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 are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
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 <option>-XPrintExplicitForalls</option>,
60 <option>-XForeignFunctionInterface</option>,
61 <option>-XUnliftedFFITypes</option>,
62 <option>-XGADTs</option>,
63 <option>-XImplicitParams</option>,
64 <option>-XScopedTypeVariables</option>,
65 <option>-XUnboxedTuples</option>,
66 <option>-XTypeSynonymInstances</option>,
67 <option>-XStandaloneDeriving</option>,
68 <option>-XDeriveDataTypeable</option>,
69 <option>-XFlexibleContexts</option>,
70 <option>-XFlexibleInstances</option>,
71 <option>-XConstrainedClassMethods</option>,
72 <option>-XMultiParamTypeClasses</option>,
73 <option>-XFunctionalDependencies</option>,
74 <option>-XMagicHash</option>,
75 <option>-XPolymorphicComponents</option>,
76 <option>-XExistentialQuantification</option>,
77 <option>-XUnicodeSyntax</option>,
78 <option>-XPostfixOperators</option>,
79 <option>-XPatternGuards</option>,
80 <option>-XLiberalTypeSynonyms</option>,
81 <option>-XExplicitForAll</option>,
82 <option>-XRankNTypes</option>,
83 <option>-XImpredicativeTypes</option>,
84 <option>-XTypeOperators</option>,
85 <option>-XDoRec</option>,
86 <option>-XParallelListComp</option>,
87 <option>-XEmptyDataDecls</option>,
88 <option>-XKindSignatures</option>,
89 <option>-XGeneralizedNewtypeDeriving</option>,
90 <option>-XTypeFamilies</option>.
91 Enabling these options is the <emphasis>only</emphasis>
92 effect of <option>-fglasgow-exts</option>.
93 We are trying to move away from this portmanteau flag,
94 and towards enabling features individually.</para>
98 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
99 <sect1 id="primitives">
100 <title>Unboxed types and primitive operations</title>
102 <para>GHC is built on a raft of primitive data types and operations;
103 "primitive" in the sense that they cannot be defined in Haskell itself.
104 While you really can use this stuff to write fast code,
105 we generally find it a lot less painful, and more satisfying in the
106 long run, to use higher-level language features and libraries. With
107 any luck, the code you write will be optimised to the efficient
108 unboxed version in any case. And if it isn't, we'd like to know
111 <para>All these primitive data types and operations are exported by the
112 library <literal>GHC.Prim</literal>, for which there is
113 <ulink url="../libraries/ghc-prim/GHC-Prim.html">detailed online documentation</ulink>.
114 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
117 If you want to mention any of the primitive data types or operations in your
118 program, you must first import <literal>GHC.Prim</literal> to bring them
119 into scope. Many of them have names ending in "#", and to mention such
120 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
123 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
124 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
125 we briefly summarise here. </para>
127 <sect2 id="glasgow-unboxed">
132 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
135 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
136 that values of that type are represented by a pointer to a heap
137 object. The representation of a Haskell <literal>Int</literal>, for
138 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
139 type, however, is represented by the value itself, no pointers or heap
140 allocation are involved.
144 Unboxed types correspond to the “raw machine” types you
145 would use in C: <literal>Int#</literal> (long int),
146 <literal>Double#</literal> (double), <literal>Addr#</literal>
147 (void *), etc. The <emphasis>primitive operations</emphasis>
148 (PrimOps) on these types are what you might expect; e.g.,
149 <literal>(+#)</literal> is addition on
150 <literal>Int#</literal>s, and is the machine-addition that we all
151 know and love—usually one instruction.
155 Primitive (unboxed) types cannot be defined in Haskell, and are
156 therefore built into the language and compiler. Primitive types are
157 always unlifted; that is, a value of a primitive type cannot be
158 bottom. We use the convention (but it is only a convention)
159 that primitive types, values, and
160 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
161 For some primitive types we have special syntax for literals, also
162 described in the <link linkend="magic-hash">same section</link>.
166 Primitive values are often represented by a simple bit-pattern, such
167 as <literal>Int#</literal>, <literal>Float#</literal>,
168 <literal>Double#</literal>. But this is not necessarily the case:
169 a primitive value might be represented by a pointer to a
170 heap-allocated object. Examples include
171 <literal>Array#</literal>, the type of primitive arrays. A
172 primitive array is heap-allocated because it is too big a value to fit
173 in a register, and would be too expensive to copy around; in a sense,
174 it is accidental that it is represented by a pointer. If a pointer
175 represents a primitive value, then it really does point to that value:
176 no unevaluated thunks, no indirections…nothing can be at the
177 other end of the pointer than the primitive value.
178 A numerically-intensive program using unboxed types can
179 go a <emphasis>lot</emphasis> faster than its “standard”
180 counterpart—we saw a threefold speedup on one example.
184 There are some restrictions on the use of primitive types:
186 <listitem><para>The main restriction
187 is that you can't pass a primitive value to a polymorphic
188 function or store one in a polymorphic data type. This rules out
189 things like <literal>[Int#]</literal> (i.e. lists of primitive
190 integers). The reason for this restriction is that polymorphic
191 arguments and constructor fields are assumed to be pointers: if an
192 unboxed integer is stored in one of these, the garbage collector would
193 attempt to follow it, leading to unpredictable space leaks. Or a
194 <function>seq</function> operation on the polymorphic component may
195 attempt to dereference the pointer, with disastrous results. Even
196 worse, the unboxed value might be larger than a pointer
197 (<literal>Double#</literal> for instance).
200 <listitem><para> You cannot define a newtype whose representation type
201 (the argument type of the data constructor) is an unboxed type. Thus,
207 <listitem><para> You cannot bind a variable with an unboxed type
208 in a <emphasis>top-level</emphasis> binding.
210 <listitem><para> You cannot bind a variable with an unboxed type
211 in a <emphasis>recursive</emphasis> binding.
213 <listitem><para> You may bind unboxed variables in a (non-recursive,
214 non-top-level) pattern binding, but you must make any such pattern-match
215 strict. For example, rather than:
217 data Foo = Foo Int Int#
219 f x = let (Foo a b, w) = ..rhs.. in ..body..
223 data Foo = Foo Int Int#
225 f x = let !(Foo a b, w) = ..rhs.. in ..body..
227 since <literal>b</literal> has type <literal>Int#</literal>.
235 <sect2 id="unboxed-tuples">
236 <title>Unboxed Tuples
240 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
241 they're available by default with <option>-fglasgow-exts</option>. An
242 unboxed tuple looks like this:
254 where <literal>e_1..e_n</literal> are expressions of any
255 type (primitive or non-primitive). The type of an unboxed tuple looks
260 Unboxed tuples are used for functions that need to return multiple
261 values, but they avoid the heap allocation normally associated with
262 using fully-fledged tuples. When an unboxed tuple is returned, the
263 components are put directly into registers or on the stack; the
264 unboxed tuple itself does not have a composite representation. Many
265 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
267 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
268 tuples to avoid unnecessary allocation during sequences of operations.
272 There are some pretty stringent restrictions on the use of unboxed tuples:
277 Values of unboxed tuple types are subject to the same restrictions as
278 other unboxed types; i.e. they may not be stored in polymorphic data
279 structures or passed to polymorphic functions.
286 No variable can have an unboxed tuple type, nor may a constructor or function
287 argument have an unboxed tuple type. The following are all illegal:
291 data Foo = Foo (# Int, Int #)
293 f :: (# Int, Int #) -> (# Int, Int #)
296 g :: (# Int, Int #) -> Int
299 h x = let y = (# x,x #) in ...
306 The typical use of unboxed tuples is simply to return multiple values,
307 binding those multiple results with a <literal>case</literal> expression, thus:
309 f x y = (# x+1, y-1 #)
310 g x = case f x x of { (# a, b #) -> a + b }
312 You can have an unboxed tuple in a pattern binding, thus
314 f x = let (# p,q #) = h x in ..body..
316 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
317 the resulting binding is lazy like any other Haskell pattern binding. The
318 above example desugars like this:
320 f x = let t = case h x o f{ (# p,q #) -> (p,q)
325 Indeed, the bindings can even be recursive.
332 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
334 <sect1 id="syntax-extns">
335 <title>Syntactic extensions</title>
337 <sect2 id="unicode-syntax">
338 <title>Unicode syntax</title>
340 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
341 enables Unicode characters to be used to stand for certain ASCII
342 character sequences. The following alternatives are provided:</para>
345 <tgroup cols="2" align="left" colsep="1" rowsep="1">
349 <entry>Unicode alternative</entry>
350 <entry>Code point</entry>
356 <entry><literal>::</literal></entry>
357 <entry>::</entry> <!-- no special char, apparently -->
358 <entry>0x2237</entry>
359 <entry>PROPORTION</entry>
364 <entry><literal>=></literal></entry>
365 <entry>⇒</entry>
366 <entry>0x21D2</entry>
367 <entry>RIGHTWARDS DOUBLE ARROW</entry>
372 <entry><literal>forall</literal></entry>
373 <entry>∀</entry>
374 <entry>0x2200</entry>
375 <entry>FOR ALL</entry>
380 <entry><literal>-></literal></entry>
381 <entry>→</entry>
382 <entry>0x2192</entry>
383 <entry>RIGHTWARDS ARROW</entry>
388 <entry><literal><-</literal></entry>
389 <entry>←</entry>
390 <entry>0x2190</entry>
391 <entry>LEFTWARDS ARROW</entry>
397 <entry>…</entry>
398 <entry>0x22EF</entry>
399 <entry>MIDLINE HORIZONTAL ELLIPSIS</entry>
406 <sect2 id="magic-hash">
407 <title>The magic hash</title>
408 <para>The language extension <option>-XMagicHash</option> allows "#" as a
409 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
410 a valid type constructor or data constructor.</para>
412 <para>The hash sign does not change sematics at all. We tend to use variable
413 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
414 but there is no requirement to do so; they are just plain ordinary variables.
415 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
416 For example, to bring <literal>Int#</literal> into scope you must
417 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
418 the <option>-XMagicHash</option> extension
419 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
420 that is now in scope.</para>
421 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
423 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
424 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
425 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
426 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
427 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
428 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
429 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
430 is a <literal>Word#</literal>. </para> </listitem>
431 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
432 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
437 <sect2 id="new-qualified-operators">
438 <title>New qualified operator syntax</title>
440 <para>A new syntax for referencing qualified operators is
441 planned to be introduced by Haskell', and is enabled in GHC
443 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
444 option. In the new syntax, the prefix form of a qualified
446 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
447 (in Haskell 98 this would
448 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
449 and the infix form is
450 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
451 (in Haskell 98 this would
452 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
455 add x y = Prelude.(+) x y
456 subtract y = (`Prelude.(-)` y)
458 The new form of qualified operators is intended to regularise
459 the syntax by eliminating odd cases
460 like <literal>Prelude..</literal>. For example,
461 when <literal>NewQualifiedOperators</literal> is on, it is possible to
462 write the enumerated sequence <literal>[Monday..]</literal>
463 without spaces, whereas in Haskell 98 this would be a
464 reference to the operator ‘<literal>.</literal>‘
465 from module <literal>Monday</literal>.</para>
467 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
468 98 syntax for qualified operators is not accepted, so this
469 option may cause existing Haskell 98 code to break.</para>
474 <!-- ====================== HIERARCHICAL MODULES ======================= -->
477 <sect2 id="hierarchical-modules">
478 <title>Hierarchical Modules</title>
480 <para>GHC supports a small extension to the syntax of module
481 names: a module name is allowed to contain a dot
482 <literal>‘.’</literal>. This is also known as the
483 “hierarchical module namespace” extension, because
484 it extends the normally flat Haskell module namespace into a
485 more flexible hierarchy of modules.</para>
487 <para>This extension has very little impact on the language
488 itself; modules names are <emphasis>always</emphasis> fully
489 qualified, so you can just think of the fully qualified module
490 name as <quote>the module name</quote>. In particular, this
491 means that the full module name must be given after the
492 <literal>module</literal> keyword at the beginning of the
493 module; for example, the module <literal>A.B.C</literal> must
496 <programlisting>module A.B.C</programlisting>
499 <para>It is a common strategy to use the <literal>as</literal>
500 keyword to save some typing when using qualified names with
501 hierarchical modules. For example:</para>
504 import qualified Control.Monad.ST.Strict as ST
507 <para>For details on how GHC searches for source and interface
508 files in the presence of hierarchical modules, see <xref
509 linkend="search-path"/>.</para>
511 <para>GHC comes with a large collection of libraries arranged
512 hierarchically; see the accompanying <ulink
513 url="../libraries/index.html">library
514 documentation</ulink>. More libraries to install are available
516 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
519 <!-- ====================== PATTERN GUARDS ======================= -->
521 <sect2 id="pattern-guards">
522 <title>Pattern guards</title>
525 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
526 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.)
530 Suppose we have an abstract data type of finite maps, with a
534 lookup :: FiniteMap -> Int -> Maybe Int
537 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
538 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
542 clunky env var1 var2 | ok1 && ok2 = val1 + val2
543 | otherwise = var1 + var2
554 The auxiliary functions are
558 maybeToBool :: Maybe a -> Bool
559 maybeToBool (Just x) = True
560 maybeToBool Nothing = False
562 expectJust :: Maybe a -> a
563 expectJust (Just x) = x
564 expectJust Nothing = error "Unexpected Nothing"
568 What is <function>clunky</function> doing? The guard <literal>ok1 &&
569 ok2</literal> checks that both lookups succeed, using
570 <function>maybeToBool</function> to convert the <function>Maybe</function>
571 types to booleans. The (lazily evaluated) <function>expectJust</function>
572 calls extract the values from the results of the lookups, and binds the
573 returned values to <varname>val1</varname> and <varname>val2</varname>
574 respectively. If either lookup fails, then clunky takes the
575 <literal>otherwise</literal> case and returns the sum of its arguments.
579 This is certainly legal Haskell, but it is a tremendously verbose and
580 un-obvious way to achieve the desired effect. Arguably, a more direct way
581 to write clunky would be to use case expressions:
585 clunky env var1 var2 = case lookup env var1 of
587 Just val1 -> case lookup env var2 of
589 Just val2 -> val1 + val2
595 This is a bit shorter, but hardly better. Of course, we can rewrite any set
596 of pattern-matching, guarded equations as case expressions; that is
597 precisely what the compiler does when compiling equations! The reason that
598 Haskell provides guarded equations is because they allow us to write down
599 the cases we want to consider, one at a time, independently of each other.
600 This structure is hidden in the case version. Two of the right-hand sides
601 are really the same (<function>fail</function>), and the whole expression
602 tends to become more and more indented.
606 Here is how I would write clunky:
611 | Just val1 <- lookup env var1
612 , Just val2 <- lookup env var2
614 ...other equations for clunky...
618 The semantics should be clear enough. The qualifiers are matched in order.
619 For a <literal><-</literal> qualifier, which I call a pattern guard, the
620 right hand side is evaluated and matched against the pattern on the left.
621 If the match fails then the whole guard fails and the next equation is
622 tried. If it succeeds, then the appropriate binding takes place, and the
623 next qualifier is matched, in the augmented environment. Unlike list
624 comprehensions, however, the type of the expression to the right of the
625 <literal><-</literal> is the same as the type of the pattern to its
626 left. The bindings introduced by pattern guards scope over all the
627 remaining guard qualifiers, and over the right hand side of the equation.
631 Just as with list comprehensions, boolean expressions can be freely mixed
632 with among the pattern guards. For example:
643 Haskell's current guards therefore emerge as a special case, in which the
644 qualifier list has just one element, a boolean expression.
648 <!-- ===================== View patterns =================== -->
650 <sect2 id="view-patterns">
655 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
656 More information and examples of view patterns can be found on the
657 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
662 View patterns are somewhat like pattern guards that can be nested inside
663 of other patterns. They are a convenient way of pattern-matching
664 against values of abstract types. For example, in a programming language
665 implementation, we might represent the syntax of the types of the
674 view :: Type -> TypeView
676 -- additional operations for constructing Typ's ...
679 The representation of Typ is held abstract, permitting implementations
680 to use a fancy representation (e.g., hash-consing to manage sharing).
682 Without view patterns, using this signature a little inconvenient:
684 size :: Typ -> Integer
685 size t = case view t of
687 Arrow t1 t2 -> size t1 + size t2
690 It is necessary to iterate the case, rather than using an equational
691 function definition. And the situation is even worse when the matching
692 against <literal>t</literal> is buried deep inside another pattern.
696 View patterns permit calling the view function inside the pattern and
697 matching against the result:
699 size (view -> Unit) = 1
700 size (view -> Arrow t1 t2) = size t1 + size t2
703 That is, we add a new form of pattern, written
704 <replaceable>expression</replaceable> <literal>-></literal>
705 <replaceable>pattern</replaceable> that means "apply the expression to
706 whatever we're trying to match against, and then match the result of
707 that application against the pattern". The expression can be any Haskell
708 expression of function type, and view patterns can be used wherever
713 The semantics of a pattern <literal>(</literal>
714 <replaceable>exp</replaceable> <literal>-></literal>
715 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
721 <para>The variables bound by the view pattern are the variables bound by
722 <replaceable>pat</replaceable>.
726 Any variables in <replaceable>exp</replaceable> are bound occurrences,
727 but variables bound "to the left" in a pattern are in scope. This
728 feature permits, for example, one argument to a function to be used in
729 the view of another argument. For example, the function
730 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
731 written using view patterns as follows:
734 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
735 ...other equations for clunky...
740 More precisely, the scoping rules are:
744 In a single pattern, variables bound by patterns to the left of a view
745 pattern expression are in scope. For example:
747 example :: Maybe ((String -> Integer,Integer), String) -> Bool
748 example Just ((f,_), f -> 4) = True
751 Additionally, in function definitions, variables bound by matching earlier curried
752 arguments may be used in view pattern expressions in later arguments:
754 example :: (String -> Integer) -> String -> Bool
755 example f (f -> 4) = True
757 That is, the scoping is the same as it would be if the curried arguments
758 were collected into a tuple.
764 In mutually recursive bindings, such as <literal>let</literal>,
765 <literal>where</literal>, or the top level, view patterns in one
766 declaration may not mention variables bound by other declarations. That
767 is, each declaration must be self-contained. For example, the following
768 program is not allowed:
775 restriction in the future; the only cost is that type checking patterns
776 would get a little more complicated.)
786 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
787 <replaceable>T1</replaceable> <literal>-></literal>
788 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
789 a <replaceable>T2</replaceable>, then the whole view pattern matches a
790 <replaceable>T1</replaceable>.
793 <listitem><para> Matching: To the equations in Section 3.17.3 of the
794 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
795 Report</ulink>, add the following:
797 case v of { (e -> p) -> e1 ; _ -> e2 }
799 case (e v) of { p -> e1 ; _ -> e2 }
801 That is, to match a variable <replaceable>v</replaceable> against a pattern
802 <literal>(</literal> <replaceable>exp</replaceable>
803 <literal>-></literal> <replaceable>pat</replaceable>
804 <literal>)</literal>, evaluate <literal>(</literal>
805 <replaceable>exp</replaceable> <replaceable> v</replaceable>
806 <literal>)</literal> and match the result against
807 <replaceable>pat</replaceable>.
810 <listitem><para> Efficiency: When the same view function is applied in
811 multiple branches of a function definition or a case expression (e.g.,
812 in <literal>size</literal> above), GHC makes an attempt to collect these
813 applications into a single nested case expression, so that the view
814 function is only applied once. Pattern compilation in GHC follows the
815 matrix algorithm described in Chapter 4 of <ulink
816 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
817 Implementation of Functional Programming Languages</ulink>. When the
818 top rows of the first column of a matrix are all view patterns with the
819 "same" expression, these patterns are transformed into a single nested
820 case. This includes, for example, adjacent view patterns that line up
823 f ((view -> A, p1), p2) = e1
824 f ((view -> B, p3), p4) = e2
828 <para> The current notion of when two view pattern expressions are "the
829 same" is very restricted: it is not even full syntactic equality.
830 However, it does include variables, literals, applications, and tuples;
831 e.g., two instances of <literal>view ("hi", "there")</literal> will be
832 collected. However, the current implementation does not compare up to
833 alpha-equivalence, so two instances of <literal>(x, view x ->
834 y)</literal> will not be coalesced.
844 <!-- ===================== n+k patterns =================== -->
846 <sect2 id="n-k-patterns">
847 <title>n+k patterns</title>
848 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
851 <literal>n+k</literal> pattern support is enabled by default. To disable
852 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
857 <!-- ===================== Recursive do-notation =================== -->
859 <sect2 id="mdo-notation">
860 <title>The recursive do-notation
864 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
865 that is, the variables bound in a do-expression are visible only in the textually following
866 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
867 group. It turns out that several applications can benefit from recursive bindings in
868 the do-notation. The <option>-XDoRec</option> flag provides the necessary syntactic support.
871 Here is a simple (albeit contrived) example:
873 {-# LANGUAGE DoRec #-}
874 import Control.Monad.Fix
876 justOnes = do { rec { xs <- Just (1:xs) }
877 ; return (map negate xs) }
879 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
882 The background and motivation for recusrive do-notation is described in
883 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
884 by Levent Erkok, John Launchbury,
885 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
886 This paper is essential reading for anyone making non-trivial use of mdo-notation,
887 and we do not repeat it here. However, note that GHC uses a different syntax than the one
892 <title>Details of recursive do-notation</title>
894 The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
895 the LANGUAGE pragma <option>DoRec</option>. It introduces the single new keyword "<literal>rec</literal>",
896 which wraps a mutually-recursive group of monadic statements,
897 producing a single statement.
899 <para>Similar to a <literal>let</literal>
900 statement, the variables bound in the <literal>rec</literal> are
901 visible throughout the <literal>rec</literal> group, and below it.
904 do { a <- getChar do { a <- getChar
905 ; let { r1 = f a r2 ; rec { r1 <- f a r2
906 ; r2 = g r1 } ; r2 <- g r1 }
907 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
909 In both cases, <literal>r1</literal> and <literal>r2</literal> are
910 available both throughout the <literal>let</literal> or <literal>rec</literal> block, and
911 in the statements that follow it. The difference is that <literal>let</literal> is non-monadic,
912 while <literal>rec</literal> is monadic. (In Haskell <literal>let</literal> is
913 really <literal>letrec</literal>, of course.)
916 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. Its definition is:
919 class Monad m => MonadFix m where
920 mfix :: (a -> m a) -> m a
923 The function <literal>mfix</literal>
924 dictates how the required recursion operation should be performed. For example,
925 <literal>justOnes</literal> desugars as follows:
927 justOnes = do { xs <- mfix (\xs' -> do { xs <- Just (1:xs'); return xs })
928 ; return (map negate xs) }
930 In general, the statment <literal>rec <replaceable>ss</replaceable></literal>
931 is desugared to the statement
933 <replaceable>vs</replaceable> <- mfix (\~<replaceable>vs</replaceable> -> do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
935 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
936 Moreover, the original <literal>rec</literal> typechecks exactly
937 when the above desugared version would do so. (For example, this means that
938 the variables <replaceable>vs</replaceable> are all monomorphic in the statements
939 following the <literal>rec</literal>, because they are bound by a lambda.)
942 Here are some other important points in using the recursive-do notation:
945 It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
946 <literal>-fglasgow-exts</literal>.
950 If recursive bindings are required for a monad,
951 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
955 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
956 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
957 for Haskell's internal state monad (strict and lazy, respectively).
961 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
962 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
963 be distinct (Section 3.3 of the paper).
967 Similar to let-bindings, GHC implements the segmentation technique described in Section 3.2 of
968 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
969 to break up a single <literal>rec</literal> statement into a sequence of statements with
970 <literal>rec</literal> groups of minimal size. This
971 improves polymorphism, reduces the size of the recursive "knot", and, as the paper
972 describes, also has a semantic effect (unless the monad satisfies the right-shrinking law).
978 <sect3> <title> Mdo-notation (deprecated) </title>
980 <para> GHC used to support the flag <option>-XREecursiveDo</option>,
981 which enabled the keyword <literal>mdo</literal>, precisely as described in
982 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
983 but this is now deprecated. Instead of <literal>mdo { Q; e }</literal>, write
984 <literal>do { rec Q; e }</literal>.
987 Historical note: The old implementation of the mdo-notation (and most
988 of the existing documents) used the name
989 <literal>MonadRec</literal> for the class and the corresponding library.
990 This name is not supported by GHC.
997 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
999 <sect2 id="parallel-list-comprehensions">
1000 <title>Parallel List Comprehensions</title>
1001 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1003 <indexterm><primary>parallel list comprehensions</primary>
1006 <para>Parallel list comprehensions are a natural extension to list
1007 comprehensions. List comprehensions can be thought of as a nice
1008 syntax for writing maps and filters. Parallel comprehensions
1009 extend this to include the zipWith family.</para>
1011 <para>A parallel list comprehension has multiple independent
1012 branches of qualifier lists, each separated by a `|' symbol. For
1013 example, the following zips together two lists:</para>
1016 [ (x, y) | x <- xs | y <- ys ]
1019 <para>The behavior of parallel list comprehensions follows that of
1020 zip, in that the resulting list will have the same length as the
1021 shortest branch.</para>
1023 <para>We can define parallel list comprehensions by translation to
1024 regular comprehensions. Here's the basic idea:</para>
1026 <para>Given a parallel comprehension of the form: </para>
1029 [ e | p1 <- e11, p2 <- e12, ...
1030 | q1 <- e21, q2 <- e22, ...
1035 <para>This will be translated to: </para>
1038 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1039 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1044 <para>where `zipN' is the appropriate zip for the given number of
1049 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1051 <sect2 id="generalised-list-comprehensions">
1052 <title>Generalised (SQL-Like) List Comprehensions</title>
1053 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1055 <indexterm><primary>extended list comprehensions</primary>
1057 <indexterm><primary>group</primary></indexterm>
1058 <indexterm><primary>sql</primary></indexterm>
1061 <para>Generalised list comprehensions are a further enhancement to the
1062 list comprehension syntactic sugar to allow operations such as sorting
1063 and grouping which are familiar from SQL. They are fully described in the
1064 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1065 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1066 except that the syntax we use differs slightly from the paper.</para>
1067 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1068 <para>Here is an example:
1070 employees = [ ("Simon", "MS", 80)
1071 , ("Erik", "MS", 100)
1072 , ("Phil", "Ed", 40)
1073 , ("Gordon", "Ed", 45)
1074 , ("Paul", "Yale", 60)]
1076 output = [ (the dept, sum salary)
1077 | (name, dept, salary) <- employees
1078 , then group by dept
1079 , then sortWith by (sum salary)
1082 In this example, the list <literal>output</literal> would take on
1086 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1089 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1090 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1091 function that is exported by <literal>GHC.Exts</literal>.)</para>
1093 <para>There are five new forms of comprehension qualifier,
1094 all introduced by the (existing) keyword <literal>then</literal>:
1102 This statement requires that <literal>f</literal> have the type <literal>
1103 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1104 motivating example, as this form is used to apply <literal>take 5</literal>.
1115 This form is similar to the previous one, but allows you to create a function
1116 which will be passed as the first argument to f. As a consequence f must have
1117 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1118 from the type, this function lets f "project out" some information
1119 from the elements of the list it is transforming.</para>
1121 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1122 is supplied with a function that lets it find out the <literal>sum salary</literal>
1123 for any item in the list comprehension it transforms.</para>
1131 then group by e using f
1134 <para>This is the most general of the grouping-type statements. In this form,
1135 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1136 As with the <literal>then f by e</literal> case above, the first argument
1137 is a function supplied to f by the compiler which lets it compute e on every
1138 element of the list being transformed. However, unlike the non-grouping case,
1139 f additionally partitions the list into a number of sublists: this means that
1140 at every point after this statement, binders occurring before it in the comprehension
1141 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1142 this, let's look at an example:</para>
1145 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1146 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1147 groupRuns f = groupBy (\x y -> f x == f y)
1149 output = [ (the x, y)
1150 | x <- ([1..3] ++ [1..2])
1152 , then group by x using groupRuns ]
1155 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1158 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1161 <para>Note that we have used the <literal>the</literal> function to change the type
1162 of x from a list to its original numeric type. The variable y, in contrast, is left
1163 unchanged from the list form introduced by the grouping.</para>
1173 <para>This form of grouping is essentially the same as the one described above. However,
1174 since no function to use for the grouping has been supplied it will fall back on the
1175 <literal>groupWith</literal> function defined in
1176 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1177 is the form of the group statement that we made use of in the opening example.</para>
1188 <para>With this form of the group statement, f is required to simply have the type
1189 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1190 comprehension so far directly. An example of this form is as follows:</para>
1196 , then group using inits]
1199 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1202 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1210 <!-- ===================== REBINDABLE SYNTAX =================== -->
1212 <sect2 id="rebindable-syntax">
1213 <title>Rebindable syntax and the implicit Prelude import</title>
1215 <para><indexterm><primary>-XNoImplicitPrelude
1216 option</primary></indexterm> GHC normally imports
1217 <filename>Prelude.hi</filename> files for you. If you'd
1218 rather it didn't, then give it a
1219 <option>-XNoImplicitPrelude</option> option. The idea is
1220 that you can then import a Prelude of your own. (But don't
1221 call it <literal>Prelude</literal>; the Haskell module
1222 namespace is flat, and you must not conflict with any
1223 Prelude module.)</para>
1225 <para>Suppose you are importing a Prelude of your own
1226 in order to define your own numeric class
1227 hierarchy. It completely defeats that purpose if the
1228 literal "1" means "<literal>Prelude.fromInteger
1229 1</literal>", which is what the Haskell Report specifies.
1230 So the <option>-XNoImplicitPrelude</option>
1231 flag <emphasis>also</emphasis> causes
1232 the following pieces of built-in syntax to refer to
1233 <emphasis>whatever is in scope</emphasis>, not the Prelude
1237 <para>An integer literal <literal>368</literal> means
1238 "<literal>fromInteger (368::Integer)</literal>", rather than
1239 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1242 <listitem><para>Fractional literals are handed in just the same way,
1243 except that the translation is
1244 <literal>fromRational (3.68::Rational)</literal>.
1247 <listitem><para>The equality test in an overloaded numeric pattern
1248 uses whatever <literal>(==)</literal> is in scope.
1251 <listitem><para>The subtraction operation, and the
1252 greater-than-or-equal test, in <literal>n+k</literal> patterns
1253 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1257 <para>Negation (e.g. "<literal>- (f x)</literal>")
1258 means "<literal>negate (f x)</literal>", both in numeric
1259 patterns, and expressions.
1263 <para>"Do" notation is translated using whatever
1264 functions <literal>(>>=)</literal>,
1265 <literal>(>>)</literal>, and <literal>fail</literal>,
1266 are in scope (not the Prelude
1267 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1268 comprehensions, are unaffected. </para></listitem>
1272 notation (see <xref linkend="arrow-notation"/>)
1273 uses whatever <literal>arr</literal>,
1274 <literal>(>>>)</literal>, <literal>first</literal>,
1275 <literal>app</literal>, <literal>(|||)</literal> and
1276 <literal>loop</literal> functions are in scope. But unlike the
1277 other constructs, the types of these functions must match the
1278 Prelude types very closely. Details are in flux; if you want
1282 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1283 even if that is a little unexpected. For example, the
1284 static semantics of the literal <literal>368</literal>
1285 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1286 <literal>fromInteger</literal> to have any of the types:
1288 fromInteger :: Integer -> Integer
1289 fromInteger :: forall a. Foo a => Integer -> a
1290 fromInteger :: Num a => a -> Integer
1291 fromInteger :: Integer -> Bool -> Bool
1295 <para>Be warned: this is an experimental facility, with
1296 fewer checks than usual. Use <literal>-dcore-lint</literal>
1297 to typecheck the desugared program. If Core Lint is happy
1298 you should be all right.</para>
1302 <sect2 id="postfix-operators">
1303 <title>Postfix operators</title>
1306 The <option>-XPostfixOperators</option> flag enables a small
1307 extension to the syntax of left operator sections, which allows you to
1308 define postfix operators. The extension is this: the left section
1312 is equivalent (from the point of view of both type checking and execution) to the expression
1316 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1317 The strict Haskell 98 interpretation is that the section is equivalent to
1321 That is, the operator must be a function of two arguments. GHC allows it to
1322 take only one argument, and that in turn allows you to write the function
1325 <para>The extension does not extend to the left-hand side of function
1326 definitions; you must define such a function in prefix form.</para>
1330 <sect2 id="tuple-sections">
1331 <title>Tuple sections</title>
1334 The <option>-XTupleSections</option> flag enables Python-style partially applied
1335 tuple constructors. For example, the following program
1339 is considered to be an alternative notation for the more unwieldy alternative
1343 You can omit any combination of arguments to the tuple, as in the following
1345 (, "I", , , "Love", , 1337)
1349 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1354 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1355 will also be available for them, like so
1359 Because there is no unboxed unit tuple, the following expression
1363 continues to stand for the unboxed singleton tuple data constructor.
1368 <sect2 id="disambiguate-fields">
1369 <title>Record field disambiguation</title>
1371 In record construction and record pattern matching
1372 it is entirely unambiguous which field is referred to, even if there are two different
1373 data types in scope with a common field name. For example:
1376 data S = MkS { x :: Int, y :: Bool }
1381 data T = MkT { x :: Int }
1383 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1384 ok2 n = MkT { x = n+1 } -- Unambiguous
1386 bad1 k = k { x = 3 } -- Ambiguous
1387 bad2 k = x k -- Ambiguous
1389 Even though there are two <literal>x</literal>'s in scope,
1390 it is clear that the <literal>x</literal> in the pattern in the
1391 definition of <literal>ok1</literal> can only mean the field
1392 <literal>x</literal> from type <literal>S</literal>. Similarly for
1393 the function <literal>ok2</literal>. However, in the record update
1394 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1395 it is not clear which of the two types is intended.
1398 Haskell 98 regards all four as ambiguous, but with the
1399 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1400 the former two. The rules are precisely the same as those for instance
1401 declarations in Haskell 98, where the method names on the left-hand side
1402 of the method bindings in an instance declaration refer unambiguously
1403 to the method of that class (provided they are in scope at all), even
1404 if there are other variables in scope with the same name.
1405 This reduces the clutter of qualified names when you import two
1406 records from different modules that use the same field name.
1412 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1417 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1422 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1423 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1424 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1427 import qualified M -- Note qualified
1429 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1431 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1432 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1433 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1434 is not. (In effect, it is qualified by the constructor.)
1441 <!-- ===================== Record puns =================== -->
1443 <sect2 id="record-puns">
1448 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1452 When using records, it is common to write a pattern that binds a
1453 variable with the same name as a record field, such as:
1456 data C = C {a :: Int}
1462 Record punning permits the variable name to be elided, so one can simply
1469 to mean the same pattern as above. That is, in a record pattern, the
1470 pattern <literal>a</literal> expands into the pattern <literal>a =
1471 a</literal> for the same name <literal>a</literal>.
1478 Record punning can also be used in an expression, writing, for example,
1484 let a = 1 in C {a = a}
1486 The expansion is purely syntactic, so the expanded right-hand side
1487 expression refers to the nearest enclosing variable that is spelled the
1488 same as the field name.
1492 Puns and other patterns can be mixed in the same record:
1494 data C = C {a :: Int, b :: Int}
1495 f (C {a, b = 4}) = a
1500 Puns can be used wherever record patterns occur (e.g. in
1501 <literal>let</literal> bindings or at the top-level).
1505 A pun on a qualified field name is expanded by stripping off the module qualifier.
1512 f (M.C {M.a = a}) = a
1514 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1515 is only in scope in qualified form.)
1523 <!-- ===================== Record wildcards =================== -->
1525 <sect2 id="record-wildcards">
1526 <title>Record wildcards
1530 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1531 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1535 For records with many fields, it can be tiresome to write out each field
1536 individually in a record pattern, as in
1538 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1539 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1544 Record wildcard syntax permits a "<literal>..</literal>" in a record
1545 pattern, where each elided field <literal>f</literal> is replaced by the
1546 pattern <literal>f = f</literal>. For example, the above pattern can be
1549 f (C {a = 1, ..}) = b + c + d
1557 Wildcards can be mixed with other patterns, including puns
1558 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1559 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1560 wherever record patterns occur, including in <literal>let</literal>
1561 bindings and at the top-level. For example, the top-level binding
1565 defines <literal>b</literal>, <literal>c</literal>, and
1566 <literal>d</literal>.
1570 Record wildcards can also be used in expressions, writing, for example,
1572 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1576 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1578 The expansion is purely syntactic, so the record wildcard
1579 expression refers to the nearest enclosing variables that are spelled
1580 the same as the omitted field names.
1584 The "<literal>..</literal>" expands to the missing
1585 <emphasis>in-scope</emphasis> record fields, where "in scope"
1586 includes both unqualified and qualified-only.
1587 Any fields that are not in scope are not filled in. For example
1590 data R = R { a,b,c :: Int }
1592 import qualified M( R(a,b) )
1595 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1596 omitting <literal>c</literal> since it is not in scope at all.
1603 <!-- ===================== Local fixity declarations =================== -->
1605 <sect2 id="local-fixity-declarations">
1606 <title>Local Fixity Declarations
1609 <para>A careful reading of the Haskell 98 Report reveals that fixity
1610 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1611 <literal>infixr</literal>) are permitted to appear inside local bindings
1612 such those introduced by <literal>let</literal> and
1613 <literal>where</literal>. However, the Haskell Report does not specify
1614 the semantics of such bindings very precisely.
1617 <para>In GHC, a fixity declaration may accompany a local binding:
1624 and the fixity declaration applies wherever the binding is in scope.
1625 For example, in a <literal>let</literal>, it applies in the right-hand
1626 sides of other <literal>let</literal>-bindings and the body of the
1627 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1628 expressions (<xref linkend="mdo-notation"/>), the local fixity
1629 declarations of a <literal>let</literal> statement scope over other
1630 statements in the group, just as the bound name does.
1634 Moreover, a local fixity declaration *must* accompany a local binding of
1635 that name: it is not possible to revise the fixity of name bound
1638 let infixr 9 $ in ...
1641 Because local fixity declarations are technically Haskell 98, no flag is
1642 necessary to enable them.
1646 <sect2 id="package-imports">
1647 <title>Package-qualified imports</title>
1649 <para>With the <option>-XPackageImports</option> flag, GHC allows
1650 import declarations to be qualified by the package name that the
1651 module is intended to be imported from. For example:</para>
1654 import "network" Network.Socket
1657 <para>would import the module <literal>Network.Socket</literal> from
1658 the package <literal>network</literal> (any version). This may
1659 be used to disambiguate an import when the same module is
1660 available from multiple packages, or is present in both the
1661 current package being built and an external package.</para>
1663 <para>Note: you probably don't need to use this feature, it was
1664 added mainly so that we can build backwards-compatible versions of
1665 packages when APIs change. It can lead to fragile dependencies in
1666 the common case: modules occasionally move from one package to
1667 another, rendering any package-qualified imports broken.</para>
1670 <sect2 id="syntax-stolen">
1671 <title>Summary of stolen syntax</title>
1673 <para>Turning on an option that enables special syntax
1674 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1675 to compile, perhaps because it uses a variable name which has
1676 become a reserved word. This section lists the syntax that is
1677 "stolen" by language extensions.
1679 notation and nonterminal names from the Haskell 98 lexical syntax
1680 (see the Haskell 98 Report).
1681 We only list syntax changes here that might affect
1682 existing working programs (i.e. "stolen" syntax). Many of these
1683 extensions will also enable new context-free syntax, but in all
1684 cases programs written to use the new syntax would not be
1685 compilable without the option enabled.</para>
1687 <para>There are two classes of special
1692 <para>New reserved words and symbols: character sequences
1693 which are no longer available for use as identifiers in the
1697 <para>Other special syntax: sequences of characters that have
1698 a different meaning when this particular option is turned
1703 The following syntax is stolen:
1708 <literal>forall</literal>
1709 <indexterm><primary><literal>forall</literal></primary></indexterm>
1712 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1713 <option>-XScopedTypeVariables</option>,
1714 <option>-XLiberalTypeSynonyms</option>,
1715 <option>-XRank2Types</option>,
1716 <option>-XRankNTypes</option>,
1717 <option>-XPolymorphicComponents</option>,
1718 <option>-XExistentialQuantification</option>
1724 <literal>mdo</literal>
1725 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1728 Stolen by: <option>-XRecursiveDo</option>,
1734 <literal>foreign</literal>
1735 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1738 Stolen by: <option>-XForeignFunctionInterface</option>,
1744 <literal>rec</literal>,
1745 <literal>proc</literal>, <literal>-<</literal>,
1746 <literal>>-</literal>, <literal>-<<</literal>,
1747 <literal>>>-</literal>, and <literal>(|</literal>,
1748 <literal>|)</literal> brackets
1749 <indexterm><primary><literal>proc</literal></primary></indexterm>
1752 Stolen by: <option>-XArrows</option>,
1758 <literal>?<replaceable>varid</replaceable></literal>,
1759 <literal>%<replaceable>varid</replaceable></literal>
1760 <indexterm><primary>implicit parameters</primary></indexterm>
1763 Stolen by: <option>-XImplicitParams</option>,
1769 <literal>[|</literal>,
1770 <literal>[e|</literal>, <literal>[p|</literal>,
1771 <literal>[d|</literal>, <literal>[t|</literal>,
1772 <literal>$(</literal>,
1773 <literal>$<replaceable>varid</replaceable></literal>
1774 <indexterm><primary>Template Haskell</primary></indexterm>
1777 Stolen by: <option>-XTemplateHaskell</option>,
1783 <literal>[:<replaceable>varid</replaceable>|</literal>
1784 <indexterm><primary>quasi-quotation</primary></indexterm>
1787 Stolen by: <option>-XQuasiQuotes</option>,
1793 <replaceable>varid</replaceable>{<literal>#</literal>},
1794 <replaceable>char</replaceable><literal>#</literal>,
1795 <replaceable>string</replaceable><literal>#</literal>,
1796 <replaceable>integer</replaceable><literal>#</literal>,
1797 <replaceable>float</replaceable><literal>#</literal>,
1798 <replaceable>float</replaceable><literal>##</literal>,
1799 <literal>(#</literal>, <literal>#)</literal>,
1802 Stolen by: <option>-XMagicHash</option>,
1811 <!-- TYPE SYSTEM EXTENSIONS -->
1812 <sect1 id="data-type-extensions">
1813 <title>Extensions to data types and type synonyms</title>
1815 <sect2 id="nullary-types">
1816 <title>Data types with no constructors</title>
1818 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1819 a data type with no constructors. For example:</para>
1823 data T a -- T :: * -> *
1826 <para>Syntactically, the declaration lacks the "= constrs" part. The
1827 type can be parameterised over types of any kind, but if the kind is
1828 not <literal>*</literal> then an explicit kind annotation must be used
1829 (see <xref linkend="kinding"/>).</para>
1831 <para>Such data types have only one value, namely bottom.
1832 Nevertheless, they can be useful when defining "phantom types".</para>
1835 <sect2 id="infix-tycons">
1836 <title>Infix type constructors, classes, and type variables</title>
1839 GHC allows type constructors, classes, and type variables to be operators, and
1840 to be written infix, very much like expressions. More specifically:
1843 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1844 The lexical syntax is the same as that for data constructors.
1847 Data type and type-synonym declarations can be written infix, parenthesised
1848 if you want further arguments. E.g.
1850 data a :*: b = Foo a b
1851 type a :+: b = Either a b
1852 class a :=: b where ...
1854 data (a :**: b) x = Baz a b x
1855 type (a :++: b) y = Either (a,b) y
1859 Types, and class constraints, can be written infix. For example
1862 f :: (a :=: b) => a -> b
1866 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1867 The lexical syntax is the same as that for variable operators, excluding "(.)",
1868 "(!)", and "(*)". In a binding position, the operator must be
1869 parenthesised. For example:
1871 type T (+) = Int + Int
1875 liftA2 :: Arrow (~>)
1876 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1882 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1883 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1886 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1887 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1888 sets the fixity for a data constructor and the corresponding type constructor. For example:
1892 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1893 and similarly for <literal>:*:</literal>.
1894 <literal>Int `a` Bool</literal>.
1897 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1904 <sect2 id="type-synonyms">
1905 <title>Liberalised type synonyms</title>
1908 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1909 on individual synonym declarations.
1910 With the <option>-XLiberalTypeSynonyms</option> extension,
1911 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1912 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1915 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1916 in a type synonym, thus:
1918 type Discard a = forall b. Show b => a -> b -> (a, String)
1923 g :: Discard Int -> (Int,String) -- A rank-2 type
1930 If you also use <option>-XUnboxedTuples</option>,
1931 you can write an unboxed tuple in a type synonym:
1933 type Pr = (# Int, Int #)
1941 You can apply a type synonym to a forall type:
1943 type Foo a = a -> a -> Bool
1945 f :: Foo (forall b. b->b)
1947 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1949 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1954 You can apply a type synonym to a partially applied type synonym:
1956 type Generic i o = forall x. i x -> o x
1959 foo :: Generic Id []
1961 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1963 foo :: forall x. x -> [x]
1971 GHC currently does kind checking before expanding synonyms (though even that
1975 After expanding type synonyms, GHC does validity checking on types, looking for
1976 the following mal-formedness which isn't detected simply by kind checking:
1979 Type constructor applied to a type involving for-alls.
1982 Unboxed tuple on left of an arrow.
1985 Partially-applied type synonym.
1989 this will be rejected:
1991 type Pr = (# Int, Int #)
1996 because GHC does not allow unboxed tuples on the left of a function arrow.
2001 <sect2 id="existential-quantification">
2002 <title>Existentially quantified data constructors
2006 The idea of using existential quantification in data type declarations
2007 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2008 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2009 London, 1991). It was later formalised by Laufer and Odersky
2010 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2011 TOPLAS, 16(5), pp1411-1430, 1994).
2012 It's been in Lennart
2013 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2014 proved very useful. Here's the idea. Consider the declaration:
2020 data Foo = forall a. MkFoo a (a -> Bool)
2027 The data type <literal>Foo</literal> has two constructors with types:
2033 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2040 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2041 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2042 For example, the following expression is fine:
2048 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2054 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2055 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2056 isUpper</function> packages a character with a compatible function. These
2057 two things are each of type <literal>Foo</literal> and can be put in a list.
2061 What can we do with a value of type <literal>Foo</literal>?. In particular,
2062 what happens when we pattern-match on <function>MkFoo</function>?
2068 f (MkFoo val fn) = ???
2074 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2075 are compatible, the only (useful) thing we can do with them is to
2076 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2083 f (MkFoo val fn) = fn val
2089 What this allows us to do is to package heterogeneous values
2090 together with a bunch of functions that manipulate them, and then treat
2091 that collection of packages in a uniform manner. You can express
2092 quite a bit of object-oriented-like programming this way.
2095 <sect3 id="existential">
2096 <title>Why existential?
2100 What has this to do with <emphasis>existential</emphasis> quantification?
2101 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2107 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2113 But Haskell programmers can safely think of the ordinary
2114 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2115 adding a new existential quantification construct.
2120 <sect3 id="existential-with-context">
2121 <title>Existentials and type classes</title>
2124 An easy extension is to allow
2125 arbitrary contexts before the constructor. For example:
2131 data Baz = forall a. Eq a => Baz1 a a
2132 | forall b. Show b => Baz2 b (b -> b)
2138 The two constructors have the types you'd expect:
2144 Baz1 :: forall a. Eq a => a -> a -> Baz
2145 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2151 But when pattern matching on <function>Baz1</function> the matched values can be compared
2152 for equality, and when pattern matching on <function>Baz2</function> the first matched
2153 value can be converted to a string (as well as applying the function to it).
2154 So this program is legal:
2161 f (Baz1 p q) | p == q = "Yes"
2163 f (Baz2 v fn) = show (fn v)
2169 Operationally, in a dictionary-passing implementation, the
2170 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2171 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2172 extract it on pattern matching.
2177 <sect3 id="existential-records">
2178 <title>Record Constructors</title>
2181 GHC allows existentials to be used with records syntax as well. For example:
2184 data Counter a = forall self. NewCounter
2186 , _inc :: self -> self
2187 , _display :: self -> IO ()
2191 Here <literal>tag</literal> is a public field, with a well-typed selector
2192 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2193 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2194 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2195 compile-time error. In other words, <emphasis>GHC defines a record selector function
2196 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2197 (This example used an underscore in the fields for which record selectors
2198 will not be defined, but that is only programming style; GHC ignores them.)
2202 To make use of these hidden fields, we need to create some helper functions:
2205 inc :: Counter a -> Counter a
2206 inc (NewCounter x i d t) = NewCounter
2207 { _this = i x, _inc = i, _display = d, tag = t }
2209 display :: Counter a -> IO ()
2210 display NewCounter{ _this = x, _display = d } = d x
2213 Now we can define counters with different underlying implementations:
2216 counterA :: Counter String
2217 counterA = NewCounter
2218 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2220 counterB :: Counter String
2221 counterB = NewCounter
2222 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2225 display (inc counterA) -- prints "1"
2226 display (inc (inc counterB)) -- prints "##"
2229 Record update syntax is supported for existentials (and GADTs):
2231 setTag :: Counter a -> a -> Counter a
2232 setTag obj t = obj{ tag = t }
2234 The rule for record update is this: <emphasis>
2235 the types of the updated fields may
2236 mention only the universally-quantified type variables
2237 of the data constructor. For GADTs, the field may mention only types
2238 that appear as a simple type-variable argument in the constructor's result
2239 type</emphasis>. For example:
2241 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2242 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2243 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2244 -- existentially quantified)
2246 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2247 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2248 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2249 -- type-variable argument in G1's result type)
2257 <title>Restrictions</title>
2260 There are several restrictions on the ways in which existentially-quantified
2261 constructors can be use.
2270 When pattern matching, each pattern match introduces a new,
2271 distinct, type for each existential type variable. These types cannot
2272 be unified with any other type, nor can they escape from the scope of
2273 the pattern match. For example, these fragments are incorrect:
2281 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2282 is the result of <function>f1</function>. One way to see why this is wrong is to
2283 ask what type <function>f1</function> has:
2287 f1 :: Foo -> a -- Weird!
2291 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2296 f1 :: forall a. Foo -> a -- Wrong!
2300 The original program is just plain wrong. Here's another sort of error
2304 f2 (Baz1 a b) (Baz1 p q) = a==q
2308 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2309 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2310 from the two <function>Baz1</function> constructors.
2318 You can't pattern-match on an existentially quantified
2319 constructor in a <literal>let</literal> or <literal>where</literal> group of
2320 bindings. So this is illegal:
2324 f3 x = a==b where { Baz1 a b = x }
2327 Instead, use a <literal>case</literal> expression:
2330 f3 x = case x of Baz1 a b -> a==b
2333 In general, you can only pattern-match
2334 on an existentially-quantified constructor in a <literal>case</literal> expression or
2335 in the patterns of a function definition.
2337 The reason for this restriction is really an implementation one.
2338 Type-checking binding groups is already a nightmare without
2339 existentials complicating the picture. Also an existential pattern
2340 binding at the top level of a module doesn't make sense, because it's
2341 not clear how to prevent the existentially-quantified type "escaping".
2342 So for now, there's a simple-to-state restriction. We'll see how
2350 You can't use existential quantification for <literal>newtype</literal>
2351 declarations. So this is illegal:
2355 newtype T = forall a. Ord a => MkT a
2359 Reason: a value of type <literal>T</literal> must be represented as a
2360 pair of a dictionary for <literal>Ord t</literal> and a value of type
2361 <literal>t</literal>. That contradicts the idea that
2362 <literal>newtype</literal> should have no concrete representation.
2363 You can get just the same efficiency and effect by using
2364 <literal>data</literal> instead of <literal>newtype</literal>. If
2365 there is no overloading involved, then there is more of a case for
2366 allowing an existentially-quantified <literal>newtype</literal>,
2367 because the <literal>data</literal> version does carry an
2368 implementation cost, but single-field existentially quantified
2369 constructors aren't much use. So the simple restriction (no
2370 existential stuff on <literal>newtype</literal>) stands, unless there
2371 are convincing reasons to change it.
2379 You can't use <literal>deriving</literal> to define instances of a
2380 data type with existentially quantified data constructors.
2382 Reason: in most cases it would not make sense. For example:;
2385 data T = forall a. MkT [a] deriving( Eq )
2388 To derive <literal>Eq</literal> in the standard way we would need to have equality
2389 between the single component of two <function>MkT</function> constructors:
2393 (MkT a) == (MkT b) = ???
2396 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2397 It's just about possible to imagine examples in which the derived instance
2398 would make sense, but it seems altogether simpler simply to prohibit such
2399 declarations. Define your own instances!
2410 <!-- ====================== Generalised algebraic data types ======================= -->
2412 <sect2 id="gadt-style">
2413 <title>Declaring data types with explicit constructor signatures</title>
2415 <para>GHC allows you to declare an algebraic data type by
2416 giving the type signatures of constructors explicitly. For example:
2420 Just :: a -> Maybe a
2422 The form is called a "GADT-style declaration"
2423 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2424 can only be declared using this form.</para>
2425 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2426 For example, these two declarations are equivalent:
2428 data Foo = forall a. MkFoo a (a -> Bool)
2429 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2432 <para>Any data type that can be declared in standard Haskell-98 syntax
2433 can also be declared using GADT-style syntax.
2434 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2435 they treat class constraints on the data constructors differently.
2436 Specifically, if the constructor is given a type-class context, that
2437 context is made available by pattern matching. For example:
2440 MkSet :: Eq a => [a] -> Set a
2442 makeSet :: Eq a => [a] -> Set a
2443 makeSet xs = MkSet (nub xs)
2445 insert :: a -> Set a -> Set a
2446 insert a (MkSet as) | a `elem` as = MkSet as
2447 | otherwise = MkSet (a:as)
2449 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2450 gives rise to a <literal>(Eq a)</literal>
2451 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2452 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2453 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2454 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2455 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2456 In the example, the equality dictionary is used to satisfy the equality constraint
2457 generated by the call to <literal>elem</literal>, so that the type of
2458 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2461 For example, one possible application is to reify dictionaries:
2463 data NumInst a where
2464 MkNumInst :: Num a => NumInst a
2466 intInst :: NumInst Int
2469 plus :: NumInst a -> a -> a -> a
2470 plus MkNumInst p q = p + q
2472 Here, a value of type <literal>NumInst a</literal> is equivalent
2473 to an explicit <literal>(Num a)</literal> dictionary.
2476 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2477 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2481 = Num a => MkNumInst (NumInst a)
2483 Notice that, unlike the situation when declaring an existential, there is
2484 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2485 data type's universally quantified type variable <literal>a</literal>.
2486 A constructor may have both universal and existential type variables: for example,
2487 the following two declarations are equivalent:
2490 = forall b. (Num a, Eq b) => MkT1 a b
2492 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2495 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2496 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2497 In Haskell 98 the definition
2499 data Eq a => Set' a = MkSet' [a]
2501 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2502 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2503 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2504 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2505 GHC's behaviour is much more useful, as well as much more intuitive.
2509 The rest of this section gives further details about GADT-style data
2514 The result type of each data constructor must begin with the type constructor being defined.
2515 If the result type of all constructors
2516 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2517 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2518 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2522 As with other type signatures, you can give a single signature for several data constructors.
2523 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2532 The type signature of
2533 each constructor is independent, and is implicitly universally quantified as usual.
2534 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2535 have no scope, and different constructors may have different universally-quantified type variables:
2537 data T a where -- The 'a' has no scope
2538 T1,T2 :: b -> T b -- Means forall b. b -> T b
2539 T3 :: T a -- Means forall a. T a
2544 A constructor signature may mention type class constraints, which can differ for
2545 different constructors. For example, this is fine:
2548 T1 :: Eq b => b -> b -> T b
2549 T2 :: (Show c, Ix c) => c -> [c] -> T c
2551 When patten matching, these constraints are made available to discharge constraints
2552 in the body of the match. For example:
2555 f (T1 x y) | x==y = "yes"
2559 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2560 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2561 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2565 Unlike a Haskell-98-style
2566 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2567 have no scope. Indeed, one can write a kind signature instead:
2569 data Set :: * -> * where ...
2571 or even a mixture of the two:
2573 data Bar a :: (* -> *) -> * where ...
2575 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2578 data Bar a (b :: * -> *) where ...
2584 You can use strictness annotations, in the obvious places
2585 in the constructor type:
2588 Lit :: !Int -> Term Int
2589 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2590 Pair :: Term a -> Term b -> Term (a,b)
2595 You can use a <literal>deriving</literal> clause on a GADT-style data type
2596 declaration. For example, these two declarations are equivalent
2598 data Maybe1 a where {
2599 Nothing1 :: Maybe1 a ;
2600 Just1 :: a -> Maybe1 a
2601 } deriving( Eq, Ord )
2603 data Maybe2 a = Nothing2 | Just2 a
2609 The type signature may have quantified type variables that do not appear
2613 MkFoo :: a -> (a->Bool) -> Foo
2616 Here the type variable <literal>a</literal> does not appear in the result type
2617 of either constructor.
2618 Although it is universally quantified in the type of the constructor, such
2619 a type variable is often called "existential".
2620 Indeed, the above declaration declares precisely the same type as
2621 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2623 The type may contain a class context too, of course:
2626 MkShowable :: Show a => a -> Showable
2631 You can use record syntax on a GADT-style data type declaration:
2635 Adult :: { name :: String, children :: [Person] } -> Person
2636 Child :: Show a => { name :: !String, funny :: a } -> Person
2638 As usual, for every constructor that has a field <literal>f</literal>, the type of
2639 field <literal>f</literal> must be the same (modulo alpha conversion).
2640 The <literal>Child</literal> constructor above shows that the signature
2641 may have a context, existentially-quantified variables, and strictness annotations,
2642 just as in the non-record case. (NB: the "type" that follows the double-colon
2643 is not really a type, because of the record syntax and strictness annotations.
2644 A "type" of this form can appear only in a constructor signature.)
2648 Record updates are allowed with GADT-style declarations,
2649 only fields that have the following property: the type of the field
2650 mentions no existential type variables.
2654 As in the case of existentials declared using the Haskell-98-like record syntax
2655 (<xref linkend="existential-records"/>),
2656 record-selector functions are generated only for those fields that have well-typed
2658 Here is the example of that section, in GADT-style syntax:
2660 data Counter a where
2661 NewCounter { _this :: self
2662 , _inc :: self -> self
2663 , _display :: self -> IO ()
2668 As before, only one selector function is generated here, that for <literal>tag</literal>.
2669 Nevertheless, you can still use all the field names in pattern matching and record construction.
2671 </itemizedlist></para>
2675 <title>Generalised Algebraic Data Types (GADTs)</title>
2677 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2678 by allowing constructors to have richer return types. Here is an example:
2681 Lit :: Int -> Term Int
2682 Succ :: Term Int -> Term Int
2683 IsZero :: Term Int -> Term Bool
2684 If :: Term Bool -> Term a -> Term a -> Term a
2685 Pair :: Term a -> Term b -> Term (a,b)
2687 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2688 case with ordinary data types. This generality allows us to
2689 write a well-typed <literal>eval</literal> function
2690 for these <literal>Terms</literal>:
2694 eval (Succ t) = 1 + eval t
2695 eval (IsZero t) = eval t == 0
2696 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2697 eval (Pair e1 e2) = (eval e1, eval e2)
2699 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2700 For example, in the right hand side of the equation
2705 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2706 A precise specification of the type rules is beyond what this user manual aspires to,
2707 but the design closely follows that described in
2709 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2710 unification-based type inference for GADTs</ulink>,
2712 The general principle is this: <emphasis>type refinement is only carried out
2713 based on user-supplied type annotations</emphasis>.
2714 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2715 and lots of obscure error messages will
2716 occur. However, the refinement is quite general. For example, if we had:
2718 eval :: Term a -> a -> a
2719 eval (Lit i) j = i+j
2721 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2722 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2723 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2726 These and many other examples are given in papers by Hongwei Xi, and
2727 Tim Sheard. There is a longer introduction
2728 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2730 <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
2731 may use different notation to that implemented in GHC.
2734 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2735 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2738 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2739 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2740 The result type of each constructor must begin with the type constructor being defined,
2741 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2742 For example, in the <literal>Term</literal> data
2743 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2744 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2749 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2750 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2751 whose result type is not just <literal>T a b</literal>.
2755 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2756 an ordinary data type.
2760 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2764 Lit { val :: Int } :: Term Int
2765 Succ { num :: Term Int } :: Term Int
2766 Pred { num :: Term Int } :: Term Int
2767 IsZero { arg :: Term Int } :: Term Bool
2768 Pair { arg1 :: Term a
2771 If { cnd :: Term Bool
2776 However, for GADTs there is the following additional constraint:
2777 every constructor that has a field <literal>f</literal> must have
2778 the same result type (modulo alpha conversion)
2779 Hence, in the above example, we cannot merge the <literal>num</literal>
2780 and <literal>arg</literal> fields above into a
2781 single name. Although their field types are both <literal>Term Int</literal>,
2782 their selector functions actually have different types:
2785 num :: Term Int -> Term Int
2786 arg :: Term Bool -> Term Int
2791 When pattern-matching against data constructors drawn from a GADT,
2792 for example in a <literal>case</literal> expression, the following rules apply:
2794 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2795 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2796 <listitem><para>The type of any free variable mentioned in any of
2797 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2799 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2800 way to ensure that a variable a rigid type is to give it a type signature.
2801 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2802 Simple unification-based type inference for GADTs
2803 </ulink>. The criteria implemented by GHC are given in the Appendix.
2813 <!-- ====================== End of Generalised algebraic data types ======================= -->
2815 <sect1 id="deriving">
2816 <title>Extensions to the "deriving" mechanism</title>
2818 <sect2 id="deriving-inferred">
2819 <title>Inferred context for deriving clauses</title>
2822 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2825 data T0 f a = MkT0 a deriving( Eq )
2826 data T1 f a = MkT1 (f a) deriving( Eq )
2827 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2829 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2831 instance Eq a => Eq (T0 f a) where ...
2832 instance Eq (f a) => Eq (T1 f a) where ...
2833 instance Eq (f (f a)) => Eq (T2 f a) where ...
2835 The first of these is obviously fine. The second is still fine, although less obviously.
2836 The third is not Haskell 98, and risks losing termination of instances.
2839 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2840 each constraint in the inferred instance context must consist only of type variables,
2841 with no repetitions.
2844 This rule is applied regardless of flags. If you want a more exotic context, you can write
2845 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2849 <sect2 id="stand-alone-deriving">
2850 <title>Stand-alone deriving declarations</title>
2853 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2855 data Foo a = Bar a | Baz String
2857 deriving instance Eq a => Eq (Foo a)
2859 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2860 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2861 Note the following points:
2864 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2865 exactly as you would in an ordinary instance declaration.
2866 (In contrast, in a <literal>deriving</literal> clause
2867 attached to a data type declaration, the context is inferred.)
2871 A <literal>deriving instance</literal> declaration
2872 must obey the same rules concerning form and termination as ordinary instance declarations,
2873 controlled by the same flags; see <xref linkend="instance-decls"/>.
2877 Unlike a <literal>deriving</literal>
2878 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2879 than the data type (assuming you also use
2880 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2883 data Foo a = Bar a | Baz String
2885 deriving instance Eq a => Eq (Foo [a])
2886 deriving instance Eq a => Eq (Foo (Maybe a))
2888 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2889 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2893 Unlike a <literal>deriving</literal>
2894 declaration attached to a <literal>data</literal> declaration,
2895 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2896 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2897 your problem. (GHC will show you the offending code if it has a type error.)
2898 The merit of this is that you can derive instances for GADTs and other exotic
2899 data types, providing only that the boilerplate code does indeed typecheck. For example:
2905 deriving instance Show (T a)
2907 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2908 data type declaration for <literal>T</literal>,
2909 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2910 the instance declaration using stand-alone deriving.
2915 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2916 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2919 newtype Foo a = MkFoo (State Int a)
2921 deriving instance MonadState Int Foo
2923 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2924 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2926 </itemizedlist></para>
2931 <sect2 id="deriving-typeable">
2932 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2935 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2936 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2937 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2938 classes <literal>Eq</literal>, <literal>Ord</literal>,
2939 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2942 GHC extends this list with several more classes that may be automatically derived:
2944 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2945 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2946 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2948 <para>An instance of <literal>Typeable</literal> can only be derived if the
2949 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2950 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2952 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2953 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2955 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2956 are used, and only <literal>Typeable1</literal> up to
2957 <literal>Typeable7</literal> are provided in the library.)
2958 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2959 class, whose kind suits that of the data type constructor, and
2960 then writing the data type instance by hand.
2964 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2965 the class <literal>Functor</literal>,
2966 defined in <literal>GHC.Base</literal>.
2969 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2970 the class <literal>Foldable</literal>,
2971 defined in <literal>Data.Foldable</literal>.
2974 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2975 the class <literal>Traversable</literal>,
2976 defined in <literal>Data.Traversable</literal>.
2979 In each case the appropriate class must be in scope before it
2980 can be mentioned in the <literal>deriving</literal> clause.
2984 <sect2 id="newtype-deriving">
2985 <title>Generalised derived instances for newtypes</title>
2988 When you define an abstract type using <literal>newtype</literal>, you may want
2989 the new type to inherit some instances from its representation. In
2990 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2991 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2992 other classes you have to write an explicit instance declaration. For
2993 example, if you define
2996 newtype Dollars = Dollars Int
2999 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3000 explicitly define an instance of <literal>Num</literal>:
3003 instance Num Dollars where
3004 Dollars a + Dollars b = Dollars (a+b)
3007 All the instance does is apply and remove the <literal>newtype</literal>
3008 constructor. It is particularly galling that, since the constructor
3009 doesn't appear at run-time, this instance declaration defines a
3010 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3011 dictionary, only slower!
3015 <sect3> <title> Generalising the deriving clause </title>
3017 GHC now permits such instances to be derived instead,
3018 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3021 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3024 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3025 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3026 derives an instance declaration of the form
3029 instance Num Int => Num Dollars
3032 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3036 We can also derive instances of constructor classes in a similar
3037 way. For example, suppose we have implemented state and failure monad
3038 transformers, such that
3041 instance Monad m => Monad (State s m)
3042 instance Monad m => Monad (Failure m)
3044 In Haskell 98, we can define a parsing monad by
3046 type Parser tok m a = State [tok] (Failure m) a
3049 which is automatically a monad thanks to the instance declarations
3050 above. With the extension, we can make the parser type abstract,
3051 without needing to write an instance of class <literal>Monad</literal>, via
3054 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3057 In this case the derived instance declaration is of the form
3059 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3062 Notice that, since <literal>Monad</literal> is a constructor class, the
3063 instance is a <emphasis>partial application</emphasis> of the new type, not the
3064 entire left hand side. We can imagine that the type declaration is
3065 "eta-converted" to generate the context of the instance
3070 We can even derive instances of multi-parameter classes, provided the
3071 newtype is the last class parameter. In this case, a ``partial
3072 application'' of the class appears in the <literal>deriving</literal>
3073 clause. For example, given the class
3076 class StateMonad s m | m -> s where ...
3077 instance Monad m => StateMonad s (State s m) where ...
3079 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3081 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3082 deriving (Monad, StateMonad [tok])
3085 The derived instance is obtained by completing the application of the
3086 class to the new type:
3089 instance StateMonad [tok] (State [tok] (Failure m)) =>
3090 StateMonad [tok] (Parser tok m)
3095 As a result of this extension, all derived instances in newtype
3096 declarations are treated uniformly (and implemented just by reusing
3097 the dictionary for the representation type), <emphasis>except</emphasis>
3098 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3099 the newtype and its representation.
3103 <sect3> <title> A more precise specification </title>
3105 Derived instance declarations are constructed as follows. Consider the
3106 declaration (after expansion of any type synonyms)
3109 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3115 The <literal>ci</literal> are partial applications of
3116 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3117 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3120 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3123 The type <literal>t</literal> is an arbitrary type.
3126 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3127 nor in the <literal>ci</literal>, and
3130 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3131 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3132 should not "look through" the type or its constructor. You can still
3133 derive these classes for a newtype, but it happens in the usual way, not
3134 via this new mechanism.
3137 Then, for each <literal>ci</literal>, the derived instance
3140 instance ci t => ci (T v1...vk)
3142 As an example which does <emphasis>not</emphasis> work, consider
3144 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3146 Here we cannot derive the instance
3148 instance Monad (State s m) => Monad (NonMonad m)
3151 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3152 and so cannot be "eta-converted" away. It is a good thing that this
3153 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3154 not, in fact, a monad --- for the same reason. Try defining
3155 <literal>>>=</literal> with the correct type: you won't be able to.
3159 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3160 important, since we can only derive instances for the last one. If the
3161 <literal>StateMonad</literal> class above were instead defined as
3164 class StateMonad m s | m -> s where ...
3167 then we would not have been able to derive an instance for the
3168 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3169 classes usually have one "main" parameter for which deriving new
3170 instances is most interesting.
3172 <para>Lastly, all of this applies only for classes other than
3173 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3174 and <literal>Data</literal>, for which the built-in derivation applies (section
3175 4.3.3. of the Haskell Report).
3176 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3177 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3178 the standard method is used or the one described here.)
3185 <!-- TYPE SYSTEM EXTENSIONS -->
3186 <sect1 id="type-class-extensions">
3187 <title>Class and instances declarations</title>
3189 <sect2 id="multi-param-type-classes">
3190 <title>Class declarations</title>
3193 This section, and the next one, documents GHC's type-class extensions.
3194 There's lots of background in the paper <ulink
3195 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3196 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3197 Jones, Erik Meijer).
3200 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3204 <title>Multi-parameter type classes</title>
3206 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3211 class Collection c a where
3212 union :: c a -> c a -> c a
3219 <sect3 id="superclass-rules">
3220 <title>The superclasses of a class declaration</title>
3223 In Haskell 98 the context of a class declaration (which introduces superclasses)
3224 must be simple; that is, each predicate must consist of a class applied to
3225 type variables. The flag <option>-XFlexibleContexts</option>
3226 (<xref linkend="flexible-contexts"/>)
3227 lifts this restriction,
3228 so that the only restriction on the context in a class declaration is
3229 that the class hierarchy must be acyclic. So these class declarations are OK:
3233 class Functor (m k) => FiniteMap m k where
3236 class (Monad m, Monad (t m)) => Transform t m where
3237 lift :: m a -> (t m) a
3243 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3244 of "acyclic" involves only the superclass relationships. For example,
3250 op :: D b => a -> b -> b
3253 class C a => D a where { ... }
3257 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3258 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3259 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3266 <sect3 id="class-method-types">
3267 <title>Class method types</title>
3270 Haskell 98 prohibits class method types to mention constraints on the
3271 class type variable, thus:
3274 fromList :: [a] -> s a
3275 elem :: Eq a => a -> s a -> Bool
3277 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3278 contains the constraint <literal>Eq a</literal>, constrains only the
3279 class type variable (in this case <literal>a</literal>).
3280 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3287 <sect2 id="functional-dependencies">
3288 <title>Functional dependencies
3291 <para> Functional dependencies are implemented as described by Mark Jones
3292 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3293 In Proceedings of the 9th European Symposium on Programming,
3294 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3298 Functional dependencies are introduced by a vertical bar in the syntax of a
3299 class declaration; e.g.
3301 class (Monad m) => MonadState s m | m -> s where ...
3303 class Foo a b c | a b -> c where ...
3305 There should be more documentation, but there isn't (yet). Yell if you need it.
3308 <sect3><title>Rules for functional dependencies </title>
3310 In a class declaration, all of the class type variables must be reachable (in the sense
3311 mentioned in <xref linkend="flexible-contexts"/>)
3312 from the free variables of each method type.
3316 class Coll s a where
3318 insert :: s -> a -> s
3321 is not OK, because the type of <literal>empty</literal> doesn't mention
3322 <literal>a</literal>. Functional dependencies can make the type variable
3325 class Coll s a | s -> a where
3327 insert :: s -> a -> s
3330 Alternatively <literal>Coll</literal> might be rewritten
3333 class Coll s a where
3335 insert :: s a -> a -> s a
3339 which makes the connection between the type of a collection of
3340 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3341 Occasionally this really doesn't work, in which case you can split the
3349 class CollE s => Coll s a where
3350 insert :: s -> a -> s
3357 <title>Background on functional dependencies</title>
3359 <para>The following description of the motivation and use of functional dependencies is taken
3360 from the Hugs user manual, reproduced here (with minor changes) by kind
3361 permission of Mark Jones.
3364 Consider the following class, intended as part of a
3365 library for collection types:
3367 class Collects e ce where
3369 insert :: e -> ce -> ce
3370 member :: e -> ce -> Bool
3372 The type variable e used here represents the element type, while ce is the type
3373 of the container itself. Within this framework, we might want to define
3374 instances of this class for lists or characteristic functions (both of which
3375 can be used to represent collections of any equality type), bit sets (which can
3376 be used to represent collections of characters), or hash tables (which can be
3377 used to represent any collection whose elements have a hash function). Omitting
3378 standard implementation details, this would lead to the following declarations:
3380 instance Eq e => Collects e [e] where ...
3381 instance Eq e => Collects e (e -> Bool) where ...
3382 instance Collects Char BitSet where ...
3383 instance (Hashable e, Collects a ce)
3384 => Collects e (Array Int ce) where ...
3386 All this looks quite promising; we have a class and a range of interesting
3387 implementations. Unfortunately, there are some serious problems with the class
3388 declaration. First, the empty function has an ambiguous type:
3390 empty :: Collects e ce => ce
3392 By "ambiguous" we mean that there is a type variable e that appears on the left
3393 of the <literal>=></literal> symbol, but not on the right. The problem with
3394 this is that, according to the theoretical foundations of Haskell overloading,
3395 we cannot guarantee a well-defined semantics for any term with an ambiguous
3399 We can sidestep this specific problem by removing the empty member from the
3400 class declaration. However, although the remaining members, insert and member,
3401 do not have ambiguous types, we still run into problems when we try to use
3402 them. For example, consider the following two functions:
3404 f x y = insert x . insert y
3407 for which GHC infers the following types:
3409 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3410 g :: (Collects Bool c, Collects Char c) => c -> c
3412 Notice that the type for f allows the two parameters x and y to be assigned
3413 different types, even though it attempts to insert each of the two values, one
3414 after the other, into the same collection. If we're trying to model collections
3415 that contain only one type of value, then this is clearly an inaccurate
3416 type. Worse still, the definition for g is accepted, without causing a type
3417 error. As a result, the error in this code will not be flagged at the point
3418 where it appears. Instead, it will show up only when we try to use g, which
3419 might even be in a different module.
3422 <sect4><title>An attempt to use constructor classes</title>
3425 Faced with the problems described above, some Haskell programmers might be
3426 tempted to use something like the following version of the class declaration:
3428 class Collects e c where
3430 insert :: e -> c e -> c e
3431 member :: e -> c e -> Bool
3433 The key difference here is that we abstract over the type constructor c that is
3434 used to form the collection type c e, and not over that collection type itself,
3435 represented by ce in the original class declaration. This avoids the immediate
3436 problems that we mentioned above: empty has type <literal>Collects e c => c
3437 e</literal>, which is not ambiguous.
3440 The function f from the previous section has a more accurate type:
3442 f :: (Collects e c) => e -> e -> c e -> c e
3444 The function g from the previous section is now rejected with a type error as
3445 we would hope because the type of f does not allow the two arguments to have
3447 This, then, is an example of a multiple parameter class that does actually work
3448 quite well in practice, without ambiguity problems.
3449 There is, however, a catch. This version of the Collects class is nowhere near
3450 as general as the original class seemed to be: only one of the four instances
3451 for <literal>Collects</literal>
3452 given above can be used with this version of Collects because only one of
3453 them---the instance for lists---has a collection type that can be written in
3454 the form c e, for some type constructor c, and element type e.
3458 <sect4><title>Adding functional dependencies</title>
3461 To get a more useful version of the Collects class, Hugs provides a mechanism
3462 that allows programmers to specify dependencies between the parameters of a
3463 multiple parameter class (For readers with an interest in theoretical
3464 foundations and previous work: The use of dependency information can be seen
3465 both as a generalization of the proposal for `parametric type classes' that was
3466 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3467 later framework for "improvement" of qualified types. The
3468 underlying ideas are also discussed in a more theoretical and abstract setting
3469 in a manuscript [implparam], where they are identified as one point in a
3470 general design space for systems of implicit parameterization.).
3472 To start with an abstract example, consider a declaration such as:
3474 class C a b where ...
3476 which tells us simply that C can be thought of as a binary relation on types
3477 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3478 included in the definition of classes to add information about dependencies
3479 between parameters, as in the following examples:
3481 class D a b | a -> b where ...
3482 class E a b | a -> b, b -> a where ...
3484 The notation <literal>a -> b</literal> used here between the | and where
3485 symbols --- not to be
3486 confused with a function type --- indicates that the a parameter uniquely
3487 determines the b parameter, and might be read as "a determines b." Thus D is
3488 not just a relation, but actually a (partial) function. Similarly, from the two
3489 dependencies that are included in the definition of E, we can see that E
3490 represents a (partial) one-one mapping between types.
3493 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3494 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3495 m>=0, meaning that the y parameters are uniquely determined by the x
3496 parameters. Spaces can be used as separators if more than one variable appears
3497 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3498 annotated with multiple dependencies using commas as separators, as in the
3499 definition of E above. Some dependencies that we can write in this notation are
3500 redundant, and will be rejected because they don't serve any useful
3501 purpose, and may instead indicate an error in the program. Examples of
3502 dependencies like this include <literal>a -> a </literal>,
3503 <literal>a -> a a </literal>,
3504 <literal>a -> </literal>, etc. There can also be
3505 some redundancy if multiple dependencies are given, as in
3506 <literal>a->b</literal>,
3507 <literal>b->c </literal>, <literal>a->c </literal>, and
3508 in which some subset implies the remaining dependencies. Examples like this are
3509 not treated as errors. Note that dependencies appear only in class
3510 declarations, and not in any other part of the language. In particular, the
3511 syntax for instance declarations, class constraints, and types is completely
3515 By including dependencies in a class declaration, we provide a mechanism for
3516 the programmer to specify each multiple parameter class more precisely. The
3517 compiler, on the other hand, is responsible for ensuring that the set of
3518 instances that are in scope at any given point in the program is consistent
3519 with any declared dependencies. For example, the following pair of instance
3520 declarations cannot appear together in the same scope because they violate the
3521 dependency for D, even though either one on its own would be acceptable:
3523 instance D Bool Int where ...
3524 instance D Bool Char where ...
3526 Note also that the following declaration is not allowed, even by itself:
3528 instance D [a] b where ...
3530 The problem here is that this instance would allow one particular choice of [a]
3531 to be associated with more than one choice for b, which contradicts the
3532 dependency specified in the definition of D. More generally, this means that,
3533 in any instance of the form:
3535 instance D t s where ...
3537 for some particular types t and s, the only variables that can appear in s are
3538 the ones that appear in t, and hence, if the type t is known, then s will be
3539 uniquely determined.
3542 The benefit of including dependency information is that it allows us to define
3543 more general multiple parameter classes, without ambiguity problems, and with
3544 the benefit of more accurate types. To illustrate this, we return to the
3545 collection class example, and annotate the original definition of <literal>Collects</literal>
3546 with a simple dependency:
3548 class Collects e ce | ce -> e where
3550 insert :: e -> ce -> ce
3551 member :: e -> ce -> Bool
3553 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3554 determined by the type of the collection ce. Note that both parameters of
3555 Collects are of kind *; there are no constructor classes here. Note too that
3556 all of the instances of Collects that we gave earlier can be used
3557 together with this new definition.
3560 What about the ambiguity problems that we encountered with the original
3561 definition? The empty function still has type Collects e ce => ce, but it is no
3562 longer necessary to regard that as an ambiguous type: Although the variable e
3563 does not appear on the right of the => symbol, the dependency for class
3564 Collects tells us that it is uniquely determined by ce, which does appear on
3565 the right of the => symbol. Hence the context in which empty is used can still
3566 give enough information to determine types for both ce and e, without
3567 ambiguity. More generally, we need only regard a type as ambiguous if it
3568 contains a variable on the left of the => that is not uniquely determined
3569 (either directly or indirectly) by the variables on the right.
3572 Dependencies also help to produce more accurate types for user defined
3573 functions, and hence to provide earlier detection of errors, and less cluttered
3574 types for programmers to work with. Recall the previous definition for a
3577 f x y = insert x y = insert x . insert y
3579 for which we originally obtained a type:
3581 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3583 Given the dependency information that we have for Collects, however, we can
3584 deduce that a and b must be equal because they both appear as the second
3585 parameter in a Collects constraint with the same first parameter c. Hence we
3586 can infer a shorter and more accurate type for f:
3588 f :: (Collects a c) => a -> a -> c -> c
3590 In a similar way, the earlier definition of g will now be flagged as a type error.
3593 Although we have given only a few examples here, it should be clear that the
3594 addition of dependency information can help to make multiple parameter classes
3595 more useful in practice, avoiding ambiguity problems, and allowing more general
3596 sets of instance declarations.
3602 <sect2 id="instance-decls">
3603 <title>Instance declarations</title>
3605 <para>An instance declaration has the form
3607 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 ...
3609 The part before the "<literal>=></literal>" is the
3610 <emphasis>context</emphasis>, while the part after the
3611 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3614 <sect3 id="flexible-instance-head">
3615 <title>Relaxed rules for the instance head</title>
3618 In Haskell 98 the head of an instance declaration
3619 must be of the form <literal>C (T a1 ... an)</literal>, where
3620 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3621 and the <literal>a1 ... an</literal> are distinct type variables.
3622 GHC relaxes these rules in two ways.
3626 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3627 declaration to mention arbitrary nested types.
3628 For example, this becomes a legal instance declaration
3630 instance C (Maybe Int) where ...
3632 See also the <link linkend="instance-overlap">rules on overlap</link>.
3635 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3636 synonyms. As always, using a type synonym is just shorthand for
3637 writing the RHS of the type synonym definition. For example:
3641 type Point = (Int,Int)
3642 instance C Point where ...
3643 instance C [Point] where ...
3647 is legal. However, if you added
3651 instance C (Int,Int) where ...
3655 as well, then the compiler will complain about the overlapping
3656 (actually, identical) instance declarations. As always, type synonyms
3657 must be fully applied. You cannot, for example, write:
3661 instance Monad P where ...
3669 <sect3 id="instance-rules">
3670 <title>Relaxed rules for instance contexts</title>
3672 <para>In Haskell 98, the assertions in the context of the instance declaration
3673 must be of the form <literal>C a</literal> where <literal>a</literal>
3674 is a type variable that occurs in the head.
3678 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3679 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3680 With this flag the context of the instance declaration can each consist of arbitrary
3681 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3685 The Paterson Conditions: for each assertion in the context
3687 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3688 <listitem><para>The assertion has fewer constructors and variables (taken together
3689 and counting repetitions) than the head</para></listitem>
3693 <listitem><para>The Coverage Condition. For each functional dependency,
3694 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3695 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3696 every type variable in
3697 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3698 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3699 substitution mapping each type variable in the class declaration to the
3700 corresponding type in the instance declaration.
3703 These restrictions ensure that context reduction terminates: each reduction
3704 step makes the problem smaller by at least one
3705 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3706 if you give the <option>-XUndecidableInstances</option>
3707 flag (<xref linkend="undecidable-instances"/>).
3708 You can find lots of background material about the reason for these
3709 restrictions in the paper <ulink
3710 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3711 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3714 For example, these are OK:
3716 instance C Int [a] -- Multiple parameters
3717 instance Eq (S [a]) -- Structured type in head
3719 -- Repeated type variable in head
3720 instance C4 a a => C4 [a] [a]
3721 instance Stateful (ST s) (MutVar s)
3723 -- Head can consist of type variables only
3725 instance (Eq a, Show b) => C2 a b
3727 -- Non-type variables in context
3728 instance Show (s a) => Show (Sized s a)
3729 instance C2 Int a => C3 Bool [a]
3730 instance C2 Int a => C3 [a] b
3734 -- Context assertion no smaller than head
3735 instance C a => C a where ...
3736 -- (C b b) has more more occurrences of b than the head
3737 instance C b b => Foo [b] where ...
3742 The same restrictions apply to instances generated by
3743 <literal>deriving</literal> clauses. Thus the following is accepted:
3745 data MinHeap h a = H a (h a)
3748 because the derived instance
3750 instance (Show a, Show (h a)) => Show (MinHeap h a)
3752 conforms to the above rules.
3756 A useful idiom permitted by the above rules is as follows.
3757 If one allows overlapping instance declarations then it's quite
3758 convenient to have a "default instance" declaration that applies if
3759 something more specific does not:
3767 <sect3 id="undecidable-instances">
3768 <title>Undecidable instances</title>
3771 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3772 For example, sometimes you might want to use the following to get the
3773 effect of a "class synonym":
3775 class (C1 a, C2 a, C3 a) => C a where { }
3777 instance (C1 a, C2 a, C3 a) => C a where { }
3779 This allows you to write shorter signatures:
3785 f :: (C1 a, C2 a, C3 a) => ...
3787 The restrictions on functional dependencies (<xref
3788 linkend="functional-dependencies"/>) are particularly troublesome.
3789 It is tempting to introduce type variables in the context that do not appear in
3790 the head, something that is excluded by the normal rules. For example:
3792 class HasConverter a b | a -> b where
3795 data Foo a = MkFoo a
3797 instance (HasConverter a b,Show b) => Show (Foo a) where
3798 show (MkFoo value) = show (convert value)
3800 This is dangerous territory, however. Here, for example, is a program that would make the
3805 instance F [a] [[a]]
3806 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3808 Similarly, it can be tempting to lift the coverage condition:
3810 class Mul a b c | a b -> c where
3811 (.*.) :: a -> b -> c
3813 instance Mul Int Int Int where (.*.) = (*)
3814 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3815 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3817 The third instance declaration does not obey the coverage condition;
3818 and indeed the (somewhat strange) definition:
3820 f = \ b x y -> if b then x .*. [y] else y
3822 makes instance inference go into a loop, because it requires the constraint
3823 <literal>(Mul a [b] b)</literal>.
3826 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3827 the experimental flag <option>-XUndecidableInstances</option>
3828 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3829 both the Paterson Conditions and the Coverage Condition
3830 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3831 fixed-depth recursion stack. If you exceed the stack depth you get a
3832 sort of backtrace, and the opportunity to increase the stack depth
3833 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3839 <sect3 id="instance-overlap">
3840 <title>Overlapping instances</title>
3842 In general, <emphasis>GHC requires that that it be unambiguous which instance
3844 should be used to resolve a type-class constraint</emphasis>. This behaviour
3845 can be modified by two flags: <option>-XOverlappingInstances</option>
3846 <indexterm><primary>-XOverlappingInstances
3847 </primary></indexterm>
3848 and <option>-XIncoherentInstances</option>
3849 <indexterm><primary>-XIncoherentInstances
3850 </primary></indexterm>, as this section discusses. Both these
3851 flags are dynamic flags, and can be set on a per-module basis, using
3852 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3854 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3855 it tries to match every instance declaration against the
3857 by instantiating the head of the instance declaration. For example, consider
3860 instance context1 => C Int a where ... -- (A)
3861 instance context2 => C a Bool where ... -- (B)
3862 instance context3 => C Int [a] where ... -- (C)
3863 instance context4 => C Int [Int] where ... -- (D)
3865 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3866 but (C) and (D) do not. When matching, GHC takes
3867 no account of the context of the instance declaration
3868 (<literal>context1</literal> etc).
3869 GHC's default behaviour is that <emphasis>exactly one instance must match the
3870 constraint it is trying to resolve</emphasis>.
3871 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3872 including both declarations (A) and (B), say); an error is only reported if a
3873 particular constraint matches more than one.
3877 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3878 more than one instance to match, provided there is a most specific one. For
3879 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3880 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3881 most-specific match, the program is rejected.
3884 However, GHC is conservative about committing to an overlapping instance. For example:
3889 Suppose that from the RHS of <literal>f</literal> we get the constraint
3890 <literal>C Int [b]</literal>. But
3891 GHC does not commit to instance (C), because in a particular
3892 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3893 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3894 So GHC rejects the program.
3895 (If you add the flag <option>-XIncoherentInstances</option>,
3896 GHC will instead pick (C), without complaining about
3897 the problem of subsequent instantiations.)
3900 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3901 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3902 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3903 it instead. In this case, GHC will refrain from
3904 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3905 as before) but, rather than rejecting the program, it will infer the type
3907 f :: C Int [b] => [b] -> [b]
3909 That postpones the question of which instance to pick to the
3910 call site for <literal>f</literal>
3911 by which time more is known about the type <literal>b</literal>.
3912 You can write this type signature yourself if you use the
3913 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3917 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3921 instance Foo [b] where
3924 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3925 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3926 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3927 declaration. The solution is to postpone the choice by adding the constraint to the context
3928 of the instance declaration, thus:
3930 instance C Int [b] => Foo [b] where
3933 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3936 The willingness to be overlapped or incoherent is a property of
3937 the <emphasis>instance declaration</emphasis> itself, controlled by the
3938 presence or otherwise of the <option>-XOverlappingInstances</option>
3939 and <option>-XIncoherentInstances</option> flags when that module is
3940 being defined. Neither flag is required in a module that imports and uses the
3941 instance declaration. Specifically, during the lookup process:
3944 An instance declaration is ignored during the lookup process if (a) a more specific
3945 match is found, and (b) the instance declaration was compiled with
3946 <option>-XOverlappingInstances</option>. The flag setting for the
3947 more-specific instance does not matter.
3950 Suppose an instance declaration does not match the constraint being looked up, but
3951 does unify with it, so that it might match when the constraint is further
3952 instantiated. Usually GHC will regard this as a reason for not committing to
3953 some other constraint. But if the instance declaration was compiled with
3954 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3955 check for that declaration.
3958 These rules make it possible for a library author to design a library that relies on
3959 overlapping instances without the library client having to know.
3962 If an instance declaration is compiled without
3963 <option>-XOverlappingInstances</option>,
3964 then that instance can never be overlapped. This could perhaps be
3965 inconvenient. Perhaps the rule should instead say that the
3966 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3967 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3968 at a usage site should be permitted regardless of how the instance declarations
3969 are compiled, if the <option>-XOverlappingInstances</option> flag is
3970 used at the usage site. (Mind you, the exact usage site can occasionally be
3971 hard to pin down.) We are interested to receive feedback on these points.
3973 <para>The <option>-XIncoherentInstances</option> flag implies the
3974 <option>-XOverlappingInstances</option> flag, but not vice versa.
3982 <sect2 id="overloaded-strings">
3983 <title>Overloaded string literals
3987 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3988 string literal has type <literal>String</literal>, but with overloaded string
3989 literals enabled (with <literal>-XOverloadedStrings</literal>)
3990 a string literal has type <literal>(IsString a) => a</literal>.
3993 This means that the usual string syntax can be used, e.g., for packed strings
3994 and other variations of string like types. String literals behave very much
3995 like integer literals, i.e., they can be used in both expressions and patterns.
3996 If used in a pattern the literal with be replaced by an equality test, in the same
3997 way as an integer literal is.
4000 The class <literal>IsString</literal> is defined as:
4002 class IsString a where
4003 fromString :: String -> a
4005 The only predefined instance is the obvious one to make strings work as usual:
4007 instance IsString [Char] where
4010 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4011 it explicitly (for example, to give an instance declaration for it), you can import it
4012 from module <literal>GHC.Exts</literal>.
4015 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4019 Each type in a default declaration must be an
4020 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4024 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4025 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4026 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4027 <emphasis>or</emphasis> <literal>IsString</literal>.
4036 import GHC.Exts( IsString(..) )
4038 newtype MyString = MyString String deriving (Eq, Show)
4039 instance IsString MyString where
4040 fromString = MyString
4042 greet :: MyString -> MyString
4043 greet "hello" = "world"
4047 print $ greet "hello"
4048 print $ greet "fool"
4052 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4053 to work since it gets translated into an equality comparison.
4059 <sect1 id="type-families">
4060 <title>Type families</title>
4063 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4064 facilitate type-level
4065 programming. Type families are a generalisation of <firstterm>associated
4066 data types</firstterm>
4067 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4068 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4069 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4070 Symposium on Principles of Programming Languages (POPL'05)”, pages
4071 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4072 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4073 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4075 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4076 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4077 themselves are described in the paper “<ulink
4078 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4079 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4081 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4082 13th ACM SIGPLAN International Conference on Functional
4083 Programming”, ACM Press, pages 51-62, 2008. Type families
4084 essentially provide type-indexed data types and named functions on types,
4085 which are useful for generic programming and highly parameterised library
4086 interfaces as well as interfaces with enhanced static information, much like
4087 dependent types. They might also be regarded as an alternative to functional
4088 dependencies, but provide a more functional style of type-level programming
4089 than the relational style of functional dependencies.
4092 Indexed type families, or type families for short, are type constructors that
4093 represent sets of types. Set members are denoted by supplying the type family
4094 constructor with type parameters, which are called <firstterm>type
4095 indices</firstterm>. The
4096 difference between vanilla parametrised type constructors and family
4097 constructors is much like between parametrically polymorphic functions and
4098 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4099 behave the same at all type instances, whereas class methods can change their
4100 behaviour in dependence on the class type parameters. Similarly, vanilla type
4101 constructors imply the same data representation for all type instances, but
4102 family constructors can have varying representation types for varying type
4106 Indexed type families come in two flavours: <firstterm>data
4107 families</firstterm> and <firstterm>type synonym
4108 families</firstterm>. They are the indexed family variants of algebraic
4109 data types and type synonyms, respectively. The instances of data families
4110 can be data types and newtypes.
4113 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4114 Additional information on the use of type families in GHC is available on
4115 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4116 Haskell wiki page on type families</ulink>.
4119 <sect2 id="data-families">
4120 <title>Data families</title>
4123 Data families appear in two flavours: (1) they can be defined on the
4125 or (2) they can appear inside type classes (in which case they are known as
4126 associated types). The former is the more general variant, as it lacks the
4127 requirement for the type-indexes to coincide with the class
4128 parameters. However, the latter can lead to more clearly structured code and
4129 compiler warnings if some type instances were - possibly accidentally -
4130 omitted. In the following, we always discuss the general toplevel form first
4131 and then cover the additional constraints placed on associated types.
4134 <sect3 id="data-family-declarations">
4135 <title>Data family declarations</title>
4138 Indexed data families are introduced by a signature, such as
4140 data family GMap k :: * -> *
4142 The special <literal>family</literal> distinguishes family from standard
4143 data declarations. The result kind annotation is optional and, as
4144 usual, defaults to <literal>*</literal> if omitted. An example is
4148 Named arguments can also be given explicit kind signatures if needed.
4150 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4151 declarations] named arguments are entirely optional, so that we can
4152 declare <literal>Array</literal> alternatively with
4154 data family Array :: * -> *
4158 <sect4 id="assoc-data-family-decl">
4159 <title>Associated data family declarations</title>
4161 When a data family is declared as part of a type class, we drop
4162 the <literal>family</literal> special. The <literal>GMap</literal>
4163 declaration takes the following form
4165 class GMapKey k where
4166 data GMap k :: * -> *
4169 In contrast to toplevel declarations, named arguments must be used for
4170 all type parameters that are to be used as type-indexes. Moreover,
4171 the argument names must be class parameters. Each class parameter may
4172 only be used at most once per associated type, but some may be omitted
4173 and they may be in an order other than in the class head. Hence, the
4174 following contrived example is admissible:
4183 <sect3 id="data-instance-declarations">
4184 <title>Data instance declarations</title>
4187 Instance declarations of data and newtype families are very similar to
4188 standard data and newtype declarations. The only two differences are
4189 that the keyword <literal>data</literal> or <literal>newtype</literal>
4190 is followed by <literal>instance</literal> and that some or all of the
4191 type arguments can be non-variable types, but may not contain forall
4192 types or type synonym families. However, data families are generally
4193 allowed in type parameters, and type synonyms are allowed as long as
4194 they are fully applied and expand to a type that is itself admissible -
4195 exactly as this is required for occurrences of type synonyms in class
4196 instance parameters. For example, the <literal>Either</literal>
4197 instance for <literal>GMap</literal> is
4199 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4201 In this example, the declaration has only one variant. In general, it
4205 Data and newtype instance declarations are only permitted when an
4206 appropriate family declaration is in scope - just as a class instance declaratoin
4207 requires the class declaration to be visible. Moreover, each instance
4208 declaration has to conform to the kind determined by its family
4209 declaration. This implies that the number of parameters of an instance
4210 declaration matches the arity determined by the kind of the family.
4213 A data family instance declaration can use the full exprssiveness of
4214 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4216 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4217 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4218 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4221 data instance T Int = T1 Int | T2 Bool
4222 newtype instance T Char = TC Bool
4225 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4226 and indeed can define a GADT. For example:
4229 data instance G [a] b where
4230 G1 :: c -> G [Int] b
4234 <listitem><para> You can use a <literal>deriving</literal> clause on a
4235 <literal>data instance</literal> or <literal>newtype instance</literal>
4242 Even if type families are defined as toplevel declarations, functions
4243 that perform different computations for different family instances may still
4244 need to be defined as methods of type classes. In particular, the
4245 following is not possible:
4248 data instance T Int = A
4249 data instance T Char = B
4251 foo A = 1 -- WRONG: These two equations together...
4252 foo B = 2 -- ...will produce a type error.
4254 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4258 instance Foo Int where
4260 instance Foo Char where
4263 (Given the functionality provided by GADTs (Generalised Algebraic Data
4264 Types), it might seem as if a definition, such as the above, should be
4265 feasible. However, type families are - in contrast to GADTs - are
4266 <emphasis>open;</emphasis> i.e., new instances can always be added,
4268 modules. Supporting pattern matching across different data instances
4269 would require a form of extensible case construct.)
4272 <sect4 id="assoc-data-inst">
4273 <title>Associated data instances</title>
4275 When an associated data family instance is declared within a type
4276 class instance, we drop the <literal>instance</literal> keyword in the
4277 family instance. So, the <literal>Either</literal> instance
4278 for <literal>GMap</literal> becomes:
4280 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4281 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4284 The most important point about associated family instances is that the
4285 type indexes corresponding to class parameters must be identical to
4286 the type given in the instance head; here this is the first argument
4287 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4288 which coincides with the only class parameter. Any parameters to the
4289 family constructor that do not correspond to class parameters, need to
4290 be variables in every instance; here this is the
4291 variable <literal>v</literal>.
4294 Instances for an associated family can only appear as part of
4295 instances declarations of the class in which the family was declared -
4296 just as with the equations of the methods of a class. Also in
4297 correspondence to how methods are handled, declarations of associated
4298 types can be omitted in class instances. If an associated family
4299 instance is omitted, the corresponding instance type is not inhabited;
4300 i.e., only diverging expressions, such
4301 as <literal>undefined</literal>, can assume the type.
4305 <sect4 id="scoping-class-params">
4306 <title>Scoping of class parameters</title>
4308 In the case of multi-parameter type classes, the visibility of class
4309 parameters in the right-hand side of associated family instances
4310 depends <emphasis>solely</emphasis> on the parameters of the data
4311 family. As an example, consider the simple class declaration
4316 Only one of the two class parameters is a parameter to the data
4317 family. Hence, the following instance declaration is invalid:
4319 instance C [c] d where
4320 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4322 Here, the right-hand side of the data instance mentions the type
4323 variable <literal>d</literal> that does not occur in its left-hand
4324 side. We cannot admit such data instances as they would compromise
4329 <sect4 id="family-class-inst">
4330 <title>Type class instances of family instances</title>
4332 Type class instances of instances of data families can be defined as
4333 usual, and in particular data instance declarations can
4334 have <literal>deriving</literal> clauses. For example, we can write
4336 data GMap () v = GMapUnit (Maybe v)
4339 which implicitly defines an instance of the form
4341 instance Show v => Show (GMap () v) where ...
4345 Note that class instances are always for
4346 particular <emphasis>instances</emphasis> of a data family and never
4347 for an entire family as a whole. This is for essentially the same
4348 reasons that we cannot define a toplevel function that performs
4349 pattern matching on the data constructors
4350 of <emphasis>different</emphasis> instances of a single type family.
4351 It would require a form of extensible case construct.
4355 <sect4 id="data-family-overlap">
4356 <title>Overlap of data instances</title>
4358 The instance declarations of a data family used in a single program
4359 may not overlap at all, independent of whether they are associated or
4360 not. In contrast to type class instances, this is not only a matter
4361 of consistency, but one of type safety.
4367 <sect3 id="data-family-import-export">
4368 <title>Import and export</title>
4371 The association of data constructors with type families is more dynamic
4372 than that is the case with standard data and newtype declarations. In
4373 the standard case, the notation <literal>T(..)</literal> in an import or
4374 export list denotes the type constructor and all the data constructors
4375 introduced in its declaration. However, a family declaration never
4376 introduces any data constructors; instead, data constructors are
4377 introduced by family instances. As a result, which data constructors
4378 are associated with a type family depends on the currently visible
4379 instance declarations for that family. Consequently, an import or
4380 export item of the form <literal>T(..)</literal> denotes the family
4381 constructor and all currently visible data constructors - in the case of
4382 an export item, these may be either imported or defined in the current
4383 module. The treatment of import and export items that explicitly list
4384 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4388 <sect4 id="data-family-impexp-assoc">
4389 <title>Associated families</title>
4391 As expected, an import or export item of the
4392 form <literal>C(..)</literal> denotes all of the class' methods and
4393 associated types. However, when associated types are explicitly
4394 listed as subitems of a class, we need some new syntax, as uppercase
4395 identifiers as subitems are usually data constructors, not type
4396 constructors. To clarify that we denote types here, each associated
4397 type name needs to be prefixed by the keyword <literal>type</literal>.
4398 So for example, when explicitly listing the components of
4399 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4400 GMap, empty, lookup, insert)</literal>.
4404 <sect4 id="data-family-impexp-examples">
4405 <title>Examples</title>
4407 Assuming our running <literal>GMapKey</literal> class example, let us
4408 look at some export lists and their meaning:
4411 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4412 just the class name.</para>
4415 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4416 Exports the class, the associated type <literal>GMap</literal>
4418 functions <literal>empty</literal>, <literal>lookup</literal>,
4419 and <literal>insert</literal>. None of the data constructors is
4423 <para><literal>module GMap (GMapKey(..), GMap(..))
4424 where...</literal>: As before, but also exports all the data
4425 constructors <literal>GMapInt</literal>,
4426 <literal>GMapChar</literal>,
4427 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4428 and <literal>GMapUnit</literal>.</para>
4431 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4432 GMap(..)) where...</literal>: As before.</para>
4435 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4436 where...</literal>: As before.</para>
4441 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4442 both the class <literal>GMapKey</literal> as well as its associated
4443 type <literal>GMap</literal>. However, you cannot
4444 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4445 sub-component specifications cannot be nested. To
4446 specify <literal>GMap</literal>'s data constructors, you have to list
4451 <sect4 id="data-family-impexp-instances">
4452 <title>Instances</title>
4454 Family instances are implicitly exported, just like class instances.
4455 However, this applies only to the heads of instances, not to the data
4456 constructors an instance defines.
4464 <sect2 id="synonym-families">
4465 <title>Synonym families</title>
4468 Type families appear in two flavours: (1) they can be defined on the
4469 toplevel or (2) they can appear inside type classes (in which case they
4470 are known as associated type synonyms). The former is the more general
4471 variant, as it lacks the requirement for the type-indexes to coincide with
4472 the class parameters. However, the latter can lead to more clearly
4473 structured code and compiler warnings if some type instances were -
4474 possibly accidentally - omitted. In the following, we always discuss the
4475 general toplevel form first and then cover the additional constraints
4476 placed on associated types.
4479 <sect3 id="type-family-declarations">
4480 <title>Type family declarations</title>
4483 Indexed type families are introduced by a signature, such as
4485 type family Elem c :: *
4487 The special <literal>family</literal> distinguishes family from standard
4488 type declarations. The result kind annotation is optional and, as
4489 usual, defaults to <literal>*</literal> if omitted. An example is
4493 Parameters can also be given explicit kind signatures if needed. We
4494 call the number of parameters in a type family declaration, the family's
4495 arity, and all applications of a type family must be fully saturated
4496 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4497 and it implies that the kind of a type family is not sufficient to
4498 determine a family's arity, and hence in general, also insufficient to
4499 determine whether a type family application is well formed. As an
4500 example, consider the following declaration:
4502 type family F a b :: * -> * -- F's arity is 2,
4503 -- although its overall kind is * -> * -> * -> *
4505 Given this declaration the following are examples of well-formed and
4508 F Char [Int] -- OK! Kind: * -> *
4509 F Char [Int] Bool -- OK! Kind: *
4510 F IO Bool -- WRONG: kind mismatch in the first argument
4511 F Bool -- WRONG: unsaturated application
4515 <sect4 id="assoc-type-family-decl">
4516 <title>Associated type family declarations</title>
4518 When a type family is declared as part of a type class, we drop
4519 the <literal>family</literal> special. The <literal>Elem</literal>
4520 declaration takes the following form
4522 class Collects ce where
4526 The argument names of the type family must be class parameters. Each
4527 class parameter may only be used at most once per associated type, but
4528 some may be omitted and they may be in an order other than in the
4529 class head. Hence, the following contrived example is admissible:
4534 These rules are exactly as for associated data families.
4539 <sect3 id="type-instance-declarations">
4540 <title>Type instance declarations</title>
4542 Instance declarations of type families are very similar to standard type
4543 synonym declarations. The only two differences are that the
4544 keyword <literal>type</literal> is followed
4545 by <literal>instance</literal> and that some or all of the type
4546 arguments can be non-variable types, but may not contain forall types or
4547 type synonym families. However, data families are generally allowed, and
4548 type synonyms are allowed as long as they are fully applied and expand
4549 to a type that is admissible - these are the exact same requirements as
4550 for data instances. For example, the <literal>[e]</literal> instance
4551 for <literal>Elem</literal> is
4553 type instance Elem [e] = e
4557 Type family instance declarations are only legitimate when an
4558 appropriate family declaration is in scope - just like class instances
4559 require the class declaration to be visible. Moreover, each instance
4560 declaration has to conform to the kind determined by its family
4561 declaration, and the number of type parameters in an instance
4562 declaration must match the number of type parameters in the family
4563 declaration. Finally, the right-hand side of a type instance must be a
4564 monotype (i.e., it may not include foralls) and after the expansion of
4565 all saturated vanilla type synonyms, no synonyms, except family synonyms
4566 may remain. Here are some examples of admissible and illegal type
4569 type family F a :: *
4570 type instance F [Int] = Int -- OK!
4571 type instance F String = Char -- OK!
4572 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4573 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4574 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4576 type family G a b :: * -> *
4577 type instance G Int = (,) -- WRONG: must be two type parameters
4578 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4582 <sect4 id="assoc-type-instance">
4583 <title>Associated type instance declarations</title>
4585 When an associated family instance is declared within a type class
4586 instance, we drop the <literal>instance</literal> keyword in the family
4587 instance. So, the <literal>[e]</literal> instance
4588 for <literal>Elem</literal> becomes:
4590 instance (Eq (Elem [e])) => Collects ([e]) where
4594 The most important point about associated family instances is that the
4595 type indexes corresponding to class parameters must be identical to the
4596 type given in the instance head; here this is <literal>[e]</literal>,
4597 which coincides with the only class parameter.
4600 Instances for an associated family can only appear as part of instances
4601 declarations of the class in which the family was declared - just as
4602 with the equations of the methods of a class. Also in correspondence to
4603 how methods are handled, declarations of associated types can be omitted
4604 in class instances. If an associated family instance is omitted, the
4605 corresponding instance type is not inhabited; i.e., only diverging
4606 expressions, such as <literal>undefined</literal>, can assume the type.
4610 <sect4 id="type-family-overlap">
4611 <title>Overlap of type synonym instances</title>
4613 The instance declarations of a type family used in a single program
4614 may only overlap if the right-hand sides of the overlapping instances
4615 coincide for the overlapping types. More formally, two instance
4616 declarations overlap if there is a substitution that makes the
4617 left-hand sides of the instances syntactically the same. Whenever
4618 that is the case, the right-hand sides of the instances must also be
4619 syntactically equal under the same substitution. This condition is
4620 independent of whether the type family is associated or not, and it is
4621 not only a matter of consistency, but one of type safety.
4624 Here are two example to illustrate the condition under which overlap
4627 type instance F (a, Int) = [a]
4628 type instance F (Int, b) = [b] -- overlap permitted
4630 type instance G (a, Int) = [a]
4631 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4636 <sect4 id="type-family-decidability">
4637 <title>Decidability of type synonym instances</title>
4639 In order to guarantee that type inference in the presence of type
4640 families decidable, we need to place a number of additional
4641 restrictions on the formation of type instance declarations (c.f.,
4642 Definition 5 (Relaxed Conditions) of “<ulink
4643 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4644 Checking with Open Type Functions</ulink>”). Instance
4645 declarations have the general form
4647 type instance F t1 .. tn = t
4649 where we require that for every type family application <literal>(G s1
4650 .. sm)</literal> in <literal>t</literal>,
4653 <para><literal>s1 .. sm</literal> do not contain any type family
4654 constructors,</para>
4657 <para>the total number of symbols (data type constructors and type
4658 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4659 in <literal>t1 .. tn</literal>, and</para>
4662 <para>for every type
4663 variable <literal>a</literal>, <literal>a</literal> occurs
4664 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4665 .. tn</literal>.</para>
4668 These restrictions are easily verified and ensure termination of type
4669 inference. However, they are not sufficient to guarantee completeness
4670 of type inference in the presence of, so called, ''loopy equalities'',
4671 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4672 a type variable is underneath a family application and data
4673 constructor application - see the above mentioned paper for details.
4676 If the option <option>-XUndecidableInstances</option> is passed to the
4677 compiler, the above restrictions are not enforced and it is on the
4678 programmer to ensure termination of the normalisation of type families
4679 during type inference.
4684 <sect3 id-="equality-constraints">
4685 <title>Equality constraints</title>
4687 Type context can include equality constraints of the form <literal>t1 ~
4688 t2</literal>, which denote that the types <literal>t1</literal>
4689 and <literal>t2</literal> need to be the same. In the presence of type
4690 families, whether two types are equal cannot generally be decided
4691 locally. Hence, the contexts of function signatures may include
4692 equality constraints, as in the following example:
4694 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4696 where we require that the element type of <literal>c1</literal>
4697 and <literal>c2</literal> are the same. In general, the
4698 types <literal>t1</literal> and <literal>t2</literal> of an equality
4699 constraint may be arbitrary monotypes; i.e., they may not contain any
4700 quantifiers, independent of whether higher-rank types are otherwise
4704 Equality constraints can also appear in class and instance contexts.
4705 The former enable a simple translation of programs using functional
4706 dependencies into programs using family synonyms instead. The general
4707 idea is to rewrite a class declaration of the form
4709 class C a b | a -> b
4713 class (F a ~ b) => C a b where
4716 That is, we represent every functional dependency (FD) <literal>a1 .. an
4717 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4718 superclass context equality <literal>F a1 .. an ~ b</literal>,
4719 essentially giving a name to the functional dependency. In class
4720 instances, we define the type instances of FD families in accordance
4721 with the class head. Method signatures are not affected by that
4725 NB: Equalities in superclass contexts are not fully implemented in
4730 <sect3 id-="ty-fams-in-instances">
4731 <title>Type families and instance declarations</title>
4732 <para>Type families require us to extend the rules for
4733 the form of instance heads, which are given
4734 in <xref linkend="flexible-instance-head"/>.
4737 <listitem><para>Data type families may appear in an instance head</para></listitem>
4738 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4740 The reason for the latter restriction is that there is no way to check for. Consider
4743 type instance F Bool = Int
4750 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4751 The situation is especially bad because the type instance for <literal>F Bool</literal>
4752 might be in another module, or even in a module that is not yet written.
4759 <sect1 id="other-type-extensions">
4760 <title>Other type system extensions</title>
4762 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4764 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4765 is used, the keyword <literal>forall</literal>
4766 allows us to say exactly what this means. For example:
4774 g :: forall b. (b -> b)
4776 The two are treated identically.
4779 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4780 a type variable any more!
4785 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4787 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4788 that the type-class constraints in a type signature must have the
4789 form <emphasis>(class type-variable)</emphasis> or
4790 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4791 With <option>-XFlexibleContexts</option>
4792 these type signatures are perfectly OK
4795 g :: Ord (T a ()) => ...
4797 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4798 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4799 (<xref linkend="instance-rules"/>).
4803 GHC imposes the following restrictions on the constraints in a type signature.
4807 forall tv1..tvn (c1, ...,cn) => type
4810 (Here, we write the "foralls" explicitly, although the Haskell source
4811 language omits them; in Haskell 98, all the free type variables of an
4812 explicit source-language type signature are universally quantified,
4813 except for the class type variables in a class declaration. However,
4814 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4823 <emphasis>Each universally quantified type variable
4824 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4826 A type variable <literal>a</literal> is "reachable" if it appears
4827 in the same constraint as either a type variable free in
4828 <literal>type</literal>, or another reachable type variable.
4829 A value with a type that does not obey
4830 this reachability restriction cannot be used without introducing
4831 ambiguity; that is why the type is rejected.
4832 Here, for example, is an illegal type:
4836 forall a. Eq a => Int
4840 When a value with this type was used, the constraint <literal>Eq tv</literal>
4841 would be introduced where <literal>tv</literal> is a fresh type variable, and
4842 (in the dictionary-translation implementation) the value would be
4843 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4844 can never know which instance of <literal>Eq</literal> to use because we never
4845 get any more information about <literal>tv</literal>.
4849 that the reachability condition is weaker than saying that <literal>a</literal> is
4850 functionally dependent on a type variable free in
4851 <literal>type</literal> (see <xref
4852 linkend="functional-dependencies"/>). The reason for this is there
4853 might be a "hidden" dependency, in a superclass perhaps. So
4854 "reachable" is a conservative approximation to "functionally dependent".
4855 For example, consider:
4857 class C a b | a -> b where ...
4858 class C a b => D a b where ...
4859 f :: forall a b. D a b => a -> a
4861 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4862 but that is not immediately apparent from <literal>f</literal>'s type.
4868 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4869 universally quantified type variables <literal>tvi</literal></emphasis>.
4871 For example, this type is OK because <literal>C a b</literal> mentions the
4872 universally quantified type variable <literal>b</literal>:
4876 forall a. C a b => burble
4880 The next type is illegal because the constraint <literal>Eq b</literal> does not
4881 mention <literal>a</literal>:
4885 forall a. Eq b => burble
4889 The reason for this restriction is milder than the other one. The
4890 excluded types are never useful or necessary (because the offending
4891 context doesn't need to be witnessed at this point; it can be floated
4892 out). Furthermore, floating them out increases sharing. Lastly,
4893 excluding them is a conservative choice; it leaves a patch of
4894 territory free in case we need it later.
4905 <sect2 id="implicit-parameters">
4906 <title>Implicit parameters</title>
4908 <para> Implicit parameters are implemented as described in
4909 "Implicit parameters: dynamic scoping with static types",
4910 J Lewis, MB Shields, E Meijer, J Launchbury,
4911 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4915 <para>(Most of the following, still rather incomplete, documentation is
4916 due to Jeff Lewis.)</para>
4918 <para>Implicit parameter support is enabled with the option
4919 <option>-XImplicitParams</option>.</para>
4922 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4923 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4924 context. In Haskell, all variables are statically bound. Dynamic
4925 binding of variables is a notion that goes back to Lisp, but was later
4926 discarded in more modern incarnations, such as Scheme. Dynamic binding
4927 can be very confusing in an untyped language, and unfortunately, typed
4928 languages, in particular Hindley-Milner typed languages like Haskell,
4929 only support static scoping of variables.
4932 However, by a simple extension to the type class system of Haskell, we
4933 can support dynamic binding. Basically, we express the use of a
4934 dynamically bound variable as a constraint on the type. These
4935 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4936 function uses a dynamically-bound variable <literal>?x</literal>
4937 of type <literal>t'</literal>". For
4938 example, the following expresses the type of a sort function,
4939 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4941 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4943 The dynamic binding constraints are just a new form of predicate in the type class system.
4946 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4947 where <literal>x</literal> is
4948 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4949 Use of this construct also introduces a new
4950 dynamic-binding constraint in the type of the expression.
4951 For example, the following definition
4952 shows how we can define an implicitly parameterized sort function in
4953 terms of an explicitly parameterized <literal>sortBy</literal> function:
4955 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4957 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4963 <title>Implicit-parameter type constraints</title>
4965 Dynamic binding constraints behave just like other type class
4966 constraints in that they are automatically propagated. Thus, when a
4967 function is used, its implicit parameters are inherited by the
4968 function that called it. For example, our <literal>sort</literal> function might be used
4969 to pick out the least value in a list:
4971 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4972 least xs = head (sort xs)
4974 Without lifting a finger, the <literal>?cmp</literal> parameter is
4975 propagated to become a parameter of <literal>least</literal> as well. With explicit
4976 parameters, the default is that parameters must always be explicit
4977 propagated. With implicit parameters, the default is to always
4981 An implicit-parameter type constraint differs from other type class constraints in the
4982 following way: All uses of a particular implicit parameter must have
4983 the same type. This means that the type of <literal>(?x, ?x)</literal>
4984 is <literal>(?x::a) => (a,a)</literal>, and not
4985 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4989 <para> You can't have an implicit parameter in the context of a class or instance
4990 declaration. For example, both these declarations are illegal:
4992 class (?x::Int) => C a where ...
4993 instance (?x::a) => Foo [a] where ...
4995 Reason: exactly which implicit parameter you pick up depends on exactly where
4996 you invoke a function. But the ``invocation'' of instance declarations is done
4997 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4998 Easiest thing is to outlaw the offending types.</para>
5000 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5002 f :: (?x :: [a]) => Int -> Int
5005 g :: (Read a, Show a) => String -> String
5008 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5009 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5010 quite unambiguous, and fixes the type <literal>a</literal>.
5015 <title>Implicit-parameter bindings</title>
5018 An implicit parameter is <emphasis>bound</emphasis> using the standard
5019 <literal>let</literal> or <literal>where</literal> binding forms.
5020 For example, we define the <literal>min</literal> function by binding
5021 <literal>cmp</literal>.
5024 min = let ?cmp = (<=) in least
5028 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5029 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5030 (including in a list comprehension, or do-notation, or pattern guards),
5031 or a <literal>where</literal> clause.
5032 Note the following points:
5035 An implicit-parameter binding group must be a
5036 collection of simple bindings to implicit-style variables (no
5037 function-style bindings, and no type signatures); these bindings are
5038 neither polymorphic or recursive.
5041 You may not mix implicit-parameter bindings with ordinary bindings in a
5042 single <literal>let</literal>
5043 expression; use two nested <literal>let</literal>s instead.
5044 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5048 You may put multiple implicit-parameter bindings in a
5049 single binding group; but they are <emphasis>not</emphasis> treated
5050 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5051 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5052 parameter. The bindings are not nested, and may be re-ordered without changing
5053 the meaning of the program.
5054 For example, consider:
5056 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5058 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5059 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5061 f :: (?x::Int) => Int -> Int
5069 <sect3><title>Implicit parameters and polymorphic recursion</title>
5072 Consider these two definitions:
5075 len1 xs = let ?acc = 0 in len_acc1 xs
5078 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5083 len2 xs = let ?acc = 0 in len_acc2 xs
5085 len_acc2 :: (?acc :: Int) => [a] -> Int
5087 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5089 The only difference between the two groups is that in the second group
5090 <literal>len_acc</literal> is given a type signature.
5091 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5092 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5093 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5094 has a type signature, the recursive call is made to the
5095 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5096 as an implicit parameter. So we get the following results in GHCi:
5103 Adding a type signature dramatically changes the result! This is a rather
5104 counter-intuitive phenomenon, worth watching out for.
5108 <sect3><title>Implicit parameters and monomorphism</title>
5110 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5111 Haskell Report) to implicit parameters. For example, consider:
5119 Since the binding for <literal>y</literal> falls under the Monomorphism
5120 Restriction it is not generalised, so the type of <literal>y</literal> is
5121 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5122 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5123 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5124 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5125 <literal>y</literal> in the body of the <literal>let</literal> will see the
5126 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5127 <literal>14</literal>.
5132 <!-- ======================= COMMENTED OUT ========================
5134 We intend to remove linear implicit parameters, so I'm at least removing
5135 them from the 6.6 user manual
5137 <sect2 id="linear-implicit-parameters">
5138 <title>Linear implicit parameters</title>
5140 Linear implicit parameters are an idea developed by Koen Claessen,
5141 Mark Shields, and Simon PJ. They address the long-standing
5142 problem that monads seem over-kill for certain sorts of problem, notably:
5145 <listitem> <para> distributing a supply of unique names </para> </listitem>
5146 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5147 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5151 Linear implicit parameters are just like ordinary implicit parameters,
5152 except that they are "linear"; that is, they cannot be copied, and
5153 must be explicitly "split" instead. Linear implicit parameters are
5154 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5155 (The '/' in the '%' suggests the split!)
5160 import GHC.Exts( Splittable )
5162 data NameSupply = ...
5164 splitNS :: NameSupply -> (NameSupply, NameSupply)
5165 newName :: NameSupply -> Name
5167 instance Splittable NameSupply where
5171 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5172 f env (Lam x e) = Lam x' (f env e)
5175 env' = extend env x x'
5176 ...more equations for f...
5178 Notice that the implicit parameter %ns is consumed
5180 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5181 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5185 So the translation done by the type checker makes
5186 the parameter explicit:
5188 f :: NameSupply -> Env -> Expr -> Expr
5189 f ns env (Lam x e) = Lam x' (f ns1 env e)
5191 (ns1,ns2) = splitNS ns
5193 env = extend env x x'
5195 Notice the call to 'split' introduced by the type checker.
5196 How did it know to use 'splitNS'? Because what it really did
5197 was to introduce a call to the overloaded function 'split',
5198 defined by the class <literal>Splittable</literal>:
5200 class Splittable a where
5203 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5204 split for name supplies. But we can simply write
5210 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5212 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5213 <literal>GHC.Exts</literal>.
5218 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5219 are entirely distinct implicit parameters: you
5220 can use them together and they won't interfere with each other. </para>
5223 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5225 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5226 in the context of a class or instance declaration. </para></listitem>
5230 <sect3><title>Warnings</title>
5233 The monomorphism restriction is even more important than usual.
5234 Consider the example above:
5236 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5237 f env (Lam x e) = Lam x' (f env e)
5240 env' = extend env x x'
5242 If we replaced the two occurrences of x' by (newName %ns), which is
5243 usually a harmless thing to do, we get:
5245 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5246 f env (Lam x e) = Lam (newName %ns) (f env e)
5248 env' = extend env x (newName %ns)
5250 But now the name supply is consumed in <emphasis>three</emphasis> places
5251 (the two calls to newName,and the recursive call to f), so
5252 the result is utterly different. Urk! We don't even have
5256 Well, this is an experimental change. With implicit
5257 parameters we have already lost beta reduction anyway, and
5258 (as John Launchbury puts it) we can't sensibly reason about
5259 Haskell programs without knowing their typing.
5264 <sect3><title>Recursive functions</title>
5265 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5268 foo :: %x::T => Int -> [Int]
5270 foo n = %x : foo (n-1)
5272 where T is some type in class Splittable.</para>
5274 Do you get a list of all the same T's or all different T's
5275 (assuming that split gives two distinct T's back)?
5277 If you supply the type signature, taking advantage of polymorphic
5278 recursion, you get what you'd probably expect. Here's the
5279 translated term, where the implicit param is made explicit:
5282 foo x n = let (x1,x2) = split x
5283 in x1 : foo x2 (n-1)
5285 But if you don't supply a type signature, GHC uses the Hindley
5286 Milner trick of using a single monomorphic instance of the function
5287 for the recursive calls. That is what makes Hindley Milner type inference
5288 work. So the translation becomes
5292 foom n = x : foom (n-1)
5296 Result: 'x' is not split, and you get a list of identical T's. So the
5297 semantics of the program depends on whether or not foo has a type signature.
5300 You may say that this is a good reason to dislike linear implicit parameters
5301 and you'd be right. That is why they are an experimental feature.
5307 ================ END OF Linear Implicit Parameters commented out -->
5309 <sect2 id="kinding">
5310 <title>Explicitly-kinded quantification</title>
5313 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5314 to give the kind explicitly as (machine-checked) documentation,
5315 just as it is nice to give a type signature for a function. On some occasions,
5316 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5317 John Hughes had to define the data type:
5319 data Set cxt a = Set [a]
5320 | Unused (cxt a -> ())
5322 The only use for the <literal>Unused</literal> constructor was to force the correct
5323 kind for the type variable <literal>cxt</literal>.
5326 GHC now instead allows you to specify the kind of a type variable directly, wherever
5327 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5330 This flag enables kind signatures in the following places:
5332 <listitem><para><literal>data</literal> declarations:
5334 data Set (cxt :: * -> *) a = Set [a]
5335 </screen></para></listitem>
5336 <listitem><para><literal>type</literal> declarations:
5338 type T (f :: * -> *) = f Int
5339 </screen></para></listitem>
5340 <listitem><para><literal>class</literal> declarations:
5342 class (Eq a) => C (f :: * -> *) a where ...
5343 </screen></para></listitem>
5344 <listitem><para><literal>forall</literal>'s in type signatures:
5346 f :: forall (cxt :: * -> *). Set cxt Int
5347 </screen></para></listitem>
5352 The parentheses are required. Some of the spaces are required too, to
5353 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5354 will get a parse error, because "<literal>::*->*</literal>" is a
5355 single lexeme in Haskell.
5359 As part of the same extension, you can put kind annotations in types
5362 f :: (Int :: *) -> Int
5363 g :: forall a. a -> (a :: *)
5367 atype ::= '(' ctype '::' kind ')
5369 The parentheses are required.
5374 <sect2 id="universal-quantification">
5375 <title>Arbitrary-rank polymorphism
5379 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5380 explicit universal quantification in
5382 For example, all the following types are legal:
5384 f1 :: forall a b. a -> b -> a
5385 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5387 f2 :: (forall a. a->a) -> Int -> Int
5388 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5390 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5392 f4 :: Int -> (forall a. a -> a)
5394 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5395 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5396 The <literal>forall</literal> makes explicit the universal quantification that
5397 is implicitly added by Haskell.
5400 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5401 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5402 shows, the polymorphic type on the left of the function arrow can be overloaded.
5405 The function <literal>f3</literal> has a rank-3 type;
5406 it has rank-2 types on the left of a function arrow.
5409 GHC has three flags to control higher-rank types:
5412 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5415 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5418 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5419 That is, you can nest <literal>forall</literal>s
5420 arbitrarily deep in function arrows.
5421 In particular, a forall-type (also called a "type scheme"),
5422 including an operational type class context, is legal:
5424 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5425 of a function arrow </para> </listitem>
5426 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5427 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5428 field type signatures.</para> </listitem>
5429 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5430 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5442 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5443 the types of the constructor arguments. Here are several examples:
5449 data T a = T1 (forall b. b -> b -> b) a
5451 data MonadT m = MkMonad { return :: forall a. a -> m a,
5452 bind :: forall a b. m a -> (a -> m b) -> m b
5455 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5461 The constructors have rank-2 types:
5467 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5468 MkMonad :: forall m. (forall a. a -> m a)
5469 -> (forall a b. m a -> (a -> m b) -> m b)
5471 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5477 Notice that you don't need to use a <literal>forall</literal> if there's an
5478 explicit context. For example in the first argument of the
5479 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5480 prefixed to the argument type. The implicit <literal>forall</literal>
5481 quantifies all type variables that are not already in scope, and are
5482 mentioned in the type quantified over.
5486 As for type signatures, implicit quantification happens for non-overloaded
5487 types too. So if you write this:
5490 data T a = MkT (Either a b) (b -> b)
5493 it's just as if you had written this:
5496 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5499 That is, since the type variable <literal>b</literal> isn't in scope, it's
5500 implicitly universally quantified. (Arguably, it would be better
5501 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5502 where that is what is wanted. Feedback welcomed.)
5506 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5507 the constructor to suitable values, just as usual. For example,
5518 a3 = MkSwizzle reverse
5521 a4 = let r x = Just x
5528 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5529 mkTs f x y = [T1 f x, T1 f y]
5535 The type of the argument can, as usual, be more general than the type
5536 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5537 does not need the <literal>Ord</literal> constraint.)
5541 When you use pattern matching, the bound variables may now have
5542 polymorphic types. For example:
5548 f :: T a -> a -> (a, Char)
5549 f (T1 w k) x = (w k x, w 'c' 'd')
5551 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5552 g (MkSwizzle s) xs f = s (map f (s xs))
5554 h :: MonadT m -> [m a] -> m [a]
5555 h m [] = return m []
5556 h m (x:xs) = bind m x $ \y ->
5557 bind m (h m xs) $ \ys ->
5564 In the function <function>h</function> we use the record selectors <literal>return</literal>
5565 and <literal>bind</literal> to extract the polymorphic bind and return functions
5566 from the <literal>MonadT</literal> data structure, rather than using pattern
5572 <title>Type inference</title>
5575 In general, type inference for arbitrary-rank types is undecidable.
5576 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5577 to get a decidable algorithm by requiring some help from the programmer.
5578 We do not yet have a formal specification of "some help" but the rule is this:
5581 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5582 provides an explicit polymorphic type for x, or GHC's type inference will assume
5583 that x's type has no foralls in it</emphasis>.
5586 What does it mean to "provide" an explicit type for x? You can do that by
5587 giving a type signature for x directly, using a pattern type signature
5588 (<xref linkend="scoped-type-variables"/>), thus:
5590 \ f :: (forall a. a->a) -> (f True, f 'c')
5592 Alternatively, you can give a type signature to the enclosing
5593 context, which GHC can "push down" to find the type for the variable:
5595 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5597 Here the type signature on the expression can be pushed inwards
5598 to give a type signature for f. Similarly, and more commonly,
5599 one can give a type signature for the function itself:
5601 h :: (forall a. a->a) -> (Bool,Char)
5602 h f = (f True, f 'c')
5604 You don't need to give a type signature if the lambda bound variable
5605 is a constructor argument. Here is an example we saw earlier:
5607 f :: T a -> a -> (a, Char)
5608 f (T1 w k) x = (w k x, w 'c' 'd')
5610 Here we do not need to give a type signature to <literal>w</literal>, because
5611 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5618 <sect3 id="implicit-quant">
5619 <title>Implicit quantification</title>
5622 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5623 user-written types, if and only if there is no explicit <literal>forall</literal>,
5624 GHC finds all the type variables mentioned in the type that are not already
5625 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5629 f :: forall a. a -> a
5636 h :: forall b. a -> b -> b
5642 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5645 f :: (a -> a) -> Int
5647 f :: forall a. (a -> a) -> Int
5649 f :: (forall a. a -> a) -> Int
5652 g :: (Ord a => a -> a) -> Int
5653 -- MEANS the illegal type
5654 g :: forall a. (Ord a => a -> a) -> Int
5656 g :: (forall a. Ord a => a -> a) -> Int
5658 The latter produces an illegal type, which you might think is silly,
5659 but at least the rule is simple. If you want the latter type, you
5660 can write your for-alls explicitly. Indeed, doing so is strongly advised
5667 <sect2 id="impredicative-polymorphism">
5668 <title>Impredicative polymorphism
5670 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5671 enabled with <option>-XImpredicativeTypes</option>.
5673 that you can call a polymorphic function at a polymorphic type, and
5674 parameterise data structures over polymorphic types. For example:
5676 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5677 f (Just g) = Just (g [3], g "hello")
5680 Notice here that the <literal>Maybe</literal> type is parameterised by the
5681 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5684 <para>The technical details of this extension are described in the paper
5685 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5686 type inference for higher-rank types and impredicativity</ulink>,
5687 which appeared at ICFP 2006.
5691 <sect2 id="scoped-type-variables">
5692 <title>Lexically scoped type variables
5696 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5697 which some type signatures are simply impossible to write. For example:
5699 f :: forall a. [a] -> [a]
5705 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5706 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5707 The type variables bound by a <literal>forall</literal> scope over
5708 the entire definition of the accompanying value declaration.
5709 In this example, the type variable <literal>a</literal> scopes over the whole
5710 definition of <literal>f</literal>, including over
5711 the type signature for <varname>ys</varname>.
5712 In Haskell 98 it is not possible to declare
5713 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5714 it becomes possible to do so.
5716 <para>Lexically-scoped type variables are enabled by
5717 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5719 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5720 variables work, compared to earlier releases. Read this section
5724 <title>Overview</title>
5726 <para>The design follows the following principles
5728 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5729 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5730 design.)</para></listitem>
5731 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5732 type variables. This means that every programmer-written type signature
5733 (including one that contains free scoped type variables) denotes a
5734 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5735 checker, and no inference is involved.</para></listitem>
5736 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5737 changing the program.</para></listitem>
5741 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5743 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5744 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5745 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5746 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5750 In Haskell, a programmer-written type signature is implicitly quantified over
5751 its free type variables (<ulink
5752 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5754 of the Haskell Report).
5755 Lexically scoped type variables affect this implicit quantification rules
5756 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5757 quantified. For example, if type variable <literal>a</literal> is in scope,
5760 (e :: a -> a) means (e :: a -> a)
5761 (e :: b -> b) means (e :: forall b. b->b)
5762 (e :: a -> b) means (e :: forall b. a->b)
5770 <sect3 id="decl-type-sigs">
5771 <title>Declaration type signatures</title>
5772 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5773 quantification (using <literal>forall</literal>) brings into scope the
5774 explicitly-quantified
5775 type variables, in the definition of the named function. For example:
5777 f :: forall a. [a] -> [a]
5778 f (x:xs) = xs ++ [ x :: a ]
5780 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5781 the definition of "<literal>f</literal>".
5783 <para>This only happens if:
5785 <listitem><para> The quantification in <literal>f</literal>'s type
5786 signature is explicit. For example:
5789 g (x:xs) = xs ++ [ x :: a ]
5791 This program will be rejected, because "<literal>a</literal>" does not scope
5792 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5793 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5794 quantification rules.
5796 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5797 not a pattern binding.
5800 f1 :: forall a. [a] -> [a]
5801 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5803 f2 :: forall a. [a] -> [a]
5804 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5806 f3 :: forall a. [a] -> [a]
5807 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5809 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5810 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5811 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5812 the type signature brings <literal>a</literal> into scope.
5818 <sect3 id="exp-type-sigs">
5819 <title>Expression type signatures</title>
5821 <para>An expression type signature that has <emphasis>explicit</emphasis>
5822 quantification (using <literal>forall</literal>) brings into scope the
5823 explicitly-quantified
5824 type variables, in the annotated expression. For example:
5826 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5828 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5829 type variable <literal>s</literal> into scope, in the annotated expression
5830 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5835 <sect3 id="pattern-type-sigs">
5836 <title>Pattern type signatures</title>
5838 A type signature may occur in any pattern; this is a <emphasis>pattern type
5839 signature</emphasis>.
5842 -- f and g assume that 'a' is already in scope
5843 f = \(x::Int, y::a) -> x
5845 h ((x,y) :: (Int,Bool)) = (y,x)
5847 In the case where all the type variables in the pattern type signature are
5848 already in scope (i.e. bound by the enclosing context), matters are simple: the
5849 signature simply constrains the type of the pattern in the obvious way.
5852 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5853 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5854 that are already in scope. For example:
5856 f :: forall a. [a] -> (Int, [a])
5859 (ys::[a], n) = (reverse xs, length xs) -- OK
5860 zs::[a] = xs ++ ys -- OK
5862 Just (v::b) = ... -- Not OK; b is not in scope
5864 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5865 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5869 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5870 type signature may mention a type variable that is not in scope; in this case,
5871 <emphasis>the signature brings that type variable into scope</emphasis>.
5872 This is particularly important for existential data constructors. For example:
5874 data T = forall a. MkT [a]
5877 k (MkT [t::a]) = MkT t3
5881 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5882 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5883 because it is bound by the pattern match. GHC's rule is that in this situation
5884 (and only then), a pattern type signature can mention a type variable that is
5885 not already in scope; the effect is to bring it into scope, standing for the
5886 existentially-bound type variable.
5889 When a pattern type signature binds a type variable in this way, GHC insists that the
5890 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5891 This means that any user-written type signature always stands for a completely known type.
5894 If all this seems a little odd, we think so too. But we must have
5895 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5896 could not name existentially-bound type variables in subsequent type signatures.
5899 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5900 signature is allowed to mention a lexical variable that is not already in
5902 For example, both <literal>f</literal> and <literal>g</literal> would be
5903 illegal if <literal>a</literal> was not already in scope.
5909 <!-- ==================== Commented out part about result type signatures
5911 <sect3 id="result-type-sigs">
5912 <title>Result type signatures</title>
5915 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5918 {- f assumes that 'a' is already in scope -}
5919 f x y :: [a] = [x,y,x]
5921 g = \ x :: [Int] -> [3,4]
5923 h :: forall a. [a] -> a
5927 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5928 the result of the function. Similarly, the body of the lambda in the RHS of
5929 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5930 alternative in <literal>h</literal> is <literal>a</literal>.
5932 <para> A result type signature never brings new type variables into scope.</para>
5934 There are a couple of syntactic wrinkles. First, notice that all three
5935 examples would parse quite differently with parentheses:
5937 {- f assumes that 'a' is already in scope -}
5938 f x (y :: [a]) = [x,y,x]
5940 g = \ (x :: [Int]) -> [3,4]
5942 h :: forall a. [a] -> a
5946 Now the signature is on the <emphasis>pattern</emphasis>; and
5947 <literal>h</literal> would certainly be ill-typed (since the pattern
5948 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5950 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5951 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5952 token or a parenthesised type of some sort). To see why,
5953 consider how one would parse this:
5962 <sect3 id="cls-inst-scoped-tyvars">
5963 <title>Class and instance declarations</title>
5966 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5967 scope over the methods defined in the <literal>where</literal> part. For example:
5985 <sect2 id="typing-binds">
5986 <title>Generalised typing of mutually recursive bindings</title>
5989 The Haskell Report specifies that a group of bindings (at top level, or in a
5990 <literal>let</literal> or <literal>where</literal>) should be sorted into
5991 strongly-connected components, and then type-checked in dependency order
5992 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5993 Report, Section 4.5.1</ulink>).
5994 As each group is type-checked, any binders of the group that
5996 an explicit type signature are put in the type environment with the specified
5998 and all others are monomorphic until the group is generalised
5999 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6002 <para>Following a suggestion of Mark Jones, in his paper
6003 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6005 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6007 <emphasis>the dependency analysis ignores references to variables that have an explicit
6008 type signature</emphasis>.
6009 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6010 typecheck. For example, consider:
6012 f :: Eq a => a -> Bool
6013 f x = (x == x) || g True || g "Yes"
6015 g y = (y <= y) || f True
6017 This is rejected by Haskell 98, but under Jones's scheme the definition for
6018 <literal>g</literal> is typechecked first, separately from that for
6019 <literal>f</literal>,
6020 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6021 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6022 type is generalised, to get
6024 g :: Ord a => a -> Bool
6026 Now, the definition for <literal>f</literal> is typechecked, with this type for
6027 <literal>g</literal> in the type environment.
6031 The same refined dependency analysis also allows the type signatures of
6032 mutually-recursive functions to have different contexts, something that is illegal in
6033 Haskell 98 (Section 4.5.2, last sentence). With
6034 <option>-XRelaxedPolyRec</option>
6035 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6036 type signatures; in practice this means that only variables bound by the same
6037 pattern binding must have the same context. For example, this is fine:
6039 f :: Eq a => a -> Bool
6040 f x = (x == x) || g True
6042 g :: Ord a => a -> Bool
6043 g y = (y <= y) || f True
6048 <sect2 id="mono-local-binds">
6049 <title>Monomorphic local bindings</title>
6051 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6052 The rationale is described in the paper
6053 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6056 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6057 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6058 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6059 If you supply a type signature, then the flag has no effect.
6064 <!-- ==================== End of type system extensions ================= -->
6066 <!-- ====================== TEMPLATE HASKELL ======================= -->
6068 <sect1 id="template-haskell">
6069 <title>Template Haskell</title>
6071 <para>Template Haskell allows you to do compile-time meta-programming in
6074 the main technical innovations is discussed in "<ulink
6075 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6076 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6079 There is a Wiki page about
6080 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6081 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6085 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6086 Haskell library reference material</ulink>
6087 (look for module <literal>Language.Haskell.TH</literal>).
6088 Many changes to the original design are described in
6089 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6090 Notes on Template Haskell version 2</ulink>.
6091 Not all of these changes are in GHC, however.
6094 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6095 as a worked example to help get you started.
6099 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6100 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6105 <title>Syntax</title>
6107 <para> Template Haskell has the following new syntactic
6108 constructions. You need to use the flag
6109 <option>-XTemplateHaskell</option>
6110 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6111 </indexterm>to switch these syntactic extensions on
6112 (<option>-XTemplateHaskell</option> is no longer implied by
6113 <option>-fglasgow-exts</option>).</para>
6117 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6118 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6119 There must be no space between the "$" and the identifier or parenthesis. This use
6120 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6121 of "." as an infix operator. If you want the infix operator, put spaces around it.
6123 <para> A splice can occur in place of
6125 <listitem><para> an expression; the spliced expression must
6126 have type <literal>Q Exp</literal></para></listitem>
6127 <listitem><para> an type; the spliced expression must
6128 have type <literal>Q Typ</literal></para></listitem>
6129 <listitem><para> a list of top-level declarations; the spliced expression
6130 must have type <literal>Q [Dec]</literal></para></listitem>
6132 Inside a splice you can can only call functions defined in imported modules,
6133 not functions defined elsewhere in the same module.</para></listitem>
6136 A expression quotation is written in Oxford brackets, thus:
6138 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6139 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6140 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6141 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6142 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6143 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6144 </itemizedlist></para></listitem>
6147 A quasi-quotation can appear in either a pattern context or an
6148 expression context and is also written in Oxford brackets:
6150 <listitem><para> <literal>[$<replaceable>varid</replaceable>| ... |]</literal>,
6151 where the "..." is an arbitrary string; a full description of the
6152 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6153 </itemizedlist></para></listitem>
6156 A name can be quoted with either one or two prefix single quotes:
6158 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6159 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6160 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6162 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6163 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6166 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6167 may also be given as an argument to the <literal>reify</literal> function.
6171 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6172 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6179 $(deriveStuff 'f) -- Uses the $(...) notation
6183 deriveStuff 'g -- Omits the $(...)
6187 This abbreviation makes top-level declaration slices quieter and less intimidating.
6192 (Compared to the original paper, there are many differences of detail.
6193 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6194 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6195 Pattern splices and quotations are not implemented.)
6199 <sect2> <title> Using Template Haskell </title>
6203 The data types and monadic constructor functions for Template Haskell are in the library
6204 <literal>Language.Haskell.THSyntax</literal>.
6208 You can only run a function at compile time if it is imported from another module. That is,
6209 you can't define a function in a module, and call it from within a splice in the same module.
6210 (It would make sense to do so, but it's hard to implement.)
6214 You can only run a function at compile time if it is imported
6215 from another module <emphasis>that is not part of a mutually-recursive group of modules
6216 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6217 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6218 splice is to be run.</para>
6220 For example, when compiling module A,
6221 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6222 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6226 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6229 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6230 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6231 compiles and runs a program, and then looks at the result. So it's important that
6232 the program it compiles produces results whose representations are identical to
6233 those of the compiler itself.
6237 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6238 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6243 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6244 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6245 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6252 -- Import our template "pr"
6253 import Printf ( pr )
6255 -- The splice operator $ takes the Haskell source code
6256 -- generated at compile time by "pr" and splices it into
6257 -- the argument of "putStrLn".
6258 main = putStrLn ( $(pr "Hello") )
6264 -- Skeletal printf from the paper.
6265 -- It needs to be in a separate module to the one where
6266 -- you intend to use it.
6268 -- Import some Template Haskell syntax
6269 import Language.Haskell.TH
6271 -- Describe a format string
6272 data Format = D | S | L String
6274 -- Parse a format string. This is left largely to you
6275 -- as we are here interested in building our first ever
6276 -- Template Haskell program and not in building printf.
6277 parse :: String -> [Format]
6280 -- Generate Haskell source code from a parsed representation
6281 -- of the format string. This code will be spliced into
6282 -- the module which calls "pr", at compile time.
6283 gen :: [Format] -> Q Exp
6284 gen [D] = [| \n -> show n |]
6285 gen [S] = [| \s -> s |]
6286 gen [L s] = stringE s
6288 -- Here we generate the Haskell code for the splice
6289 -- from an input format string.
6290 pr :: String -> Q Exp
6291 pr s = gen (parse s)
6294 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6297 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6300 <para>Run "main.exe" and here is your output:</para>
6310 <title>Using Template Haskell with Profiling</title>
6311 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6313 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6314 interpreter to run the splice expressions. The bytecode interpreter
6315 runs the compiled expression on top of the same runtime on which GHC
6316 itself is running; this means that the compiled code referred to by
6317 the interpreted expression must be compatible with this runtime, and
6318 in particular this means that object code that is compiled for
6319 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6320 expression, because profiled object code is only compatible with the
6321 profiling version of the runtime.</para>
6323 <para>This causes difficulties if you have a multi-module program
6324 containing Template Haskell code and you need to compile it for
6325 profiling, because GHC cannot load the profiled object code and use it
6326 when executing the splices. Fortunately GHC provides a workaround.
6327 The basic idea is to compile the program twice:</para>
6331 <para>Compile the program or library first the normal way, without
6332 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6335 <para>Then compile it again with <option>-prof</option>, and
6336 additionally use <option>-osuf
6337 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6338 to name the object files differently (you can choose any suffix
6339 that isn't the normal object suffix here). GHC will automatically
6340 load the object files built in the first step when executing splice
6341 expressions. If you omit the <option>-osuf</option> flag when
6342 building with <option>-prof</option> and Template Haskell is used,
6343 GHC will emit an error message. </para>
6348 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6349 <para>Quasi-quotation allows patterns and expressions to be written using
6350 programmer-defined concrete syntax; the motivation behind the extension and
6351 several examples are documented in
6352 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6353 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6354 2007). The example below shows how to write a quasiquoter for a simple
6355 expression language.</para>
6358 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6359 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6360 functions for quoting expressions and patterns, respectively. The first argument
6361 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6362 context of the quasi-quotation statement determines which of the two parsers is
6363 called: if the quasi-quotation occurs in an expression context, the expression
6364 parser is called, and if it occurs in a pattern context, the pattern parser is
6368 Note that in the example we make use of an antiquoted
6369 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6370 (this syntax for anti-quotation was defined by the parser's
6371 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6372 integer value argument of the constructor <literal>IntExpr</literal> when
6373 pattern matching. Please see the referenced paper for further details regarding
6374 anti-quotation as well as the description of a technique that uses SYB to
6375 leverage a single parser of type <literal>String -> a</literal> to generate both
6376 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6377 pattern parser that returns a value of type <literal>Q Pat</literal>.
6380 <para>In general, a quasi-quote has the form
6381 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6382 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6383 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6384 can be arbitrary, and may contain newlines.
6387 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6388 the example, <literal>expr</literal> cannot be defined
6389 in <literal>Main.hs</literal> where it is used, but must be imported.
6400 main = do { print $ eval [$expr|1 + 2|]
6402 { [$expr|'int:n|] -> print n
6411 import qualified Language.Haskell.TH as TH
6412 import Language.Haskell.TH.Quote
6414 data Expr = IntExpr Integer
6415 | AntiIntExpr String
6416 | BinopExpr BinOp Expr Expr
6418 deriving(Show, Typeable, Data)
6424 deriving(Show, Typeable, Data)
6426 eval :: Expr -> Integer
6427 eval (IntExpr n) = n
6428 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6435 expr = QuasiQuoter parseExprExp parseExprPat
6437 -- Parse an Expr, returning its representation as
6438 -- either a Q Exp or a Q Pat. See the referenced paper
6439 -- for how to use SYB to do this by writing a single
6440 -- parser of type String -> Expr instead of two
6441 -- separate parsers.
6443 parseExprExp :: String -> Q Exp
6446 parseExprPat :: String -> Q Pat
6450 <para>Now run the compiler:
6453 $ ghc --make -XQuasiQuotes Main.hs -o main
6456 <para>Run "main" and here is your output:</para>
6468 <!-- ===================== Arrow notation =================== -->
6470 <sect1 id="arrow-notation">
6471 <title>Arrow notation
6474 <para>Arrows are a generalization of monads introduced by John Hughes.
6475 For more details, see
6480 “Generalising Monads to Arrows”,
6481 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6482 pp67–111, May 2000.
6483 The paper that introduced arrows: a friendly introduction, motivated with
6484 programming examples.
6490 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6491 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6492 Introduced the notation described here.
6498 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6499 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6506 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6507 John Hughes, in <citetitle>5th International Summer School on
6508 Advanced Functional Programming</citetitle>,
6509 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6511 This paper includes another introduction to the notation,
6512 with practical examples.
6518 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6519 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6520 A terse enumeration of the formal rules used
6521 (extracted from comments in the source code).
6527 The arrows web page at
6528 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6533 With the <option>-XArrows</option> flag, GHC supports the arrow
6534 notation described in the second of these papers,
6535 translating it using combinators from the
6536 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6538 What follows is a brief introduction to the notation;
6539 it won't make much sense unless you've read Hughes's paper.
6542 <para>The extension adds a new kind of expression for defining arrows:
6544 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6545 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6547 where <literal>proc</literal> is a new keyword.
6548 The variables of the pattern are bound in the body of the
6549 <literal>proc</literal>-expression,
6550 which is a new sort of thing called a <firstterm>command</firstterm>.
6551 The syntax of commands is as follows:
6553 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6554 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6555 | <replaceable>cmd</replaceable><superscript>0</superscript>
6557 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6558 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6559 infix operators as for expressions, and
6561 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6562 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6563 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6564 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6565 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6566 | <replaceable>fcmd</replaceable>
6568 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6569 | ( <replaceable>cmd</replaceable> )
6570 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6572 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6573 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6574 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6575 | <replaceable>cmd</replaceable>
6577 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6578 except that the bodies are commands instead of expressions.
6582 Commands produce values, but (like monadic computations)
6583 may yield more than one value,
6584 or none, and may do other things as well.
6585 For the most part, familiarity with monadic notation is a good guide to
6587 However the values of expressions, even monadic ones,
6588 are determined by the values of the variables they contain;
6589 this is not necessarily the case for commands.
6593 A simple example of the new notation is the expression
6595 proc x -> f -< x+1
6597 We call this a <firstterm>procedure</firstterm> or
6598 <firstterm>arrow abstraction</firstterm>.
6599 As with a lambda expression, the variable <literal>x</literal>
6600 is a new variable bound within the <literal>proc</literal>-expression.
6601 It refers to the input to the arrow.
6602 In the above example, <literal>-<</literal> is not an identifier but an
6603 new reserved symbol used for building commands from an expression of arrow
6604 type and an expression to be fed as input to that arrow.
6605 (The weird look will make more sense later.)
6606 It may be read as analogue of application for arrows.
6607 The above example is equivalent to the Haskell expression
6609 arr (\ x -> x+1) >>> f
6611 That would make no sense if the expression to the left of
6612 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6613 More generally, the expression to the left of <literal>-<</literal>
6614 may not involve any <firstterm>local variable</firstterm>,
6615 i.e. a variable bound in the current arrow abstraction.
6616 For such a situation there is a variant <literal>-<<</literal>, as in
6618 proc x -> f x -<< x+1
6620 which is equivalent to
6622 arr (\ x -> (f x, x+1)) >>> app
6624 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6626 Such an arrow is equivalent to a monad, so if you're using this form
6627 you may find a monadic formulation more convenient.
6631 <title>do-notation for commands</title>
6634 Another form of command is a form of <literal>do</literal>-notation.
6635 For example, you can write
6644 You can read this much like ordinary <literal>do</literal>-notation,
6645 but with commands in place of monadic expressions.
6646 The first line sends the value of <literal>x+1</literal> as an input to
6647 the arrow <literal>f</literal>, and matches its output against
6648 <literal>y</literal>.
6649 In the next line, the output is discarded.
6650 The arrow <function>returnA</function> is defined in the
6651 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6652 module as <literal>arr id</literal>.
6653 The above example is treated as an abbreviation for
6655 arr (\ x -> (x, x)) >>>
6656 first (arr (\ x -> x+1) >>> f) >>>
6657 arr (\ (y, x) -> (y, (x, y))) >>>
6658 first (arr (\ y -> 2*y) >>> g) >>>
6660 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6661 first (arr (\ (x, z) -> x*z) >>> h) >>>
6662 arr (\ (t, z) -> t+z) >>>
6665 Note that variables not used later in the composition are projected out.
6666 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6668 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6669 module, this reduces to
6671 arr (\ x -> (x+1, x)) >>>
6673 arr (\ (y, x) -> (2*y, (x, y))) >>>
6675 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6677 arr (\ (t, z) -> t+z)
6679 which is what you might have written by hand.
6680 With arrow notation, GHC keeps track of all those tuples of variables for you.
6684 Note that although the above translation suggests that
6685 <literal>let</literal>-bound variables like <literal>z</literal> must be
6686 monomorphic, the actual translation produces Core,
6687 so polymorphic variables are allowed.
6691 It's also possible to have mutually recursive bindings,
6692 using the new <literal>rec</literal> keyword, as in the following example:
6694 counter :: ArrowCircuit a => a Bool Int
6695 counter = proc reset -> do
6696 rec output <- returnA -< if reset then 0 else next
6697 next <- delay 0 -< output+1
6698 returnA -< output
6700 The translation of such forms uses the <function>loop</function> combinator,
6701 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6707 <title>Conditional commands</title>
6710 In the previous example, we used a conditional expression to construct the
6712 Sometimes we want to conditionally execute different commands, as in
6719 which is translated to
6721 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6722 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6724 Since the translation uses <function>|||</function>,
6725 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6729 There are also <literal>case</literal> commands, like
6735 y <- h -< (x1, x2)
6739 The syntax is the same as for <literal>case</literal> expressions,
6740 except that the bodies of the alternatives are commands rather than expressions.
6741 The translation is similar to that of <literal>if</literal> commands.
6747 <title>Defining your own control structures</title>
6750 As we're seen, arrow notation provides constructs,
6751 modelled on those for expressions,
6752 for sequencing, value recursion and conditionals.
6753 But suitable combinators,
6754 which you can define in ordinary Haskell,
6755 may also be used to build new commands out of existing ones.
6756 The basic idea is that a command defines an arrow from environments to values.
6757 These environments assign values to the free local variables of the command.
6758 Thus combinators that produce arrows from arrows
6759 may also be used to build commands from commands.
6760 For example, the <literal>ArrowChoice</literal> class includes a combinator
6762 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6764 so we can use it to build commands:
6766 expr' = proc x -> do
6769 symbol Plus -< ()
6770 y <- term -< ()
6773 symbol Minus -< ()
6774 y <- term -< ()
6777 (The <literal>do</literal> on the first line is needed to prevent the first
6778 <literal><+> ...</literal> from being interpreted as part of the
6779 expression on the previous line.)
6780 This is equivalent to
6782 expr' = (proc x -> returnA -< x)
6783 <+> (proc x -> do
6784 symbol Plus -< ()
6785 y <- term -< ()
6787 <+> (proc x -> do
6788 symbol Minus -< ()
6789 y <- term -< ()
6792 It is essential that this operator be polymorphic in <literal>e</literal>
6793 (representing the environment input to the command
6794 and thence to its subcommands)
6795 and satisfy the corresponding naturality property
6797 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6799 at least for strict <literal>k</literal>.
6800 (This should be automatic if you're not using <function>seq</function>.)
6801 This ensures that environments seen by the subcommands are environments
6802 of the whole command,
6803 and also allows the translation to safely trim these environments.
6804 The operator must also not use any variable defined within the current
6809 We could define our own operator
6811 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6812 untilA body cond = proc x ->
6813 b <- cond -< x
6814 if b then returnA -< ()
6817 untilA body cond -< x
6819 and use it in the same way.
6820 Of course this infix syntax only makes sense for binary operators;
6821 there is also a more general syntax involving special brackets:
6825 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6832 <title>Primitive constructs</title>
6835 Some operators will need to pass additional inputs to their subcommands.
6836 For example, in an arrow type supporting exceptions,
6837 the operator that attaches an exception handler will wish to pass the
6838 exception that occurred to the handler.
6839 Such an operator might have a type
6841 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6843 where <literal>Ex</literal> is the type of exceptions handled.
6844 You could then use this with arrow notation by writing a command
6846 body `handleA` \ ex -> handler
6848 so that if an exception is raised in the command <literal>body</literal>,
6849 the variable <literal>ex</literal> is bound to the value of the exception
6850 and the command <literal>handler</literal>,
6851 which typically refers to <literal>ex</literal>, is entered.
6852 Though the syntax here looks like a functional lambda,
6853 we are talking about commands, and something different is going on.
6854 The input to the arrow represented by a command consists of values for
6855 the free local variables in the command, plus a stack of anonymous values.
6856 In all the prior examples, this stack was empty.
6857 In the second argument to <function>handleA</function>,
6858 this stack consists of one value, the value of the exception.
6859 The command form of lambda merely gives this value a name.
6864 the values on the stack are paired to the right of the environment.
6865 So operators like <function>handleA</function> that pass
6866 extra inputs to their subcommands can be designed for use with the notation
6867 by pairing the values with the environment in this way.
6868 More precisely, the type of each argument of the operator (and its result)
6869 should have the form
6871 a (...(e,t1), ... tn) t
6873 where <replaceable>e</replaceable> is a polymorphic variable
6874 (representing the environment)
6875 and <replaceable>ti</replaceable> are the types of the values on the stack,
6876 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6877 The polymorphic variable <replaceable>e</replaceable> must not occur in
6878 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6879 <replaceable>t</replaceable>.
6880 However the arrows involved need not be the same.
6881 Here are some more examples of suitable operators:
6883 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6884 runReader :: ... => a e c -> a' (e,State) c
6885 runState :: ... => a e c -> a' (e,State) (c,State)
6887 We can supply the extra input required by commands built with the last two
6888 by applying them to ordinary expressions, as in
6892 (|runReader (do { ... })|) s
6894 which adds <literal>s</literal> to the stack of inputs to the command
6895 built using <function>runReader</function>.
6899 The command versions of lambda abstraction and application are analogous to
6900 the expression versions.
6901 In particular, the beta and eta rules describe equivalences of commands.
6902 These three features (operators, lambda abstraction and application)
6903 are the core of the notation; everything else can be built using them,
6904 though the results would be somewhat clumsy.
6905 For example, we could simulate <literal>do</literal>-notation by defining
6907 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6908 u `bind` f = returnA &&& u >>> f
6910 bind_ :: Arrow a => a e b -> a e c -> a e c
6911 u `bind_` f = u `bind` (arr fst >>> f)
6913 We could simulate <literal>if</literal> by defining
6915 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6916 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6923 <title>Differences with the paper</title>
6928 <para>Instead of a single form of arrow application (arrow tail) with two
6929 translations, the implementation provides two forms
6930 <quote><literal>-<</literal></quote> (first-order)
6931 and <quote><literal>-<<</literal></quote> (higher-order).
6936 <para>User-defined operators are flagged with banana brackets instead of
6937 a new <literal>form</literal> keyword.
6946 <title>Portability</title>
6949 Although only GHC implements arrow notation directly,
6950 there is also a preprocessor
6952 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6953 that translates arrow notation into Haskell 98
6954 for use with other Haskell systems.
6955 You would still want to check arrow programs with GHC;
6956 tracing type errors in the preprocessor output is not easy.
6957 Modules intended for both GHC and the preprocessor must observe some
6958 additional restrictions:
6963 The module must import
6964 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6970 The preprocessor cannot cope with other Haskell extensions.
6971 These would have to go in separate modules.
6977 Because the preprocessor targets Haskell (rather than Core),
6978 <literal>let</literal>-bound variables are monomorphic.
6989 <!-- ==================== BANG PATTERNS ================= -->
6991 <sect1 id="bang-patterns">
6992 <title>Bang patterns
6993 <indexterm><primary>Bang patterns</primary></indexterm>
6995 <para>GHC supports an extension of pattern matching called <emphasis>bang
6996 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6997 Bang patterns are under consideration for Haskell Prime.
6999 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7000 prime feature description</ulink> contains more discussion and examples
7001 than the material below.
7004 The key change is the addition of a new rule to the
7005 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7006 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7007 against a value <replaceable>v</replaceable> behaves as follows:
7009 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7010 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7014 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7017 <sect2 id="bang-patterns-informal">
7018 <title>Informal description of bang patterns
7021 The main idea is to add a single new production to the syntax of patterns:
7025 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7026 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7031 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7032 whereas without the bang it would be lazy.
7033 Bang patterns can be nested of course:
7037 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7038 <literal>y</literal>.
7039 A bang only really has an effect if it precedes a variable or wild-card pattern:
7044 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7045 putting a bang before a pattern that
7046 forces evaluation anyway does nothing.
7049 There is one (apparent) exception to this general rule that a bang only
7050 makes a difference when it precedes a variable or wild-card: a bang at the
7051 top level of a <literal>let</literal> or <literal>where</literal>
7052 binding makes the binding strict, regardless of the pattern. For example:
7056 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7057 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7058 (We say "apparent" exception because the Right Way to think of it is that the bang
7059 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7060 is part of the syntax of the <emphasis>binding</emphasis>.)
7061 Nested bangs in a pattern binding behave uniformly with all other forms of
7062 pattern matching. For example
7064 let (!x,[y]) = e in b
7066 is equivalent to this:
7068 let { t = case e of (x,[y]) -> x `seq` (x,y)
7073 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7074 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7075 evaluation of <literal>x</literal>.
7078 Bang patterns work in <literal>case</literal> expressions too, of course:
7080 g5 x = let y = f x in body
7081 g6 x = case f x of { y -> body }
7082 g7 x = case f x of { !y -> body }
7084 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7085 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7086 result, and then evaluates <literal>body</literal>.
7091 <sect2 id="bang-patterns-sem">
7092 <title>Syntax and semantics
7096 We add a single new production to the syntax of patterns:
7100 There is one problem with syntactic ambiguity. Consider:
7104 Is this a definition of the infix function "<literal>(!)</literal>",
7105 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7106 ambiguity in favour of the latter. If you want to define
7107 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7112 The semantics of Haskell pattern matching is described in <ulink
7113 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7114 Section 3.17.2</ulink> of the Haskell Report. To this description add
7115 one extra item 10, saying:
7116 <itemizedlist><listitem><para>Matching
7117 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7118 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7119 <listitem><para>otherwise, <literal>pat</literal> is matched against
7120 <literal>v</literal></para></listitem>
7122 </para></listitem></itemizedlist>
7123 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7124 Section 3.17.3</ulink>, add a new case (t):
7126 case v of { !pat -> e; _ -> e' }
7127 = v `seq` case v of { pat -> e; _ -> e' }
7130 That leaves let expressions, whose translation is given in
7131 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7133 of the Haskell Report.
7134 In the translation box, first apply
7135 the following transformation: for each pattern <literal>pi</literal> that is of
7136 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7137 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7138 have a bang at the top, apply the rules in the existing box.
7140 <para>The effect of the let rule is to force complete matching of the pattern
7141 <literal>qi</literal> before evaluation of the body is begun. The bang is
7142 retained in the translated form in case <literal>qi</literal> is a variable,
7150 The let-binding can be recursive. However, it is much more common for
7151 the let-binding to be non-recursive, in which case the following law holds:
7152 <literal>(let !p = rhs in body)</literal>
7154 <literal>(case rhs of !p -> body)</literal>
7157 A pattern with a bang at the outermost level is not allowed at the top level of
7163 <!-- ==================== ASSERTIONS ================= -->
7165 <sect1 id="assertions">
7167 <indexterm><primary>Assertions</primary></indexterm>
7171 If you want to make use of assertions in your standard Haskell code, you
7172 could define a function like the following:
7178 assert :: Bool -> a -> a
7179 assert False x = error "assertion failed!"
7186 which works, but gives you back a less than useful error message --
7187 an assertion failed, but which and where?
7191 One way out is to define an extended <function>assert</function> function which also
7192 takes a descriptive string to include in the error message and
7193 perhaps combine this with the use of a pre-processor which inserts
7194 the source location where <function>assert</function> was used.
7198 Ghc offers a helping hand here, doing all of this for you. For every
7199 use of <function>assert</function> in the user's source:
7205 kelvinToC :: Double -> Double
7206 kelvinToC k = assert (k >= 0.0) (k+273.15)
7212 Ghc will rewrite this to also include the source location where the
7219 assert pred val ==> assertError "Main.hs|15" pred val
7225 The rewrite is only performed by the compiler when it spots
7226 applications of <function>Control.Exception.assert</function>, so you
7227 can still define and use your own versions of
7228 <function>assert</function>, should you so wish. If not, import
7229 <literal>Control.Exception</literal> to make use
7230 <function>assert</function> in your code.
7234 GHC ignores assertions when optimisation is turned on with the
7235 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7236 <literal>assert pred e</literal> will be rewritten to
7237 <literal>e</literal>. You can also disable assertions using the
7238 <option>-fignore-asserts</option>
7239 option<indexterm><primary><option>-fignore-asserts</option></primary>
7240 </indexterm>.</para>
7243 Assertion failures can be caught, see the documentation for the
7244 <literal>Control.Exception</literal> library for the details.
7250 <!-- =============================== PRAGMAS =========================== -->
7252 <sect1 id="pragmas">
7253 <title>Pragmas</title>
7255 <indexterm><primary>pragma</primary></indexterm>
7257 <para>GHC supports several pragmas, or instructions to the
7258 compiler placed in the source code. Pragmas don't normally affect
7259 the meaning of the program, but they might affect the efficiency
7260 of the generated code.</para>
7262 <para>Pragmas all take the form
7264 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7266 where <replaceable>word</replaceable> indicates the type of
7267 pragma, and is followed optionally by information specific to that
7268 type of pragma. Case is ignored in
7269 <replaceable>word</replaceable>. The various values for
7270 <replaceable>word</replaceable> that GHC understands are described
7271 in the following sections; any pragma encountered with an
7272 unrecognised <replaceable>word</replaceable> is
7273 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7274 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7276 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7280 pragma must precede the <literal>module</literal> keyword in the file.
7283 There can be as many file-header pragmas as you please, and they can be
7284 preceded or followed by comments.
7287 File-header pragmas are read once only, before
7288 pre-processing the file (e.g. with cpp).
7291 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7292 <literal>{-# OPTIONS_GHC #-}</literal>, and
7293 <literal>{-# INCLUDE #-}</literal>.
7298 <sect2 id="language-pragma">
7299 <title>LANGUAGE pragma</title>
7301 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7302 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7304 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7306 It is the intention that all Haskell compilers support the
7307 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7308 all extensions are supported by all compilers, of
7309 course. The <literal>LANGUAGE</literal> pragma should be used instead
7310 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7312 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7314 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7316 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7318 <para>Every language extension can also be turned into a command-line flag
7319 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7320 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7323 <para>A list of all supported language extensions can be obtained by invoking
7324 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7326 <para>Any extension from the <literal>Extension</literal> type defined in
7328 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7329 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7333 <sect2 id="options-pragma">
7334 <title>OPTIONS_GHC pragma</title>
7335 <indexterm><primary>OPTIONS_GHC</primary>
7337 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7340 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7341 additional options that are given to the compiler when compiling
7342 this source file. See <xref linkend="source-file-options"/> for
7345 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7346 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7349 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7351 <sect2 id="include-pragma">
7352 <title>INCLUDE pragma</title>
7354 <para>The <literal>INCLUDE</literal> used to be necessary for
7355 specifying header files to be included when using the FFI and
7356 compiling via C. It is no longer required for GHC, but is
7357 accepted (and ignored) for compatibility with other
7361 <sect2 id="warning-deprecated-pragma">
7362 <title>WARNING and DEPRECATED pragmas</title>
7363 <indexterm><primary>WARNING</primary></indexterm>
7364 <indexterm><primary>DEPRECATED</primary></indexterm>
7366 <para>The WARNING pragma allows you to attach an arbitrary warning
7367 to a particular function, class, or type.
7368 A DEPRECATED pragma lets you specify that
7369 a particular function, class, or type is deprecated.
7370 There are two ways of using these pragmas.
7374 <para>You can work on an entire module thus:</para>
7376 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7381 module Wibble {-# WARNING "This is an unstable interface." #-} where
7384 <para>When you compile any module that import
7385 <literal>Wibble</literal>, GHC will print the specified
7390 <para>You can attach a warning to a function, class, type, or data constructor, with the
7391 following top-level declarations:</para>
7393 {-# DEPRECATED f, C, T "Don't use these" #-}
7394 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7396 <para>When you compile any module that imports and uses any
7397 of the specified entities, GHC will print the specified
7399 <para> You can only attach to entities declared at top level in the module
7400 being compiled, and you can only use unqualified names in the list of
7401 entities. A capitalised name, such as <literal>T</literal>
7402 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7403 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7404 both are in scope. If both are in scope, there is currently no way to
7405 specify one without the other (c.f. fixities
7406 <xref linkend="infix-tycons"/>).</para>
7409 Warnings and deprecations are not reported for
7410 (a) uses within the defining module, and
7411 (b) uses in an export list.
7412 The latter reduces spurious complaints within a library
7413 in which one module gathers together and re-exports
7414 the exports of several others.
7416 <para>You can suppress the warnings with the flag
7417 <option>-fno-warn-warnings-deprecations</option>.</para>
7420 <sect2 id="inline-noinline-pragma">
7421 <title>INLINE and NOINLINE pragmas</title>
7423 <para>These pragmas control the inlining of function
7426 <sect3 id="inline-pragma">
7427 <title>INLINE pragma</title>
7428 <indexterm><primary>INLINE</primary></indexterm>
7430 <para>GHC (with <option>-O</option>, as always) tries to
7431 inline (or “unfold”) functions/values that are
7432 “small enough,” thus avoiding the call overhead
7433 and possibly exposing other more-wonderful optimisations.
7434 Normally, if GHC decides a function is “too
7435 expensive” to inline, it will not do so, nor will it
7436 export that unfolding for other modules to use.</para>
7438 <para>The sledgehammer you can bring to bear is the
7439 <literal>INLINE</literal><indexterm><primary>INLINE
7440 pragma</primary></indexterm> pragma, used thusly:</para>
7443 key_function :: Int -> String -> (Bool, Double)
7444 {-# INLINE key_function #-}
7447 <para>The major effect of an <literal>INLINE</literal> pragma
7448 is to declare a function's “cost” to be very low.
7449 The normal unfolding machinery will then be very keen to
7450 inline it. However, an <literal>INLINE</literal> pragma for a
7451 function "<literal>f</literal>" has a number of other effects:
7454 No functions are inlined into <literal>f</literal>. Otherwise
7455 GHC might inline a big function into <literal>f</literal>'s right hand side,
7456 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7459 The float-in, float-out, and common-sub-expression transformations are not
7460 applied to the body of <literal>f</literal>.
7463 An INLINE function is not worker/wrappered by strictness analysis.
7464 It's going to be inlined wholesale instead.
7467 All of these effects are aimed at ensuring that what gets inlined is
7468 exactly what you asked for, no more and no less.
7470 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7471 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7472 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7473 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7474 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7475 when there is no choice even an INLINE function can be selected, in which case
7476 the INLINE pragma is ignored.
7477 For example, for a self-recursive function, the loop breaker can only be the function
7478 itself, so an INLINE pragma is always ignored.</para>
7480 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7481 function can be put anywhere its type signature could be
7484 <para><literal>INLINE</literal> pragmas are a particularly
7486 <literal>then</literal>/<literal>return</literal> (or
7487 <literal>bind</literal>/<literal>unit</literal>) functions in
7488 a monad. For example, in GHC's own
7489 <literal>UniqueSupply</literal> monad code, we have:</para>
7492 {-# INLINE thenUs #-}
7493 {-# INLINE returnUs #-}
7496 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7497 linkend="noinline-pragma"/>).</para>
7499 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7500 so if you want your code to be HBC-compatible you'll have to surround
7501 the pragma with C pre-processor directives
7502 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7506 <sect3 id="noinline-pragma">
7507 <title>NOINLINE pragma</title>
7509 <indexterm><primary>NOINLINE</primary></indexterm>
7510 <indexterm><primary>NOTINLINE</primary></indexterm>
7512 <para>The <literal>NOINLINE</literal> pragma does exactly what
7513 you'd expect: it stops the named function from being inlined
7514 by the compiler. You shouldn't ever need to do this, unless
7515 you're very cautious about code size.</para>
7517 <para><literal>NOTINLINE</literal> is a synonym for
7518 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7519 specified by Haskell 98 as the standard way to disable
7520 inlining, so it should be used if you want your code to be
7524 <sect3 id="phase-control">
7525 <title>Phase control</title>
7527 <para> Sometimes you want to control exactly when in GHC's
7528 pipeline the INLINE pragma is switched on. Inlining happens
7529 only during runs of the <emphasis>simplifier</emphasis>. Each
7530 run of the simplifier has a different <emphasis>phase
7531 number</emphasis>; the phase number decreases towards zero.
7532 If you use <option>-dverbose-core2core</option> you'll see the
7533 sequence of phase numbers for successive runs of the
7534 simplifier. In an INLINE pragma you can optionally specify a
7538 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7539 <literal>f</literal>
7540 until phase <literal>k</literal>, but from phase
7541 <literal>k</literal> onwards be very keen to inline it.
7544 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7545 <literal>f</literal>
7546 until phase <literal>k</literal>, but from phase
7547 <literal>k</literal> onwards do not inline it.
7550 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7551 <literal>f</literal>
7552 until phase <literal>k</literal>, but from phase
7553 <literal>k</literal> onwards be willing to inline it (as if
7554 there was no pragma).
7557 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7558 <literal>f</literal>
7559 until phase <literal>k</literal>, but from phase
7560 <literal>k</literal> onwards do not inline it.
7563 The same information is summarised here:
7565 -- Before phase 2 Phase 2 and later
7566 {-# INLINE [2] f #-} -- No Yes
7567 {-# INLINE [~2] f #-} -- Yes No
7568 {-# NOINLINE [2] f #-} -- No Maybe
7569 {-# NOINLINE [~2] f #-} -- Maybe No
7571 {-# INLINE f #-} -- Yes Yes
7572 {-# NOINLINE f #-} -- No No
7574 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7575 function body is small, or it is applied to interesting-looking arguments etc).
7576 Another way to understand the semantics is this:
7578 <listitem><para>For both INLINE and NOINLINE, the phase number says
7579 when inlining is allowed at all.</para></listitem>
7580 <listitem><para>The INLINE pragma has the additional effect of making the
7581 function body look small, so that when inlining is allowed it is very likely to
7586 <para>The same phase-numbering control is available for RULES
7587 (<xref linkend="rewrite-rules"/>).</para>
7591 <sect2 id="annotation-pragmas">
7592 <title>ANN pragmas</title>
7594 <para>GHC offers the ability to annotate various code constructs with additional
7595 data by using three pragmas. This data can then be inspected at a later date by
7596 using GHC-as-a-library.</para>
7598 <sect3 id="ann-pragma">
7599 <title>Annotating values</title>
7601 <indexterm><primary>ANN</primary></indexterm>
7603 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7604 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7605 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7606 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7607 you would do this:</para>
7610 {-# ANN foo (Just "Hello") #-}
7615 A number of restrictions apply to use of annotations:
7617 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7618 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7619 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7620 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7621 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7623 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7624 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7627 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7628 please give the GHC team a shout</ulink>.
7631 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7632 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7635 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7640 <sect3 id="typeann-pragma">
7641 <title>Annotating types</title>
7643 <indexterm><primary>ANN type</primary></indexterm>
7644 <indexterm><primary>ANN</primary></indexterm>
7646 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7649 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7654 <sect3 id="modann-pragma">
7655 <title>Annotating modules</title>
7657 <indexterm><primary>ANN module</primary></indexterm>
7658 <indexterm><primary>ANN</primary></indexterm>
7660 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7663 {-# ANN module (Just "A `Maybe String' annotation") #-}
7668 <sect2 id="line-pragma">
7669 <title>LINE pragma</title>
7671 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7672 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7673 <para>This pragma is similar to C's <literal>#line</literal>
7674 pragma, and is mainly for use in automatically generated Haskell
7675 code. It lets you specify the line number and filename of the
7676 original code; for example</para>
7678 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7680 <para>if you'd generated the current file from something called
7681 <filename>Foo.vhs</filename> and this line corresponds to line
7682 42 in the original. GHC will adjust its error messages to refer
7683 to the line/file named in the <literal>LINE</literal>
7688 <title>RULES pragma</title>
7690 <para>The RULES pragma lets you specify rewrite rules. It is
7691 described in <xref linkend="rewrite-rules"/>.</para>
7694 <sect2 id="specialize-pragma">
7695 <title>SPECIALIZE pragma</title>
7697 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7698 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7699 <indexterm><primary>overloading, death to</primary></indexterm>
7701 <para>(UK spelling also accepted.) For key overloaded
7702 functions, you can create extra versions (NB: more code space)
7703 specialised to particular types. Thus, if you have an
7704 overloaded function:</para>
7707 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7710 <para>If it is heavily used on lists with
7711 <literal>Widget</literal> keys, you could specialise it as
7715 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7718 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7719 be put anywhere its type signature could be put.</para>
7721 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7722 (a) a specialised version of the function and (b) a rewrite rule
7723 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7724 un-specialised function into a call to the specialised one.</para>
7726 <para>The type in a SPECIALIZE pragma can be any type that is less
7727 polymorphic than the type of the original function. In concrete terms,
7728 if the original function is <literal>f</literal> then the pragma
7730 {-# SPECIALIZE f :: <type> #-}
7732 is valid if and only if the definition
7734 f_spec :: <type>
7737 is valid. Here are some examples (where we only give the type signature
7738 for the original function, not its code):
7740 f :: Eq a => a -> b -> b
7741 {-# SPECIALISE f :: Int -> b -> b #-}
7743 g :: (Eq a, Ix b) => a -> b -> b
7744 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7746 h :: Eq a => a -> a -> a
7747 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7749 The last of these examples will generate a
7750 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7751 well. If you use this kind of specialisation, let us know how well it works.
7754 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7755 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7756 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7757 The <literal>INLINE</literal> pragma affects the specialised version of the
7758 function (only), and applies even if the function is recursive. The motivating
7761 -- A GADT for arrays with type-indexed representation
7763 ArrInt :: !Int -> ByteArray# -> Arr Int
7764 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7766 (!:) :: Arr e -> Int -> e
7767 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7768 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7769 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7770 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7772 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7773 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7774 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7775 the specialised function will be inlined. It has two calls to
7776 <literal>(!:)</literal>,
7777 both at type <literal>Int</literal>. Both these calls fire the first
7778 specialisation, whose body is also inlined. The result is a type-based
7779 unrolling of the indexing function.</para>
7780 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7781 on an ordinarily-recursive function.</para>
7783 <para>Note: In earlier versions of GHC, it was possible to provide your own
7784 specialised function for a given type:
7787 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7790 This feature has been removed, as it is now subsumed by the
7791 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7795 <sect2 id="specialize-instance-pragma">
7796 <title>SPECIALIZE instance pragma
7800 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7801 <indexterm><primary>overloading, death to</primary></indexterm>
7802 Same idea, except for instance declarations. For example:
7805 instance (Eq a) => Eq (Foo a) where {
7806 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7810 The pragma must occur inside the <literal>where</literal> part
7811 of the instance declaration.
7814 Compatible with HBC, by the way, except perhaps in the placement
7820 <sect2 id="unpack-pragma">
7821 <title>UNPACK pragma</title>
7823 <indexterm><primary>UNPACK</primary></indexterm>
7825 <para>The <literal>UNPACK</literal> indicates to the compiler
7826 that it should unpack the contents of a constructor field into
7827 the constructor itself, removing a level of indirection. For
7831 data T = T {-# UNPACK #-} !Float
7832 {-# UNPACK #-} !Float
7835 <para>will create a constructor <literal>T</literal> containing
7836 two unboxed floats. This may not always be an optimisation: if
7837 the <function>T</function> constructor is scrutinised and the
7838 floats passed to a non-strict function for example, they will
7839 have to be reboxed (this is done automatically by the
7842 <para>Unpacking constructor fields should only be used in
7843 conjunction with <option>-O</option>, in order to expose
7844 unfoldings to the compiler so the reboxing can be removed as
7845 often as possible. For example:</para>
7849 f (T f1 f2) = f1 + f2
7852 <para>The compiler will avoid reboxing <function>f1</function>
7853 and <function>f2</function> by inlining <function>+</function>
7854 on floats, but only when <option>-O</option> is on.</para>
7856 <para>Any single-constructor data is eligible for unpacking; for
7860 data T = T {-# UNPACK #-} !(Int,Int)
7863 <para>will store the two <literal>Int</literal>s directly in the
7864 <function>T</function> constructor, by flattening the pair.
7865 Multi-level unpacking is also supported:
7868 data T = T {-# UNPACK #-} !S
7869 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7872 will store two unboxed <literal>Int#</literal>s
7873 directly in the <function>T</function> constructor. The
7874 unpacker can see through newtypes, too.</para>
7876 <para>If a field cannot be unpacked, you will not get a warning,
7877 so it might be an idea to check the generated code with
7878 <option>-ddump-simpl</option>.</para>
7880 <para>See also the <option>-funbox-strict-fields</option> flag,
7881 which essentially has the effect of adding
7882 <literal>{-# UNPACK #-}</literal> to every strict
7883 constructor field.</para>
7886 <sect2 id="source-pragma">
7887 <title>SOURCE pragma</title>
7889 <indexterm><primary>SOURCE</primary></indexterm>
7890 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7891 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7897 <!-- ======================= REWRITE RULES ======================== -->
7899 <sect1 id="rewrite-rules">
7900 <title>Rewrite rules
7902 <indexterm><primary>RULES pragma</primary></indexterm>
7903 <indexterm><primary>pragma, RULES</primary></indexterm>
7904 <indexterm><primary>rewrite rules</primary></indexterm></title>
7907 The programmer can specify rewrite rules as part of the source program
7913 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7918 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7919 If you need more information, then <option>-ddump-rule-firings</option> shows you
7920 each individual rule firing in detail.
7924 <title>Syntax</title>
7927 From a syntactic point of view:
7933 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7934 may be generated by the layout rule).
7940 The layout rule applies in a pragma.
7941 Currently no new indentation level
7942 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7943 you must lay out the starting in the same column as the enclosing definitions.
7946 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7947 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7950 Furthermore, the closing <literal>#-}</literal>
7951 should start in a column to the right of the opening <literal>{-#</literal>.
7957 Each rule has a name, enclosed in double quotes. The name itself has
7958 no significance at all. It is only used when reporting how many times the rule fired.
7964 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7965 immediately after the name of the rule. Thus:
7968 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7971 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7972 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7981 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7982 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7983 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7984 by spaces, just like in a type <literal>forall</literal>.
7990 A pattern variable may optionally have a type signature.
7991 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7992 For example, here is the <literal>foldr/build</literal> rule:
7995 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7996 foldr k z (build g) = g k z
7999 Since <function>g</function> has a polymorphic type, it must have a type signature.
8006 The left hand side of a rule must consist of a top-level variable applied
8007 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8010 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8011 "wrong2" forall f. f True = True
8014 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8021 A rule does not need to be in the same module as (any of) the
8022 variables it mentions, though of course they need to be in scope.
8028 All rules are implicitly exported from the module, and are therefore
8029 in force in any module that imports the module that defined the rule, directly
8030 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8031 in force when compiling A.) The situation is very similar to that for instance
8039 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8040 any other flag settings. Furthermore, inside a RULE, the language extension
8041 <option>-XScopedTypeVariables</option> is automatically enabled; see
8042 <xref linkend="scoped-type-variables"/>.
8048 Like other pragmas, RULE pragmas are always checked for scope errors, and
8049 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8050 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8051 if the <option>-fenable-rewrite-rules</option> flag is
8052 on (see <xref linkend="rule-semantics"/>).
8061 <sect2 id="rule-semantics">
8062 <title>Semantics</title>
8065 From a semantic point of view:
8070 Rules are enabled (that is, used during optimisation)
8071 by the <option>-fenable-rewrite-rules</option> flag.
8072 This flag is implied by <option>-O</option>, and may be switched
8073 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8074 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8075 may not do what you expect, though, because without <option>-O</option> GHC
8076 ignores all optimisation information in interface files;
8077 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8078 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8079 has no effect on parsing or typechecking.
8085 Rules are regarded as left-to-right rewrite rules.
8086 When GHC finds an expression that is a substitution instance of the LHS
8087 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8088 By "a substitution instance" we mean that the LHS can be made equal to the
8089 expression by substituting for the pattern variables.
8096 GHC makes absolutely no attempt to verify that the LHS and RHS
8097 of a rule have the same meaning. That is undecidable in general, and
8098 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8105 GHC makes no attempt to make sure that the rules are confluent or
8106 terminating. For example:
8109 "loop" forall x y. f x y = f y x
8112 This rule will cause the compiler to go into an infinite loop.
8119 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8125 GHC currently uses a very simple, syntactic, matching algorithm
8126 for matching a rule LHS with an expression. It seeks a substitution
8127 which makes the LHS and expression syntactically equal modulo alpha
8128 conversion. The pattern (rule), but not the expression, is eta-expanded if
8129 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8130 But not beta conversion (that's called higher-order matching).
8134 Matching is carried out on GHC's intermediate language, which includes
8135 type abstractions and applications. So a rule only matches if the
8136 types match too. See <xref linkend="rule-spec"/> below.
8142 GHC keeps trying to apply the rules as it optimises the program.
8143 For example, consider:
8152 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8153 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8154 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8155 not be substituted, and the rule would not fire.
8162 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8163 results. Consider this (artificial) example
8166 {-# RULES "f" f True = False #-}
8172 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8177 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8179 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8180 would have been a better chance that <literal>f</literal>'s RULE might fire.
8183 The way to get predictable behaviour is to use a NOINLINE
8184 pragma on <literal>f</literal>, to ensure
8185 that it is not inlined until its RULEs have had a chance to fire.
8195 <title>List fusion</title>
8198 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8199 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8200 intermediate list should be eliminated entirely.
8204 The following are good producers:
8216 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8222 Explicit lists (e.g. <literal>[True, False]</literal>)
8228 The cons constructor (e.g <literal>3:4:[]</literal>)
8234 <function>++</function>
8240 <function>map</function>
8246 <function>take</function>, <function>filter</function>
8252 <function>iterate</function>, <function>repeat</function>
8258 <function>zip</function>, <function>zipWith</function>
8267 The following are good consumers:
8279 <function>array</function> (on its second argument)
8285 <function>++</function> (on its first argument)
8291 <function>foldr</function>
8297 <function>map</function>
8303 <function>take</function>, <function>filter</function>
8309 <function>concat</function>
8315 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8321 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8322 will fuse with one but not the other)
8328 <function>partition</function>
8334 <function>head</function>
8340 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8346 <function>sequence_</function>
8352 <function>msum</function>
8358 <function>sortBy</function>
8367 So, for example, the following should generate no intermediate lists:
8370 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8376 This list could readily be extended; if there are Prelude functions that you use
8377 a lot which are not included, please tell us.
8381 If you want to write your own good consumers or producers, look at the
8382 Prelude definitions of the above functions to see how to do so.
8387 <sect2 id="rule-spec">
8388 <title>Specialisation
8392 Rewrite rules can be used to get the same effect as a feature
8393 present in earlier versions of GHC.
8394 For example, suppose that:
8397 genericLookup :: Ord a => Table a b -> a -> b
8398 intLookup :: Table Int b -> Int -> b
8401 where <function>intLookup</function> is an implementation of
8402 <function>genericLookup</function> that works very fast for
8403 keys of type <literal>Int</literal>. You might wish
8404 to tell GHC to use <function>intLookup</function> instead of
8405 <function>genericLookup</function> whenever the latter was called with
8406 type <literal>Table Int b -> Int -> b</literal>.
8407 It used to be possible to write
8410 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8413 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8416 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8419 This slightly odd-looking rule instructs GHC to replace
8420 <function>genericLookup</function> by <function>intLookup</function>
8421 <emphasis>whenever the types match</emphasis>.
8422 What is more, this rule does not need to be in the same
8423 file as <function>genericLookup</function>, unlike the
8424 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8425 have an original definition available to specialise).
8428 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8429 <function>intLookup</function> really behaves as a specialised version
8430 of <function>genericLookup</function>!!!</para>
8432 <para>An example in which using <literal>RULES</literal> for
8433 specialisation will Win Big:
8436 toDouble :: Real a => a -> Double
8437 toDouble = fromRational . toRational
8439 {-# RULES "toDouble/Int" toDouble = i2d #-}
8440 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8443 The <function>i2d</function> function is virtually one machine
8444 instruction; the default conversion—via an intermediate
8445 <literal>Rational</literal>—is obscenely expensive by
8452 <title>Controlling what's going on</title>
8460 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8466 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8467 If you add <option>-dppr-debug</option> you get a more detailed listing.
8473 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8476 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8477 {-# INLINE build #-}
8481 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8482 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8483 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8484 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8491 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8492 see how to write rules that will do fusion and yet give an efficient
8493 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8503 <sect2 id="core-pragma">
8504 <title>CORE pragma</title>
8506 <indexterm><primary>CORE pragma</primary></indexterm>
8507 <indexterm><primary>pragma, CORE</primary></indexterm>
8508 <indexterm><primary>core, annotation</primary></indexterm>
8511 The external core format supports <quote>Note</quote> annotations;
8512 the <literal>CORE</literal> pragma gives a way to specify what these
8513 should be in your Haskell source code. Syntactically, core
8514 annotations are attached to expressions and take a Haskell string
8515 literal as an argument. The following function definition shows an
8519 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8522 Semantically, this is equivalent to:
8530 However, when external core is generated (via
8531 <option>-fext-core</option>), there will be Notes attached to the
8532 expressions <function>show</function> and <varname>x</varname>.
8533 The core function declaration for <function>f</function> is:
8537 f :: %forall a . GHCziShow.ZCTShow a ->
8538 a -> GHCziBase.ZMZN GHCziBase.Char =
8539 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8541 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8543 (tpl1::GHCziBase.Int ->
8545 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8547 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8548 (tpl3::GHCziBase.ZMZN a ->
8549 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8557 Here, we can see that the function <function>show</function> (which
8558 has been expanded out to a case expression over the Show dictionary)
8559 has a <literal>%note</literal> attached to it, as does the
8560 expression <varname>eta</varname> (which used to be called
8561 <varname>x</varname>).
8568 <sect1 id="special-ids">
8569 <title>Special built-in functions</title>
8570 <para>GHC has a few built-in functions with special behaviour. These
8571 are now described in the module <ulink
8572 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8573 in the library documentation.</para>
8577 <sect1 id="generic-classes">
8578 <title>Generic classes</title>
8581 The ideas behind this extension are described in detail in "Derivable type classes",
8582 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8583 An example will give the idea:
8591 fromBin :: [Int] -> (a, [Int])
8593 toBin {| Unit |} Unit = []
8594 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8595 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8596 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8598 fromBin {| Unit |} bs = (Unit, bs)
8599 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8600 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8601 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8602 (y,bs'') = fromBin bs'
8605 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8606 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8607 which are defined thus in the library module <literal>Generics</literal>:
8611 data a :+: b = Inl a | Inr b
8612 data a :*: b = a :*: b
8615 Now you can make a data type into an instance of Bin like this:
8617 instance (Bin a, Bin b) => Bin (a,b)
8618 instance Bin a => Bin [a]
8620 That is, just leave off the "where" clause. Of course, you can put in the
8621 where clause and over-ride whichever methods you please.
8625 <title> Using generics </title>
8626 <para>To use generics you need to</para>
8629 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8630 <option>-XGenerics</option> (to generate extra per-data-type code),
8631 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8635 <para>Import the module <literal>Generics</literal> from the
8636 <literal>lang</literal> package. This import brings into
8637 scope the data types <literal>Unit</literal>,
8638 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8639 don't need this import if you don't mention these types
8640 explicitly; for example, if you are simply giving instance
8641 declarations.)</para>
8646 <sect2> <title> Changes wrt the paper </title>
8648 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8649 can be written infix (indeed, you can now use
8650 any operator starting in a colon as an infix type constructor). Also note that
8651 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8652 Finally, note that the syntax of the type patterns in the class declaration
8653 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8654 alone would ambiguous when they appear on right hand sides (an extension we
8655 anticipate wanting).
8659 <sect2> <title>Terminology and restrictions</title>
8661 Terminology. A "generic default method" in a class declaration
8662 is one that is defined using type patterns as above.
8663 A "polymorphic default method" is a default method defined as in Haskell 98.
8664 A "generic class declaration" is a class declaration with at least one
8665 generic default method.
8673 Alas, we do not yet implement the stuff about constructor names and
8680 A generic class can have only one parameter; you can't have a generic
8681 multi-parameter class.
8687 A default method must be defined entirely using type patterns, or entirely
8688 without. So this is illegal:
8691 op :: a -> (a, Bool)
8692 op {| Unit |} Unit = (Unit, True)
8695 However it is perfectly OK for some methods of a generic class to have
8696 generic default methods and others to have polymorphic default methods.
8702 The type variable(s) in the type pattern for a generic method declaration
8703 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:
8707 op {| p :*: q |} (x :*: y) = op (x :: p)
8715 The type patterns in a generic default method must take one of the forms:
8721 where "a" and "b" are type variables. Furthermore, all the type patterns for
8722 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8723 must use the same type variables. So this is illegal:
8727 op {| a :+: b |} (Inl x) = True
8728 op {| p :+: q |} (Inr y) = False
8730 The type patterns must be identical, even in equations for different methods of the class.
8731 So this too is illegal:
8735 op1 {| a :*: b |} (x :*: y) = True
8738 op2 {| p :*: q |} (x :*: y) = False
8740 (The reason for this restriction is that we gather all the equations for a particular type constructor
8741 into a single generic instance declaration.)
8747 A generic method declaration must give a case for each of the three type constructors.
8753 The type for a generic method can be built only from:
8755 <listitem> <para> Function arrows </para> </listitem>
8756 <listitem> <para> Type variables </para> </listitem>
8757 <listitem> <para> Tuples </para> </listitem>
8758 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8760 Here are some example type signatures for generic methods:
8763 op2 :: Bool -> (a,Bool)
8764 op3 :: [Int] -> a -> a
8767 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8771 This restriction is an implementation restriction: we just haven't got around to
8772 implementing the necessary bidirectional maps over arbitrary type constructors.
8773 It would be relatively easy to add specific type constructors, such as Maybe and list,
8774 to the ones that are allowed.</para>
8779 In an instance declaration for a generic class, the idea is that the compiler
8780 will fill in the methods for you, based on the generic templates. However it can only
8785 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8790 No constructor of the instance type has unboxed fields.
8794 (Of course, these things can only arise if you are already using GHC extensions.)
8795 However, you can still give an instance declarations for types which break these rules,
8796 provided you give explicit code to override any generic default methods.
8804 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8805 what the compiler does with generic declarations.
8810 <sect2> <title> Another example </title>
8812 Just to finish with, here's another example I rather like:
8816 nCons {| Unit |} _ = 1
8817 nCons {| a :*: b |} _ = 1
8818 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8821 tag {| Unit |} _ = 1
8822 tag {| a :*: b |} _ = 1
8823 tag {| a :+: b |} (Inl x) = tag x
8824 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8830 <sect1 id="monomorphism">
8831 <title>Control over monomorphism</title>
8833 <para>GHC supports two flags that control the way in which generalisation is
8834 carried out at let and where bindings.
8838 <title>Switching off the dreaded Monomorphism Restriction</title>
8839 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8841 <para>Haskell's monomorphism restriction (see
8842 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8844 of the Haskell Report)
8845 can be completely switched off by
8846 <option>-XNoMonomorphismRestriction</option>.
8851 <title>Monomorphic pattern bindings</title>
8852 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8853 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8855 <para> As an experimental change, we are exploring the possibility of
8856 making pattern bindings monomorphic; that is, not generalised at all.
8857 A pattern binding is a binding whose LHS has no function arguments,
8858 and is not a simple variable. For example:
8860 f x = x -- Not a pattern binding
8861 f = \x -> x -- Not a pattern binding
8862 f :: Int -> Int = \x -> x -- Not a pattern binding
8864 (g,h) = e -- A pattern binding
8865 (f) = e -- A pattern binding
8866 [x] = e -- A pattern binding
8868 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8869 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8878 ;;; Local Variables: ***
8880 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8881 ;;; ispell-local-dictionary: "british" ***
projects / ghc-hetmet.git / blob