal>Child</literal> constructor above shows that the signature
2663 may have a context, existentially-quantified variables, and strictness annotations,
2664 just as in the non-record case. (NB: the "type" that follows the double-colon
2665 is not really a type, because of the record syntax and strictness annotations.
2666 A "type" of this form can appear only in a constructor signature.)
2670 Record updates are allowed with GADT-style declarations,
2671 only fields that have the following property: the type of the field
2672 mentions no existential type variables.
2676 As in the case of existentials declared using the Haskell-98-like record syntax
2677 (<xref linkend="existential-records"/>),
2678 record-selector functions are generated only for those fields that have well-typed
2680 Here is the example of that section, in GADT-style syntax:
2682 data Counter a where
2683 NewCounter { _this :: self
2684 , _inc :: self -> self
2685 , _display :: self -> IO ()
2690 As before, only one selector function is generated here, that for <literal>tag</literal>.
2691 Nevertheless, you can still use all the field names in pattern matching and record construction.
2693 </itemizedlist></para>
2697 <title>Generalised Algebraic Data Types (GADTs)</title>
2699 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2700 by allowing constructors to have richer return types. Here is an example:
2703 Lit :: Int -> Term Int
2704 Succ :: Term Int -> Term Int
2705 IsZero :: Term Int -> Term Bool
2706 If :: Term Bool -> Term a -> Term a -> Term a
2707 Pair :: Term a -> Term b -> Term (a,b)
2709 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2710 case with ordinary data types. This generality allows us to
2711 write a well-typed <literal>eval</literal> function
2712 for these <literal>Terms</literal>:
2716 eval (Succ t) = 1 + eval t
2717 eval (IsZero t) = eval t == 0
2718 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2719 eval (Pair e1 e2) = (eval e1, eval e2)
2721 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2722 For example, in the right hand side of the equation
2727 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2728 A precise specification of the type rules is beyond what this user manual aspires to,
2729 but the design closely follows that described in
2731 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2732 unification-based type inference for GADTs</ulink>,
2734 The general principle is this: <emphasis>type refinement is only carried out
2735 based on user-supplied type annotations</emphasis>.
2736 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2737 and lots of obscure error messages will
2738 occur. However, the refinement is quite general. For example, if we had:
2740 eval :: Term a -> a -> a
2741 eval (Lit i) j = i+j
2743 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2744 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2745 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2748 These and many other examples are given in papers by Hongwei Xi, and
2749 Tim Sheard. There is a longer introduction
2750 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2752 <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
2753 may use different notation to that implemented in GHC.
2756 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2757 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2760 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2761 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2762 The result type of each constructor must begin with the type constructor being defined,
2763 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2764 For example, in the <literal>Term</literal> data
2765 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2766 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2771 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2772 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2773 whose result type is not just <literal>T a b</literal>.
2777 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2778 an ordinary data type.
2782 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2786 Lit { val :: Int } :: Term Int
2787 Succ { num :: Term Int } :: Term Int
2788 Pred { num :: Term Int } :: Term Int
2789 IsZero { arg :: Term Int } :: Term Bool
2790 Pair { arg1 :: Term a
2793 If { cnd :: Term Bool
2798 However, for GADTs there is the following additional constraint:
2799 every constructor that has a field <literal>f</literal> must have
2800 the same result type (modulo alpha conversion)
2801 Hence, in the above example, we cannot merge the <literal>num</literal>
2802 and <literal>arg</literal> fields above into a
2803 single name. Although their field types are both <literal>Term Int</literal>,
2804 their selector functions actually have different types:
2807 num :: Term Int -> Term Int
2808 arg :: Term Bool -> Term Int
2813 When pattern-matching against data constructors drawn from a GADT,
2814 for example in a <literal>case</literal> expression, the following rules apply:
2816 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2817 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2818 <listitem><para>The type of any free variable mentioned in any of
2819 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2821 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2822 way to ensure that a variable a rigid type is to give it a type signature.
2823 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2824 Simple unification-based type inference for GADTs
2825 </ulink>. The criteria implemented by GHC are given in the Appendix.
2835 <!-- ====================== End of Generalised algebraic data types ======================= -->
2837 <sect1 id="deriving">
2838 <title>Extensions to the "deriving" mechanism</title>
2840 <sect2 id="deriving-inferred">
2841 <title>Inferred context for deriving clauses</title>
2844 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2847 data T0 f a = MkT0 a deriving( Eq )
2848 data T1 f a = MkT1 (f a) deriving( Eq )
2849 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2851 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2853 instance Eq a => Eq (T0 f a) where ...
2854 instance Eq (f a) => Eq (T1 f a) where ...
2855 instance Eq (f (f a)) => Eq (T2 f a) where ...
2857 The first of these is obviously fine. The second is still fine, although less obviously.
2858 The third is not Haskell 98, and risks losing termination of instances.
2861 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2862 each constraint in the inferred instance context must consist only of type variables,
2863 with no repetitions.
2866 This rule is applied regardless of flags. If you want a more exotic context, you can write
2867 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2871 <sect2 id="stand-alone-deriving">
2872 <title>Stand-alone deriving declarations</title>
2875 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2877 data Foo a = Bar a | Baz String
2879 deriving instance Eq a => Eq (Foo a)
2881 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2882 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2883 Note the following points:
2886 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2887 exactly as you would in an ordinary instance declaration.
2888 (In contrast, in a <literal>deriving</literal> clause
2889 attached to a data type declaration, the context is inferred.)
2893 A <literal>deriving instance</literal> declaration
2894 must obey the same rules concerning form and termination as ordinary instance declarations,
2895 controlled by the same flags; see <xref linkend="instance-decls"/>.
2899 Unlike a <literal>deriving</literal>
2900 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2901 than the data type (assuming you also use
2902 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2905 data Foo a = Bar a | Baz String
2907 deriving instance Eq a => Eq (Foo [a])
2908 deriving instance Eq a => Eq (Foo (Maybe a))
2910 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2911 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2915 Unlike a <literal>deriving</literal>
2916 declaration attached to a <literal>data</literal> declaration,
2917 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2918 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2919 your problem. (GHC will show you the offending code if it has a type error.)
2920 The merit of this is that you can derive instances for GADTs and other exotic
2921 data types, providing only that the boilerplate code does indeed typecheck. For example:
2927 deriving instance Show (T a)
2929 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2930 data type declaration for <literal>T</literal>,
2931 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2932 the instance declaration using stand-alone deriving.
2937 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2938 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2941 newtype Foo a = MkFoo (State Int a)
2943 deriving instance MonadState Int Foo
2945 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2946 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2948 </itemizedlist></para>
2953 <sect2 id="deriving-typeable">
2954 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2957 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2958 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2959 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2960 classes <literal>Eq</literal>, <literal>Ord</literal>,
2961 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2964 GHC extends this list with several more classes that may be automatically derived:
2966 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2967 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2968 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2970 <para>An instance of <literal>Typeable</literal> can only be derived if the
2971 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2972 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2974 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2975 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2977 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2978 are used, and only <literal>Typeable1</literal> up to
2979 <literal>Typeable7</literal> are provided in the library.)
2980 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2981 class, whose kind suits that of the data type constructor, and
2982 then writing the data type instance by hand.
2986 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2987 the class <literal>Functor</literal>,
2988 defined in <literal>GHC.Base</literal>.
2991 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2992 the class <literal>Foldable</literal>,
2993 defined in <literal>Data.Foldable</literal>.
2996 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2997 the class <literal>Traversable</literal>,
2998 defined in <literal>Data.Traversable</literal>.
3001 In each case the appropriate class must be in scope before it
3002 can be mentioned in the <literal>deriving</literal> clause.
3006 <sect2 id="newtype-deriving">
3007 <title>Generalised derived instances for newtypes</title>
3010 When you define an abstract type using <literal>newtype</literal>, you may want
3011 the new type to inherit some instances from its representation. In
3012 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3013 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3014 other classes you have to write an explicit instance declaration. For
3015 example, if you define
3018 newtype Dollars = Dollars Int
3021 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3022 explicitly define an instance of <literal>Num</literal>:
3025 instance Num Dollars where
3026 Dollars a + Dollars b = Dollars (a+b)
3029 All the instance does is apply and remove the <literal>newtype</literal>
3030 constructor. It is particularly galling that, since the constructor
3031 doesn't appear at run-time, this instance declaration defines a
3032 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3033 dictionary, only slower!
3037 <sect3> <title> Generalising the deriving clause </title>
3039 GHC now permits such instances to be derived instead,
3040 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3043 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3046 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3047 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3048 derives an instance declaration of the form
3051 instance Num Int => Num Dollars
3054 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3058 We can also derive instances of constructor classes in a similar
3059 way. For example, suppose we have implemented state and failure monad
3060 transformers, such that
3063 instance Monad m => Monad (State s m)
3064 instance Monad m => Monad (Failure m)
3066 In Haskell 98, we can define a parsing monad by
3068 type Parser tok m a = State [tok] (Failure m) a
3071 which is automatically a monad thanks to the instance declarations
3072 above. With the extension, we can make the parser type abstract,
3073 without needing to write an instance of class <literal>Monad</literal>, via
3076 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3079 In this case the derived instance declaration is of the form
3081 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3084 Notice that, since <literal>Monad</literal> is a constructor class, the
3085 instance is a <emphasis>partial application</emphasis> of the new type, not the
3086 entire left hand side. We can imagine that the type declaration is
3087 "eta-converted" to generate the context of the instance
3092 We can even derive instances of multi-parameter classes, provided the
3093 newtype is the last class parameter. In this case, a ``partial
3094 application'' of the class appears in the <literal>deriving</literal>
3095 clause. For example, given the class
3098 class StateMonad s m | m -> s where ...
3099 instance Monad m => StateMonad s (State s m) where ...
3101 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3103 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3104 deriving (Monad, StateMonad [tok])
3107 The derived instance is obtained by completing the application of the
3108 class to the new type:
3111 instance StateMonad [tok] (State [tok] (Failure m)) =>
3112 StateMonad [tok] (Parser tok m)
3117 As a result of this extension, all derived instances in newtype
3118 declarations are treated uniformly (and implemented just by reusing
3119 the dictionary for the representation type), <emphasis>except</emphasis>
3120 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3121 the newtype and its representation.
3125 <sect3> <title> A more precise specification </title>
3127 Derived instance declarations are constructed as follows. Consider the
3128 declaration (after expansion of any type synonyms)
3131 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3137 The <literal>ci</literal> are partial applications of
3138 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3139 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3142 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3145 The type <literal>t</literal> is an arbitrary type.
3148 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3149 nor in the <literal>ci</literal>, and
3152 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3153 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3154 should not "look through" the type or its constructor. You can still
3155 derive these classes for a newtype, but it happens in the usual way, not
3156 via this new mechanism.
3159 Then, for each <literal>ci</literal>, the derived instance
3162 instance ci t => ci (T v1...vk)
3164 As an example which does <emphasis>not</emphasis> work, consider
3166 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3168 Here we cannot derive the instance
3170 instance Monad (State s m) => Monad (NonMonad m)
3173 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3174 and so cannot be "eta-converted" away. It is a good thing that this
3175 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3176 not, in fact, a monad --- for the same reason. Try defining
3177 <literal>>>=</literal> with the correct type: you won't be able to.
3181 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3182 important, since we can only derive instances for the last one. If the
3183 <literal>StateMonad</literal> class above were instead defined as
3186 class StateMonad m s | m -> s where ...
3189 then we would not have been able to derive an instance for the
3190 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3191 classes usually have one "main" parameter for which deriving new
3192 instances is most interesting.
3194 <para>Lastly, all of this applies only for classes other than
3195 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3196 and <literal>Data</literal>, for which the built-in derivation applies (section
3197 4.3.3. of the Haskell Report).
3198 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3199 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3200 the standard method is used or the one described here.)
3207 <!-- TYPE SYSTEM EXTENSIONS -->
3208 <sect1 id="type-class-extensions">
3209 <title>Class and instances declarations</title>
3211 <sect2 id="multi-param-type-classes">
3212 <title>Class declarations</title>
3215 This section, and the next one, documents GHC's type-class extensions.
3216 There's lots of background in the paper <ulink
3217 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3218 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3219 Jones, Erik Meijer).
3222 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3226 <title>Multi-parameter type classes</title>
3228 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3233 class Collection c a where
3234 union :: c a -> c a -> c a
3241 <sect3 id="superclass-rules">
3242 <title>The superclasses of a class declaration</title>
3245 In Haskell 98 the context of a class declaration (which introduces superclasses)
3246 must be simple; that is, each predicate must consist of a class applied to
3247 type variables. The flag <option>-XFlexibleContexts</option>
3248 (<xref linkend="flexible-contexts"/>)
3249 lifts this restriction,
3250 so that the only restriction on the context in a class declaration is
3251 that the class hierarchy must be acyclic. So these class declarations are OK:
3255 class Functor (m k) => FiniteMap m k where
3258 class (Monad m, Monad (t m)) => Transform t m where
3259 lift :: m a -> (t m) a
3265 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3266 of "acyclic" involves only the superclass relationships. For example,
3272 op :: D b => a -> b -> b
3275 class C a => D a where { ... }
3279 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3280 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3281 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3288 <sect3 id="class-method-types">
3289 <title>Class method types</title>
3292 Haskell 98 prohibits class method types to mention constraints on the
3293 class type variable, thus:
3296 fromList :: [a] -> s a
3297 elem :: Eq a => a -> s a -> Bool
3299 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3300 contains the constraint <literal>Eq a</literal>, constrains only the
3301 class type variable (in this case <literal>a</literal>).
3302 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3309 <sect2 id="functional-dependencies">
3310 <title>Functional dependencies
3313 <para> Functional dependencies are implemented as described by Mark Jones
3314 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3315 In Proceedings of the 9th European Symposium on Programming,
3316 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3320 Functional dependencies are introduced by a vertical bar in the syntax of a
3321 class declaration; e.g.
3323 class (Monad m) => MonadState s m | m -> s where ...
3325 class Foo a b c | a b -> c where ...
3327 There should be more documentation, but there isn't (yet). Yell if you need it.
3330 <sect3><title>Rules for functional dependencies </title>
3332 In a class declaration, all of the class type variables must be reachable (in the sense
3333 mentioned in <xref linkend="flexible-contexts"/>)
3334 from the free variables of each method type.
3338 class Coll s a where
3340 insert :: s -> a -> s
3343 is not OK, because the type of <literal>empty</literal> doesn't mention
3344 <literal>a</literal>. Functional dependencies can make the type variable
3347 class Coll s a | s -> a where
3349 insert :: s -> a -> s
3352 Alternatively <literal>Coll</literal> might be rewritten
3355 class Coll s a where
3357 insert :: s a -> a -> s a
3361 which makes the connection between the type of a collection of
3362 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3363 Occasionally this really doesn't work, in which case you can split the
3371 class CollE s => Coll s a where
3372 insert :: s -> a -> s
3379 <title>Background on functional dependencies</title>
3381 <para>The following description of the motivation and use of functional dependencies is taken
3382 from the Hugs user manual, reproduced here (with minor changes) by kind
3383 permission of Mark Jones.
3386 Consider the following class, intended as part of a
3387 library for collection types:
3389 class Collects e ce where
3391 insert :: e -> ce -> ce
3392 member :: e -> ce -> Bool
3394 The type variable e used here represents the element type, while ce is the type
3395 of the container itself. Within this framework, we might want to define
3396 instances of this class for lists or characteristic functions (both of which
3397 can be used to represent collections of any equality type), bit sets (which can
3398 be used to represent collections of characters), or hash tables (which can be
3399 used to represent any collection whose elements have a hash function). Omitting
3400 standard implementation details, this would lead to the following declarations:
3402 instance Eq e => Collects e [e] where ...
3403 instance Eq e => Collects e (e -> Bool) where ...
3404 instance Collects Char BitSet where ...
3405 instance (Hashable e, Collects a ce)
3406 => Collects e (Array Int ce) where ...
3408 All this looks quite promising; we have a class and a range of interesting
3409 implementations. Unfortunately, there are some serious problems with the class
3410 declaration. First, the empty function has an ambiguous type:
3412 empty :: Collects e ce => ce
3414 By "ambiguous" we mean that there is a type variable e that appears on the left
3415 of the <literal>=></literal> symbol, but not on the right. The problem with
3416 this is that, according to the theoretical foundations of Haskell overloading,
3417 we cannot guarantee a well-defined semantics for any term with an ambiguous
3421 We can sidestep this specific problem by removing the empty member from the
3422 class declaration. However, although the remaining members, insert and member,
3423 do not have ambiguous types, we still run into problems when we try to use
3424 them. For example, consider the following two functions:
3426 f x y = insert x . insert y
3429 for which GHC infers the following types:
3431 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3432 g :: (Collects Bool c, Collects Char c) => c -> c
3434 Notice that the type for f allows the two parameters x and y to be assigned
3435 different types, even though it attempts to insert each of the two values, one
3436 after the other, into the same collection. If we're trying to model collections
3437 that contain only one type of value, then this is clearly an inaccurate
3438 type. Worse still, the definition for g is accepted, without causing a type
3439 error. As a result, the error in this code will not be flagged at the point
3440 where it appears. Instead, it will show up only when we try to use g, which
3441 might even be in a different module.
3444 <sect4><title>An attempt to use constructor classes</title>
3447 Faced with the problems described above, some Haskell programmers might be
3448 tempted to use something like the following version of the class declaration:
3450 class Collects e c where
3452 insert :: e -> c e -> c e
3453 member :: e -> c e -> Bool
3455 The key difference here is that we abstract over the type constructor c that is
3456 used to form the collection type c e, and not over that collection type itself,
3457 represented by ce in the original class declaration. This avoids the immediate
3458 problems that we mentioned above: empty has type <literal>Collects e c => c
3459 e</literal>, which is not ambiguous.
3462 The function f from the previous section has a more accurate type:
3464 f :: (Collects e c) => e -> e -> c e -> c e
3466 The function g from the previous section is now rejected with a type error as
3467 we would hope because the type of f does not allow the two arguments to have
3469 This, then, is an example of a multiple parameter class that does actually work
3470 quite well in practice, without ambiguity problems.
3471 There is, however, a catch. This version of the Collects class is nowhere near
3472 as general as the original class seemed to be: only one of the four instances
3473 for <literal>Collects</literal>
3474 given above can be used with this version of Collects because only one of
3475 them---the instance for lists---has a collection type that can be written in
3476 the form c e, for some type constructor c, and element type e.
3480 <sect4><title>Adding functional dependencies</title>
3483 To get a more useful version of the Collects class, Hugs provides a mechanism
3484 that allows programmers to specify dependencies between the parameters of a
3485 multiple parameter class (For readers with an interest in theoretical
3486 foundations and previous work: The use of dependency information can be seen
3487 both as a generalization of the proposal for `parametric type classes' that was
3488 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3489 later framework for "improvement" of qualified types. The
3490 underlying ideas are also discussed in a more theoretical and abstract setting
3491 in a manuscript [implparam], where they are identified as one point in a
3492 general design space for systems of implicit parameterization.).
3494 To start with an abstract example, consider a declaration such as:
3496 class C a b where ...
3498 which tells us simply that C can be thought of as a binary relation on types
3499 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3500 included in the definition of classes to add information about dependencies
3501 between parameters, as in the following examples:
3503 class D a b | a -> b where ...
3504 class E a b | a -> b, b -> a where ...
3506 The notation <literal>a -> b</literal> used here between the | and where
3507 symbols --- not to be
3508 confused with a function type --- indicates that the a parameter uniquely
3509 determines the b parameter, and might be read as "a determines b." Thus D is
3510 not just a relation, but actually a (partial) function. Similarly, from the two
3511 dependencies that are included in the definition of E, we can see that E
3512 represents a (partial) one-one mapping between types.
3515 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3516 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3517 m>=0, meaning that the y parameters are uniquely determined by the x
3518 parameters. Spaces can be used as separators if more than one variable appears
3519 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3520 annotated with multiple dependencies using commas as separators, as in the
3521 definition of E above. Some dependencies that we can write in this notation are
3522 redundant, and will be rejected because they don't serve any useful
3523 purpose, and may instead indicate an error in the program. Examples of
3524 dependencies like this include <literal>a -> a </literal>,
3525 <literal>a -> a a </literal>,
3526 <literal>a -> </literal>, etc. There can also be
3527 some redundancy if multiple dependencies are given, as in
3528 <literal>a->b</literal>,
3529 <literal>b->c </literal>, <literal>a->c </literal>, and
3530 in which some subset implies the remaining dependencies. Examples like this are
3531 not treated as errors. Note that dependencies appear only in class
3532 declarations, and not in any other part of the language. In particular, the
3533 syntax for instance declarations, class constraints, and types is completely
3537 By including dependencies in a class declaration, we provide a mechanism for
3538 the programmer to specify each multiple parameter class more precisely. The
3539 compiler, on the other hand, is responsible for ensuring that the set of
3540 instances that are in scope at any given point in the program is consistent
3541 with any declared dependencies. For example, the following pair of instance
3542 declarations cannot appear together in the same scope because they violate the
3543 dependency for D, even though either one on its own would be acceptable:
3545 instance D Bool Int where ...
3546 instance D Bool Char where ...
3548 Note also that the following declaration is not allowed, even by itself:
3550 instance D [a] b where ...
3552 The problem here is that this instance would allow one particular choice of [a]
3553 to be associated with more than one choice for b, which contradicts the
3554 dependency specified in the definition of D. More generally, this means that,
3555 in any instance of the form:
3557 instance D t s where ...
3559 for some particular types t and s, the only variables that can appear in s are
3560 the ones that appear in t, and hence, if the type t is known, then s will be
3561 uniquely determined.
3564 The benefit of including dependency information is that it allows us to define
3565 more general multiple parameter classes, without ambiguity problems, and with
3566 the benefit of more accurate types. To illustrate this, we return to the
3567 collection class example, and annotate the original definition of <literal>Collects</literal>
3568 with a simple dependency:
3570 class Collects e ce | ce -> e where
3572 insert :: e -> ce -> ce
3573 member :: e -> ce -> Bool
3575 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3576 determined by the type of the collection ce. Note that both parameters of
3577 Collects are of kind *; there are no constructor classes here. Note too that
3578 all of the instances of Collects that we gave earlier can be used
3579 together with this new definition.
3582 What about the ambiguity problems that we encountered with the original
3583 definition? The empty function still has type Collects e ce => ce, but it is no
3584 longer necessary to regard that as an ambiguous type: Although the variable e
3585 does not appear on the right of the => symbol, the dependency for class
3586 Collects tells us that it is uniquely determined by ce, which does appear on
3587 the right of the => symbol. Hence the context in which empty is used can still
3588 give enough information to determine types for both ce and e, without
3589 ambiguity. More generally, we need only regard a type as ambiguous if it
3590 contains a variable on the left of the => that is not uniquely determined
3591 (either directly or indirectly) by the variables on the right.
3594 Dependencies also help to produce more accurate types for user defined
3595 functions, and hence to provide earlier detection of errors, and less cluttered
3596 types for programmers to work with. Recall the previous definition for a
3599 f x y = insert x y = insert x . insert y
3601 for which we originally obtained a type:
3603 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3605 Given the dependency information that we have for Collects, however, we can
3606 deduce that a and b must be equal because they both appear as the second
3607 parameter in a Collects constraint with the same first parameter c. Hence we
3608 can infer a shorter and more accurate type for f:
3610 f :: (Collects a c) => a -> a -> c -> c
3612 In a similar way, the earlier definition of g will now be flagged as a type error.
3615 Although we have given only a few examples here, it should be clear that the
3616 addition of dependency information can help to make multiple parameter classes
3617 more useful in practice, avoiding ambiguity problems, and allowing more general
3618 sets of instance declarations.
3624 <sect2 id="instance-decls">
3625 <title>Instance declarations</title>
3627 <para>An instance declaration has the form
3629 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 ...
3631 The part before the "<literal>=></literal>" is the
3632 <emphasis>context</emphasis>, while the part after the
3633 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3636 <sect3 id="flexible-instance-head">
3637 <title>Relaxed rules for the instance head</title>
3640 In Haskell 98 the head of an instance declaration
3641 must be of the form <literal>C (T a1 ... an)</literal>, where
3642 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3643 and the <literal>a1 ... an</literal> are distinct type variables.
3644 GHC relaxes these rules in two ways.
3648 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3649 declaration to mention arbitrary nested types.
3650 For example, this becomes a legal instance declaration
3652 instance C (Maybe Int) where ...
3654 See also the <link linkend="instance-overlap">rules on overlap</link>.
3657 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3658 synonyms. As always, using a type synonym is just shorthand for
3659 writing the RHS of the type synonym definition. For example:
3663 type Point = (Int,Int)
3664 instance C Point where ...
3665 instance C [Point] where ...
3669 is legal. However, if you added
3673 instance C (Int,Int) where ...
3677 as well, then the compiler will complain about the overlapping
3678 (actually, identical) instance declarations. As always, type synonyms
3679 must be fully applied. You cannot, for example, write:
3683 instance Monad P where ...
3691 <sect3 id="instance-rules">
3692 <title>Relaxed rules for instance contexts</title>
3694 <para>In Haskell 98, the assertions in the context of the instance declaration
3695 must be of the form <literal>C a</literal> where <literal>a</literal>
3696 is a type variable that occurs in the head.
3700 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3701 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3702 With this flag the context of the instance declaration can each consist of arbitrary
3703 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3707 The Paterson Conditions: for each assertion in the context
3709 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3710 <listitem><para>The assertion has fewer constructors and variables (taken together
3711 and counting repetitions) than the head</para></listitem>
3715 <listitem><para>The Coverage Condition. For each functional dependency,
3716 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3717 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3718 every type variable in
3719 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3720 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3721 substitution mapping each type variable in the class declaration to the
3722 corresponding type in the instance declaration.
3725 These restrictions ensure that context reduction terminates: each reduction
3726 step makes the problem smaller by at least one
3727 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3728 if you give the <option>-XUndecidableInstances</option>
3729 flag (<xref linkend="undecidable-instances"/>).
3730 You can find lots of background material about the reason for these
3731 restrictions in the paper <ulink
3732 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3733 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3736 For example, these are OK:
3738 instance C Int [a] -- Multiple parameters
3739 instance Eq (S [a]) -- Structured type in head
3741 -- Repeated type variable in head
3742 instance C4 a a => C4 [a] [a]
3743 instance Stateful (ST s) (MutVar s)
3745 -- Head can consist of type variables only
3747 instance (Eq a, Show b) => C2 a b
3749 -- Non-type variables in context
3750 instance Show (s a) => Show (Sized s a)
3751 instance C2 Int a => C3 Bool [a]
3752 instance C2 Int a => C3 [a] b
3756 -- Context assertion no smaller than head
3757 instance C a => C a where ...
3758 -- (C b b) has more more occurrences of b than the head
3759 instance C b b => Foo [b] where ...
3764 The same restrictions apply to instances generated by
3765 <literal>deriving</literal> clauses. Thus the following is accepted:
3767 data MinHeap h a = H a (h a)
3770 because the derived instance
3772 instance (Show a, Show (h a)) => Show (MinHeap h a)
3774 conforms to the above rules.
3778 A useful idiom permitted by the above rules is as follows.
3779 If one allows overlapping instance declarations then it's quite
3780 convenient to have a "default instance" declaration that applies if
3781 something more specific does not:
3789 <sect3 id="undecidable-instances">
3790 <title>Undecidable instances</title>
3793 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3794 For example, sometimes you might want to use the following to get the
3795 effect of a "class synonym":
3797 class (C1 a, C2 a, C3 a) => C a where { }
3799 instance (C1 a, C2 a, C3 a) => C a where { }
3801 This allows you to write shorter signatures:
3807 f :: (C1 a, C2 a, C3 a) => ...
3809 The restrictions on functional dependencies (<xref
3810 linkend="functional-dependencies"/>) are particularly troublesome.
3811 It is tempting to introduce type variables in the context that do not appear in
3812 the head, something that is excluded by the normal rules. For example:
3814 class HasConverter a b | a -> b where
3817 data Foo a = MkFoo a
3819 instance (HasConverter a b,Show b) => Show (Foo a) where
3820 show (MkFoo value) = show (convert value)
3822 This is dangerous territory, however. Here, for example, is a program that would make the
3827 instance F [a] [[a]]
3828 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3830 Similarly, it can be tempting to lift the coverage condition:
3832 class Mul a b c | a b -> c where
3833 (.*.) :: a -> b -> c
3835 instance Mul Int Int Int where (.*.) = (*)
3836 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3837 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3839 The third instance declaration does not obey the coverage condition;
3840 and indeed the (somewhat strange) definition:
3842 f = \ b x y -> if b then x .*. [y] else y
3844 makes instance inference go into a loop, because it requires the constraint
3845 <literal>(Mul a [b] b)</literal>.
3848 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3849 the experimental flag <option>-XUndecidableInstances</option>
3850 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3851 both the Paterson Conditions and the Coverage Condition
3852 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3853 fixed-depth recursion stack. If you exceed the stack depth you get a
3854 sort of backtrace, and the opportunity to increase the stack depth
3855 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3861 <sect3 id="instance-overlap">
3862 <title>Overlapping instances</title>
3864 In general, <emphasis>GHC requires that that it be unambiguous which instance
3866 should be used to resolve a type-class constraint</emphasis>. This behaviour
3867 can be modified by two flags: <option>-XOverlappingInstances</option>
3868 <indexterm><primary>-XOverlappingInstances
3869 </primary></indexterm>
3870 and <option>-XIncoherentInstances</option>
3871 <indexterm><primary>-XIncoherentInstances
3872 </primary></indexterm>, as this section discusses. Both these
3873 flags are dynamic flags, and can be set on a per-module basis, using
3874 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3876 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3877 it tries to match every instance declaration against the
3879 by instantiating the head of the instance declaration. For example, consider
3882 instance context1 => C Int a where ... -- (A)
3883 instance context2 => C a Bool where ... -- (B)
3884 instance context3 => C Int [a] where ... -- (C)
3885 instance context4 => C Int [Int] where ... -- (D)
3887 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3888 but (C) and (D) do not. When matching, GHC takes
3889 no account of the context of the instance declaration
3890 (<literal>context1</literal> etc).
3891 GHC's default behaviour is that <emphasis>exactly one instance must match the
3892 constraint it is trying to resolve</emphasis>.
3893 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3894 including both declarations (A) and (B), say); an error is only reported if a
3895 particular constraint matches more than one.
3899 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3900 more than one instance to match, provided there is a most specific one. For
3901 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3902 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3903 most-specific match, the program is rejected.
3906 However, GHC is conservative about committing to an overlapping instance. For example:
3911 Suppose that from the RHS of <literal>f</literal> we get the constraint
3912 <literal>C Int [b]</literal>. But
3913 GHC does not commit to instance (C), because in a particular
3914 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3915 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3916 So GHC rejects the program.
3917 (If you add the flag <option>-XIncoherentInstances</option>,
3918 GHC will instead pick (C), without complaining about
3919 the problem of subsequent instantiations.)
3922 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3923 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3924 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3925 it instead. In this case, GHC will refrain from
3926 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3927 as before) but, rather than rejecting the program, it will infer the type
3929 f :: C Int [b] => [b] -> [b]
3931 That postpones the question of which instance to pick to the
3932 call site for <literal>f</literal>
3933 by which time more is known about the type <literal>b</literal>.
3934 You can write this type signature yourself if you use the
3935 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3939 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3943 instance Foo [b] where
3946 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3947 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3948 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3949 declaration. The solution is to postpone the choice by adding the constraint to the context
3950 of the instance declaration, thus:
3952 instance C Int [b] => Foo [b] where
3955 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3958 Warning: overlapping instances must be used with care. They
3959 can give rise to incoherence (ie different instance choices are made
3960 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
3962 {-# LANGUAGE OverlappingInstances #-}
3965 class MyShow a where
3966 myshow :: a -> String
3968 instance MyShow a => MyShow [a] where
3969 myshow xs = concatMap myshow xs
3971 showHelp :: MyShow a => [a] -> String
3972 showHelp xs = myshow xs
3974 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
3980 instance MyShow T where
3981 myshow x = "Used generic instance"
3983 instance MyShow [T] where
3984 myshow xs = "Used more specific instance"
3986 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
3988 In function <literal>showHelp</literal> GHC sees no overlapping
3989 instances, and so uses the <literal>MyShow [a]</literal> instance
3990 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
3991 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
3992 instance declaration in module <literal>Main</literal>. As a result,
3995 "Used more specific instance"
3996 "Used generic instance"
3998 (An alternative possible behaviour, not currently implemented,
3999 would be to reject module <literal>Help</literal>
4000 on the grounds that a later instance declaration might overlap the local one.)
4003 The willingness to be overlapped or incoherent is a property of
4004 the <emphasis>instance declaration</emphasis> itself, controlled by the
4005 presence or otherwise of the <option>-XOverlappingInstances</option>
4006 and <option>-XIncoherentInstances</option> flags when that module is
4007 being defined. Specifically, during the lookup process:
4010 If the constraint being looked up matches two instance declarations IA and IB,
4013 <listitem><para>IB is a substitution instance of IA (but not vice versa);
4014 that is, IB is strictly more specific than IA</para></listitem>
4015 <listitem><para>either IA or IB was compiled with <option>-XOverlappingInstances</option></para></listitem>
4017 then the less-specific instance IA is ignored.
4020 Suppose an instance declaration does not match the constraint being looked up, but
4021 does <emphasis>unify</emphasis> with it, so that it might match when the constraint is further
4022 instantiated. Usually GHC will regard this as a reason for not committing to
4023 some other constraint. But if the instance declaration was compiled with
4024 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4025 check for that declaration.
4028 These rules make it possible for a library author to design a library that relies on
4029 overlapping instances without the library client having to know.
4031 <para>The <option>-XIncoherentInstances</option> flag implies the
4032 <option>-XOverlappingInstances</option> flag, but not vice versa.
4040 <sect2 id="overloaded-strings">
4041 <title>Overloaded string literals
4045 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4046 string literal has type <literal>String</literal>, but with overloaded string
4047 literals enabled (with <literal>-XOverloadedStrings</literal>)
4048 a string literal has type <literal>(IsString a) => a</literal>.
4051 This means that the usual string syntax can be used, e.g., for packed strings
4052 and other variations of string like types. String literals behave very much
4053 like integer literals, i.e., they can be used in both expressions and patterns.
4054 If used in a pattern the literal with be replaced by an equality test, in the same
4055 way as an integer literal is.
4058 The class <literal>IsString</literal> is defined as:
4060 class IsString a where
4061 fromString :: String -> a
4063 The only predefined instance is the obvious one to make strings work as usual:
4065 instance IsString [Char] where
4068 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4069 it explicitly (for example, to give an instance declaration for it), you can import it
4070 from module <literal>GHC.Exts</literal>.
4073 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4077 Each type in a default declaration must be an
4078 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4082 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4083 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4084 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4085 <emphasis>or</emphasis> <literal>IsString</literal>.
4094 import GHC.Exts( IsString(..) )
4096 newtype MyString = MyString String deriving (Eq, Show)
4097 instance IsString MyString where
4098 fromString = MyString
4100 greet :: MyString -> MyString
4101 greet "hello" = "world"
4105 print $ greet "hello"
4106 print $ greet "fool"
4110 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4111 to work since it gets translated into an equality comparison.
4117 <sect1 id="type-families">
4118 <title>Type families</title>
4121 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4122 facilitate type-level
4123 programming. Type families are a generalisation of <firstterm>associated
4124 data types</firstterm>
4125 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4126 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4127 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4128 Symposium on Principles of Programming Languages (POPL'05)”, pages
4129 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4130 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4131 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4133 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4134 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4135 themselves are described in the paper “<ulink
4136 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4137 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4139 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4140 13th ACM SIGPLAN International Conference on Functional
4141 Programming”, ACM Press, pages 51-62, 2008. Type families
4142 essentially provide type-indexed data types and named functions on types,
4143 which are useful for generic programming and highly parameterised library
4144 interfaces as well as interfaces with enhanced static information, much like
4145 dependent types. They might also be regarded as an alternative to functional
4146 dependencies, but provide a more functional style of type-level programming
4147 than the relational style of functional dependencies.
4150 Indexed type families, or type families for short, are type constructors that
4151 represent sets of types. Set members are denoted by supplying the type family
4152 constructor with type parameters, which are called <firstterm>type
4153 indices</firstterm>. The
4154 difference between vanilla parametrised type constructors and family
4155 constructors is much like between parametrically polymorphic functions and
4156 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4157 behave the same at all type instances, whereas class methods can change their
4158 behaviour in dependence on the class type parameters. Similarly, vanilla type
4159 constructors imply the same data representation for all type instances, but
4160 family constructors can have varying representation types for varying type
4164 Indexed type families come in two flavours: <firstterm>data
4165 families</firstterm> and <firstterm>type synonym
4166 families</firstterm>. They are the indexed family variants of algebraic
4167 data types and type synonyms, respectively. The instances of data families
4168 can be data types and newtypes.
4171 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4172 Additional information on the use of type families in GHC is available on
4173 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4174 Haskell wiki page on type families</ulink>.
4177 <sect2 id="data-families">
4178 <title>Data families</title>
4181 Data families appear in two flavours: (1) they can be defined on the
4183 or (2) they can appear inside type classes (in which case they are known as
4184 associated types). The former is the more general variant, as it lacks the
4185 requirement for the type-indexes to coincide with the class
4186 parameters. However, the latter can lead to more clearly structured code and
4187 compiler warnings if some type instances were - possibly accidentally -
4188 omitted. In the following, we always discuss the general toplevel form first
4189 and then cover the additional constraints placed on associated types.
4192 <sect3 id="data-family-declarations">
4193 <title>Data family declarations</title>
4196 Indexed data families are introduced by a signature, such as
4198 data family GMap k :: * -> *
4200 The special <literal>family</literal> distinguishes family from standard
4201 data declarations. The result kind annotation is optional and, as
4202 usual, defaults to <literal>*</literal> if omitted. An example is
4206 Named arguments can also be given explicit kind signatures if needed.
4208 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4209 declarations] named arguments are entirely optional, so that we can
4210 declare <literal>Array</literal> alternatively with
4212 data family Array :: * -> *
4216 <sect4 id="assoc-data-family-decl">
4217 <title>Associated data family declarations</title>
4219 When a data family is declared as part of a type class, we drop
4220 the <literal>family</literal> special. The <literal>GMap</literal>
4221 declaration takes the following form
4223 class GMapKey k where
4224 data GMap k :: * -> *
4227 In contrast to toplevel declarations, named arguments must be used for
4228 all type parameters that are to be used as type-indexes. Moreover,
4229 the argument names must be class parameters. Each class parameter may
4230 only be used at most once per associated type, but some may be omitted
4231 and they may be in an order other than in the class head. Hence, the
4232 following contrived example is admissible:
4241 <sect3 id="data-instance-declarations">
4242 <title>Data instance declarations</title>
4245 Instance declarations of data and newtype families are very similar to
4246 standard data and newtype declarations. The only two differences are
4247 that the keyword <literal>data</literal> or <literal>newtype</literal>
4248 is followed by <literal>instance</literal> and that some or all of the
4249 type arguments can be non-variable types, but may not contain forall
4250 types or type synonym families. However, data families are generally
4251 allowed in type parameters, and type synonyms are allowed as long as
4252 they are fully applied and expand to a type that is itself admissible -
4253 exactly as this is required for occurrences of type synonyms in class
4254 instance parameters. For example, the <literal>Either</literal>
4255 instance for <literal>GMap</literal> is
4257 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4259 In this example, the declaration has only one variant. In general, it
4263 Data and newtype instance declarations are only permitted when an
4264 appropriate family declaration is in scope - just as a class instance declaratoin
4265 requires the class declaration to be visible. Moreover, each instance
4266 declaration has to conform to the kind determined by its family
4267 declaration. This implies that the number of parameters of an instance
4268 declaration matches the arity determined by the kind of the family.
4271 A data family instance declaration can use the full exprssiveness of
4272 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4274 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4275 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4276 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4279 data instance T Int = T1 Int | T2 Bool
4280 newtype instance T Char = TC Bool
4283 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4284 and indeed can define a GADT. For example:
4287 data instance G [a] b where
4288 G1 :: c -> G [Int] b
4292 <listitem><para> You can use a <literal>deriving</literal> clause on a
4293 <literal>data instance</literal> or <literal>newtype instance</literal>
4300 Even if type families are defined as toplevel declarations, functions
4301 that perform different computations for different family instances may still
4302 need to be defined as methods of type classes. In particular, the
4303 following is not possible:
4306 data instance T Int = A
4307 data instance T Char = B
4309 foo A = 1 -- WRONG: These two equations together...
4310 foo B = 2 -- ...will produce a type error.
4312 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4316 instance Foo Int where
4318 instance Foo Char where
4321 (Given the functionality provided by GADTs (Generalised Algebraic Data
4322 Types), it might seem as if a definition, such as the above, should be
4323 feasible. However, type families are - in contrast to GADTs - are
4324 <emphasis>open;</emphasis> i.e., new instances can always be added,
4326 modules. Supporting pattern matching across different data instances
4327 would require a form of extensible case construct.)
4330 <sect4 id="assoc-data-inst">
4331 <title>Associated data instances</title>
4333 When an associated data family instance is declared within a type
4334 class instance, we drop the <literal>instance</literal> keyword in the
4335 family instance. So, the <literal>Either</literal> instance
4336 for <literal>GMap</literal> becomes:
4338 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4339 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4342 The most important point about associated family instances is that the
4343 type indexes corresponding to class parameters must be identical to
4344 the type given in the instance head; here this is the first argument
4345 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4346 which coincides with the only class parameter. Any parameters to the
4347 family constructor that do not correspond to class parameters, need to
4348 be variables in every instance; here this is the
4349 variable <literal>v</literal>.
4352 Instances for an associated family can only appear as part of
4353 instances declarations of the class in which the family was declared -
4354 just as with the equations of the methods of a class. Also in
4355 correspondence to how methods are handled, declarations of associated
4356 types can be omitted in class instances. If an associated family
4357 instance is omitted, the corresponding instance type is not inhabited;
4358 i.e., only diverging expressions, such
4359 as <literal>undefined</literal>, can assume the type.
4363 <sect4 id="scoping-class-params">
4364 <title>Scoping of class parameters</title>
4366 In the case of multi-parameter type classes, the visibility of class
4367 parameters in the right-hand side of associated family instances
4368 depends <emphasis>solely</emphasis> on the parameters of the data
4369 family. As an example, consider the simple class declaration
4374 Only one of the two class parameters is a parameter to the data
4375 family. Hence, the following instance declaration is invalid:
4377 instance C [c] d where
4378 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4380 Here, the right-hand side of the data instance mentions the type
4381 variable <literal>d</literal> that does not occur in its left-hand
4382 side. We cannot admit such data instances as they would compromise
4387 <sect4 id="family-class-inst">
4388 <title>Type class instances of family instances</title>
4390 Type class instances of instances of data families can be defined as
4391 usual, and in particular data instance declarations can
4392 have <literal>deriving</literal> clauses. For example, we can write
4394 data GMap () v = GMapUnit (Maybe v)
4397 which implicitly defines an instance of the form
4399 instance Show v => Show (GMap () v) where ...
4403 Note that class instances are always for
4404 particular <emphasis>instances</emphasis> of a data family and never
4405 for an entire family as a whole. This is for essentially the same
4406 reasons that we cannot define a toplevel function that performs
4407 pattern matching on the data constructors
4408 of <emphasis>different</emphasis> instances of a single type family.
4409 It would require a form of extensible case construct.
4413 <sect4 id="data-family-overlap">
4414 <title>Overlap of data instances</title>
4416 The instance declarations of a data family used in a single program
4417 may not overlap at all, independent of whether they are associated or
4418 not. In contrast to type class instances, this is not only a matter
4419 of consistency, but one of type safety.
4425 <sect3 id="data-family-import-export">
4426 <title>Import and export</title>
4429 The association of data constructors with type families is more dynamic
4430 than that is the case with standard data and newtype declarations. In
4431 the standard case, the notation <literal>T(..)</literal> in an import or
4432 export list denotes the type constructor and all the data constructors
4433 introduced in its declaration. However, a family declaration never
4434 introduces any data constructors; instead, data constructors are
4435 introduced by family instances. As a result, which data constructors
4436 are associated with a type family depends on the currently visible
4437 instance declarations for that family. Consequently, an import or
4438 export item of the form <literal>T(..)</literal> denotes the family
4439 constructor and all currently visible data constructors - in the case of
4440 an export item, these may be either imported or defined in the current
4441 module. The treatment of import and export items that explicitly list
4442 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4446 <sect4 id="data-family-impexp-assoc">
4447 <title>Associated families</title>
4449 As expected, an import or export item of the
4450 form <literal>C(..)</literal> denotes all of the class' methods and
4451 associated types. However, when associated types are explicitly
4452 listed as subitems of a class, we need some new syntax, as uppercase
4453 identifiers as subitems are usually data constructors, not type
4454 constructors. To clarify that we denote types here, each associated
4455 type name needs to be prefixed by the keyword <literal>type</literal>.
4456 So for example, when explicitly listing the components of
4457 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4458 GMap, empty, lookup, insert)</literal>.
4462 <sect4 id="data-family-impexp-examples">
4463 <title>Examples</title>
4465 Assuming our running <literal>GMapKey</literal> class example, let us
4466 look at some export lists and their meaning:
4469 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4470 just the class name.</para>
4473 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4474 Exports the class, the associated type <literal>GMap</literal>
4476 functions <literal>empty</literal>, <literal>lookup</literal>,
4477 and <literal>insert</literal>. None of the data constructors is
4481 <para><literal>module GMap (GMapKey(..), GMap(..))
4482 where...</literal>: As before, but also exports all the data
4483 constructors <literal>GMapInt</literal>,
4484 <literal>GMapChar</literal>,
4485 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4486 and <literal>GMapUnit</literal>.</para>
4489 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4490 GMap(..)) where...</literal>: As before.</para>
4493 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4494 where...</literal>: As before.</para>
4499 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4500 both the class <literal>GMapKey</literal> as well as its associated
4501 type <literal>GMap</literal>. However, you cannot
4502 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4503 sub-component specifications cannot be nested. To
4504 specify <literal>GMap</literal>'s data constructors, you have to list
4509 <sect4 id="data-family-impexp-instances">
4510 <title>Instances</title>
4512 Family instances are implicitly exported, just like class instances.
4513 However, this applies only to the heads of instances, not to the data
4514 constructors an instance defines.
4522 <sect2 id="synonym-families">
4523 <title>Synonym families</title>
4526 Type families appear in two flavours: (1) they can be defined on the
4527 toplevel or (2) they can appear inside type classes (in which case they
4528 are known as associated type synonyms). The former is the more general
4529 variant, as it lacks the requirement for the type-indexes to coincide with
4530 the class parameters. However, the latter can lead to more clearly
4531 structured code and compiler warnings if some type instances were -
4532 possibly accidentally - omitted. In the following, we always discuss the
4533 general toplevel form first and then cover the additional constraints
4534 placed on associated types.
4537 <sect3 id="type-family-declarations">
4538 <title>Type family declarations</title>
4541 Indexed type families are introduced by a signature, such as
4543 type family Elem c :: *
4545 The special <literal>family</literal> distinguishes family from standard
4546 type declarations. The result kind annotation is optional and, as
4547 usual, defaults to <literal>*</literal> if omitted. An example is
4551 Parameters can also be given explicit kind signatures if needed. We
4552 call the number of parameters in a type family declaration, the family's
4553 arity, and all applications of a type family must be fully saturated
4554 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4555 and it implies that the kind of a type family is not sufficient to
4556 determine a family's arity, and hence in general, also insufficient to
4557 determine whether a type family application is well formed. As an
4558 example, consider the following declaration:
4560 type family F a b :: * -> * -- F's arity is 2,
4561 -- although its overall kind is * -> * -> * -> *
4563 Given this declaration the following are examples of well-formed and
4566 F Char [Int] -- OK! Kind: * -> *
4567 F Char [Int] Bool -- OK! Kind: *
4568 F IO Bool -- WRONG: kind mismatch in the first argument
4569 F Bool -- WRONG: unsaturated application
4573 <sect4 id="assoc-type-family-decl">
4574 <title>Associated type family declarations</title>
4576 When a type family is declared as part of a type class, we drop
4577 the <literal>family</literal> special. The <literal>Elem</literal>
4578 declaration takes the following form
4580 class Collects ce where
4584 The argument names of the type family must be class parameters. Each
4585 class parameter may only be used at most once per associated type, but
4586 some may be omitted and they may be in an order other than in the
4587 class head. Hence, the following contrived example is admissible:
4592 These rules are exactly as for associated data families.
4597 <sect3 id="type-instance-declarations">
4598 <title>Type instance declarations</title>
4600 Instance declarations of type families are very similar to standard type
4601 synonym declarations. The only two differences are that the
4602 keyword <literal>type</literal> is followed
4603 by <literal>instance</literal> and that some or all of the type
4604 arguments can be non-variable types, but may not contain forall types or
4605 type synonym families. However, data families are generally allowed, and
4606 type synonyms are allowed as long as they are fully applied and expand
4607 to a type that is admissible - these are the exact same requirements as
4608 for data instances. For example, the <literal>[e]</literal> instance
4609 for <literal>Elem</literal> is
4611 type instance Elem [e] = e
4615 Type family instance declarations are only legitimate when an
4616 appropriate family declaration is in scope - just like class instances
4617 require the class declaration to be visible. Moreover, each instance
4618 declaration has to conform to the kind determined by its family
4619 declaration, and the number of type parameters in an instance
4620 declaration must match the number of type parameters in the family
4621 declaration. Finally, the right-hand side of a type instance must be a
4622 monotype (i.e., it may not include foralls) and after the expansion of
4623 all saturated vanilla type synonyms, no synonyms, except family synonyms
4624 may remain. Here are some examples of admissible and illegal type
4627 type family F a :: *
4628 type instance F [Int] = Int -- OK!
4629 type instance F String = Char -- OK!
4630 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4631 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4632 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4634 type family G a b :: * -> *
4635 type instance G Int = (,) -- WRONG: must be two type parameters
4636 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4640 <sect4 id="assoc-type-instance">
4641 <title>Associated type instance declarations</title>
4643 When an associated family instance is declared within a type class
4644 instance, we drop the <literal>instance</literal> keyword in the family
4645 instance. So, the <literal>[e]</literal> instance
4646 for <literal>Elem</literal> becomes:
4648 instance (Eq (Elem [e])) => Collects ([e]) where
4652 The most important point about associated family instances is that the
4653 type indexes corresponding to class parameters must be identical to the
4654 type given in the instance head; here this is <literal>[e]</literal>,
4655 which coincides with the only class parameter.
4658 Instances for an associated family can only appear as part of instances
4659 declarations of the class in which the family was declared - just as
4660 with the equations of the methods of a class. Also in correspondence to
4661 how methods are handled, declarations of associated types can be omitted
4662 in class instances. If an associated family instance is omitted, the
4663 corresponding instance type is not inhabited; i.e., only diverging
4664 expressions, such as <literal>undefined</literal>, can assume the type.
4668 <sect4 id="type-family-overlap">
4669 <title>Overlap of type synonym instances</title>
4671 The instance declarations of a type family used in a single program
4672 may only overlap if the right-hand sides of the overlapping instances
4673 coincide for the overlapping types. More formally, two instance
4674 declarations overlap if there is a substitution that makes the
4675 left-hand sides of the instances syntactically the same. Whenever
4676 that is the case, the right-hand sides of the instances must also be
4677 syntactically equal under the same substitution. This condition is
4678 independent of whether the type family is associated or not, and it is
4679 not only a matter of consistency, but one of type safety.
4682 Here are two example to illustrate the condition under which overlap
4685 type instance F (a, Int) = [a]
4686 type instance F (Int, b) = [b] -- overlap permitted
4688 type instance G (a, Int) = [a]
4689 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4694 <sect4 id="type-family-decidability">
4695 <title>Decidability of type synonym instances</title>
4697 In order to guarantee that type inference in the presence of type
4698 families decidable, we need to place a number of additional
4699 restrictions on the formation of type instance declarations (c.f.,
4700 Definition 5 (Relaxed Conditions) of “<ulink
4701 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4702 Checking with Open Type Functions</ulink>”). Instance
4703 declarations have the general form
4705 type instance F t1 .. tn = t
4707 where we require that for every type family application <literal>(G s1
4708 .. sm)</literal> in <literal>t</literal>,
4711 <para><literal>s1 .. sm</literal> do not contain any type family
4712 constructors,</para>
4715 <para>the total number of symbols (data type constructors and type
4716 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4717 in <literal>t1 .. tn</literal>, and</para>
4720 <para>for every type
4721 variable <literal>a</literal>, <literal>a</literal> occurs
4722 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4723 .. tn</literal>.</para>
4726 These restrictions are easily verified and ensure termination of type
4727 inference. However, they are not sufficient to guarantee completeness
4728 of type inference in the presence of, so called, ''loopy equalities'',
4729 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4730 a type variable is underneath a family application and data
4731 constructor application - see the above mentioned paper for details.
4734 If the option <option>-XUndecidableInstances</option> is passed to the
4735 compiler, the above restrictions are not enforced and it is on the
4736 programmer to ensure termination of the normalisation of type families
4737 during type inference.
4742 <sect3 id-="equality-constraints">
4743 <title>Equality constraints</title>
4745 Type context can include equality constraints of the form <literal>t1 ~
4746 t2</literal>, which denote that the types <literal>t1</literal>
4747 and <literal>t2</literal> need to be the same. In the presence of type
4748 families, whether two types are equal cannot generally be decided
4749 locally. Hence, the contexts of function signatures may include
4750 equality constraints, as in the following example:
4752 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4754 where we require that the element type of <literal>c1</literal>
4755 and <literal>c2</literal> are the same. In general, the
4756 types <literal>t1</literal> and <literal>t2</literal> of an equality
4757 constraint may be arbitrary monotypes; i.e., they may not contain any
4758 quantifiers, independent of whether higher-rank types are otherwise
4762 Equality constraints can also appear in class and instance contexts.
4763 The former enable a simple translation of programs using functional
4764 dependencies into programs using family synonyms instead. The general
4765 idea is to rewrite a class declaration of the form
4767 class C a b | a -> b
4771 class (F a ~ b) => C a b where
4774 That is, we represent every functional dependency (FD) <literal>a1 .. an
4775 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4776 superclass context equality <literal>F a1 .. an ~ b</literal>,
4777 essentially giving a name to the functional dependency. In class
4778 instances, we define the type instances of FD families in accordance
4779 with the class head. Method signatures are not affected by that
4783 NB: Equalities in superclass contexts are not fully implemented in
4788 <sect3 id-="ty-fams-in-instances">
4789 <title>Type families and instance declarations</title>
4790 <para>Type families require us to extend the rules for
4791 the form of instance heads, which are given
4792 in <xref linkend="flexible-instance-head"/>.
4795 <listitem><para>Data type families may appear in an instance head</para></listitem>
4796 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4798 The reason for the latter restriction is that there is no way to check for. Consider
4801 type instance F Bool = Int
4808 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4809 The situation is especially bad because the type instance for <literal>F Bool</literal>
4810 might be in another module, or even in a module that is not yet written.
4817 <sect1 id="other-type-extensions">
4818 <title>Other type system extensions</title>
4820 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4822 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4823 is used, the keyword <literal>forall</literal>
4824 allows us to say exactly what this means. For example:
4832 g :: forall b. (b -> b)
4834 The two are treated identically.
4837 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4838 a type variable any more!
4843 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4845 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4846 that the type-class constraints in a type signature must have the
4847 form <emphasis>(class type-variable)</emphasis> or
4848 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4849 With <option>-XFlexibleContexts</option>
4850 these type signatures are perfectly OK
4853 g :: Ord (T a ()) => ...
4855 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4856 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4857 (<xref linkend="instance-rules"/>).
4861 GHC imposes the following restrictions on the constraints in a type signature.
4865 forall tv1..tvn (c1, ...,cn) => type
4868 (Here, we write the "foralls" explicitly, although the Haskell source
4869 language omits them; in Haskell 98, all the free type variables of an
4870 explicit source-language type signature are universally quantified,
4871 except for the class type variables in a class declaration. However,
4872 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4881 <emphasis>Each universally quantified type variable
4882 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4884 A type variable <literal>a</literal> is "reachable" if it appears
4885 in the same constraint as either a type variable free in
4886 <literal>type</literal>, or another reachable type variable.
4887 A value with a type that does not obey
4888 this reachability restriction cannot be used without introducing
4889 ambiguity; that is why the type is rejected.
4890 Here, for example, is an illegal type:
4894 forall a. Eq a => Int
4898 When a value with this type was used, the constraint <literal>Eq tv</literal>
4899 would be introduced where <literal>tv</literal> is a fresh type variable, and
4900 (in the dictionary-translation implementation) the value would be
4901 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4902 can never know which instance of <literal>Eq</literal> to use because we never
4903 get any more information about <literal>tv</literal>.
4907 that the reachability condition is weaker than saying that <literal>a</literal> is
4908 functionally dependent on a type variable free in
4909 <literal>type</literal> (see <xref
4910 linkend="functional-dependencies"/>). The reason for this is there
4911 might be a "hidden" dependency, in a superclass perhaps. So
4912 "reachable" is a conservative approximation to "functionally dependent".
4913 For example, consider:
4915 class C a b | a -> b where ...
4916 class C a b => D a b where ...
4917 f :: forall a b. D a b => a -> a
4919 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4920 but that is not immediately apparent from <literal>f</literal>'s type.
4926 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4927 universally quantified type variables <literal>tvi</literal></emphasis>.
4929 For example, this type is OK because <literal>C a b</literal> mentions the
4930 universally quantified type variable <literal>b</literal>:
4934 forall a. C a b => burble
4938 The next type is illegal because the constraint <literal>Eq b</literal> does not
4939 mention <literal>a</literal>:
4943 forall a. Eq b => burble
4947 The reason for this restriction is milder than the other one. The
4948 excluded types are never useful or necessary (because the offending
4949 context doesn't need to be witnessed at this point; it can be floated
4950 out). Furthermore, floating them out increases sharing. Lastly,
4951 excluding them is a conservative choice; it leaves a patch of
4952 territory free in case we need it later.
4963 <sect2 id="implicit-parameters">
4964 <title>Implicit parameters</title>
4966 <para> Implicit parameters are implemented as described in
4967 "Implicit parameters: dynamic scoping with static types",
4968 J Lewis, MB Shields, E Meijer, J Launchbury,
4969 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4973 <para>(Most of the following, still rather incomplete, documentation is
4974 due to Jeff Lewis.)</para>
4976 <para>Implicit parameter support is enabled with the option
4977 <option>-XImplicitParams</option>.</para>
4980 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4981 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4982 context. In Haskell, all variables are statically bound. Dynamic
4983 binding of variables is a notion that goes back to Lisp, but was later
4984 discarded in more modern incarnations, such as Scheme. Dynamic binding
4985 can be very confusing in an untyped language, and unfortunately, typed
4986 languages, in particular Hindley-Milner typed languages like Haskell,
4987 only support static scoping of variables.
4990 However, by a simple extension to the type class system of Haskell, we
4991 can support dynamic binding. Basically, we express the use of a
4992 dynamically bound variable as a constraint on the type. These
4993 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4994 function uses a dynamically-bound variable <literal>?x</literal>
4995 of type <literal>t'</literal>". For
4996 example, the following expresses the type of a sort function,
4997 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4999 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5001 The dynamic binding constraints are just a new form of predicate in the type class system.
5004 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5005 where <literal>x</literal> is
5006 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5007 Use of this construct also introduces a new
5008 dynamic-binding constraint in the type of the expression.
5009 For example, the following definition
5010 shows how we can define an implicitly parameterized sort function in
5011 terms of an explicitly parameterized <literal>sortBy</literal> function:
5013 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5015 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5021 <title>Implicit-parameter type constraints</title>
5023 Dynamic binding constraints behave just like other type class
5024 constraints in that they are automatically propagated. Thus, when a
5025 function is used, its implicit parameters are inherited by the
5026 function that called it. For example, our <literal>sort</literal> function might be used
5027 to pick out the least value in a list:
5029 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5030 least xs = head (sort xs)
5032 Without lifting a finger, the <literal>?cmp</literal> parameter is
5033 propagated to become a parameter of <literal>least</literal> as well. With explicit
5034 parameters, the default is that parameters must always be explicit
5035 propagated. With implicit parameters, the default is to always
5039 An implicit-parameter type constraint differs from other type class constraints in the
5040 following way: All uses of a particular implicit parameter must have
5041 the same type. This means that the type of <literal>(?x, ?x)</literal>
5042 is <literal>(?x::a) => (a,a)</literal>, and not
5043 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5047 <para> You can't have an implicit parameter in the context of a class or instance
5048 declaration. For example, both these declarations are illegal:
5050 class (?x::Int) => C a where ...
5051 instance (?x::a) => Foo [a] where ...
5053 Reason: exactly which implicit parameter you pick up depends on exactly where
5054 you invoke a function. But the ``invocation'' of instance declarations is done
5055 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5056 Easiest thing is to outlaw the offending types.</para>
5058 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5060 f :: (?x :: [a]) => Int -> Int
5063 g :: (Read a, Show a) => String -> String
5066 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5067 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5068 quite unambiguous, and fixes the type <literal>a</literal>.
5073 <title>Implicit-parameter bindings</title>
5076 An implicit parameter is <emphasis>bound</emphasis> using the standard
5077 <literal>let</literal> or <literal>where</literal> binding forms.
5078 For example, we define the <literal>min</literal> function by binding
5079 <literal>cmp</literal>.
5082 min = let ?cmp = (<=) in least
5086 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5087 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5088 (including in a list comprehension, or do-notation, or pattern guards),
5089 or a <literal>where</literal> clause.
5090 Note the following points:
5093 An implicit-parameter binding group must be a
5094 collection of simple bindings to implicit-style variables (no
5095 function-style bindings, and no type signatures); these bindings are
5096 neither polymorphic or recursive.
5099 You may not mix implicit-parameter bindings with ordinary bindings in a
5100 single <literal>let</literal>
5101 expression; use two nested <literal>let</literal>s instead.
5102 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5106 You may put multiple implicit-parameter bindings in a
5107 single binding group; but they are <emphasis>not</emphasis> treated
5108 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5109 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5110 parameter. The bindings are not nested, and may be re-ordered without changing
5111 the meaning of the program.
5112 For example, consider:
5114 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5116 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5117 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5119 f :: (?x::Int) => Int -> Int
5127 <sect3><title>Implicit parameters and polymorphic recursion</title>
5130 Consider these two definitions:
5133 len1 xs = let ?acc = 0 in len_acc1 xs
5136 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5141 len2 xs = let ?acc = 0 in len_acc2 xs
5143 len_acc2 :: (?acc :: Int) => [a] -> Int
5145 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5147 The only difference between the two groups is that in the second group
5148 <literal>len_acc</literal> is given a type signature.
5149 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5150 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5151 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5152 has a type signature, the recursive call is made to the
5153 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5154 as an implicit parameter. So we get the following results in GHCi:
5161 Adding a type signature dramatically changes the result! This is a rather
5162 counter-intuitive phenomenon, worth watching out for.
5166 <sect3><title>Implicit parameters and monomorphism</title>
5168 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5169 Haskell Report) to implicit parameters. For example, consider:
5177 Since the binding for <literal>y</literal> falls under the Monomorphism
5178 Restriction it is not generalised, so the type of <literal>y</literal> is
5179 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5180 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5181 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5182 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5183 <literal>y</literal> in the body of the <literal>let</literal> will see the
5184 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5185 <literal>14</literal>.
5190 <!-- ======================= COMMENTED OUT ========================
5192 We intend to remove linear implicit parameters, so I'm at least removing
5193 them from the 6.6 user manual
5195 <sect2 id="linear-implicit-parameters">
5196 <title>Linear implicit parameters</title>
5198 Linear implicit parameters are an idea developed by Koen Claessen,
5199 Mark Shields, and Simon PJ. They address the long-standing
5200 problem that monads seem over-kill for certain sorts of problem, notably:
5203 <listitem> <para> distributing a supply of unique names </para> </listitem>
5204 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5205 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5209 Linear implicit parameters are just like ordinary implicit parameters,
5210 except that they are "linear"; that is, they cannot be copied, and
5211 must be explicitly "split" instead. Linear implicit parameters are
5212 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5213 (The '/' in the '%' suggests the split!)
5218 import GHC.Exts( Splittable )
5220 data NameSupply = ...
5222 splitNS :: NameSupply -> (NameSupply, NameSupply)
5223 newName :: NameSupply -> Name
5225 instance Splittable NameSupply where
5229 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5230 f env (Lam x e) = Lam x' (f env e)
5233 env' = extend env x x'
5234 ...more equations for f...
5236 Notice that the implicit parameter %ns is consumed
5238 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5239 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5243 So the translation done by the type checker makes
5244 the parameter explicit:
5246 f :: NameSupply -> Env -> Expr -> Expr
5247 f ns env (Lam x e) = Lam x' (f ns1 env e)
5249 (ns1,ns2) = splitNS ns
5251 env = extend env x x'
5253 Notice the call to 'split' introduced by the type checker.
5254 How did it know to use 'splitNS'? Because what it really did
5255 was to introduce a call to the overloaded function 'split',
5256 defined by the class <literal>Splittable</literal>:
5258 class Splittable a where
5261 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5262 split for name supplies. But we can simply write
5268 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5270 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5271 <literal>GHC.Exts</literal>.
5276 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5277 are entirely distinct implicit parameters: you
5278 can use them together and they won't interfere with each other. </para>
5281 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5283 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5284 in the context of a class or instance declaration. </para></listitem>
5288 <sect3><title>Warnings</title>
5291 The monomorphism restriction is even more important than usual.
5292 Consider the example above:
5294 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5295 f env (Lam x e) = Lam x' (f env e)
5298 env' = extend env x x'
5300 If we replaced the two occurrences of x' by (newName %ns), which is
5301 usually a harmless thing to do, we get:
5303 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5304 f env (Lam x e) = Lam (newName %ns) (f env e)
5306 env' = extend env x (newName %ns)
5308 But now the name supply is consumed in <emphasis>three</emphasis> places
5309 (the two calls to newName,and the recursive call to f), so
5310 the result is utterly different. Urk! We don't even have
5314 Well, this is an experimental change. With implicit
5315 parameters we have already lost beta reduction anyway, and
5316 (as John Launchbury puts it) we can't sensibly reason about
5317 Haskell programs without knowing their typing.
5322 <sect3><title>Recursive functions</title>
5323 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5326 foo :: %x::T => Int -> [Int]
5328 foo n = %x : foo (n-1)
5330 where T is some type in class Splittable.</para>
5332 Do you get a list of all the same T's or all different T's
5333 (assuming that split gives two distinct T's back)?
5335 If you supply the type signature, taking advantage of polymorphic
5336 recursion, you get what you'd probably expect. Here's the
5337 translated term, where the implicit param is made explicit:
5340 foo x n = let (x1,x2) = split x
5341 in x1 : foo x2 (n-1)
5343 But if you don't supply a type signature, GHC uses the Hindley
5344 Milner trick of using a single monomorphic instance of the function
5345 for the recursive calls. That is what makes Hindley Milner type inference
5346 work. So the translation becomes
5350 foom n = x : foom (n-1)
5354 Result: 'x' is not split, and you get a list of identical T's. So the
5355 semantics of the program depends on whether or not foo has a type signature.
5358 You may say that this is a good reason to dislike linear implicit parameters
5359 and you'd be right. That is why they are an experimental feature.
5365 ================ END OF Linear Implicit Parameters commented out -->
5367 <sect2 id="kinding">
5368 <title>Explicitly-kinded quantification</title>
5371 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5372 to give the kind explicitly as (machine-checked) documentation,
5373 just as it is nice to give a type signature for a function. On some occasions,
5374 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5375 John Hughes had to define the data type:
5377 data Set cxt a = Set [a]
5378 | Unused (cxt a -> ())
5380 The only use for the <literal>Unused</literal> constructor was to force the correct
5381 kind for the type variable <literal>cxt</literal>.
5384 GHC now instead allows you to specify the kind of a type variable directly, wherever
5385 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5388 This flag enables kind signatures in the following places:
5390 <listitem><para><literal>data</literal> declarations:
5392 data Set (cxt :: * -> *) a = Set [a]
5393 </screen></para></listitem>
5394 <listitem><para><literal>type</literal> declarations:
5396 type T (f :: * -> *) = f Int
5397 </screen></para></listitem>
5398 <listitem><para><literal>class</literal> declarations:
5400 class (Eq a) => C (f :: * -> *) a where ...
5401 </screen></para></listitem>
5402 <listitem><para><literal>forall</literal>'s in type signatures:
5404 f :: forall (cxt :: * -> *). Set cxt Int
5405 </screen></para></listitem>
5410 The parentheses are required. Some of the spaces are required too, to
5411 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5412 will get a parse error, because "<literal>::*->*</literal>" is a
5413 single lexeme in Haskell.
5417 As part of the same extension, you can put kind annotations in types
5420 f :: (Int :: *) -> Int
5421 g :: forall a. a -> (a :: *)
5425 atype ::= '(' ctype '::' kind ')
5427 The parentheses are required.
5432 <sect2 id="universal-quantification">
5433 <title>Arbitrary-rank polymorphism
5437 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5438 explicit universal quantification in
5440 For example, all the following types are legal:
5442 f1 :: forall a b. a -> b -> a
5443 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5445 f2 :: (forall a. a->a) -> Int -> Int
5446 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5448 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5450 f4 :: Int -> (forall a. a -> a)
5452 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5453 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5454 The <literal>forall</literal> makes explicit the universal quantification that
5455 is implicitly added by Haskell.
5458 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5459 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5460 shows, the polymorphic type on the left of the function arrow can be overloaded.
5463 The function <literal>f3</literal> has a rank-3 type;
5464 it has rank-2 types on the left of a function arrow.
5467 GHC has three flags to control higher-rank types:
5470 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5473 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5476 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5477 That is, you can nest <literal>forall</literal>s
5478 arbitrarily deep in function arrows.
5479 In particular, a forall-type (also called a "type scheme"),
5480 including an operational type class context, is legal:
5482 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5483 of a function arrow </para> </listitem>
5484 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5485 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5486 field type signatures.</para> </listitem>
5487 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5488 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5500 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5501 the types of the constructor arguments. Here are several examples:
5507 data T a = T1 (forall b. b -> b -> b) a
5509 data MonadT m = MkMonad { return :: forall a. a -> m a,
5510 bind :: forall a b. m a -> (a -> m b) -> m b
5513 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5519 The constructors have rank-2 types:
5525 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5526 MkMonad :: forall m. (forall a. a -> m a)
5527 -> (forall a b. m a -> (a -> m b) -> m b)
5529 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5535 Notice that you don't need to use a <literal>forall</literal> if there's an
5536 explicit context. For example in the first argument of the
5537 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5538 prefixed to the argument type. The implicit <literal>forall</literal>
5539 quantifies all type variables that are not already in scope, and are
5540 mentioned in the type quantified over.
5544 As for type signatures, implicit quantification happens for non-overloaded
5545 types too. So if you write this:
5548 data T a = MkT (Either a b) (b -> b)
5551 it's just as if you had written this:
5554 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5557 That is, since the type variable <literal>b</literal> isn't in scope, it's
5558 implicitly universally quantified. (Arguably, it would be better
5559 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5560 where that is what is wanted. Feedback welcomed.)
5564 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5565 the constructor to suitable values, just as usual. For example,
5576 a3 = MkSwizzle reverse
5579 a4 = let r x = Just x
5586 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5587 mkTs f x y = [T1 f x, T1 f y]
5593 The type of the argument can, as usual, be more general than the type
5594 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5595 does not need the <literal>Ord</literal> constraint.)
5599 When you use pattern matching, the bound variables may now have
5600 polymorphic types. For example:
5606 f :: T a -> a -> (a, Char)
5607 f (T1 w k) x = (w k x, w 'c' 'd')
5609 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5610 g (MkSwizzle s) xs f = s (map f (s xs))
5612 h :: MonadT m -> [m a] -> m [a]
5613 h m [] = return m []
5614 h m (x:xs) = bind m x $ \y ->
5615 bind m (h m xs) $ \ys ->
5622 In the function <function>h</function> we use the record selectors <literal>return</literal>
5623 and <literal>bind</literal> to extract the polymorphic bind and return functions
5624 from the <literal>MonadT</literal> data structure, rather than using pattern
5630 <title>Type inference</title>
5633 In general, type inference for arbitrary-rank types is undecidable.
5634 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5635 to get a decidable algorithm by requiring some help from the programmer.
5636 We do not yet have a formal specification of "some help" but the rule is this:
5639 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5640 provides an explicit polymorphic type for x, or GHC's type inference will assume
5641 that x's type has no foralls in it</emphasis>.
5644 What does it mean to "provide" an explicit type for x? You can do that by
5645 giving a type signature for x directly, using a pattern type signature
5646 (<xref linkend="scoped-type-variables"/>), thus:
5648 \ f :: (forall a. a->a) -> (f True, f 'c')
5650 Alternatively, you can give a type signature to the enclosing
5651 context, which GHC can "push down" to find the type for the variable:
5653 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5655 Here the type signature on the expression can be pushed inwards
5656 to give a type signature for f. Similarly, and more commonly,
5657 one can give a type signature for the function itself:
5659 h :: (forall a. a->a) -> (Bool,Char)
5660 h f = (f True, f 'c')
5662 You don't need to give a type signature if the lambda bound variable
5663 is a constructor argument. Here is an example we saw earlier:
5665 f :: T a -> a -> (a, Char)
5666 f (T1 w k) x = (w k x, w 'c' 'd')
5668 Here we do not need to give a type signature to <literal>w</literal>, because
5669 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5676 <sect3 id="implicit-quant">
5677 <title>Implicit quantification</title>
5680 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5681 user-written types, if and only if there is no explicit <literal>forall</literal>,
5682 GHC finds all the type variables mentioned in the type that are not already
5683 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5687 f :: forall a. a -> a
5694 h :: forall b. a -> b -> b
5700 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5703 f :: (a -> a) -> Int
5705 f :: forall a. (a -> a) -> Int
5707 f :: (forall a. a -> a) -> Int
5710 g :: (Ord a => a -> a) -> Int
5711 -- MEANS the illegal type
5712 g :: forall a. (Ord a => a -> a) -> Int
5714 g :: (forall a. Ord a => a -> a) -> Int
5716 The latter produces an illegal type, which you might think is silly,
5717 but at least the rule is simple. If you want the latter type, you
5718 can write your for-alls explicitly. Indeed, doing so is strongly advised
5725 <sect2 id="impredicative-polymorphism">
5726 <title>Impredicative polymorphism
5728 <para><emphasis>NOTE: the impredicative-polymorphism feature is deprecated in GHC 6.12, and
5729 will be removed or replaced in GHC 6.14.</emphasis></para>
5731 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5732 enabled with <option>-XImpredicativeTypes</option>.
5734 that you can call a polymorphic function at a polymorphic type, and
5735 parameterise data structures over polymorphic types. For example:
5737 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5738 f (Just g) = Just (g [3], g "hello")
5741 Notice here that the <literal>Maybe</literal> type is parameterised by the
5742 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5745 <para>The technical details of this extension are described in the paper
5746 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5747 type inference for higher-rank types and impredicativity</ulink>,
5748 which appeared at ICFP 2006.
5752 <sect2 id="scoped-type-variables">
5753 <title>Lexically scoped type variables
5757 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5758 which some type signatures are simply impossible to write. For example:
5760 f :: forall a. [a] -> [a]
5766 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5767 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5768 The type variables bound by a <literal>forall</literal> scope over
5769 the entire definition of the accompanying value declaration.
5770 In this example, the type variable <literal>a</literal> scopes over the whole
5771 definition of <literal>f</literal>, including over
5772 the type signature for <varname>ys</varname>.
5773 In Haskell 98 it is not possible to declare
5774 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5775 it becomes possible to do so.
5777 <para>Lexically-scoped type variables are enabled by
5778 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5780 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5781 variables work, compared to earlier releases. Read this section
5785 <title>Overview</title>
5787 <para>The design follows the following principles
5789 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5790 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5791 design.)</para></listitem>
5792 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5793 type variables. This means that every programmer-written type signature
5794 (including one that contains free scoped type variables) denotes a
5795 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5796 checker, and no inference is involved.</para></listitem>
5797 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5798 changing the program.</para></listitem>
5802 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5804 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5805 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5806 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5807 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5811 In Haskell, a programmer-written type signature is implicitly quantified over
5812 its free type variables (<ulink
5813 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5815 of the Haskell Report).
5816 Lexically scoped type variables affect this implicit quantification rules
5817 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5818 quantified. For example, if type variable <literal>a</literal> is in scope,
5821 (e :: a -> a) means (e :: a -> a)
5822 (e :: b -> b) means (e :: forall b. b->b)
5823 (e :: a -> b) means (e :: forall b. a->b)
5831 <sect3 id="decl-type-sigs">
5832 <title>Declaration type signatures</title>
5833 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5834 quantification (using <literal>forall</literal>) brings into scope the
5835 explicitly-quantified
5836 type variables, in the definition of the named function. For example:
5838 f :: forall a. [a] -> [a]
5839 f (x:xs) = xs ++ [ x :: a ]
5841 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5842 the definition of "<literal>f</literal>".
5844 <para>This only happens if:
5846 <listitem><para> The quantification in <literal>f</literal>'s type
5847 signature is explicit. For example:
5850 g (x:xs) = xs ++ [ x :: a ]
5852 This program will be rejected, because "<literal>a</literal>" does not scope
5853 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5854 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5855 quantification rules.
5857 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5858 not a pattern binding.
5861 f1 :: forall a. [a] -> [a]
5862 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5864 f2 :: forall a. [a] -> [a]
5865 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5867 f3 :: forall a. [a] -> [a]
5868 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5870 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5871 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5872 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5873 the type signature brings <literal>a</literal> into scope.
5879 <sect3 id="exp-type-sigs">
5880 <title>Expression type signatures</title>
5882 <para>An expression type signature that has <emphasis>explicit</emphasis>
5883 quantification (using <literal>forall</literal>) brings into scope the
5884 explicitly-quantified
5885 type variables, in the annotated expression. For example:
5887 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5889 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5890 type variable <literal>s</literal> into scope, in the annotated expression
5891 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5896 <sect3 id="pattern-type-sigs">
5897 <title>Pattern type signatures</title>
5899 A type signature may occur in any pattern; this is a <emphasis>pattern type
5900 signature</emphasis>.
5903 -- f and g assume that 'a' is already in scope
5904 f = \(x::Int, y::a) -> x
5906 h ((x,y) :: (Int,Bool)) = (y,x)
5908 In the case where all the type variables in the pattern type signature are
5909 already in scope (i.e. bound by the enclosing context), matters are simple: the
5910 signature simply constrains the type of the pattern in the obvious way.
5913 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5914 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5915 that are already in scope. For example:
5917 f :: forall a. [a] -> (Int, [a])
5920 (ys::[a], n) = (reverse xs, length xs) -- OK
5921 zs::[a] = xs ++ ys -- OK
5923 Just (v::b) = ... -- Not OK; b is not in scope
5925 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5926 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5930 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5931 type signature may mention a type variable that is not in scope; in this case,
5932 <emphasis>the signature brings that type variable into scope</emphasis>.
5933 This is particularly important for existential data constructors. For example:
5935 data T = forall a. MkT [a]
5938 k (MkT [t::a]) = MkT t3
5942 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5943 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5944 because it is bound by the pattern match. GHC's rule is that in this situation
5945 (and only then), a pattern type signature can mention a type variable that is
5946 not already in scope; the effect is to bring it into scope, standing for the
5947 existentially-bound type variable.
5950 When a pattern type signature binds a type variable in this way, GHC insists that the
5951 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5952 This means that any user-written type signature always stands for a completely known type.
5955 If all this seems a little odd, we think so too. But we must have
5956 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5957 could not name existentially-bound type variables in subsequent type signatures.
5960 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5961 signature is allowed to mention a lexical variable that is not already in
5963 For example, both <literal>f</literal> and <literal>g</literal> would be
5964 illegal if <literal>a</literal> was not already in scope.
5970 <!-- ==================== Commented out part about result type signatures
5972 <sect3 id="result-type-sigs">
5973 <title>Result type signatures</title>
5976 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5979 {- f assumes that 'a' is already in scope -}
5980 f x y :: [a] = [x,y,x]
5982 g = \ x :: [Int] -> [3,4]
5984 h :: forall a. [a] -> a
5988 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5989 the result of the function. Similarly, the body of the lambda in the RHS of
5990 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5991 alternative in <literal>h</literal> is <literal>a</literal>.
5993 <para> A result type signature never brings new type variables into scope.</para>
5995 There are a couple of syntactic wrinkles. First, notice that all three
5996 examples would parse quite differently with parentheses:
5998 {- f assumes that 'a' is already in scope -}
5999 f x (y :: [a]) = [x,y,x]
6001 g = \ (x :: [Int]) -> [3,4]
6003 h :: forall a. [a] -> a
6007 Now the signature is on the <emphasis>pattern</emphasis>; and
6008 <literal>h</literal> would certainly be ill-typed (since the pattern
6009 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6011 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6012 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6013 token or a parenthesised type of some sort). To see why,
6014 consider how one would parse this:
6023 <sect3 id="cls-inst-scoped-tyvars">
6024 <title>Class and instance declarations</title>
6027 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6028 scope over the methods defined in the <literal>where</literal> part. For example:
6046 <sect2 id="typing-binds">
6047 <title>Generalised typing of mutually recursive bindings</title>
6050 The Haskell Report specifies that a group of bindings (at top level, or in a
6051 <literal>let</literal> or <literal>where</literal>) should be sorted into
6052 strongly-connected components, and then type-checked in dependency order
6053 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6054 Report, Section 4.5.1</ulink>).
6055 As each group is type-checked, any binders of the group that
6057 an explicit type signature are put in the type environment with the specified
6059 and all others are monomorphic until the group is generalised
6060 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6063 <para>Following a suggestion of Mark Jones, in his paper
6064 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6066 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6068 <emphasis>the dependency analysis ignores references to variables that have an explicit
6069 type signature</emphasis>.
6070 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6071 typecheck. For example, consider:
6073 f :: Eq a => a -> Bool
6074 f x = (x == x) || g True || g "Yes"
6076 g y = (y <= y) || f True
6078 This is rejected by Haskell 98, but under Jones's scheme the definition for
6079 <literal>g</literal> is typechecked first, separately from that for
6080 <literal>f</literal>,
6081 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6082 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6083 type is generalised, to get
6085 g :: Ord a => a -> Bool
6087 Now, the definition for <literal>f</literal> is typechecked, with this type for
6088 <literal>g</literal> in the type environment.
6092 The same refined dependency analysis also allows the type signatures of
6093 mutually-recursive functions to have different contexts, something that is illegal in
6094 Haskell 98 (Section 4.5.2, last sentence). With
6095 <option>-XRelaxedPolyRec</option>
6096 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6097 type signatures; in practice this means that only variables bound by the same
6098 pattern binding must have the same context. For example, this is fine:
6100 f :: Eq a => a -> Bool
6101 f x = (x == x) || g True
6103 g :: Ord a => a -> Bool
6104 g y = (y <= y) || f True
6109 <sect2 id="mono-local-binds">
6110 <title>Monomorphic local bindings</title>
6112 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6113 The rationale is described in the paper
6114 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6117 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6118 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6119 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6120 If you supply a type signature, then the flag has no effect.
6125 <!-- ==================== End of type system extensions ================= -->
6127 <!-- ====================== TEMPLATE HASKELL ======================= -->
6129 <sect1 id="template-haskell">
6130 <title>Template Haskell</title>
6132 <para>Template Haskell allows you to do compile-time meta-programming in
6135 the main technical innovations is discussed in "<ulink
6136 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6137 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6140 There is a Wiki page about
6141 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6142 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6146 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6147 Haskell library reference material</ulink>
6148 (look for module <literal>Language.Haskell.TH</literal>).
6149 Many changes to the original design are described in
6150 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6151 Notes on Template Haskell version 2</ulink>.
6152 Not all of these changes are in GHC, however.
6155 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6156 as a worked example to help get you started.
6160 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6161 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6166 <title>Syntax</title>
6168 <para> Template Haskell has the following new syntactic
6169 constructions. You need to use the flag
6170 <option>-XTemplateHaskell</option>
6171 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6172 </indexterm>to switch these syntactic extensions on
6173 (<option>-XTemplateHaskell</option> is no longer implied by
6174 <option>-fglasgow-exts</option>).</para>
6178 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6179 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6180 There must be no space between the "$" and the identifier or parenthesis. This use
6181 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6182 of "." as an infix operator. If you want the infix operator, put spaces around it.
6184 <para> A splice can occur in place of
6186 <listitem><para> an expression; the spliced expression must
6187 have type <literal>Q Exp</literal></para></listitem>
6188 <listitem><para> an type; the spliced expression must
6189 have type <literal>Q Typ</literal></para></listitem>
6190 <listitem><para> a list of top-level declarations; the spliced expression
6191 must have type <literal>Q [Dec]</literal></para></listitem>
6193 Note that pattern splices are not supported.
6194 Inside a splice you can can only call functions defined in imported modules,
6195 not functions defined elsewhere in the same module.</para></listitem>
6198 A expression quotation is written in Oxford brackets, thus:
6200 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6201 where the "..." is an expression;
6202 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6203 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6204 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6205 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6206 the quotation has type <literal>Q Type</literal>.</para></listitem>
6207 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6208 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6209 </itemizedlist></para></listitem>
6212 A quasi-quotation can appear in either a pattern context or an
6213 expression context and is also written in Oxford brackets:
6215 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6216 where the "..." is an arbitrary string; a full description of the
6217 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6218 </itemizedlist></para></listitem>
6221 A name can be quoted with either one or two prefix single quotes:
6223 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6224 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6225 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6227 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6228 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6231 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6232 may also be given as an argument to the <literal>reify</literal> function.
6236 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6237 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6244 $(deriveStuff 'f) -- Uses the $(...) notation
6248 deriveStuff 'g -- Omits the $(...)
6252 This abbreviation makes top-level declaration slices quieter and less intimidating.
6257 (Compared to the original paper, there are many differences of detail.
6258 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6259 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6260 Pattern splices and quotations are not implemented.)
6264 <sect2> <title> Using Template Haskell </title>
6268 The data types and monadic constructor functions for Template Haskell are in the library
6269 <literal>Language.Haskell.THSyntax</literal>.
6273 You can only run a function at compile time if it is imported from another module. That is,
6274 you can't define a function in a module, and call it from within a splice in the same module.
6275 (It would make sense to do so, but it's hard to implement.)
6279 You can only run a function at compile time if it is imported
6280 from another module <emphasis>that is not part of a mutually-recursive group of modules
6281 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6282 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6283 splice is to be run.</para>
6285 For example, when compiling module A,
6286 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6287 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6291 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6294 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6295 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6296 compiles and runs a program, and then looks at the result. So it's important that
6297 the program it compiles produces results whose representations are identical to
6298 those of the compiler itself.
6302 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6303 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6308 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6309 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6310 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6317 -- Import our template "pr"
6318 import Printf ( pr )
6320 -- The splice operator $ takes the Haskell source code
6321 -- generated at compile time by "pr" and splices it into
6322 -- the argument of "putStrLn".
6323 main = putStrLn ( $(pr "Hello") )
6329 -- Skeletal printf from the paper.
6330 -- It needs to be in a separate module to the one where
6331 -- you intend to use it.
6333 -- Import some Template Haskell syntax
6334 import Language.Haskell.TH
6336 -- Describe a format string
6337 data Format = D | S | L String
6339 -- Parse a format string. This is left largely to you
6340 -- as we are here interested in building our first ever
6341 -- Template Haskell program and not in building printf.
6342 parse :: String -> [Format]
6345 -- Generate Haskell source code from a parsed representation
6346 -- of the format string. This code will be spliced into
6347 -- the module which calls "pr", at compile time.
6348 gen :: [Format] -> Q Exp
6349 gen [D] = [| \n -> show n |]
6350 gen [S] = [| \s -> s |]
6351 gen [L s] = stringE s
6353 -- Here we generate the Haskell code for the splice
6354 -- from an input format string.
6355 pr :: String -> Q Exp
6356 pr s = gen (parse s)
6359 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6362 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6365 <para>Run "main.exe" and here is your output:</para>
6375 <title>Using Template Haskell with Profiling</title>
6376 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6378 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6379 interpreter to run the splice expressions. The bytecode interpreter
6380 runs the compiled expression on top of the same runtime on which GHC
6381 itself is running; this means that the compiled code referred to by
6382 the interpreted expression must be compatible with this runtime, and
6383 in particular this means that object code that is compiled for
6384 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6385 expression, because profiled object code is only compatible with the
6386 profiling version of the runtime.</para>
6388 <para>This causes difficulties if you have a multi-module program
6389 containing Template Haskell code and you need to compile it for
6390 profiling, because GHC cannot load the profiled object code and use it
6391 when executing the splices. Fortunately GHC provides a workaround.
6392 The basic idea is to compile the program twice:</para>
6396 <para>Compile the program or library first the normal way, without
6397 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6400 <para>Then compile it again with <option>-prof</option>, and
6401 additionally use <option>-osuf
6402 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6403 to name the object files differently (you can choose any suffix
6404 that isn't the normal object suffix here). GHC will automatically
6405 load the object files built in the first step when executing splice
6406 expressions. If you omit the <option>-osuf</option> flag when
6407 building with <option>-prof</option> and Template Haskell is used,
6408 GHC will emit an error message. </para>
6413 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6414 <para>Quasi-quotation allows patterns and expressions to be written using
6415 programmer-defined concrete syntax; the motivation behind the extension and
6416 several examples are documented in
6417 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6418 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6419 2007). The example below shows how to write a quasiquoter for a simple
6420 expression language.</para>
6422 Here are the salient features
6425 A quasi-quote has the form
6426 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6429 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6430 quoter; it cannot be an arbitrary expression.
6433 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6434 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6435 those overlap with Template Haskell quotations.
6438 There must be no spaces in the token
6439 <literal>[<replaceable>quoter</replaceable>|</literal>.
6442 The quoted <replaceable>string</replaceable>
6443 can be arbitrary, and may contain newlines.
6449 A quasiquote may appear in place of
6451 <listitem><para>An expression</para></listitem>
6452 <listitem><para>A pattern</para></listitem>
6453 <listitem><para>A type</para></listitem>
6454 <listitem><para>A top-level declaration</para></listitem>
6456 (Only the first two are described in the paper.)
6460 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6461 which is defined thus:
6463 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6464 quotePat :: String -> Q Pat,
6465 quoteType :: String -> Q Type,
6466 quoteDec :: String -> Q [Dec] }
6468 That is, a quoter is a tuple of four parsers, one for each of the contexts
6469 in which a quasi-quote can occur.
6472 A quasi-quote is expanded by applying the appropriate parser to the string
6473 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6474 type, declaration) determines which of the parsers is called.
6479 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6480 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6481 The example makes use of an antiquoted
6482 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6483 (this syntax for anti-quotation was defined by the parser's
6484 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6485 integer value argument of the constructor <literal>IntExpr</literal> when
6486 pattern matching. Please see the referenced paper for further details regarding
6487 anti-quotation as well as the description of a technique that uses SYB to
6488 leverage a single parser of type <literal>String -> a</literal> to generate both
6489 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6490 pattern parser that returns a value of type <literal>Q Pat</literal>.
6494 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6495 the example, <literal>expr</literal> cannot be defined
6496 in <literal>Main.hs</literal> where it is used, but must be imported.
6500 {- ------------- file Main.hs --------------- -}
6506 main = do { print $ eval [expr|1 + 2|]
6508 { [expr|'int:n|] -> print n
6514 {- ------------- file Expr.hs --------------- -}
6517 import qualified Language.Haskell.TH as TH
6518 import Language.Haskell.TH.Quote
6520 data Expr = IntExpr Integer
6521 | AntiIntExpr String
6522 | BinopExpr BinOp Expr Expr
6524 deriving(Show, Typeable, Data)
6530 deriving(Show, Typeable, Data)
6532 eval :: Expr -> Integer
6533 eval (IntExpr n) = n
6534 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6541 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6543 -- Parse an Expr, returning its representation as
6544 -- either a Q Exp or a Q Pat. See the referenced paper
6545 -- for how to use SYB to do this by writing a single
6546 -- parser of type String -> Expr instead of two
6547 -- separate parsers.
6549 parseExprExp :: String -> Q Exp
6552 parseExprPat :: String -> Q Pat
6556 <para>Now run the compiler:
6558 $ ghc --make -XQuasiQuotes Main.hs -o main
6562 <para>Run "main" and here is your output:
6573 <!-- ===================== Arrow notation =================== -->
6575 <sect1 id="arrow-notation">
6576 <title>Arrow notation
6579 <para>Arrows are a generalization of monads introduced by John Hughes.
6580 For more details, see
6585 “Generalising Monads to Arrows”,
6586 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6587 pp67–111, May 2000.
6588 The paper that introduced arrows: a friendly introduction, motivated with
6589 programming examples.
6595 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6596 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6597 Introduced the notation described here.
6603 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6604 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6611 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6612 John Hughes, in <citetitle>5th International Summer School on
6613 Advanced Functional Programming</citetitle>,
6614 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6616 This paper includes another introduction to the notation,
6617 with practical examples.
6623 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6624 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6625 A terse enumeration of the formal rules used
6626 (extracted from comments in the source code).
6632 The arrows web page at
6633 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6638 With the <option>-XArrows</option> flag, GHC supports the arrow
6639 notation described in the second of these papers,
6640 translating it using combinators from the
6641 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6643 What follows is a brief introduction to the notation;
6644 it won't make much sense unless you've read Hughes's paper.
6647 <para>The extension adds a new kind of expression for defining arrows:
6649 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6650 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6652 where <literal>proc</literal> is a new keyword.
6653 The variables of the pattern are bound in the body of the
6654 <literal>proc</literal>-expression,
6655 which is a new sort of thing called a <firstterm>command</firstterm>.
6656 The syntax of commands is as follows:
6658 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6659 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6660 | <replaceable>cmd</replaceable><superscript>0</superscript>
6662 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6663 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6664 infix operators as for expressions, and
6666 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6667 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6668 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6669 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6670 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6671 | <replaceable>fcmd</replaceable>
6673 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6674 | ( <replaceable>cmd</replaceable> )
6675 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6677 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6678 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6679 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6680 | <replaceable>cmd</replaceable>
6682 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6683 except that the bodies are commands instead of expressions.
6687 Commands produce values, but (like monadic computations)
6688 may yield more than one value,
6689 or none, and may do other things as well.
6690 For the most part, familiarity with monadic notation is a good guide to
6692 However the values of expressions, even monadic ones,
6693 are determined by the values of the variables they contain;
6694 this is not necessarily the case for commands.
6698 A simple example of the new notation is the expression
6700 proc x -> f -< x+1
6702 We call this a <firstterm>procedure</firstterm> or
6703 <firstterm>arrow abstraction</firstterm>.
6704 As with a lambda expression, the variable <literal>x</literal>
6705 is a new variable bound within the <literal>proc</literal>-expression.
6706 It refers to the input to the arrow.
6707 In the above example, <literal>-<</literal> is not an identifier but an
6708 new reserved symbol used for building commands from an expression of arrow
6709 type and an expression to be fed as input to that arrow.
6710 (The weird look will make more sense later.)
6711 It may be read as analogue of application for arrows.
6712 The above example is equivalent to the Haskell expression
6714 arr (\ x -> x+1) >>> f
6716 That would make no sense if the expression to the left of
6717 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6718 More generally, the expression to the left of <literal>-<</literal>
6719 may not involve any <firstterm>local variable</firstterm>,
6720 i.e. a variable bound in the current arrow abstraction.
6721 For such a situation there is a variant <literal>-<<</literal>, as in
6723 proc x -> f x -<< x+1
6725 which is equivalent to
6727 arr (\ x -> (f x, x+1)) >>> app
6729 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6731 Such an arrow is equivalent to a monad, so if you're using this form
6732 you may find a monadic formulation more convenient.
6736 <title>do-notation for commands</title>
6739 Another form of command is a form of <literal>do</literal>-notation.
6740 For example, you can write
6749 You can read this much like ordinary <literal>do</literal>-notation,
6750 but with commands in place of monadic expressions.
6751 The first line sends the value of <literal>x+1</literal> as an input to
6752 the arrow <literal>f</literal>, and matches its output against
6753 <literal>y</literal>.
6754 In the next line, the output is discarded.
6755 The arrow <function>returnA</function> is defined in the
6756 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6757 module as <literal>arr id</literal>.
6758 The above example is treated as an abbreviation for
6760 arr (\ x -> (x, x)) >>>
6761 first (arr (\ x -> x+1) >>> f) >>>
6762 arr (\ (y, x) -> (y, (x, y))) >>>
6763 first (arr (\ y -> 2*y) >>> g) >>>
6765 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6766 first (arr (\ (x, z) -> x*z) >>> h) >>>
6767 arr (\ (t, z) -> t+z) >>>
6770 Note that variables not used later in the composition are projected out.
6771 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6773 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6774 module, this reduces to
6776 arr (\ x -> (x+1, x)) >>>
6778 arr (\ (y, x) -> (2*y, (x, y))) >>>
6780 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6782 arr (\ (t, z) -> t+z)
6784 which is what you might have written by hand.
6785 With arrow notation, GHC keeps track of all those tuples of variables for you.
6789 Note that although the above translation suggests that
6790 <literal>let</literal>-bound variables like <literal>z</literal> must be
6791 monomorphic, the actual translation produces Core,
6792 so polymorphic variables are allowed.
6796 It's also possible to have mutually recursive bindings,
6797 using the new <literal>rec</literal> keyword, as in the following example:
6799 counter :: ArrowCircuit a => a Bool Int
6800 counter = proc reset -> do
6801 rec output <- returnA -< if reset then 0 else next
6802 next <- delay 0 -< output+1
6803 returnA -< output
6805 The translation of such forms uses the <function>loop</function> combinator,
6806 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6812 <title>Conditional commands</title>
6815 In the previous example, we used a conditional expression to construct the
6817 Sometimes we want to conditionally execute different commands, as in
6824 which is translated to
6826 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6827 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6829 Since the translation uses <function>|||</function>,
6830 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6834 There are also <literal>case</literal> commands, like
6840 y <- h -< (x1, x2)
6844 The syntax is the same as for <literal>case</literal> expressions,
6845 except that the bodies of the alternatives are commands rather than expressions.
6846 The translation is similar to that of <literal>if</literal> commands.
6852 <title>Defining your own control structures</title>
6855 As we're seen, arrow notation provides constructs,
6856 modelled on those for expressions,
6857 for sequencing, value recursion and conditionals.
6858 But suitable combinators,
6859 which you can define in ordinary Haskell,
6860 may also be used to build new commands out of existing ones.
6861 The basic idea is that a command defines an arrow from environments to values.
6862 These environments assign values to the free local variables of the command.
6863 Thus combinators that produce arrows from arrows
6864 may also be used to build commands from commands.
6865 For example, the <literal>ArrowChoice</literal> class includes a combinator
6867 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6869 so we can use it to build commands:
6871 expr' = proc x -> do
6874 symbol Plus -< ()
6875 y <- term -< ()
6878 symbol Minus -< ()
6879 y <- term -< ()
6882 (The <literal>do</literal> on the first line is needed to prevent the first
6883 <literal><+> ...</literal> from being interpreted as part of the
6884 expression on the previous line.)
6885 This is equivalent to
6887 expr' = (proc x -> returnA -< x)
6888 <+> (proc x -> do
6889 symbol Plus -< ()
6890 y <- term -< ()
6892 <+> (proc x -> do
6893 symbol Minus -< ()
6894 y <- term -< ()
6897 It is essential that this operator be polymorphic in <literal>e</literal>
6898 (representing the environment input to the command
6899 and thence to its subcommands)
6900 and satisfy the corresponding naturality property
6902 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6904 at least for strict <literal>k</literal>.
6905 (This should be automatic if you're not using <function>seq</function>.)
6906 This ensures that environments seen by the subcommands are environments
6907 of the whole command,
6908 and also allows the translation to safely trim these environments.
6909 The operator must also not use any variable defined within the current
6914 We could define our own operator
6916 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6917 untilA body cond = proc x ->
6918 b <- cond -< x
6919 if b then returnA -< ()
6922 untilA body cond -< x
6924 and use it in the same way.
6925 Of course this infix syntax only makes sense for binary operators;
6926 there is also a more general syntax involving special brackets:
6930 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6937 <title>Primitive constructs</title>
6940 Some operators will need to pass additional inputs to their subcommands.
6941 For example, in an arrow type supporting exceptions,
6942 the operator that attaches an exception handler will wish to pass the
6943 exception that occurred to the handler.
6944 Such an operator might have a type
6946 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6948 where <literal>Ex</literal> is the type of exceptions handled.
6949 You could then use this with arrow notation by writing a command
6951 body `handleA` \ ex -> handler
6953 so that if an exception is raised in the command <literal>body</literal>,
6954 the variable <literal>ex</literal> is bound to the value of the exception
6955 and the command <literal>handler</literal>,
6956 which typically refers to <literal>ex</literal>, is entered.
6957 Though the syntax here looks like a functional lambda,
6958 we are talking about commands, and something different is going on.
6959 The input to the arrow represented by a command consists of values for
6960 the free local variables in the command, plus a stack of anonymous values.
6961 In all the prior examples, this stack was empty.
6962 In the second argument to <function>handleA</function>,
6963 this stack consists of one value, the value of the exception.
6964 The command form of lambda merely gives this value a name.
6969 the values on the stack are paired to the right of the environment.
6970 So operators like <function>handleA</function> that pass
6971 extra inputs to their subcommands can be designed for use with the notation
6972 by pairing the values with the environment in this way.
6973 More precisely, the type of each argument of the operator (and its result)
6974 should have the form
6976 a (...(e,t1), ... tn) t
6978 where <replaceable>e</replaceable> is a polymorphic variable
6979 (representing the environment)
6980 and <replaceable>ti</replaceable> are the types of the values on the stack,
6981 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6982 The polymorphic variable <replaceable>e</replaceable> must not occur in
6983 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6984 <replaceable>t</replaceable>.
6985 However the arrows involved need not be the same.
6986 Here are some more examples of suitable operators:
6988 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6989 runReader :: ... => a e c -> a' (e,State) c
6990 runState :: ... => a e c -> a' (e,State) (c,State)
6992 We can supply the extra input required by commands built with the last two
6993 by applying them to ordinary expressions, as in
6997 (|runReader (do { ... })|) s
6999 which adds <literal>s</literal> to the stack of inputs to the command
7000 built using <function>runReader</function>.
7004 The command versions of lambda abstraction and application are analogous to
7005 the expression versions.
7006 In particular, the beta and eta rules describe equivalences of commands.
7007 These three features (operators, lambda abstraction and application)
7008 are the core of the notation; everything else can be built using them,
7009 though the results would be somewhat clumsy.
7010 For example, we could simulate <literal>do</literal>-notation by defining
7012 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7013 u `bind` f = returnA &&& u >>> f
7015 bind_ :: Arrow a => a e b -> a e c -> a e c
7016 u `bind_` f = u `bind` (arr fst >>> f)
7018 We could simulate <literal>if</literal> by defining
7020 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7021 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7028 <title>Differences with the paper</title>
7033 <para>Instead of a single form of arrow application (arrow tail) with two
7034 translations, the implementation provides two forms
7035 <quote><literal>-<</literal></quote> (first-order)
7036 and <quote><literal>-<<</literal></quote> (higher-order).
7041 <para>User-defined operators are flagged with banana brackets instead of
7042 a new <literal>form</literal> keyword.
7051 <title>Portability</title>
7054 Although only GHC implements arrow notation directly,
7055 there is also a preprocessor
7057 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7058 that translates arrow notation into Haskell 98
7059 for use with other Haskell systems.
7060 You would still want to check arrow programs with GHC;
7061 tracing type errors in the preprocessor output is not easy.
7062 Modules intended for both GHC and the preprocessor must observe some
7063 additional restrictions:
7068 The module must import
7069 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7075 The preprocessor cannot cope with other Haskell extensions.
7076 These would have to go in separate modules.
7082 Because the preprocessor targets Haskell (rather than Core),
7083 <literal>let</literal>-bound variables are monomorphic.
7094 <!-- ==================== BANG PATTERNS ================= -->
7096 <sect1 id="bang-patterns">
7097 <title>Bang patterns
7098 <indexterm><primary>Bang patterns</primary></indexterm>
7100 <para>GHC supports an extension of pattern matching called <emphasis>bang
7101 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7102 Bang patterns are under consideration for Haskell Prime.
7104 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7105 prime feature description</ulink> contains more discussion and examples
7106 than the material below.
7109 The key change is the addition of a new rule to the
7110 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7111 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7112 against a value <replaceable>v</replaceable> behaves as follows:
7114 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7115 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7119 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7122 <sect2 id="bang-patterns-informal">
7123 <title>Informal description of bang patterns
7126 The main idea is to add a single new production to the syntax of patterns:
7130 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7131 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7136 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7137 whereas without the bang it would be lazy.
7138 Bang patterns can be nested of course:
7142 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7143 <literal>y</literal>.
7144 A bang only really has an effect if it precedes a variable or wild-card pattern:
7149 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7150 putting a bang before a pattern that
7151 forces evaluation anyway does nothing.
7154 There is one (apparent) exception to this general rule that a bang only
7155 makes a difference when it precedes a variable or wild-card: a bang at the
7156 top level of a <literal>let</literal> or <literal>where</literal>
7157 binding makes the binding strict, regardless of the pattern.
7158 (We say "apparent" exception because the Right Way to think of it is that the bang
7159 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7160 is part of the syntax of the <emphasis>binding</emphasis>,
7161 creating a "bang-pattern binding".)
7166 is a bang-pattern binding. Operationally, it behaves just like a case expression:
7168 case e of [x,y] -> b
7170 Like a case expression, a bang-pattern binding must be non-recursive, and
7173 However, <emphasis>nested</emphasis> bangs in a pattern binding behave uniformly with all other forms of
7174 pattern matching. For example
7176 let (!x,[y]) = e in b
7178 is equivalent to this:
7180 let { t = case e of (x,[y]) -> x `seq` (x,y)
7185 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7186 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7187 evaluation of <literal>x</literal>.
7190 Bang patterns work in <literal>case</literal> expressions too, of course:
7192 g5 x = let y = f x in body
7193 g6 x = case f x of { y -> body }
7194 g7 x = case f x of { !y -> body }
7196 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7197 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7198 result, and then evaluates <literal>body</literal>.
7203 <sect2 id="bang-patterns-sem">
7204 <title>Syntax and semantics
7208 We add a single new production to the syntax of patterns:
7212 There is one problem with syntactic ambiguity. Consider:
7216 Is this a definition of the infix function "<literal>(!)</literal>",
7217 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7218 ambiguity in favour of the latter. If you want to define
7219 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7224 The semantics of Haskell pattern matching is described in <ulink
7225 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7226 Section 3.17.2</ulink> of the Haskell Report. To this description add
7227 one extra item 10, saying:
7228 <itemizedlist><listitem><para>Matching
7229 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7230 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7231 <listitem><para>otherwise, <literal>pat</literal> is matched against
7232 <literal>v</literal></para></listitem>
7234 </para></listitem></itemizedlist>
7235 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7236 Section 3.17.3</ulink>, add a new case (t):
7238 case v of { !pat -> e; _ -> e' }
7239 = v `seq` case v of { pat -> e; _ -> e' }
7242 That leaves let expressions, whose translation is given in
7243 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7245 of the Haskell Report.
7246 In the translation box, first apply
7247 the following transformation: for each pattern <literal>pi</literal> that is of
7248 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7249 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7250 have a bang at the top, apply the rules in the existing box.
7252 <para>The effect of the let rule is to force complete matching of the pattern
7253 <literal>qi</literal> before evaluation of the body is begun. The bang is
7254 retained in the translated form in case <literal>qi</literal> is a variable,
7262 The let-binding can be recursive. However, it is much more common for
7263 the let-binding to be non-recursive, in which case the following law holds:
7264 <literal>(let !p = rhs in body)</literal>
7266 <literal>(case rhs of !p -> body)</literal>
7269 A pattern with a bang at the outermost level is not allowed at the top level of
7275 <!-- ==================== ASSERTIONS ================= -->
7277 <sect1 id="assertions">
7279 <indexterm><primary>Assertions</primary></indexterm>
7283 If you want to make use of assertions in your standard Haskell code, you
7284 could define a function like the following:
7290 assert :: Bool -> a -> a
7291 assert False x = error "assertion failed!"
7298 which works, but gives you back a less than useful error message --
7299 an assertion failed, but which and where?
7303 One way out is to define an extended <function>assert</function> function which also
7304 takes a descriptive string to include in the error message and
7305 perhaps combine this with the use of a pre-processor which inserts
7306 the source location where <function>assert</function> was used.
7310 Ghc offers a helping hand here, doing all of this for you. For every
7311 use of <function>assert</function> in the user's source:
7317 kelvinToC :: Double -> Double
7318 kelvinToC k = assert (k >= 0.0) (k+273.15)
7324 Ghc will rewrite this to also include the source location where the
7331 assert pred val ==> assertError "Main.hs|15" pred val
7337 The rewrite is only performed by the compiler when it spots
7338 applications of <function>Control.Exception.assert</function>, so you
7339 can still define and use your own versions of
7340 <function>assert</function>, should you so wish. If not, import
7341 <literal>Control.Exception</literal> to make use
7342 <function>assert</function> in your code.
7346 GHC ignores assertions when optimisation is turned on with the
7347 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7348 <literal>assert pred e</literal> will be rewritten to
7349 <literal>e</literal>. You can also disable assertions using the
7350 <option>-fignore-asserts</option>
7351 option<indexterm><primary><option>-fignore-asserts</option></primary>
7352 </indexterm>.</para>
7355 Assertion failures can be caught, see the documentation for the
7356 <literal>Control.Exception</literal> library for the details.
7362 <!-- =============================== PRAGMAS =========================== -->
7364 <sect1 id="pragmas">
7365 <title>Pragmas</title>
7367 <indexterm><primary>pragma</primary></indexterm>
7369 <para>GHC supports several pragmas, or instructions to the
7370 compiler placed in the source code. Pragmas don't normally affect
7371 the meaning of the program, but they might affect the efficiency
7372 of the generated code.</para>
7374 <para>Pragmas all take the form
7376 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7378 where <replaceable>word</replaceable> indicates the type of
7379 pragma, and is followed optionally by information specific to that
7380 type of pragma. Case is ignored in
7381 <replaceable>word</replaceable>. The various values for
7382 <replaceable>word</replaceable> that GHC understands are described
7383 in the following sections; any pragma encountered with an
7384 unrecognised <replaceable>word</replaceable> is
7385 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7386 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7388 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7392 pragma must precede the <literal>module</literal> keyword in the file.
7395 There can be as many file-header pragmas as you please, and they can be
7396 preceded or followed by comments.
7399 File-header pragmas are read once only, before
7400 pre-processing the file (e.g. with cpp).
7403 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7404 <literal>{-# OPTIONS_GHC #-}</literal>, and
7405 <literal>{-# INCLUDE #-}</literal>.
7410 <sect2 id="language-pragma">
7411 <title>LANGUAGE pragma</title>
7413 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7414 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7416 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7418 It is the intention that all Haskell compilers support the
7419 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7420 all extensions are supported by all compilers, of
7421 course. The <literal>LANGUAGE</literal> pragma should be used instead
7422 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7424 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7426 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7428 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7430 <para>Every language extension can also be turned into a command-line flag
7431 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7432 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7435 <para>A list of all supported language extensions can be obtained by invoking
7436 <literal>ghc --supported-extensions</literal> (see <xref linkend="modes"/>).</para>
7438 <para>Any extension from the <literal>Extension</literal> type defined in
7440 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7441 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7445 <sect2 id="options-pragma">
7446 <title>OPTIONS_GHC pragma</title>
7447 <indexterm><primary>OPTIONS_GHC</primary>
7449 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7452 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7453 additional options that are given to the compiler when compiling
7454 this source file. See <xref linkend="source-file-options"/> for
7457 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7458 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7461 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7463 <sect2 id="include-pragma">
7464 <title>INCLUDE pragma</title>
7466 <para>The <literal>INCLUDE</literal> used to be necessary for
7467 specifying header files to be included when using the FFI and
7468 compiling via C. It is no longer required for GHC, but is
7469 accepted (and ignored) for compatibility with other
7473 <sect2 id="warning-deprecated-pragma">
7474 <title>WARNING and DEPRECATED pragmas</title>
7475 <indexterm><primary>WARNING</primary></indexterm>
7476 <indexterm><primary>DEPRECATED</primary></indexterm>
7478 <para>The WARNING pragma allows you to attach an arbitrary warning
7479 to a particular function, class, or type.
7480 A DEPRECATED pragma lets you specify that
7481 a particular function, class, or type is deprecated.
7482 There are two ways of using these pragmas.
7486 <para>You can work on an entire module thus:</para>
7488 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7493 module Wibble {-# WARNING "This is an unstable interface." #-} where
7496 <para>When you compile any module that import
7497 <literal>Wibble</literal>, GHC will print the specified
7502 <para>You can attach a warning to a function, class, type, or data constructor, with the
7503 following top-level declarations:</para>
7505 {-# DEPRECATED f, C, T "Don't use these" #-}
7506 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7508 <para>When you compile any module that imports and uses any
7509 of the specified entities, GHC will print the specified
7511 <para> You can only attach to entities declared at top level in the module
7512 being compiled, and you can only use unqualified names in the list of
7513 entities. A capitalised name, such as <literal>T</literal>
7514 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7515 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7516 both are in scope. If both are in scope, there is currently no way to
7517 specify one without the other (c.f. fixities
7518 <xref linkend="infix-tycons"/>).</para>
7521 Warnings and deprecations are not reported for
7522 (a) uses within the defining module, and
7523 (b) uses in an export list.
7524 The latter reduces spurious complaints within a library
7525 in which one module gathers together and re-exports
7526 the exports of several others.
7528 <para>You can suppress the warnings with the flag
7529 <option>-fno-warn-warnings-deprecations</option>.</para>
7532 <sect2 id="inline-noinline-pragma">
7533 <title>INLINE and NOINLINE pragmas</title>
7535 <para>These pragmas control the inlining of function
7538 <sect3 id="inline-pragma">
7539 <title>INLINE pragma</title>
7540 <indexterm><primary>INLINE</primary></indexterm>
7542 <para>GHC (with <option>-O</option>, as always) tries to
7543 inline (or “unfold”) functions/values that are
7544 “small enough,” thus avoiding the call overhead
7545 and possibly exposing other more-wonderful optimisations.
7546 Normally, if GHC decides a function is “too
7547 expensive” to inline, it will not do so, nor will it
7548 export that unfolding for other modules to use.</para>
7550 <para>The sledgehammer you can bring to bear is the
7551 <literal>INLINE</literal><indexterm><primary>INLINE
7552 pragma</primary></indexterm> pragma, used thusly:</para>
7555 key_function :: Int -> String -> (Bool, Double)
7556 {-# INLINE key_function #-}
7559 <para>The major effect of an <literal>INLINE</literal> pragma
7560 is to declare a function's “cost” to be very low.
7561 The normal unfolding machinery will then be very keen to
7562 inline it. However, an <literal>INLINE</literal> pragma for a
7563 function "<literal>f</literal>" has a number of other effects:
7566 While GHC is keen to inline the function, it does not do so
7567 blindly. For example, if you write
7571 there really isn't any point in inlining <literal>key_function</literal> to get
7573 map (\x -> <replaceable>body</replaceable>) xs
7575 In general, GHC only inlines the function if there is some reason (no matter
7576 how slight) to supose that it is useful to do so.
7580 Moreover, GHC will only inline the function if it is <emphasis>fully applied</emphasis>,
7581 where "fully applied"
7582 means applied to as many arguments as appear (syntactically)
7583 on the LHS of the function
7584 definition. For example:
7586 comp1 :: (b -> c) -> (a -> b) -> a -> c
7587 {-# INLINE comp1 #-}
7588 comp1 f g = \x -> f (g x)
7590 comp2 :: (b -> c) -> (a -> b) -> a -> c
7591 {-# INLINE comp2 #-}
7592 comp2 f g x = f (g x)
7594 The two functions <literal>comp1</literal> and <literal>comp2</literal> have the
7595 same semantics, but <literal>comp1</literal> will be inlined when applied
7596 to <emphasis>two</emphasis> arguments, while <literal>comp2</literal> requires
7597 <emphasis>three</emphasis>. This might make a big difference if you say
7599 map (not `comp1` not) xs
7601 which will optimise better than the corresponding use of `comp2`.
7605 It is useful for GHC to optimise the definition of an
7606 INLINE function <literal>f</literal> just like any other non-INLINE function,
7607 in case the non-inlined version of <literal>f</literal> is
7608 ultimately called. But we don't want to inline
7609 the <emphasis>optimised</emphasis> version
7610 of <literal>f</literal>;
7611 a major reason for INLINE pragmas is to expose functions
7612 in <literal>f</literal>'s RHS that have
7613 rewrite rules, and it's no good if those functions have been optimised
7617 So <emphasis>GHC guarantees to inline precisely the code that you wrote</emphasis>, no more
7618 and no less. It does this by capturing a copy of the definition of the function to use
7619 for inlining (we call this the "inline-RHS"), which it leaves untouched,
7620 while optimising the ordinarly RHS as usual. For externally-visible functions
7621 the inline-RHS (not the optimised RHS) is recorded in the interface file.
7624 An INLINE function is not worker/wrappered by strictness analysis.
7625 It's going to be inlined wholesale instead.
7629 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7630 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7631 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7632 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7633 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7634 when there is no choice even an INLINE function can be selected, in which case
7635 the INLINE pragma is ignored.
7636 For example, for a self-recursive function, the loop breaker can only be the function
7637 itself, so an INLINE pragma is always ignored.</para>
7639 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7640 function can be put anywhere its type signature could be
7643 <para><literal>INLINE</literal> pragmas are a particularly
7645 <literal>then</literal>/<literal>return</literal> (or
7646 <literal>bind</literal>/<literal>unit</literal>) functions in
7647 a monad. For example, in GHC's own
7648 <literal>UniqueSupply</literal> monad code, we have:</para>
7651 {-# INLINE thenUs #-}
7652 {-# INLINE returnUs #-}
7655 <para>See also the <literal>NOINLINE</literal> (<xref linkend="inlinable-pragma"/>)
7656 and <literal>INLINABLE</literal> (<xref linkend="noinline-pragma"/>)
7659 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7660 so if you want your code to be HBC-compatible you'll have to surround
7661 the pragma with C pre-processor directives
7662 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7666 <sect3 id="inlinable-pragma">
7667 <title>INLINABLE pragma</title>
7669 <para>An <literal>{-# INLINABLE f #-}</literal> pragma on a
7670 function <literal>f</literal> has the following behaviour:
7673 While <literal>INLINE</literal> says "please inline me", the <literal>INLINABLE</literal>
7674 says "feel free to inline me; use your
7675 discretion". In other words the choice is left to GHC, which uses the same
7676 rules as for pragma-free functions. Unlike <literal>INLINE</literal>, that decision is made at
7677 the <emphasis>call site</emphasis>, and
7678 will therefore be affected by the inlining threshold, optimisation level etc.
7681 Like <literal>INLINE</literal>, the <literal>INLINABLE</literal> pragma retains a
7682 copy of the original RHS for
7683 inlining purposes, and persists it in the interface file, regardless of
7684 the size of the RHS.
7688 One way to use <literal>INLINABLE</literal> is in conjunction with
7689 the special function <literal>inline</literal> (<xref linkend="special-ids"/>).
7690 The call <literal>inline f</literal> tries very hard to inline <literal>f</literal>.
7691 To make sure that <literal>f</literal> can be inlined,
7692 it is a good idea to mark the definition
7693 of <literal>f</literal> as <literal>INLINABLE</literal>,
7694 so that GHC guarantees to expose an unfolding regardless of how big it is.
7695 Moreover, by annotating <literal>f</literal> as <literal>INLINABLE</literal>,
7696 you ensure that <literal>f</literal>'s original RHS is inlined, rather than
7697 whatever random optimised version of <literal>f</literal> GHC's optimiser
7702 The <literal>INLINABLE</literal> pragma also works with <literal>SPECIALISE</literal>:
7703 if you mark function <literal>f</literal> as <literal>INLINABLE</literal>, then
7704 you can subsequently <literal>SPECIALISE</literal> in another module
7705 (see <xref linkend="specialize-pragma"/>).</para></listitem>
7708 Unlike <literal>INLINE</literal>, it is OK to use
7709 an <literal>INLINABLE</literal> pragma on a recursive function.
7710 The principal reason do to so to allow later use of <literal>SPECIALISE</literal>
7717 <sect3 id="noinline-pragma">
7718 <title>NOINLINE pragma</title>
7720 <indexterm><primary>NOINLINE</primary></indexterm>
7721 <indexterm><primary>NOTINLINE</primary></indexterm>
7723 <para>The <literal>NOINLINE</literal> pragma does exactly what
7724 you'd expect: it stops the named function from being inlined
7725 by the compiler. You shouldn't ever need to do this, unless
7726 you're very cautious about code size.</para>
7728 <para><literal>NOTINLINE</literal> is a synonym for
7729 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7730 specified by Haskell 98 as the standard way to disable
7731 inlining, so it should be used if you want your code to be
7735 <sect3 id="conlike-pragma">
7736 <title>CONLIKE modifier</title>
7737 <indexterm><primary>CONLIKE</primary></indexterm>
7738 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7739 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7743 <sect3 id="phase-control">
7744 <title>Phase control</title>
7746 <para> Sometimes you want to control exactly when in GHC's
7747 pipeline the INLINE pragma is switched on. Inlining happens
7748 only during runs of the <emphasis>simplifier</emphasis>. Each
7749 run of the simplifier has a different <emphasis>phase
7750 number</emphasis>; the phase number decreases towards zero.
7751 If you use <option>-dverbose-core2core</option> you'll see the
7752 sequence of phase numbers for successive runs of the
7753 simplifier. In an INLINE pragma you can optionally specify a
7757 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7758 <literal>f</literal>
7759 until phase <literal>k</literal>, but from phase
7760 <literal>k</literal> onwards be very keen to inline it.
7763 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7764 <literal>f</literal>
7765 until phase <literal>k</literal>, but from phase
7766 <literal>k</literal> onwards do not inline it.
7769 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7770 <literal>f</literal>
7771 until phase <literal>k</literal>, but from phase
7772 <literal>k</literal> onwards be willing to inline it (as if
7773 there was no pragma).
7776 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7777 <literal>f</literal>
7778 until phase <literal>k</literal>, but from phase
7779 <literal>k</literal> onwards do not inline it.
7782 The same information is summarised here:
7784 -- Before phase 2 Phase 2 and later
7785 {-# INLINE [2] f #-} -- No Yes
7786 {-# INLINE [~2] f #-} -- Yes No
7787 {-# NOINLINE [2] f #-} -- No Maybe
7788 {-# NOINLINE [~2] f #-} -- Maybe No
7790 {-# INLINE f #-} -- Yes Yes
7791 {-# NOINLINE f #-} -- No No
7793 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7794 function body is small, or it is applied to interesting-looking arguments etc).
7795 Another way to understand the semantics is this:
7797 <listitem><para>For both INLINE and NOINLINE, the phase number says
7798 when inlining is allowed at all.</para></listitem>
7799 <listitem><para>The INLINE pragma has the additional effect of making the
7800 function body look small, so that when inlining is allowed it is very likely to
7805 <para>The same phase-numbering control is available for RULES
7806 (<xref linkend="rewrite-rules"/>).</para>
7810 <sect2 id="annotation-pragmas">
7811 <title>ANN pragmas</title>
7813 <para>GHC offers the ability to annotate various code constructs with additional
7814 data by using three pragmas. This data can then be inspected at a later date by
7815 using GHC-as-a-library.</para>
7817 <sect3 id="ann-pragma">
7818 <title>Annotating values</title>
7820 <indexterm><primary>ANN</primary></indexterm>
7822 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7823 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7824 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7825 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7826 you would do this:</para>
7829 {-# ANN foo (Just "Hello") #-}
7834 A number of restrictions apply to use of annotations:
7836 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7837 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7838 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7839 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7840 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7842 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7843 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7846 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7847 please give the GHC team a shout</ulink>.
7850 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7851 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7854 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7859 <sect3 id="typeann-pragma">
7860 <title>Annotating types</title>
7862 <indexterm><primary>ANN type</primary></indexterm>
7863 <indexterm><primary>ANN</primary></indexterm>
7865 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7868 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7873 <sect3 id="modann-pragma">
7874 <title>Annotating modules</title>
7876 <indexterm><primary>ANN module</primary></indexterm>
7877 <indexterm><primary>ANN</primary></indexterm>
7879 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7882 {-# ANN module (Just "A `Maybe String' annotation") #-}
7887 <sect2 id="line-pragma">
7888 <title>LINE pragma</title>
7890 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7891 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7892 <para>This pragma is similar to C's <literal>#line</literal>
7893 pragma, and is mainly for use in automatically generated Haskell
7894 code. It lets you specify the line number and filename of the
7895 original code; for example</para>
7897 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7899 <para>if you'd generated the current file from something called
7900 <filename>Foo.vhs</filename> and this line corresponds to line
7901 42 in the original. GHC will adjust its error messages to refer
7902 to the line/file named in the <literal>LINE</literal>
7907 <title>RULES pragma</title>
7909 <para>The RULES pragma lets you specify rewrite rules. It is
7910 described in <xref linkend="rewrite-rules"/>.</para>
7913 <sect2 id="specialize-pragma">
7914 <title>SPECIALIZE pragma</title>
7916 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7917 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7918 <indexterm><primary>overloading, death to</primary></indexterm>
7920 <para>(UK spelling also accepted.) For key overloaded
7921 functions, you can create extra versions (NB: more code space)
7922 specialised to particular types. Thus, if you have an
7923 overloaded function:</para>
7926 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7929 <para>If it is heavily used on lists with
7930 <literal>Widget</literal> keys, you could specialise it as
7934 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7937 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7938 be put anywhere its type signature could be put.</para>
7940 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7941 (a) a specialised version of the function and (b) a rewrite rule
7942 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7943 un-specialised function into a call to the specialised one.</para>
7945 <para>The type in a SPECIALIZE pragma can be any type that is less
7946 polymorphic than the type of the original function. In concrete terms,
7947 if the original function is <literal>f</literal> then the pragma
7949 {-# SPECIALIZE f :: <type> #-}
7951 is valid if and only if the definition
7953 f_spec :: <type>
7956 is valid. Here are some examples (where we only give the type signature
7957 for the original function, not its code):
7959 f :: Eq a => a -> b -> b
7960 {-# SPECIALISE f :: Int -> b -> b #-}
7962 g :: (Eq a, Ix b) => a -> b -> b
7963 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7965 h :: Eq a => a -> a -> a
7966 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7968 The last of these examples will generate a
7969 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7970 well. If you use this kind of specialisation, let us know how well it works.
7973 <sect3 id="specialize-inline">
7974 <title>SPECIALIZE INLINE</title>
7976 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7977 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7978 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7979 The <literal>INLINE</literal> pragma affects the specialised version of the
7980 function (only), and applies even if the function is recursive. The motivating
7983 -- A GADT for arrays with type-indexed representation
7985 ArrInt :: !Int -> ByteArray# -> Arr Int
7986 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7988 (!:) :: Arr e -> Int -> e
7989 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7990 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7991 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7992 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7994 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7995 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7996 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7997 the specialised function will be inlined. It has two calls to
7998 <literal>(!:)</literal>,
7999 both at type <literal>Int</literal>. Both these calls fire the first
8000 specialisation, whose body is also inlined. The result is a type-based
8001 unrolling of the indexing function.</para>
8002 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
8003 on an ordinarily-recursive function.</para>
8006 <sect3><title>SPECIALIZE for imported functions</title>
8009 Generally, you can only give a <literal>SPECIALIZE</literal> pragma
8010 for a function defined in the same module.
8011 However if a function <literal>f</literal> is given an <literal>INLINABLE</literal>
8012 pragma at its definition site, then it can subequently be specialised by
8013 importing modules (see <xref linkend="inlinable-pragma"/>).
8016 module Map( lookup, blah blah ) where
8017 lookup :: Ord key => [(key,a)] -> key -> Maybe a
8019 {-# INLINABLE lookup #-}
8022 import Map( lookup )
8024 data T = T1 | T2 deriving( Eq, Ord )
8025 {-# SPECIALISE lookup :: [(T,a)] -> T -> Maybe a
8027 Here, <literal>lookup</literal> is declared <literal>INLINABLE</literal>, but
8028 it cannot be specialised for type <literal>T</literal> at its definition site,
8029 because that type does not exist yet. Instead a client module can define <literal>T</literal>
8030 and then specialise <literal>lookup</literal> at that type.
8033 Moreover, every module that imports <literal>Client</literal> (or imports a module
8034 that imports <literal>Client</literal>, transitively) will "see", and make use of,
8035 the specialised version of <literal>lookup</literal>. You don't need to put
8036 a <literal>SPECIALIZE</literal> pragma in every module.
8039 Moreover you often don't even need the <literal>SPECIALIZE</literal> pragma in the
8040 first place. When compiling a module M,
8041 GHC's optimiser (with -O) automatically considers each top-level
8042 overloaded function declared in M, and specialises it
8043 for the different types at which it is called in M. The optimiser
8044 <emphasis>also</emphasis> considers each <emphasis>imported</emphasis>
8045 <literal>INLINABLE</literal> overloaded function, and specialises it
8046 for the different types at which it is called in M.
8047 So in our example, it would be enough for <literal>lookup</literal> to
8048 be called at type <literal>T</literal>:
8051 import Map( lookup )
8053 data T = T1 | T2 deriving( Eq, Ord )
8055 findT1 :: [(T,a)] -> Maybe a
8056 findT1 m = lookup m T1 -- A call of lookup at type T
8058 However, sometimes there are no such calls, in which case the
8059 pragma can be useful.
8063 <sect3><title>Obselete SPECIALIZE syntax</title>
8065 <para>Note: In earlier versions of GHC, it was possible to provide your own
8066 specialised function for a given type:
8069 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
8072 This feature has been removed, as it is now subsumed by the
8073 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
8078 <sect2 id="specialize-instance-pragma">
8079 <title>SPECIALIZE instance pragma
8083 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
8084 <indexterm><primary>overloading, death to</primary></indexterm>
8085 Same idea, except for instance declarations. For example:
8088 instance (Eq a) => Eq (Foo a) where {
8089 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
8093 The pragma must occur inside the <literal>where</literal> part
8094 of the instance declaration.
8097 Compatible with HBC, by the way, except perhaps in the placement
8103 <sect2 id="unpack-pragma">
8104 <title>UNPACK pragma</title>
8106 <indexterm><primary>UNPACK</primary></indexterm>
8108 <para>The <literal>UNPACK</literal> indicates to the compiler
8109 that it should unpack the contents of a constructor field into
8110 the constructor itself, removing a level of indirection. For
8114 data T = T {-# UNPACK #-} !Float
8115 {-# UNPACK #-} !Float
8118 <para>will create a constructor <literal>T</literal> containing
8119 two unboxed floats. This may not always be an optimisation: if
8120 the <function>T</function> constructor is scrutinised and the
8121 floats passed to a non-strict function for example, they will
8122 have to be reboxed (this is done automatically by the
8125 <para>Unpacking constructor fields should only be used in
8126 conjunction with <option>-O</option>, in order to expose
8127 unfoldings to the compiler so the reboxing can be removed as
8128 often as possible. For example:</para>
8132 f (T f1 f2) = f1 + f2
8135 <para>The compiler will avoid reboxing <function>f1</function>
8136 and <function>f2</function> by inlining <function>+</function>
8137 on floats, but only when <option>-O</option> is on.</para>
8139 <para>Any single-constructor data is eligible for unpacking; for
8143 data T = T {-# UNPACK #-} !(Int,Int)
8146 <para>will store the two <literal>Int</literal>s directly in the
8147 <function>T</function> constructor, by flattening the pair.
8148 Multi-level unpacking is also supported:
8151 data T = T {-# UNPACK #-} !S
8152 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8155 will store two unboxed <literal>Int#</literal>s
8156 directly in the <function>T</function> constructor. The
8157 unpacker can see through newtypes, too.</para>
8159 <para>See also the <option>-funbox-strict-fields</option> flag,
8160 which essentially has the effect of adding
8161 <literal>{-# UNPACK #-}</literal> to every strict
8162 constructor field.</para>
8165 <sect2 id="source-pragma">
8166 <title>SOURCE pragma</title>
8168 <indexterm><primary>SOURCE</primary></indexterm>
8169 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8170 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8176 <!-- ======================= REWRITE RULES ======================== -->
8178 <sect1 id="rewrite-rules">
8179 <title>Rewrite rules
8181 <indexterm><primary>RULES pragma</primary></indexterm>
8182 <indexterm><primary>pragma, RULES</primary></indexterm>
8183 <indexterm><primary>rewrite rules</primary></indexterm></title>
8186 The programmer can specify rewrite rules as part of the source program
8192 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8197 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8198 If you need more information, then <option>-ddump-rule-firings</option> shows you
8199 each individual rule firing and <option>-ddump-rule-rewrites</option> also shows what the code looks like before and after the rewrite.
8203 <title>Syntax</title>
8206 From a syntactic point of view:
8212 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8213 may be generated by the layout rule).
8219 The layout rule applies in a pragma.
8220 Currently no new indentation level
8221 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8222 you must lay out the starting in the same column as the enclosing definitions.
8225 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8226 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8229 Furthermore, the closing <literal>#-}</literal>
8230 should start in a column to the right of the opening <literal>{-#</literal>.
8236 Each rule has a name, enclosed in double quotes. The name itself has
8237 no significance at all. It is only used when reporting how many times the rule fired.
8243 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8244 immediately after the name of the rule. Thus:
8247 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8250 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8251 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8260 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8261 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8262 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8263 by spaces, just like in a type <literal>forall</literal>.
8269 A pattern variable may optionally have a type signature.
8270 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8271 For example, here is the <literal>foldr/build</literal> rule:
8274 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8275 foldr k z (build g) = g k z
8278 Since <function>g</function> has a polymorphic type, it must have a type signature.
8285 The left hand side of a rule must consist of a top-level variable applied
8286 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8289 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8290 "wrong2" forall f. f True = True
8293 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8300 A rule does not need to be in the same module as (any of) the
8301 variables it mentions, though of course they need to be in scope.
8307 All rules are implicitly exported from the module, and are therefore
8308 in force in any module that imports the module that defined the rule, directly
8309 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8310 in force when compiling A.) The situation is very similar to that for instance
8318 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8319 any other flag settings. Furthermore, inside a RULE, the language extension
8320 <option>-XScopedTypeVariables</option> is automatically enabled; see
8321 <xref linkend="scoped-type-variables"/>.
8327 Like other pragmas, RULE pragmas are always checked for scope errors, and
8328 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8329 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8330 if the <option>-fenable-rewrite-rules</option> flag is
8331 on (see <xref linkend="rule-semantics"/>).
8340 <sect2 id="rule-semantics">
8341 <title>Semantics</title>
8344 From a semantic point of view:
8349 Rules are enabled (that is, used during optimisation)
8350 by the <option>-fenable-rewrite-rules</option> flag.
8351 This flag is implied by <option>-O</option>, and may be switched
8352 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8353 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8354 may not do what you expect, though, because without <option>-O</option> GHC
8355 ignores all optimisation information in interface files;
8356 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8357 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8358 has no effect on parsing or typechecking.
8364 Rules are regarded as left-to-right rewrite rules.
8365 When GHC finds an expression that is a substitution instance of the LHS
8366 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8367 By "a substitution instance" we mean that the LHS can be made equal to the
8368 expression by substituting for the pattern variables.
8375 GHC makes absolutely no attempt to verify that the LHS and RHS
8376 of a rule have the same meaning. That is undecidable in general, and
8377 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8384 GHC makes no attempt to make sure that the rules are confluent or
8385 terminating. For example:
8388 "loop" forall x y. f x y = f y x
8391 This rule will cause the compiler to go into an infinite loop.
8398 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8404 GHC currently uses a very simple, syntactic, matching algorithm
8405 for matching a rule LHS with an expression. It seeks a substitution
8406 which makes the LHS and expression syntactically equal modulo alpha
8407 conversion. The pattern (rule), but not the expression, is eta-expanded if
8408 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8409 But not beta conversion (that's called higher-order matching).
8413 Matching is carried out on GHC's intermediate language, which includes
8414 type abstractions and applications. So a rule only matches if the
8415 types match too. See <xref linkend="rule-spec"/> below.
8421 GHC keeps trying to apply the rules as it optimises the program.
8422 For example, consider:
8431 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8432 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8433 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8434 not be substituted, and the rule would not fire.
8444 <sect2 id="conlike">
8445 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8448 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8449 results. Consider this (artificial) example
8455 {-# RULES "f" f True = False #-}
8457 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8462 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8464 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8465 would have been a better chance that <literal>f</literal>'s RULE might fire.
8468 The way to get predictable behaviour is to use a NOINLINE
8469 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8470 that it is not inlined until its RULEs have had a chance to fire.
8473 GHC is very cautious about duplicating work. For example, consider
8475 f k z xs = let xs = build g
8476 in ...(foldr k z xs)...sum xs...
8477 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8479 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8480 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8481 duplicated if the rule fired.
8484 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8485 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8486 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8488 {-# INLINE[1] CONLIKE f #-}
8489 f x = <replaceable>blah</replaceable>
8491 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8492 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8493 should be considered cheap enough to duplicate, if such a duplication would make rule
8494 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8495 have such a property.)
8496 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8497 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8498 not going to be inlined before the rule has a chance to fire.
8503 <title>List fusion</title>
8506 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8507 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8508 intermediate list should be eliminated entirely.
8512 The following are good producers:
8524 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8530 Explicit lists (e.g. <literal>[True, False]</literal>)
8536 The cons constructor (e.g <literal>3:4:[]</literal>)
8542 <function>++</function>
8548 <function>map</function>
8554 <function>take</function>, <function>filter</function>
8560 <function>iterate</function>, <function>repeat</function>
8566 <function>zip</function>, <function>zipWith</function>
8575 The following are good consumers:
8587 <function>array</function> (on its second argument)
8593 <function>++</function> (on its first argument)
8599 <function>foldr</function>
8605 <function>map</function>
8611 <function>take</function>, <function>filter</function>
8617 <function>concat</function>
8623 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8629 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8630 will fuse with one but not the other)
8636 <function>partition</function>
8642 <function>head</function>
8648 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8654 <function>sequence_</function>
8660 <function>msum</function>
8666 <function>sortBy</function>
8675 So, for example, the following should generate no intermediate lists:
8678 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8684 This list could readily be extended; if there are Prelude functions that you use
8685 a lot which are not included, please tell us.
8689 If you want to write your own good consumers or producers, look at the
8690 Prelude definitions of the above functions to see how to do so.
8695 <sect2 id="rule-spec">
8696 <title>Specialisation
8700 Rewrite rules can be used to get the same effect as a feature
8701 present in earlier versions of GHC.
8702 For example, suppose that:
8705 genericLookup :: Ord a => Table a b -> a -> b
8706 intLookup :: Table Int b -> Int -> b
8709 where <function>intLookup</function> is an implementation of
8710 <function>genericLookup</function> that works very fast for
8711 keys of type <literal>Int</literal>. You might wish
8712 to tell GHC to use <function>intLookup</function> instead of
8713 <function>genericLookup</function> whenever the latter was called with
8714 type <literal>Table Int b -> Int -> b</literal>.
8715 It used to be possible to write
8718 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8721 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8724 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8727 This slightly odd-looking rule instructs GHC to replace
8728 <function>genericLookup</function> by <function>intLookup</function>
8729 <emphasis>whenever the types match</emphasis>.
8730 What is more, this rule does not need to be in the same
8731 file as <function>genericLookup</function>, unlike the
8732 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8733 have an original definition available to specialise).
8736 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8737 <function>intLookup</function> really behaves as a specialised version
8738 of <function>genericLookup</function>!!!</para>
8740 <para>An example in which using <literal>RULES</literal> for
8741 specialisation will Win Big:
8744 toDouble :: Real a => a -> Double
8745 toDouble = fromRational . toRational
8747 {-# RULES "toDouble/Int" toDouble = i2d #-}
8748 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8751 The <function>i2d</function> function is virtually one machine
8752 instruction; the default conversion—via an intermediate
8753 <literal>Rational</literal>—is obscenely expensive by
8759 <sect2 id="controlling-rules">
8760 <title>Controlling what's going on in rewrite rules</title>
8768 Use <option>-ddump-rules</option> to see the rules that are defined
8769 <emphasis>in this module</emphasis>.
8770 This includes rules generated by the specialisation pass, but excludes
8771 rules imported from other modules.
8777 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8778 If you add <option>-dppr-debug</option> you get a more detailed listing.
8784 Use <option>-ddump-rule-firings</option> or <option>-ddump-rule-rewrites</option>
8785 to see in great detail what rules are being fired.
8786 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8792 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8795 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8796 {-# INLINE build #-}
8800 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8801 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8802 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8803 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8810 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8811 see how to write rules that will do fusion and yet give an efficient
8812 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8822 <sect2 id="core-pragma">
8823 <title>CORE pragma</title>
8825 <indexterm><primary>CORE pragma</primary></indexterm>
8826 <indexterm><primary>pragma, CORE</primary></indexterm>
8827 <indexterm><primary>core, annotation</primary></indexterm>
8830 The external core format supports <quote>Note</quote> annotations;
8831 the <literal>CORE</literal> pragma gives a way to specify what these
8832 should be in your Haskell source code. Syntactically, core
8833 annotations are attached to expressions and take a Haskell string
8834 literal as an argument. The following function definition shows an
8838 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8841 Semantically, this is equivalent to:
8849 However, when external core is generated (via
8850 <option>-fext-core</option>), there will be Notes attached to the
8851 expressions <function>show</function> and <varname>x</varname>.
8852 The core function declaration for <function>f</function> is:
8856 f :: %forall a . GHCziShow.ZCTShow a ->
8857 a -> GHCziBase.ZMZN GHCziBase.Char =
8858 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8860 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8862 (tpl1::GHCziBase.Int ->
8864 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8866 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8867 (tpl3::GHCziBase.ZMZN a ->
8868 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8876 Here, we can see that the function <function>show</function> (which
8877 has been expanded out to a case expression over the Show dictionary)
8878 has a <literal>%note</literal> attached to it, as does the
8879 expression <varname>eta</varname> (which used to be called
8880 <varname>x</varname>).
8887 <sect1 id="special-ids">
8888 <title>Special built-in functions</title>
8889 <para>GHC has a few built-in functions with special behaviour. These
8890 are now described in the module <ulink
8891 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8892 in the library documentation.
8896 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Ainline"><literal>inline</literal></ulink>
8897 allows control over inlining on a per-call-site basis.
8900 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3Alazy"><literal>lazy</literal></ulink>
8901 restrains the strictness analyser.
8904 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html#v%3AunsafeCoerce%23"><literal>lazy</literal></ulink>
8905 allows you to fool the type checker.
8912 <sect1 id="generic-classes">
8913 <title>Generic classes</title>
8916 The ideas behind this extension are described in detail in "Derivable type classes",
8917 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8918 An example will give the idea:
8926 fromBin :: [Int] -> (a, [Int])
8928 toBin {| Unit |} Unit = []
8929 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8930 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8931 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8933 fromBin {| Unit |} bs = (Unit, bs)
8934 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8935 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8936 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8937 (y,bs'') = fromBin bs'
8940 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8941 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8942 which are defined thus in the library module <literal>Generics</literal>:
8946 data a :+: b = Inl a | Inr b
8947 data a :*: b = a :*: b
8950 Now you can make a data type into an instance of Bin like this:
8952 instance (Bin a, Bin b) => Bin (a,b)
8953 instance Bin a => Bin [a]
8955 That is, just leave off the "where" clause. Of course, you can put in the
8956 where clause and over-ride whichever methods you please.
8960 <title> Using generics </title>
8961 <para>To use generics you need to</para>
8964 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8965 <option>-XGenerics</option> (to generate extra per-data-type code),
8966 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8970 <para>Import the module <literal>Generics</literal> from the
8971 <literal>lang</literal> package. This import brings into
8972 scope the data types <literal>Unit</literal>,
8973 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8974 don't need this import if you don't mention these types
8975 explicitly; for example, if you are simply giving instance
8976 declarations.)</para>
8981 <sect2> <title> Changes wrt the paper </title>
8983 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8984 can be written infix (indeed, you can now use
8985 any operator starting in a colon as an infix type constructor). Also note that
8986 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8987 Finally, note that the syntax of the type patterns in the class declaration
8988 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8989 alone would ambiguous when they appear on right hand sides (an extension we
8990 anticipate wanting).
8994 <sect2> <title>Terminology and restrictions</title>
8996 Terminology. A "generic default method" in a class declaration
8997 is one that is defined using type patterns as above.
8998 A "polymorphic default method" is a default method defined as in Haskell 98.
8999 A "generic class declaration" is a class declaration with at least one
9000 generic default method.
9008 Alas, we do not yet implement the stuff about constructor names and
9015 A generic class can have only one parameter; you can't have a generic
9016 multi-parameter class.
9022 A default method must be defined entirely using type patterns, or entirely
9023 without. So this is illegal:
9026 op :: a -> (a, Bool)
9027 op {| Unit |} Unit = (Unit, True)
9030 However it is perfectly OK for some methods of a generic class to have
9031 generic default methods and others to have polymorphic default methods.
9037 The type variable(s) in the type pattern for a generic method declaration
9038 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:
9042 op {| p :*: q |} (x :*: y) = op (x :: p)
9050 The type patterns in a generic default method must take one of the forms:
9056 where "a" and "b" are type variables. Furthermore, all the type patterns for
9057 a single type constructor (<literal>:*:</literal>, say) must be identical; they
9058 must use the same type variables. So this is illegal:
9062 op {| a :+: b |} (Inl x) = True
9063 op {| p :+: q |} (Inr y) = False
9065 The type patterns must be identical, even in equations for different methods of the class.
9066 So this too is illegal:
9070 op1 {| a :*: b |} (x :*: y) = True
9073 op2 {| p :*: q |} (x :*: y) = False
9075 (The reason for this restriction is that we gather all the equations for a particular type constructor
9076 into a single generic instance declaration.)
9082 A generic method declaration must give a case for each of the three type constructors.
9088 The type for a generic method can be built only from:
9090 <listitem> <para> Function arrows </para> </listitem>
9091 <listitem> <para> Type variables </para> </listitem>
9092 <listitem> <para> Tuples </para> </listitem>
9093 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
9095 Here are some example type signatures for generic methods:
9098 op2 :: Bool -> (a,Bool)
9099 op3 :: [Int] -> a -> a
9102 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
9106 This restriction is an implementation restriction: we just haven't got around to
9107 implementing the necessary bidirectional maps over arbitrary type constructors.
9108 It would be relatively easy to add specific type constructors, such as Maybe and list,
9109 to the ones that are allowed.</para>
9114 In an instance declaration for a generic class, the idea is that the compiler
9115 will fill in the methods for you, based on the generic templates. However it can only
9120 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
9125 No constructor of the instance type has unboxed fields.
9129 (Of course, these things can only arise if you are already using GHC extensions.)
9130 However, you can still give an instance declarations for types which break these rules,
9131 provided you give explicit code to override any generic default methods.
9139 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9140 what the compiler does with generic declarations.
9145 <sect2> <title> Another example </title>
9147 Just to finish with, here's another example I rather like:
9151 nCons {| Unit |} _ = 1
9152 nCons {| a :*: b |} _ = 1
9153 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9156 tag {| Unit |} _ = 1
9157 tag {| a :*: b |} _ = 1
9158 tag {| a :+: b |} (Inl x) = tag x
9159 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9165 <sect1 id="monomorphism">
9166 <title>Control over monomorphism</title>
9168 <para>GHC supports two flags that control the way in which generalisation is
9169 carried out at let and where bindings.
9173 <title>Switching off the dreaded Monomorphism Restriction</title>
9174 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9176 <para>Haskell's monomorphism restriction (see
9177 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9179 of the Haskell Report)
9180 can be completely switched off by
9181 <option>-XNoMonomorphismRestriction</option>.
9186 <title>Monomorphic pattern bindings</title>
9187 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9188 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9190 <para> As an experimental change, we are exploring the possibility of
9191 making pattern bindings monomorphic; that is, not generalised at all.
9192 A pattern binding is a binding whose LHS has no function arguments,
9193 and is not a simple variable. For example:
9195 f x = x -- Not a pattern binding
9196 f = \x -> x -- Not a pattern binding
9197 f :: Int -> Int = \x -> x -- Not a pattern binding
9199 (g,h) = e -- A pattern binding
9200 (f) = e -- A pattern binding
9201 [x] = e -- A pattern binding
9203 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9204 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
9213 ;;; Local Variables: ***
9214 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
9215 ;;; ispell-local-dictionary: "british" ***
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