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>-XRankNTypes</option>,
82 <option>-XImpredicativeTypes</option>,
83 <option>-XTypeOperators</option>,
84 <option>-XRecursiveDo</option>,
85 <option>-XParallelListComp</option>,
86 <option>-XEmptyDataDecls</option>,
87 <option>-XKindSignatures</option>,
88 <option>-XGeneralizedNewtypeDeriving</option>,
89 <option>-XTypeFamilies</option>.
90 Enabling these options is the <emphasis>only</emphasis>
91 effect of <option>-fglasgow-exts</option>.
92 We are trying to move away from this portmanteau flag,
93 and towards enabling features individually.</para>
97 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
98 <sect1 id="primitives">
99 <title>Unboxed types and primitive operations</title>
101 <para>GHC is built on a raft of primitive data types and operations;
102 "primitive" in the sense that they cannot be defined in Haskell itself.
103 While you really can use this stuff to write fast code,
104 we generally find it a lot less painful, and more satisfying in the
105 long run, to use higher-level language features and libraries. With
106 any luck, the code you write will be optimised to the efficient
107 unboxed version in any case. And if it isn't, we'd like to know
110 <para>All these primitive data types and operations are exported by the
111 library <literal>GHC.Prim</literal>, for which there is
112 <ulink url="../libraries/base/GHC.Prim.html">detailed online documentation</ulink>.
113 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
116 If you want to mention any of the primitive data types or operations in your
117 program, you must first import <literal>GHC.Prim</literal> to bring them
118 into scope. Many of them have names ending in "#", and to mention such
119 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
122 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
123 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
124 we briefly summarise here. </para>
126 <sect2 id="glasgow-unboxed">
131 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
134 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
135 that values of that type are represented by a pointer to a heap
136 object. The representation of a Haskell <literal>Int</literal>, for
137 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
138 type, however, is represented by the value itself, no pointers or heap
139 allocation are involved.
143 Unboxed types correspond to the “raw machine” types you
144 would use in C: <literal>Int#</literal> (long int),
145 <literal>Double#</literal> (double), <literal>Addr#</literal>
146 (void *), etc. The <emphasis>primitive operations</emphasis>
147 (PrimOps) on these types are what you might expect; e.g.,
148 <literal>(+#)</literal> is addition on
149 <literal>Int#</literal>s, and is the machine-addition that we all
150 know and love—usually one instruction.
154 Primitive (unboxed) types cannot be defined in Haskell, and are
155 therefore built into the language and compiler. Primitive types are
156 always unlifted; that is, a value of a primitive type cannot be
157 bottom. We use the convention (but it is only a convention)
158 that primitive types, values, and
159 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
160 For some primitive types we have special syntax for literals, also
161 described in the <link linkend="magic-hash">same section</link>.
165 Primitive values are often represented by a simple bit-pattern, such
166 as <literal>Int#</literal>, <literal>Float#</literal>,
167 <literal>Double#</literal>. But this is not necessarily the case:
168 a primitive value might be represented by a pointer to a
169 heap-allocated object. Examples include
170 <literal>Array#</literal>, the type of primitive arrays. A
171 primitive array is heap-allocated because it is too big a value to fit
172 in a register, and would be too expensive to copy around; in a sense,
173 it is accidental that it is represented by a pointer. If a pointer
174 represents a primitive value, then it really does point to that value:
175 no unevaluated thunks, no indirections…nothing can be at the
176 other end of the pointer than the primitive value.
177 A numerically-intensive program using unboxed types can
178 go a <emphasis>lot</emphasis> faster than its “standard”
179 counterpart—we saw a threefold speedup on one example.
183 There are some restrictions on the use of primitive types:
185 <listitem><para>The main restriction
186 is that you can't pass a primitive value to a polymorphic
187 function or store one in a polymorphic data type. This rules out
188 things like <literal>[Int#]</literal> (i.e. lists of primitive
189 integers). The reason for this restriction is that polymorphic
190 arguments and constructor fields are assumed to be pointers: if an
191 unboxed integer is stored in one of these, the garbage collector would
192 attempt to follow it, leading to unpredictable space leaks. Or a
193 <function>seq</function> operation on the polymorphic component may
194 attempt to dereference the pointer, with disastrous results. Even
195 worse, the unboxed value might be larger than a pointer
196 (<literal>Double#</literal> for instance).
199 <listitem><para> You cannot define a newtype whose representation type
200 (the argument type of the data constructor) is an unboxed type. Thus,
206 <listitem><para> You cannot bind a variable with an unboxed type
207 in a <emphasis>top-level</emphasis> binding.
209 <listitem><para> You cannot bind a variable with an unboxed type
210 in a <emphasis>recursive</emphasis> binding.
212 <listitem><para> You may bind unboxed variables in a (non-recursive,
213 non-top-level) pattern binding, but any such variable causes the entire
215 to become strict. For example:
217 data Foo = Foo Int Int#
219 f x = let (Foo a b, w) = ..rhs.. in ..body..
221 Since <literal>b</literal> has type <literal>Int#</literal>, the entire pattern
223 is strict, and the program behaves as if you had written
225 data Foo = Foo Int Int#
227 f x = case ..rhs.. of { (Foo a b, w) -> ..body.. }
236 <sect2 id="unboxed-tuples">
237 <title>Unboxed Tuples
241 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
242 they're available by default with <option>-fglasgow-exts</option>. An
243 unboxed tuple looks like this:
255 where <literal>e_1..e_n</literal> are expressions of any
256 type (primitive or non-primitive). The type of an unboxed tuple looks
261 Unboxed tuples are used for functions that need to return multiple
262 values, but they avoid the heap allocation normally associated with
263 using fully-fledged tuples. When an unboxed tuple is returned, the
264 components are put directly into registers or on the stack; the
265 unboxed tuple itself does not have a composite representation. Many
266 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
268 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
269 tuples to avoid unnecessary allocation during sequences of operations.
273 There are some pretty stringent restrictions on the use of unboxed tuples:
278 Values of unboxed tuple types are subject to the same restrictions as
279 other unboxed types; i.e. they may not be stored in polymorphic data
280 structures or passed to polymorphic functions.
287 No variable can have an unboxed tuple type, nor may a constructor or function
288 argument have an unboxed tuple type. The following are all illegal:
292 data Foo = Foo (# Int, Int #)
294 f :: (# Int, Int #) -> (# Int, Int #)
297 g :: (# Int, Int #) -> Int
300 h x = let y = (# x,x #) in ...
307 The typical use of unboxed tuples is simply to return multiple values,
308 binding those multiple results with a <literal>case</literal> expression, thus:
310 f x y = (# x+1, y-1 #)
311 g x = case f x x of { (# a, b #) -> a + b }
313 You can have an unboxed tuple in a pattern binding, thus
315 f x = let (# p,q #) = h x in ..body..
317 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
318 the resulting binding is lazy like any other Haskell pattern binding. The
319 above example desugars like this:
321 f x = let t = case h x o f{ (# p,q #) -> (p,q)
326 Indeed, the bindings can even be recursive.
333 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
335 <sect1 id="syntax-extns">
336 <title>Syntactic extensions</title>
338 <sect2 id="unicode-syntax">
339 <title>Unicode syntax</title>
341 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
342 enables Unicode characters to be used to stand for certain ASCII
343 character sequences. The following alternatives are provided:</para>
346 <tgroup cols="2" align="left" colsep="1" rowsep="1">
350 <entry>Unicode alternative</entry>
351 <entry>Code point</entry>
357 <entry><literal>::</literal></entry>
358 <entry>::</entry> <!-- no special char, apparently -->
359 <entry>0x2237</entry>
360 <entry>PROPORTION</entry>
365 <entry><literal>=></literal></entry>
366 <entry>⇒</entry>
367 <entry>0x21D2</entry>
368 <entry>RIGHTWARDS DOUBLE ARROW</entry>
373 <entry><literal>forall</literal></entry>
374 <entry>∀</entry>
375 <entry>0x2200</entry>
376 <entry>FOR ALL</entry>
381 <entry><literal>-></literal></entry>
382 <entry>→</entry>
383 <entry>0x2192</entry>
384 <entry>RIGHTWARDS ARROW</entry>
389 <entry><literal><-</literal></entry>
390 <entry>←</entry>
391 <entry>0x2190</entry>
392 <entry>LEFTWARDS ARROW</entry>
398 <entry>…</entry>
399 <entry>0x22EF</entry>
400 <entry>MIDLINE HORIZONTAL ELLIPSIS</entry>
407 <sect2 id="magic-hash">
408 <title>The magic hash</title>
409 <para>The language extension <option>-XMagicHash</option> allows "#" as a
410 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
411 a valid type constructor or data constructor.</para>
413 <para>The hash sign does not change sematics at all. We tend to use variable
414 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
415 but there is no requirement to do so; they are just plain ordinary variables.
416 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
417 For example, to bring <literal>Int#</literal> into scope you must
418 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
419 the <option>-XMagicHash</option> extension
420 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
421 that is now in scope.</para>
422 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
424 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
425 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
426 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
427 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
428 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
429 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
430 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
431 is a <literal>Word#</literal>. </para> </listitem>
432 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
433 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
438 <sect2 id="new-qualified-operators">
439 <title>New qualified operator syntax</title>
441 <para>A new syntax for referencing qualified operators is
442 planned to be introduced by Haskell', and is enabled in GHC
444 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
445 option. In the new syntax, the prefix form of a qualified
447 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
448 (in Haskell 98 this would
449 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
450 and the infix form is
451 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
452 (in Haskell 98 this would
453 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
456 add x y = Prelude.(+) x y
457 subtract y = (`Prelude.(-)` y)
459 The new form of qualified operators is intended to regularise
460 the syntax by eliminating odd cases
461 like <literal>Prelude..</literal>. For example,
462 when <literal>NewQualifiedOperators</literal> is on, it is possible to
463 write the enumerated sequence <literal>[Monday..]</literal>
464 without spaces, whereas in Haskell 98 this would be a
465 reference to the operator ‘<literal>.</literal>‘
466 from module <literal>Monday</literal>.</para>
468 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
469 98 syntax for qualified operators is not accepted, so this
470 option may cause existing Haskell 98 code to break.</para>
475 <!-- ====================== HIERARCHICAL MODULES ======================= -->
478 <sect2 id="hierarchical-modules">
479 <title>Hierarchical Modules</title>
481 <para>GHC supports a small extension to the syntax of module
482 names: a module name is allowed to contain a dot
483 <literal>‘.’</literal>. This is also known as the
484 “hierarchical module namespace” extension, because
485 it extends the normally flat Haskell module namespace into a
486 more flexible hierarchy of modules.</para>
488 <para>This extension has very little impact on the language
489 itself; modules names are <emphasis>always</emphasis> fully
490 qualified, so you can just think of the fully qualified module
491 name as <quote>the module name</quote>. In particular, this
492 means that the full module name must be given after the
493 <literal>module</literal> keyword at the beginning of the
494 module; for example, the module <literal>A.B.C</literal> must
497 <programlisting>module A.B.C</programlisting>
500 <para>It is a common strategy to use the <literal>as</literal>
501 keyword to save some typing when using qualified names with
502 hierarchical modules. For example:</para>
505 import qualified Control.Monad.ST.Strict as ST
508 <para>For details on how GHC searches for source and interface
509 files in the presence of hierarchical modules, see <xref
510 linkend="search-path"/>.</para>
512 <para>GHC comes with a large collection of libraries arranged
513 hierarchically; see the accompanying <ulink
514 url="../libraries/index.html">library
515 documentation</ulink>. More libraries to install are available
517 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
520 <!-- ====================== PATTERN GUARDS ======================= -->
522 <sect2 id="pattern-guards">
523 <title>Pattern guards</title>
526 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
527 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.)
531 Suppose we have an abstract data type of finite maps, with a
535 lookup :: FiniteMap -> Int -> Maybe Int
538 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
539 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
543 clunky env var1 var2 | ok1 && ok2 = val1 + val2
544 | otherwise = var1 + var2
555 The auxiliary functions are
559 maybeToBool :: Maybe a -> Bool
560 maybeToBool (Just x) = True
561 maybeToBool Nothing = False
563 expectJust :: Maybe a -> a
564 expectJust (Just x) = x
565 expectJust Nothing = error "Unexpected Nothing"
569 What is <function>clunky</function> doing? The guard <literal>ok1 &&
570 ok2</literal> checks that both lookups succeed, using
571 <function>maybeToBool</function> to convert the <function>Maybe</function>
572 types to booleans. The (lazily evaluated) <function>expectJust</function>
573 calls extract the values from the results of the lookups, and binds the
574 returned values to <varname>val1</varname> and <varname>val2</varname>
575 respectively. If either lookup fails, then clunky takes the
576 <literal>otherwise</literal> case and returns the sum of its arguments.
580 This is certainly legal Haskell, but it is a tremendously verbose and
581 un-obvious way to achieve the desired effect. Arguably, a more direct way
582 to write clunky would be to use case expressions:
586 clunky env var1 var2 = case lookup env var1 of
588 Just val1 -> case lookup env var2 of
590 Just val2 -> val1 + val2
596 This is a bit shorter, but hardly better. Of course, we can rewrite any set
597 of pattern-matching, guarded equations as case expressions; that is
598 precisely what the compiler does when compiling equations! The reason that
599 Haskell provides guarded equations is because they allow us to write down
600 the cases we want to consider, one at a time, independently of each other.
601 This structure is hidden in the case version. Two of the right-hand sides
602 are really the same (<function>fail</function>), and the whole expression
603 tends to become more and more indented.
607 Here is how I would write clunky:
612 | Just val1 <- lookup env var1
613 , Just val2 <- lookup env var2
615 ...other equations for clunky...
619 The semantics should be clear enough. The qualifiers are matched in order.
620 For a <literal><-</literal> qualifier, which I call a pattern guard, the
621 right hand side is evaluated and matched against the pattern on the left.
622 If the match fails then the whole guard fails and the next equation is
623 tried. If it succeeds, then the appropriate binding takes place, and the
624 next qualifier is matched, in the augmented environment. Unlike list
625 comprehensions, however, the type of the expression to the right of the
626 <literal><-</literal> is the same as the type of the pattern to its
627 left. The bindings introduced by pattern guards scope over all the
628 remaining guard qualifiers, and over the right hand side of the equation.
632 Just as with list comprehensions, boolean expressions can be freely mixed
633 with among the pattern guards. For example:
644 Haskell's current guards therefore emerge as a special case, in which the
645 qualifier list has just one element, a boolean expression.
649 <!-- ===================== View patterns =================== -->
651 <sect2 id="view-patterns">
656 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
657 More information and examples of view patterns can be found on the
658 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
663 View patterns are somewhat like pattern guards that can be nested inside
664 of other patterns. They are a convenient way of pattern-matching
665 against values of abstract types. For example, in a programming language
666 implementation, we might represent the syntax of the types of the
675 view :: Type -> TypeView
677 -- additional operations for constructing Typ's ...
680 The representation of Typ is held abstract, permitting implementations
681 to use a fancy representation (e.g., hash-consing to manage sharing).
683 Without view patterns, using this signature a little inconvenient:
685 size :: Typ -> Integer
686 size t = case view t of
688 Arrow t1 t2 -> size t1 + size t2
691 It is necessary to iterate the case, rather than using an equational
692 function definition. And the situation is even worse when the matching
693 against <literal>t</literal> is buried deep inside another pattern.
697 View patterns permit calling the view function inside the pattern and
698 matching against the result:
700 size (view -> Unit) = 1
701 size (view -> Arrow t1 t2) = size t1 + size t2
704 That is, we add a new form of pattern, written
705 <replaceable>expression</replaceable> <literal>-></literal>
706 <replaceable>pattern</replaceable> that means "apply the expression to
707 whatever we're trying to match against, and then match the result of
708 that application against the pattern". The expression can be any Haskell
709 expression of function type, and view patterns can be used wherever
714 The semantics of a pattern <literal>(</literal>
715 <replaceable>exp</replaceable> <literal>-></literal>
716 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
722 <para>The variables bound by the view pattern are the variables bound by
723 <replaceable>pat</replaceable>.
727 Any variables in <replaceable>exp</replaceable> are bound occurrences,
728 but variables bound "to the left" in a pattern are in scope. This
729 feature permits, for example, one argument to a function to be used in
730 the view of another argument. For example, the function
731 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
732 written using view patterns as follows:
735 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
736 ...other equations for clunky...
741 More precisely, the scoping rules are:
745 In a single pattern, variables bound by patterns to the left of a view
746 pattern expression are in scope. For example:
748 example :: Maybe ((String -> Integer,Integer), String) -> Bool
749 example Just ((f,_), f -> 4) = True
752 Additionally, in function definitions, variables bound by matching earlier curried
753 arguments may be used in view pattern expressions in later arguments:
755 example :: (String -> Integer) -> String -> Bool
756 example f (f -> 4) = True
758 That is, the scoping is the same as it would be if the curried arguments
759 were collected into a tuple.
765 In mutually recursive bindings, such as <literal>let</literal>,
766 <literal>where</literal>, or the top level, view patterns in one
767 declaration may not mention variables bound by other declarations. That
768 is, each declaration must be self-contained. For example, the following
769 program is not allowed:
776 restriction in the future; the only cost is that type checking patterns
777 would get a little more complicated.)
787 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
788 <replaceable>T1</replaceable> <literal>-></literal>
789 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
790 a <replaceable>T2</replaceable>, then the whole view pattern matches a
791 <replaceable>T1</replaceable>.
794 <listitem><para> Matching: To the equations in Section 3.17.3 of the
795 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
796 Report</ulink>, add the following:
798 case v of { (e -> p) -> e1 ; _ -> e2 }
800 case (e v) of { p -> e1 ; _ -> e2 }
802 That is, to match a variable <replaceable>v</replaceable> against a pattern
803 <literal>(</literal> <replaceable>exp</replaceable>
804 <literal>-></literal> <replaceable>pat</replaceable>
805 <literal>)</literal>, evaluate <literal>(</literal>
806 <replaceable>exp</replaceable> <replaceable> v</replaceable>
807 <literal>)</literal> and match the result against
808 <replaceable>pat</replaceable>.
811 <listitem><para> Efficiency: When the same view function is applied in
812 multiple branches of a function definition or a case expression (e.g.,
813 in <literal>size</literal> above), GHC makes an attempt to collect these
814 applications into a single nested case expression, so that the view
815 function is only applied once. Pattern compilation in GHC follows the
816 matrix algorithm described in Chapter 4 of <ulink
817 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
818 Implementation of Functional Programming Languages</ulink>. When the
819 top rows of the first column of a matrix are all view patterns with the
820 "same" expression, these patterns are transformed into a single nested
821 case. This includes, for example, adjacent view patterns that line up
824 f ((view -> A, p1), p2) = e1
825 f ((view -> B, p3), p4) = e2
829 <para> The current notion of when two view pattern expressions are "the
830 same" is very restricted: it is not even full syntactic equality.
831 However, it does include variables, literals, applications, and tuples;
832 e.g., two instances of <literal>view ("hi", "there")</literal> will be
833 collected. However, the current implementation does not compare up to
834 alpha-equivalence, so two instances of <literal>(x, view x ->
835 y)</literal> will not be coalesced.
845 <!-- ===================== Recursive do-notation =================== -->
847 <sect2 id="mdo-notation">
848 <title>The recursive do-notation
851 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
852 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
853 by Levent Erkok, John Launchbury,
854 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
855 This paper is essential reading for anyone making non-trivial use of mdo-notation,
856 and we do not repeat it here.
859 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
860 that is, the variables bound in a do-expression are visible only in the textually following
861 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
862 group. It turns out that several applications can benefit from recursive bindings in
863 the do-notation, and this extension provides the necessary syntactic support.
866 Here is a simple (yet contrived) example:
869 import Control.Monad.Fix
871 justOnes = mdo xs <- Just (1:xs)
875 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
879 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
882 class Monad m => MonadFix m where
883 mfix :: (a -> m a) -> m a
886 The function <literal>mfix</literal>
887 dictates how the required recursion operation should be performed. For example,
888 <literal>justOnes</literal> desugars as follows:
890 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
892 For full details of the way in which mdo is typechecked and desugared, see
893 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
894 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
897 If recursive bindings are required for a monad,
898 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
899 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
900 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
901 for Haskell's internal state monad (strict and lazy, respectively).
904 Here are some important points in using the recursive-do notation:
907 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
908 than <literal>do</literal>).
912 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
913 <literal>-fglasgow-exts</literal>.
917 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
918 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
919 be distinct (Section 3.3 of the paper).
923 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
924 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
925 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
926 and improve termination (Section 3.2 of the paper).
932 Historical note: The old implementation of the mdo-notation (and most
933 of the existing documents) used the name
934 <literal>MonadRec</literal> for the class and the corresponding library.
935 This name is not supported by GHC.
941 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
943 <sect2 id="parallel-list-comprehensions">
944 <title>Parallel List Comprehensions</title>
945 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
947 <indexterm><primary>parallel list comprehensions</primary>
950 <para>Parallel list comprehensions are a natural extension to list
951 comprehensions. List comprehensions can be thought of as a nice
952 syntax for writing maps and filters. Parallel comprehensions
953 extend this to include the zipWith family.</para>
955 <para>A parallel list comprehension has multiple independent
956 branches of qualifier lists, each separated by a `|' symbol. For
957 example, the following zips together two lists:</para>
960 [ (x, y) | x <- xs | y <- ys ]
963 <para>The behavior of parallel list comprehensions follows that of
964 zip, in that the resulting list will have the same length as the
965 shortest branch.</para>
967 <para>We can define parallel list comprehensions by translation to
968 regular comprehensions. Here's the basic idea:</para>
970 <para>Given a parallel comprehension of the form: </para>
973 [ e | p1 <- e11, p2 <- e12, ...
974 | q1 <- e21, q2 <- e22, ...
979 <para>This will be translated to: </para>
982 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
983 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
988 <para>where `zipN' is the appropriate zip for the given number of
993 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
995 <sect2 id="generalised-list-comprehensions">
996 <title>Generalised (SQL-Like) List Comprehensions</title>
997 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
999 <indexterm><primary>extended list comprehensions</primary>
1001 <indexterm><primary>group</primary></indexterm>
1002 <indexterm><primary>sql</primary></indexterm>
1005 <para>Generalised list comprehensions are a further enhancement to the
1006 list comprehension syntatic sugar to allow operations such as sorting
1007 and grouping which are familiar from SQL. They are fully described in the
1008 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1009 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1010 except that the syntax we use differs slightly from the paper.</para>
1011 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1012 <para>Here is an example:
1014 employees = [ ("Simon", "MS", 80)
1015 , ("Erik", "MS", 100)
1016 , ("Phil", "Ed", 40)
1017 , ("Gordon", "Ed", 45)
1018 , ("Paul", "Yale", 60)]
1020 output = [ (the dept, sum salary)
1021 | (name, dept, salary) <- employees
1022 , then group by dept
1023 , then sortWith by (sum salary)
1026 In this example, the list <literal>output</literal> would take on
1030 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1033 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1034 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1035 function that is exported by <literal>GHC.Exts</literal>.)</para>
1037 <para>There are five new forms of comprehension qualifier,
1038 all introduced by the (existing) keyword <literal>then</literal>:
1046 This statement requires that <literal>f</literal> have the type <literal>
1047 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1048 motivating example, as this form is used to apply <literal>take 5</literal>.
1059 This form is similar to the previous one, but allows you to create a function
1060 which will be passed as the first argument to f. As a consequence f must have
1061 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1062 from the type, this function lets f "project out" some information
1063 from the elements of the list it is transforming.</para>
1065 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1066 is supplied with a function that lets it find out the <literal>sum salary</literal>
1067 for any item in the list comprehension it transforms.</para>
1075 then group by e using f
1078 <para>This is the most general of the grouping-type statements. In this form,
1079 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1080 As with the <literal>then f by e</literal> case above, the first argument
1081 is a function supplied to f by the compiler which lets it compute e on every
1082 element of the list being transformed. However, unlike the non-grouping case,
1083 f additionally partitions the list into a number of sublists: this means that
1084 at every point after this statement, binders occurring before it in the comprehension
1085 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1086 this, let's look at an example:</para>
1089 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1090 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1091 groupRuns f = groupBy (\x y -> f x == f y)
1093 output = [ (the x, y)
1094 | x <- ([1..3] ++ [1..2])
1096 , then group by x using groupRuns ]
1099 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1102 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1105 <para>Note that we have used the <literal>the</literal> function to change the type
1106 of x from a list to its original numeric type. The variable y, in contrast, is left
1107 unchanged from the list form introduced by the grouping.</para>
1117 <para>This form of grouping is essentially the same as the one described above. However,
1118 since no function to use for the grouping has been supplied it will fall back on the
1119 <literal>groupWith</literal> function defined in
1120 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1121 is the form of the group statement that we made use of in the opening example.</para>
1132 <para>With this form of the group statement, f is required to simply have the type
1133 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1134 comprehension so far directly. An example of this form is as follows:</para>
1140 , then group using inits]
1143 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1146 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1154 <!-- ===================== REBINDABLE SYNTAX =================== -->
1156 <sect2 id="rebindable-syntax">
1157 <title>Rebindable syntax and the implicit Prelude import</title>
1159 <para><indexterm><primary>-XNoImplicitPrelude
1160 option</primary></indexterm> GHC normally imports
1161 <filename>Prelude.hi</filename> files for you. If you'd
1162 rather it didn't, then give it a
1163 <option>-XNoImplicitPrelude</option> option. The idea is
1164 that you can then import a Prelude of your own. (But don't
1165 call it <literal>Prelude</literal>; the Haskell module
1166 namespace is flat, and you must not conflict with any
1167 Prelude module.)</para>
1169 <para>Suppose you are importing a Prelude of your own
1170 in order to define your own numeric class
1171 hierarchy. It completely defeats that purpose if the
1172 literal "1" means "<literal>Prelude.fromInteger
1173 1</literal>", which is what the Haskell Report specifies.
1174 So the <option>-XNoImplicitPrelude</option>
1175 flag <emphasis>also</emphasis> causes
1176 the following pieces of built-in syntax to refer to
1177 <emphasis>whatever is in scope</emphasis>, not the Prelude
1181 <para>An integer literal <literal>368</literal> means
1182 "<literal>fromInteger (368::Integer)</literal>", rather than
1183 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1186 <listitem><para>Fractional literals are handed in just the same way,
1187 except that the translation is
1188 <literal>fromRational (3.68::Rational)</literal>.
1191 <listitem><para>The equality test in an overloaded numeric pattern
1192 uses whatever <literal>(==)</literal> is in scope.
1195 <listitem><para>The subtraction operation, and the
1196 greater-than-or-equal test, in <literal>n+k</literal> patterns
1197 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1201 <para>Negation (e.g. "<literal>- (f x)</literal>")
1202 means "<literal>negate (f x)</literal>", both in numeric
1203 patterns, and expressions.
1207 <para>"Do" notation is translated using whatever
1208 functions <literal>(>>=)</literal>,
1209 <literal>(>>)</literal>, and <literal>fail</literal>,
1210 are in scope (not the Prelude
1211 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1212 comprehensions, are unaffected. </para></listitem>
1216 notation (see <xref linkend="arrow-notation"/>)
1217 uses whatever <literal>arr</literal>,
1218 <literal>(>>>)</literal>, <literal>first</literal>,
1219 <literal>app</literal>, <literal>(|||)</literal> and
1220 <literal>loop</literal> functions are in scope. But unlike the
1221 other constructs, the types of these functions must match the
1222 Prelude types very closely. Details are in flux; if you want
1226 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1227 even if that is a little unexpected. For example, the
1228 static semantics of the literal <literal>368</literal>
1229 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1230 <literal>fromInteger</literal> to have any of the types:
1232 fromInteger :: Integer -> Integer
1233 fromInteger :: forall a. Foo a => Integer -> a
1234 fromInteger :: Num a => a -> Integer
1235 fromInteger :: Integer -> Bool -> Bool
1239 <para>Be warned: this is an experimental facility, with
1240 fewer checks than usual. Use <literal>-dcore-lint</literal>
1241 to typecheck the desugared program. If Core Lint is happy
1242 you should be all right.</para>
1246 <sect2 id="postfix-operators">
1247 <title>Postfix operators</title>
1250 The <option>-XPostfixOperators</option> flag enables a small
1251 extension to the syntax of left operator sections, which allows you to
1252 define postfix operators. The extension is this: the left section
1256 is equivalent (from the point of view of both type checking and execution) to the expression
1260 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1261 The strict Haskell 98 interpretation is that the section is equivalent to
1265 That is, the operator must be a function of two arguments. GHC allows it to
1266 take only one argument, and that in turn allows you to write the function
1269 <para>The extension does not extend to the left-hand side of function
1270 definitions; you must define such a function in prefix form.</para>
1274 <sect2 id="disambiguate-fields">
1275 <title>Record field disambiguation</title>
1277 In record construction and record pattern matching
1278 it is entirely unambiguous which field is referred to, even if there are two different
1279 data types in scope with a common field name. For example:
1282 data S = MkS { x :: Int, y :: Bool }
1287 data T = MkT { x :: Int }
1289 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1291 ok2 n = MkT { x = n+1 } -- Unambiguous
1293 bad1 k = k { x = 3 } -- Ambiguous
1294 bad2 k = x k -- Ambiguous
1296 Even though there are two <literal>x</literal>'s in scope,
1297 it is clear that the <literal>x</literal> in the pattern in the
1298 definition of <literal>ok1</literal> can only mean the field
1299 <literal>x</literal> from type <literal>S</literal>. Similarly for
1300 the function <literal>ok2</literal>. However, in the record update
1301 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1302 it is not clear which of the two types is intended.
1305 Haskell 98 regards all four as ambiguous, but with the
1306 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1307 the former two. The rules are precisely the same as those for instance
1308 declarations in Haskell 98, where the method names on the left-hand side
1309 of the method bindings in an instance declaration refer unambiguously
1310 to the method of that class (provided they are in scope at all), even
1311 if there are other variables in scope with the same name.
1312 This reduces the clutter of qualified names when you import two
1313 records from different modules that use the same field name.
1317 <!-- ===================== Record puns =================== -->
1319 <sect2 id="record-puns">
1324 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1328 When using records, it is common to write a pattern that binds a
1329 variable with the same name as a record field, such as:
1332 data C = C {a :: Int}
1338 Record punning permits the variable name to be elided, so one can simply
1345 to mean the same pattern as above. That is, in a record pattern, the
1346 pattern <literal>a</literal> expands into the pattern <literal>a =
1347 a</literal> for the same name <literal>a</literal>.
1351 Note that puns and other patterns can be mixed in the same record:
1353 data C = C {a :: Int, b :: Int}
1354 f (C {a, b = 4}) = a
1356 and that puns can be used wherever record patterns occur (e.g. in
1357 <literal>let</literal> bindings or at the top-level).
1361 Record punning can also be used in an expression, writing, for example,
1367 let a = 1 in C {a = a}
1370 Note that this expansion is purely syntactic, so the record pun
1371 expression refers to the nearest enclosing variable that is spelled the
1372 same as the field name.
1377 <!-- ===================== Record wildcards =================== -->
1379 <sect2 id="record-wildcards">
1380 <title>Record wildcards
1384 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1388 For records with many fields, it can be tiresome to write out each field
1389 individually in a record pattern, as in
1391 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1392 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1397 Record wildcard syntax permits a (<literal>..</literal>) in a record
1398 pattern, where each elided field <literal>f</literal> is replaced by the
1399 pattern <literal>f = f</literal>. For example, the above pattern can be
1402 f (C {a = 1, ..}) = b + c + d
1407 Note that wildcards can be mixed with other patterns, including puns
1408 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1409 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1410 wherever record patterns occur, including in <literal>let</literal>
1411 bindings and at the top-level. For example, the top-level binding
1415 defines <literal>b</literal>, <literal>c</literal>, and
1416 <literal>d</literal>.
1420 Record wildcards can also be used in expressions, writing, for example,
1423 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1429 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1432 Note that this expansion is purely syntactic, so the record wildcard
1433 expression refers to the nearest enclosing variables that are spelled
1434 the same as the omitted field names.
1439 <!-- ===================== Local fixity declarations =================== -->
1441 <sect2 id="local-fixity-declarations">
1442 <title>Local Fixity Declarations
1445 <para>A careful reading of the Haskell 98 Report reveals that fixity
1446 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1447 <literal>infixr</literal>) are permitted to appear inside local bindings
1448 such those introduced by <literal>let</literal> and
1449 <literal>where</literal>. However, the Haskell Report does not specify
1450 the semantics of such bindings very precisely.
1453 <para>In GHC, a fixity declaration may accompany a local binding:
1460 and the fixity declaration applies wherever the binding is in scope.
1461 For example, in a <literal>let</literal>, it applies in the right-hand
1462 sides of other <literal>let</literal>-bindings and the body of the
1463 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1464 expressions (<xref linkend="mdo-notation"/>), the local fixity
1465 declarations of a <literal>let</literal> statement scope over other
1466 statements in the group, just as the bound name does.
1470 Moreover, a local fixity declaration *must* accompany a local binding of
1471 that name: it is not possible to revise the fixity of name bound
1474 let infixr 9 $ in ...
1477 Because local fixity declarations are technically Haskell 98, no flag is
1478 necessary to enable them.
1482 <sect2 id="package-imports">
1483 <title>Package-qualified imports</title>
1485 <para>With the <option>-XPackageImports</option> flag, GHC allows
1486 import declarations to be qualified by the package name that the
1487 module is intended to be imported from. For example:</para>
1490 import "network" Network.Socket
1493 <para>would import the module <literal>Network.Socket</literal> from
1494 the package <literal>network</literal> (any version). This may
1495 be used to disambiguate an import when the same module is
1496 available from multiple packages, or is present in both the
1497 current package being built and an external package.</para>
1499 <para>Note: you probably don't need to use this feature, it was
1500 added mainly so that we can build backwards-compatible versions of
1501 packages when APIs change. It can lead to fragile dependencies in
1502 the common case: modules occasionally move from one package to
1503 another, rendering any package-qualified imports broken.</para>
1506 <sect2 id="syntax-stolen">
1507 <title>Summary of stolen syntax</title>
1509 <para>Turning on an option that enables special syntax
1510 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1511 to compile, perhaps because it uses a variable name which has
1512 become a reserved word. This section lists the syntax that is
1513 "stolen" by language extensions.
1515 notation and nonterminal names from the Haskell 98 lexical syntax
1516 (see the Haskell 98 Report).
1517 We only list syntax changes here that might affect
1518 existing working programs (i.e. "stolen" syntax). Many of these
1519 extensions will also enable new context-free syntax, but in all
1520 cases programs written to use the new syntax would not be
1521 compilable without the option enabled.</para>
1523 <para>There are two classes of special
1528 <para>New reserved words and symbols: character sequences
1529 which are no longer available for use as identifiers in the
1533 <para>Other special syntax: sequences of characters that have
1534 a different meaning when this particular option is turned
1539 The following syntax is stolen:
1544 <literal>forall</literal>
1545 <indexterm><primary><literal>forall</literal></primary></indexterm>
1548 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1549 <option>-XLiberalTypeSynonyms</option>,
1550 <option>-XRank2Types</option>,
1551 <option>-XRankNTypes</option>,
1552 <option>-XPolymorphicComponents</option>,
1553 <option>-XExistentialQuantification</option>
1559 <literal>mdo</literal>
1560 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1563 Stolen by: <option>-XRecursiveDo</option>,
1569 <literal>foreign</literal>
1570 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1573 Stolen by: <option>-XForeignFunctionInterface</option>,
1579 <literal>rec</literal>,
1580 <literal>proc</literal>, <literal>-<</literal>,
1581 <literal>>-</literal>, <literal>-<<</literal>,
1582 <literal>>>-</literal>, and <literal>(|</literal>,
1583 <literal>|)</literal> brackets
1584 <indexterm><primary><literal>proc</literal></primary></indexterm>
1587 Stolen by: <option>-XArrows</option>,
1593 <literal>?<replaceable>varid</replaceable></literal>,
1594 <literal>%<replaceable>varid</replaceable></literal>
1595 <indexterm><primary>implicit parameters</primary></indexterm>
1598 Stolen by: <option>-XImplicitParams</option>,
1604 <literal>[|</literal>,
1605 <literal>[e|</literal>, <literal>[p|</literal>,
1606 <literal>[d|</literal>, <literal>[t|</literal>,
1607 <literal>$(</literal>,
1608 <literal>$<replaceable>varid</replaceable></literal>
1609 <indexterm><primary>Template Haskell</primary></indexterm>
1612 Stolen by: <option>-XTemplateHaskell</option>,
1618 <literal>[:<replaceable>varid</replaceable>|</literal>
1619 <indexterm><primary>quasi-quotation</primary></indexterm>
1622 Stolen by: <option>-XQuasiQuotes</option>,
1628 <replaceable>varid</replaceable>{<literal>#</literal>},
1629 <replaceable>char</replaceable><literal>#</literal>,
1630 <replaceable>string</replaceable><literal>#</literal>,
1631 <replaceable>integer</replaceable><literal>#</literal>,
1632 <replaceable>float</replaceable><literal>#</literal>,
1633 <replaceable>float</replaceable><literal>##</literal>,
1634 <literal>(#</literal>, <literal>#)</literal>,
1637 Stolen by: <option>-XMagicHash</option>,
1646 <!-- TYPE SYSTEM EXTENSIONS -->
1647 <sect1 id="data-type-extensions">
1648 <title>Extensions to data types and type synonyms</title>
1650 <sect2 id="nullary-types">
1651 <title>Data types with no constructors</title>
1653 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1654 a data type with no constructors. For example:</para>
1658 data T a -- T :: * -> *
1661 <para>Syntactically, the declaration lacks the "= constrs" part. The
1662 type can be parameterised over types of any kind, but if the kind is
1663 not <literal>*</literal> then an explicit kind annotation must be used
1664 (see <xref linkend="kinding"/>).</para>
1666 <para>Such data types have only one value, namely bottom.
1667 Nevertheless, they can be useful when defining "phantom types".</para>
1670 <sect2 id="infix-tycons">
1671 <title>Infix type constructors, classes, and type variables</title>
1674 GHC allows type constructors, classes, and type variables to be operators, and
1675 to be written infix, very much like expressions. More specifically:
1678 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1679 The lexical syntax is the same as that for data constructors.
1682 Data type and type-synonym declarations can be written infix, parenthesised
1683 if you want further arguments. E.g.
1685 data a :*: b = Foo a b
1686 type a :+: b = Either a b
1687 class a :=: b where ...
1689 data (a :**: b) x = Baz a b x
1690 type (a :++: b) y = Either (a,b) y
1694 Types, and class constraints, can be written infix. For example
1697 f :: (a :=: b) => a -> b
1701 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1702 The lexical syntax is the same as that for variable operators, excluding "(.)",
1703 "(!)", and "(*)". In a binding position, the operator must be
1704 parenthesised. For example:
1706 type T (+) = Int + Int
1710 liftA2 :: Arrow (~>)
1711 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1717 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1718 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1721 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1722 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1723 sets the fixity for a data constructor and the corresponding type constructor. For example:
1727 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1728 and similarly for <literal>:*:</literal>.
1729 <literal>Int `a` Bool</literal>.
1732 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1739 <sect2 id="type-synonyms">
1740 <title>Liberalised type synonyms</title>
1743 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1744 on individual synonym declarations.
1745 With the <option>-XLiberalTypeSynonyms</option> extension,
1746 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1747 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1750 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1751 in a type synonym, thus:
1753 type Discard a = forall b. Show b => a -> b -> (a, String)
1758 g :: Discard Int -> (Int,String) -- A rank-2 type
1765 If you also use <option>-XUnboxedTuples</option>,
1766 you can write an unboxed tuple in a type synonym:
1768 type Pr = (# Int, Int #)
1776 You can apply a type synonym to a forall type:
1778 type Foo a = a -> a -> Bool
1780 f :: Foo (forall b. b->b)
1782 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1784 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1789 You can apply a type synonym to a partially applied type synonym:
1791 type Generic i o = forall x. i x -> o x
1794 foo :: Generic Id []
1796 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1798 foo :: forall x. x -> [x]
1806 GHC currently does kind checking before expanding synonyms (though even that
1810 After expanding type synonyms, GHC does validity checking on types, looking for
1811 the following mal-formedness which isn't detected simply by kind checking:
1814 Type constructor applied to a type involving for-alls.
1817 Unboxed tuple on left of an arrow.
1820 Partially-applied type synonym.
1824 this will be rejected:
1826 type Pr = (# Int, Int #)
1831 because GHC does not allow unboxed tuples on the left of a function arrow.
1836 <sect2 id="existential-quantification">
1837 <title>Existentially quantified data constructors
1841 The idea of using existential quantification in data type declarations
1842 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1843 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1844 London, 1991). It was later formalised by Laufer and Odersky
1845 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1846 TOPLAS, 16(5), pp1411-1430, 1994).
1847 It's been in Lennart
1848 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1849 proved very useful. Here's the idea. Consider the declaration:
1855 data Foo = forall a. MkFoo a (a -> Bool)
1862 The data type <literal>Foo</literal> has two constructors with types:
1868 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1875 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1876 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1877 For example, the following expression is fine:
1883 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1889 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1890 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1891 isUpper</function> packages a character with a compatible function. These
1892 two things are each of type <literal>Foo</literal> and can be put in a list.
1896 What can we do with a value of type <literal>Foo</literal>?. In particular,
1897 what happens when we pattern-match on <function>MkFoo</function>?
1903 f (MkFoo val fn) = ???
1909 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1910 are compatible, the only (useful) thing we can do with them is to
1911 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1918 f (MkFoo val fn) = fn val
1924 What this allows us to do is to package heterogeneous values
1925 together with a bunch of functions that manipulate them, and then treat
1926 that collection of packages in a uniform manner. You can express
1927 quite a bit of object-oriented-like programming this way.
1930 <sect3 id="existential">
1931 <title>Why existential?
1935 What has this to do with <emphasis>existential</emphasis> quantification?
1936 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1942 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1948 But Haskell programmers can safely think of the ordinary
1949 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1950 adding a new existential quantification construct.
1955 <sect3 id="existential-with-context">
1956 <title>Existentials and type classes</title>
1959 An easy extension is to allow
1960 arbitrary contexts before the constructor. For example:
1966 data Baz = forall a. Eq a => Baz1 a a
1967 | forall b. Show b => Baz2 b (b -> b)
1973 The two constructors have the types you'd expect:
1979 Baz1 :: forall a. Eq a => a -> a -> Baz
1980 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1986 But when pattern matching on <function>Baz1</function> the matched values can be compared
1987 for equality, and when pattern matching on <function>Baz2</function> the first matched
1988 value can be converted to a string (as well as applying the function to it).
1989 So this program is legal:
1996 f (Baz1 p q) | p == q = "Yes"
1998 f (Baz2 v fn) = show (fn v)
2004 Operationally, in a dictionary-passing implementation, the
2005 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2006 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2007 extract it on pattern matching.
2012 <sect3 id="existential-records">
2013 <title>Record Constructors</title>
2016 GHC allows existentials to be used with records syntax as well. For example:
2019 data Counter a = forall self. NewCounter
2021 , _inc :: self -> self
2022 , _display :: self -> IO ()
2026 Here <literal>tag</literal> is a public field, with a well-typed selector
2027 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2028 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2029 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2030 compile-time error. In other words, <emphasis>GHC defines a record selector function
2031 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2032 (This example used an underscore in the fields for which record selectors
2033 will not be defined, but that is only programming style; GHC ignores them.)
2037 To make use of these hidden fields, we need to create some helper functions:
2040 inc :: Counter a -> Counter a
2041 inc (NewCounter x i d t) = NewCounter
2042 { _this = i x, _inc = i, _display = d, tag = t }
2044 display :: Counter a -> IO ()
2045 display NewCounter{ _this = x, _display = d } = d x
2048 Now we can define counters with different underlying implementations:
2051 counterA :: Counter String
2052 counterA = NewCounter
2053 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2055 counterB :: Counter String
2056 counterB = NewCounter
2057 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2060 display (inc counterA) -- prints "1"
2061 display (inc (inc counterB)) -- prints "##"
2064 Record update syntax is supported for existentials (and GADTs):
2066 setTag :: Counter a -> a -> Counter a
2067 setTag obj t = obj{ tag = t }
2069 The rule for record update is this: <emphasis>
2070 the types of the updated fields may
2071 mention only the universally-quantified type variables
2072 of the data constructor. For GADTs, the field may mention only types
2073 that appear as a simple type-variable argument in the constructor's result
2074 type</emphasis>. For example:
2076 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2077 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2078 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2079 -- existentially quantified)
2081 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2082 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2083 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2084 -- type-variable argument in G1's result type)
2092 <title>Restrictions</title>
2095 There are several restrictions on the ways in which existentially-quantified
2096 constructors can be use.
2105 When pattern matching, each pattern match introduces a new,
2106 distinct, type for each existential type variable. These types cannot
2107 be unified with any other type, nor can they escape from the scope of
2108 the pattern match. For example, these fragments are incorrect:
2116 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2117 is the result of <function>f1</function>. One way to see why this is wrong is to
2118 ask what type <function>f1</function> has:
2122 f1 :: Foo -> a -- Weird!
2126 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2131 f1 :: forall a. Foo -> a -- Wrong!
2135 The original program is just plain wrong. Here's another sort of error
2139 f2 (Baz1 a b) (Baz1 p q) = a==q
2143 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2144 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2145 from the two <function>Baz1</function> constructors.
2153 You can't pattern-match on an existentially quantified
2154 constructor in a <literal>let</literal> or <literal>where</literal> group of
2155 bindings. So this is illegal:
2159 f3 x = a==b where { Baz1 a b = x }
2162 Instead, use a <literal>case</literal> expression:
2165 f3 x = case x of Baz1 a b -> a==b
2168 In general, you can only pattern-match
2169 on an existentially-quantified constructor in a <literal>case</literal> expression or
2170 in the patterns of a function definition.
2172 The reason for this restriction is really an implementation one.
2173 Type-checking binding groups is already a nightmare without
2174 existentials complicating the picture. Also an existential pattern
2175 binding at the top level of a module doesn't make sense, because it's
2176 not clear how to prevent the existentially-quantified type "escaping".
2177 So for now, there's a simple-to-state restriction. We'll see how
2185 You can't use existential quantification for <literal>newtype</literal>
2186 declarations. So this is illegal:
2190 newtype T = forall a. Ord a => MkT a
2194 Reason: a value of type <literal>T</literal> must be represented as a
2195 pair of a dictionary for <literal>Ord t</literal> and a value of type
2196 <literal>t</literal>. That contradicts the idea that
2197 <literal>newtype</literal> should have no concrete representation.
2198 You can get just the same efficiency and effect by using
2199 <literal>data</literal> instead of <literal>newtype</literal>. If
2200 there is no overloading involved, then there is more of a case for
2201 allowing an existentially-quantified <literal>newtype</literal>,
2202 because the <literal>data</literal> version does carry an
2203 implementation cost, but single-field existentially quantified
2204 constructors aren't much use. So the simple restriction (no
2205 existential stuff on <literal>newtype</literal>) stands, unless there
2206 are convincing reasons to change it.
2214 You can't use <literal>deriving</literal> to define instances of a
2215 data type with existentially quantified data constructors.
2217 Reason: in most cases it would not make sense. For example:;
2220 data T = forall a. MkT [a] deriving( Eq )
2223 To derive <literal>Eq</literal> in the standard way we would need to have equality
2224 between the single component of two <function>MkT</function> constructors:
2228 (MkT a) == (MkT b) = ???
2231 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2232 It's just about possible to imagine examples in which the derived instance
2233 would make sense, but it seems altogether simpler simply to prohibit such
2234 declarations. Define your own instances!
2245 <!-- ====================== Generalised algebraic data types ======================= -->
2247 <sect2 id="gadt-style">
2248 <title>Declaring data types with explicit constructor signatures</title>
2250 <para>GHC allows you to declare an algebraic data type by
2251 giving the type signatures of constructors explicitly. For example:
2255 Just :: a -> Maybe a
2257 The form is called a "GADT-style declaration"
2258 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2259 can only be declared using this form.</para>
2260 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2261 For example, these two declarations are equivalent:
2263 data Foo = forall a. MkFoo a (a -> Bool)
2264 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2267 <para>Any data type that can be declared in standard Haskell-98 syntax
2268 can also be declared using GADT-style syntax.
2269 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2270 they treat class constraints on the data constructors differently.
2271 Specifically, if the constructor is given a type-class context, that
2272 context is made available by pattern matching. For example:
2275 MkSet :: Eq a => [a] -> Set a
2277 makeSet :: Eq a => [a] -> Set a
2278 makeSet xs = MkSet (nub xs)
2280 insert :: a -> Set a -> Set a
2281 insert a (MkSet as) | a `elem` as = MkSet as
2282 | otherwise = MkSet (a:as)
2284 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2285 gives rise to a <literal>(Eq a)</literal>
2286 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2287 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2288 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2289 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2290 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2291 In the example, the equality dictionary is used to satisfy the equality constraint
2292 generated by the call to <literal>elem</literal>, so that the type of
2293 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2296 For example, one possible application is to reify dictionaries:
2298 data NumInst a where
2299 MkNumInst :: Num a => NumInst a
2301 intInst :: NumInst Int
2304 plus :: NumInst a -> a -> a -> a
2305 plus MkNumInst p q = p + q
2307 Here, a value of type <literal>NumInst a</literal> is equivalent
2308 to an explicit <literal>(Num a)</literal> dictionary.
2311 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2312 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2316 = Num a => MkNumInst (NumInst a)
2318 Notice that, unlike the situation when declaring an existential, there is
2319 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2320 data type's universally quantified type variable <literal>a</literal>.
2321 A constructor may have both universal and existential type variables: for example,
2322 the following two declarations are equivalent:
2325 = forall b. (Num a, Eq b) => MkT1 a b
2327 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2330 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2331 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2332 In Haskell 98 the definition
2334 data Eq a => Set' a = MkSet' [a]
2336 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2337 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2338 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2339 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2340 GHC's behaviour is much more useful, as well as much more intuitive.
2344 The rest of this section gives further details about GADT-style data
2349 The result type of each data constructor must begin with the type constructor being defined.
2350 If the result type of all constructors
2351 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2352 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2353 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2357 As with other type signatures, you can give a single signature for several data constructors.
2358 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2367 The type signature of
2368 each constructor is independent, and is implicitly universally quantified as usual.
2369 Different constructors may have different universally-quantified type variables
2370 and different type-class constraints.
2371 For example, this is fine:
2374 T1 :: Eq b => b -> T b
2375 T2 :: (Show c, Ix c) => c -> [c] -> T c
2380 Unlike a Haskell-98-style
2381 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2382 have no scope. Indeed, one can write a kind signature instead:
2384 data Set :: * -> * where ...
2386 or even a mixture of the two:
2388 data Foo a :: (* -> *) -> * where ...
2390 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2393 data Foo a (b :: * -> *) where ...
2399 You can use strictness annotations, in the obvious places
2400 in the constructor type:
2403 Lit :: !Int -> Term Int
2404 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2405 Pair :: Term a -> Term b -> Term (a,b)
2410 You can use a <literal>deriving</literal> clause on a GADT-style data type
2411 declaration. For example, these two declarations are equivalent
2413 data Maybe1 a where {
2414 Nothing1 :: Maybe1 a ;
2415 Just1 :: a -> Maybe1 a
2416 } deriving( Eq, Ord )
2418 data Maybe2 a = Nothing2 | Just2 a
2424 You can use record syntax on a GADT-style data type declaration:
2428 Adult { name :: String, children :: [Person] } :: Person
2429 Child { name :: String } :: Person
2431 As usual, for every constructor that has a field <literal>f</literal>, the type of
2432 field <literal>f</literal> must be the same (modulo alpha conversion).
2435 At the moment, record updates are not yet possible with GADT-style declarations,
2436 so support is limited to record construction, selection and pattern matching.
2439 aPerson = Adult { name = "Fred", children = [] }
2441 shortName :: Person -> Bool
2442 hasChildren (Adult { children = kids }) = not (null kids)
2443 hasChildren (Child {}) = False
2448 As in the case of existentials declared using the Haskell-98-like record syntax
2449 (<xref linkend="existential-records"/>),
2450 record-selector functions are generated only for those fields that have well-typed
2452 Here is the example of that section, in GADT-style syntax:
2454 data Counter a where
2455 NewCounter { _this :: self
2456 , _inc :: self -> self
2457 , _display :: self -> IO ()
2462 As before, only one selector function is generated here, that for <literal>tag</literal>.
2463 Nevertheless, you can still use all the field names in pattern matching and record construction.
2465 </itemizedlist></para>
2469 <title>Generalised Algebraic Data Types (GADTs)</title>
2471 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2472 by allowing constructors to have richer return types. Here is an example:
2475 Lit :: Int -> Term Int
2476 Succ :: Term Int -> Term Int
2477 IsZero :: Term Int -> Term Bool
2478 If :: Term Bool -> Term a -> Term a -> Term a
2479 Pair :: Term a -> Term b -> Term (a,b)
2481 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2482 case with ordinary data types. This generality allows us to
2483 write a well-typed <literal>eval</literal> function
2484 for these <literal>Terms</literal>:
2488 eval (Succ t) = 1 + eval t
2489 eval (IsZero t) = eval t == 0
2490 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2491 eval (Pair e1 e2) = (eval e1, eval e2)
2493 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2494 For example, in the right hand side of the equation
2499 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2500 A precise specification of the type rules is beyond what this user manual aspires to,
2501 but the design closely follows that described in
2503 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2504 unification-based type inference for GADTs</ulink>,
2506 The general principle is this: <emphasis>type refinement is only carried out
2507 based on user-supplied type annotations</emphasis>.
2508 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2509 and lots of obscure error messages will
2510 occur. However, the refinement is quite general. For example, if we had:
2512 eval :: Term a -> a -> a
2513 eval (Lit i) j = i+j
2515 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2516 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2517 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2520 These and many other examples are given in papers by Hongwei Xi, and
2521 Tim Sheard. There is a longer introduction
2522 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2524 <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
2525 may use different notation to that implemented in GHC.
2528 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2529 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2532 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2533 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2534 The result type of each constructor must begin with the type constructor being defined,
2535 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2536 For example, in the <literal>Term</literal> data
2537 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2538 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2543 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2544 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2545 whose result type is not just <literal>T a b</literal>.
2549 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2550 an ordinary data type.
2554 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2558 Lit { val :: Int } :: Term Int
2559 Succ { num :: Term Int } :: Term Int
2560 Pred { num :: Term Int } :: Term Int
2561 IsZero { arg :: Term Int } :: Term Bool
2562 Pair { arg1 :: Term a
2565 If { cnd :: Term Bool
2570 However, for GADTs there is the following additional constraint:
2571 every constructor that has a field <literal>f</literal> must have
2572 the same result type (modulo alpha conversion)
2573 Hence, in the above example, we cannot merge the <literal>num</literal>
2574 and <literal>arg</literal> fields above into a
2575 single name. Although their field types are both <literal>Term Int</literal>,
2576 their selector functions actually have different types:
2579 num :: Term Int -> Term Int
2580 arg :: Term Bool -> Term Int
2585 When pattern-matching against data constructors drawn from a GADT,
2586 for example in a <literal>case</literal> expression, the following rules apply:
2588 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2589 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2590 <listitem><para>The type of any free variable mentioned in any of
2591 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2593 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2594 way to ensure that a variable a rigid type is to give it a type signature.
2595 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2596 Simple unification-based type inference for GADTs
2597 </ulink>. The criteria implemented by GHC are given in the Appendix.
2607 <!-- ====================== End of Generalised algebraic data types ======================= -->
2609 <sect1 id="deriving">
2610 <title>Extensions to the "deriving" mechanism</title>
2612 <sect2 id="deriving-inferred">
2613 <title>Inferred context for deriving clauses</title>
2616 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2619 data T0 f a = MkT0 a deriving( Eq )
2620 data T1 f a = MkT1 (f a) deriving( Eq )
2621 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2623 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2625 instance Eq a => Eq (T0 f a) where ...
2626 instance Eq (f a) => Eq (T1 f a) where ...
2627 instance Eq (f (f a)) => Eq (T2 f a) where ...
2629 The first of these is obviously fine. The second is still fine, although less obviously.
2630 The third is not Haskell 98, and risks losing termination of instances.
2633 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2634 each constraint in the inferred instance context must consist only of type variables,
2635 with no repetitions.
2638 This rule is applied regardless of flags. If you want a more exotic context, you can write
2639 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2643 <sect2 id="stand-alone-deriving">
2644 <title>Stand-alone deriving declarations</title>
2647 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2649 data Foo a = Bar a | Baz String
2651 deriving instance Eq a => Eq (Foo a)
2653 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2654 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2655 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2656 exactly as you would in an ordinary instance declaration.
2657 (In contrast the context is inferred in a <literal>deriving</literal> clause
2658 attached to a data type declaration.)
2660 A <literal>deriving instance</literal> declaration
2661 must obey the same rules concerning form and termination as ordinary instance declarations,
2662 controlled by the same flags; see <xref linkend="instance-decls"/>.
2665 Unlike a <literal>deriving</literal>
2666 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2667 than the data type (assuming you also use
2668 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2671 data Foo a = Bar a | Baz String
2673 deriving instance Eq a => Eq (Foo [a])
2674 deriving instance Eq a => Eq (Foo (Maybe a))
2676 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2677 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2680 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2681 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2684 newtype Foo a = MkFoo (State Int a)
2686 deriving instance MonadState Int Foo
2688 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2689 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2695 <sect2 id="deriving-typeable">
2696 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2699 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2700 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2701 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2702 classes <literal>Eq</literal>, <literal>Ord</literal>,
2703 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2706 GHC extends this list with several more classes that may be automatically derived:
2708 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2709 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2710 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2712 <para>An instance of <literal>Typeable</literal> can only be derived if the
2713 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2714 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2716 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2717 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2719 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2720 are used, and only <literal>Typeable1</literal> up to
2721 <literal>Typeable7</literal> are provided in the library.)
2722 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2723 class, whose kind suits that of the data type constructor, and
2724 then writing the data type instance by hand.
2728 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2729 the class <literal>Functor</literal>,
2730 defined in <literal>GHC.Base</literal>.
2733 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2734 the class <literal>Foldable</literal>,
2735 defined in <literal>Data.Foldable</literal>.
2738 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2739 the class <literal>Traversable</literal>,
2740 defined in <literal>Data.Traversable</literal>.
2743 In each case the appropriate class must be in scope before it
2744 can be mentioned in the <literal>deriving</literal> clause.
2748 <sect2 id="newtype-deriving">
2749 <title>Generalised derived instances for newtypes</title>
2752 When you define an abstract type using <literal>newtype</literal>, you may want
2753 the new type to inherit some instances from its representation. In
2754 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2755 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2756 other classes you have to write an explicit instance declaration. For
2757 example, if you define
2760 newtype Dollars = Dollars Int
2763 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2764 explicitly define an instance of <literal>Num</literal>:
2767 instance Num Dollars where
2768 Dollars a + Dollars b = Dollars (a+b)
2771 All the instance does is apply and remove the <literal>newtype</literal>
2772 constructor. It is particularly galling that, since the constructor
2773 doesn't appear at run-time, this instance declaration defines a
2774 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2775 dictionary, only slower!
2779 <sect3> <title> Generalising the deriving clause </title>
2781 GHC now permits such instances to be derived instead,
2782 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2785 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2788 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2789 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2790 derives an instance declaration of the form
2793 instance Num Int => Num Dollars
2796 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2800 We can also derive instances of constructor classes in a similar
2801 way. For example, suppose we have implemented state and failure monad
2802 transformers, such that
2805 instance Monad m => Monad (State s m)
2806 instance Monad m => Monad (Failure m)
2808 In Haskell 98, we can define a parsing monad by
2810 type Parser tok m a = State [tok] (Failure m) a
2813 which is automatically a monad thanks to the instance declarations
2814 above. With the extension, we can make the parser type abstract,
2815 without needing to write an instance of class <literal>Monad</literal>, via
2818 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2821 In this case the derived instance declaration is of the form
2823 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2826 Notice that, since <literal>Monad</literal> is a constructor class, the
2827 instance is a <emphasis>partial application</emphasis> of the new type, not the
2828 entire left hand side. We can imagine that the type declaration is
2829 "eta-converted" to generate the context of the instance
2834 We can even derive instances of multi-parameter classes, provided the
2835 newtype is the last class parameter. In this case, a ``partial
2836 application'' of the class appears in the <literal>deriving</literal>
2837 clause. For example, given the class
2840 class StateMonad s m | m -> s where ...
2841 instance Monad m => StateMonad s (State s m) where ...
2843 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2845 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2846 deriving (Monad, StateMonad [tok])
2849 The derived instance is obtained by completing the application of the
2850 class to the new type:
2853 instance StateMonad [tok] (State [tok] (Failure m)) =>
2854 StateMonad [tok] (Parser tok m)
2859 As a result of this extension, all derived instances in newtype
2860 declarations are treated uniformly (and implemented just by reusing
2861 the dictionary for the representation type), <emphasis>except</emphasis>
2862 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2863 the newtype and its representation.
2867 <sect3> <title> A more precise specification </title>
2869 Derived instance declarations are constructed as follows. Consider the
2870 declaration (after expansion of any type synonyms)
2873 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2879 The <literal>ci</literal> are partial applications of
2880 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2881 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2884 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2887 The type <literal>t</literal> is an arbitrary type.
2890 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2891 nor in the <literal>ci</literal>, and
2894 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2895 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2896 should not "look through" the type or its constructor. You can still
2897 derive these classes for a newtype, but it happens in the usual way, not
2898 via this new mechanism.
2901 Then, for each <literal>ci</literal>, the derived instance
2904 instance ci t => ci (T v1...vk)
2906 As an example which does <emphasis>not</emphasis> work, consider
2908 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2910 Here we cannot derive the instance
2912 instance Monad (State s m) => Monad (NonMonad m)
2915 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2916 and so cannot be "eta-converted" away. It is a good thing that this
2917 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2918 not, in fact, a monad --- for the same reason. Try defining
2919 <literal>>>=</literal> with the correct type: you won't be able to.
2923 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2924 important, since we can only derive instances for the last one. If the
2925 <literal>StateMonad</literal> class above were instead defined as
2928 class StateMonad m s | m -> s where ...
2931 then we would not have been able to derive an instance for the
2932 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2933 classes usually have one "main" parameter for which deriving new
2934 instances is most interesting.
2936 <para>Lastly, all of this applies only for classes other than
2937 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2938 and <literal>Data</literal>, for which the built-in derivation applies (section
2939 4.3.3. of the Haskell Report).
2940 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2941 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2942 the standard method is used or the one described here.)
2949 <!-- TYPE SYSTEM EXTENSIONS -->
2950 <sect1 id="type-class-extensions">
2951 <title>Class and instances declarations</title>
2953 <sect2 id="multi-param-type-classes">
2954 <title>Class declarations</title>
2957 This section, and the next one, documents GHC's type-class extensions.
2958 There's lots of background in the paper <ulink
2959 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2960 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2961 Jones, Erik Meijer).
2964 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2968 <title>Multi-parameter type classes</title>
2970 Multi-parameter type classes are permitted. For example:
2974 class Collection c a where
2975 union :: c a -> c a -> c a
2983 <title>The superclasses of a class declaration</title>
2986 There are no restrictions on the context in a class declaration
2987 (which introduces superclasses), except that the class hierarchy must
2988 be acyclic. So these class declarations are OK:
2992 class Functor (m k) => FiniteMap m k where
2995 class (Monad m, Monad (t m)) => Transform t m where
2996 lift :: m a -> (t m) a
3002 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3003 of "acyclic" involves only the superclass relationships. For example,
3009 op :: D b => a -> b -> b
3012 class C a => D a where { ... }
3016 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3017 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3018 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3025 <sect3 id="class-method-types">
3026 <title>Class method types</title>
3029 Haskell 98 prohibits class method types to mention constraints on the
3030 class type variable, thus:
3033 fromList :: [a] -> s a
3034 elem :: Eq a => a -> s a -> Bool
3036 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3037 contains the constraint <literal>Eq a</literal>, constrains only the
3038 class type variable (in this case <literal>a</literal>).
3039 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3046 <sect2 id="functional-dependencies">
3047 <title>Functional dependencies
3050 <para> Functional dependencies are implemented as described by Mark Jones
3051 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3052 In Proceedings of the 9th European Symposium on Programming,
3053 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3057 Functional dependencies are introduced by a vertical bar in the syntax of a
3058 class declaration; e.g.
3060 class (Monad m) => MonadState s m | m -> s where ...
3062 class Foo a b c | a b -> c where ...
3064 There should be more documentation, but there isn't (yet). Yell if you need it.
3067 <sect3><title>Rules for functional dependencies </title>
3069 In a class declaration, all of the class type variables must be reachable (in the sense
3070 mentioned in <xref linkend="type-restrictions"/>)
3071 from the free variables of each method type.
3075 class Coll s a where
3077 insert :: s -> a -> s
3080 is not OK, because the type of <literal>empty</literal> doesn't mention
3081 <literal>a</literal>. Functional dependencies can make the type variable
3084 class Coll s a | s -> a where
3086 insert :: s -> a -> s
3089 Alternatively <literal>Coll</literal> might be rewritten
3092 class Coll s a where
3094 insert :: s a -> a -> s a
3098 which makes the connection between the type of a collection of
3099 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3100 Occasionally this really doesn't work, in which case you can split the
3108 class CollE s => Coll s a where
3109 insert :: s -> a -> s
3116 <title>Background on functional dependencies</title>
3118 <para>The following description of the motivation and use of functional dependencies is taken
3119 from the Hugs user manual, reproduced here (with minor changes) by kind
3120 permission of Mark Jones.
3123 Consider the following class, intended as part of a
3124 library for collection types:
3126 class Collects e ce where
3128 insert :: e -> ce -> ce
3129 member :: e -> ce -> Bool
3131 The type variable e used here represents the element type, while ce is the type
3132 of the container itself. Within this framework, we might want to define
3133 instances of this class for lists or characteristic functions (both of which
3134 can be used to represent collections of any equality type), bit sets (which can
3135 be used to represent collections of characters), or hash tables (which can be
3136 used to represent any collection whose elements have a hash function). Omitting
3137 standard implementation details, this would lead to the following declarations:
3139 instance Eq e => Collects e [e] where ...
3140 instance Eq e => Collects e (e -> Bool) where ...
3141 instance Collects Char BitSet where ...
3142 instance (Hashable e, Collects a ce)
3143 => Collects e (Array Int ce) where ...
3145 All this looks quite promising; we have a class and a range of interesting
3146 implementations. Unfortunately, there are some serious problems with the class
3147 declaration. First, the empty function has an ambiguous type:
3149 empty :: Collects e ce => ce
3151 By "ambiguous" we mean that there is a type variable e that appears on the left
3152 of the <literal>=></literal> symbol, but not on the right. The problem with
3153 this is that, according to the theoretical foundations of Haskell overloading,
3154 we cannot guarantee a well-defined semantics for any term with an ambiguous
3158 We can sidestep this specific problem by removing the empty member from the
3159 class declaration. However, although the remaining members, insert and member,
3160 do not have ambiguous types, we still run into problems when we try to use
3161 them. For example, consider the following two functions:
3163 f x y = insert x . insert y
3166 for which GHC infers the following types:
3168 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3169 g :: (Collects Bool c, Collects Char c) => c -> c
3171 Notice that the type for f allows the two parameters x and y to be assigned
3172 different types, even though it attempts to insert each of the two values, one
3173 after the other, into the same collection. If we're trying to model collections
3174 that contain only one type of value, then this is clearly an inaccurate
3175 type. Worse still, the definition for g is accepted, without causing a type
3176 error. As a result, the error in this code will not be flagged at the point
3177 where it appears. Instead, it will show up only when we try to use g, which
3178 might even be in a different module.
3181 <sect4><title>An attempt to use constructor classes</title>
3184 Faced with the problems described above, some Haskell programmers might be
3185 tempted to use something like the following version of the class declaration:
3187 class Collects e c where
3189 insert :: e -> c e -> c e
3190 member :: e -> c e -> Bool
3192 The key difference here is that we abstract over the type constructor c that is
3193 used to form the collection type c e, and not over that collection type itself,
3194 represented by ce in the original class declaration. This avoids the immediate
3195 problems that we mentioned above: empty has type <literal>Collects e c => c
3196 e</literal>, which is not ambiguous.
3199 The function f from the previous section has a more accurate type:
3201 f :: (Collects e c) => e -> e -> c e -> c e
3203 The function g from the previous section is now rejected with a type error as
3204 we would hope because the type of f does not allow the two arguments to have
3206 This, then, is an example of a multiple parameter class that does actually work
3207 quite well in practice, without ambiguity problems.
3208 There is, however, a catch. This version of the Collects class is nowhere near
3209 as general as the original class seemed to be: only one of the four instances
3210 for <literal>Collects</literal>
3211 given above can be used with this version of Collects because only one of
3212 them---the instance for lists---has a collection type that can be written in
3213 the form c e, for some type constructor c, and element type e.
3217 <sect4><title>Adding functional dependencies</title>
3220 To get a more useful version of the Collects class, Hugs provides a mechanism
3221 that allows programmers to specify dependencies between the parameters of a
3222 multiple parameter class (For readers with an interest in theoretical
3223 foundations and previous work: The use of dependency information can be seen
3224 both as a generalization of the proposal for `parametric type classes' that was
3225 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3226 later framework for "improvement" of qualified types. The
3227 underlying ideas are also discussed in a more theoretical and abstract setting
3228 in a manuscript [implparam], where they are identified as one point in a
3229 general design space for systems of implicit parameterization.).
3231 To start with an abstract example, consider a declaration such as:
3233 class C a b where ...
3235 which tells us simply that C can be thought of as a binary relation on types
3236 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3237 included in the definition of classes to add information about dependencies
3238 between parameters, as in the following examples:
3240 class D a b | a -> b where ...
3241 class E a b | a -> b, b -> a where ...
3243 The notation <literal>a -> b</literal> used here between the | and where
3244 symbols --- not to be
3245 confused with a function type --- indicates that the a parameter uniquely
3246 determines the b parameter, and might be read as "a determines b." Thus D is
3247 not just a relation, but actually a (partial) function. Similarly, from the two
3248 dependencies that are included in the definition of E, we can see that E
3249 represents a (partial) one-one mapping between types.
3252 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3253 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3254 m>=0, meaning that the y parameters are uniquely determined by the x
3255 parameters. Spaces can be used as separators if more than one variable appears
3256 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3257 annotated with multiple dependencies using commas as separators, as in the
3258 definition of E above. Some dependencies that we can write in this notation are
3259 redundant, and will be rejected because they don't serve any useful
3260 purpose, and may instead indicate an error in the program. Examples of
3261 dependencies like this include <literal>a -> a </literal>,
3262 <literal>a -> a a </literal>,
3263 <literal>a -> </literal>, etc. There can also be
3264 some redundancy if multiple dependencies are given, as in
3265 <literal>a->b</literal>,
3266 <literal>b->c </literal>, <literal>a->c </literal>, and
3267 in which some subset implies the remaining dependencies. Examples like this are
3268 not treated as errors. Note that dependencies appear only in class
3269 declarations, and not in any other part of the language. In particular, the
3270 syntax for instance declarations, class constraints, and types is completely
3274 By including dependencies in a class declaration, we provide a mechanism for
3275 the programmer to specify each multiple parameter class more precisely. The
3276 compiler, on the other hand, is responsible for ensuring that the set of
3277 instances that are in scope at any given point in the program is consistent
3278 with any declared dependencies. For example, the following pair of instance
3279 declarations cannot appear together in the same scope because they violate the
3280 dependency for D, even though either one on its own would be acceptable:
3282 instance D Bool Int where ...
3283 instance D Bool Char where ...
3285 Note also that the following declaration is not allowed, even by itself:
3287 instance D [a] b where ...
3289 The problem here is that this instance would allow one particular choice of [a]
3290 to be associated with more than one choice for b, which contradicts the
3291 dependency specified in the definition of D. More generally, this means that,
3292 in any instance of the form:
3294 instance D t s where ...
3296 for some particular types t and s, the only variables that can appear in s are
3297 the ones that appear in t, and hence, if the type t is known, then s will be
3298 uniquely determined.
3301 The benefit of including dependency information is that it allows us to define
3302 more general multiple parameter classes, without ambiguity problems, and with
3303 the benefit of more accurate types. To illustrate this, we return to the
3304 collection class example, and annotate the original definition of <literal>Collects</literal>
3305 with a simple dependency:
3307 class Collects e ce | ce -> e where
3309 insert :: e -> ce -> ce
3310 member :: e -> ce -> Bool
3312 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3313 determined by the type of the collection ce. Note that both parameters of
3314 Collects are of kind *; there are no constructor classes here. Note too that
3315 all of the instances of Collects that we gave earlier can be used
3316 together with this new definition.
3319 What about the ambiguity problems that we encountered with the original
3320 definition? The empty function still has type Collects e ce => ce, but it is no
3321 longer necessary to regard that as an ambiguous type: Although the variable e
3322 does not appear on the right of the => symbol, the dependency for class
3323 Collects tells us that it is uniquely determined by ce, which does appear on
3324 the right of the => symbol. Hence the context in which empty is used can still
3325 give enough information to determine types for both ce and e, without
3326 ambiguity. More generally, we need only regard a type as ambiguous if it
3327 contains a variable on the left of the => that is not uniquely determined
3328 (either directly or indirectly) by the variables on the right.
3331 Dependencies also help to produce more accurate types for user defined
3332 functions, and hence to provide earlier detection of errors, and less cluttered
3333 types for programmers to work with. Recall the previous definition for a
3336 f x y = insert x y = insert x . insert y
3338 for which we originally obtained a type:
3340 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3342 Given the dependency information that we have for Collects, however, we can
3343 deduce that a and b must be equal because they both appear as the second
3344 parameter in a Collects constraint with the same first parameter c. Hence we
3345 can infer a shorter and more accurate type for f:
3347 f :: (Collects a c) => a -> a -> c -> c
3349 In a similar way, the earlier definition of g will now be flagged as a type error.
3352 Although we have given only a few examples here, it should be clear that the
3353 addition of dependency information can help to make multiple parameter classes
3354 more useful in practice, avoiding ambiguity problems, and allowing more general
3355 sets of instance declarations.
3361 <sect2 id="instance-decls">
3362 <title>Instance declarations</title>
3364 <para>An instance declaration has the form
3366 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 ...
3368 The part before the "<literal>=></literal>" is the
3369 <emphasis>context</emphasis>, while the part after the
3370 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3373 <sect3 id="flexible-instance-head">
3374 <title>Relaxed rules for the instance head</title>
3377 In Haskell 98 the head of an instance declaration
3378 must be of the form <literal>C (T a1 ... an)</literal>, where
3379 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3380 and the <literal>a1 ... an</literal> are distinct type variables.
3381 GHC relaxes these rules in two ways.
3385 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3386 declaration to mention arbitrary nested types.
3387 For example, this becomes a legal instance declaration
3389 instance C (Maybe Int) where ...
3391 See also the <link linkend="instance-overlap">rules on overlap</link>.
3394 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3395 synonyms. As always, using a type synonym is just shorthand for
3396 writing the RHS of the type synonym definition. For example:
3400 type Point = (Int,Int)
3401 instance C Point where ...
3402 instance C [Point] where ...
3406 is legal. However, if you added
3410 instance C (Int,Int) where ...
3414 as well, then the compiler will complain about the overlapping
3415 (actually, identical) instance declarations. As always, type synonyms
3416 must be fully applied. You cannot, for example, write:
3420 instance Monad P where ...
3428 <sect3 id="instance-rules">
3429 <title>Relaxed rules for instance contexts</title>
3431 <para>In Haskell 98, the assertions in the context of the instance declaration
3432 must be of the form <literal>C a</literal> where <literal>a</literal>
3433 is a type variable that occurs in the head.
3437 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3438 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3439 With this flag the context of the instance declaration can each consist of arbitrary
3440 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3444 The Paterson Conditions: for each assertion in the context
3446 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3447 <listitem><para>The assertion has fewer constructors and variables (taken together
3448 and counting repetitions) than the head</para></listitem>
3452 <listitem><para>The Coverage Condition. For each functional dependency,
3453 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3454 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3455 every type variable in
3456 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3457 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3458 substitution mapping each type variable in the class declaration to the
3459 corresponding type in the instance declaration.
3462 These restrictions ensure that context reduction terminates: each reduction
3463 step makes the problem smaller by at least one
3464 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3465 if you give the <option>-XUndecidableInstances</option>
3466 flag (<xref linkend="undecidable-instances"/>).
3467 You can find lots of background material about the reason for these
3468 restrictions in the paper <ulink
3469 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3470 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3473 For example, these are OK:
3475 instance C Int [a] -- Multiple parameters
3476 instance Eq (S [a]) -- Structured type in head
3478 -- Repeated type variable in head
3479 instance C4 a a => C4 [a] [a]
3480 instance Stateful (ST s) (MutVar s)
3482 -- Head can consist of type variables only
3484 instance (Eq a, Show b) => C2 a b
3486 -- Non-type variables in context
3487 instance Show (s a) => Show (Sized s a)
3488 instance C2 Int a => C3 Bool [a]
3489 instance C2 Int a => C3 [a] b
3493 -- Context assertion no smaller than head
3494 instance C a => C a where ...
3495 -- (C b b) has more more occurrences of b than the head
3496 instance C b b => Foo [b] where ...
3501 The same restrictions apply to instances generated by
3502 <literal>deriving</literal> clauses. Thus the following is accepted:
3504 data MinHeap h a = H a (h a)
3507 because the derived instance
3509 instance (Show a, Show (h a)) => Show (MinHeap h a)
3511 conforms to the above rules.
3515 A useful idiom permitted by the above rules is as follows.
3516 If one allows overlapping instance declarations then it's quite
3517 convenient to have a "default instance" declaration that applies if
3518 something more specific does not:
3526 <sect3 id="undecidable-instances">
3527 <title>Undecidable instances</title>
3530 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3531 For example, sometimes you might want to use the following to get the
3532 effect of a "class synonym":
3534 class (C1 a, C2 a, C3 a) => C a where { }
3536 instance (C1 a, C2 a, C3 a) => C a where { }
3538 This allows you to write shorter signatures:
3544 f :: (C1 a, C2 a, C3 a) => ...
3546 The restrictions on functional dependencies (<xref
3547 linkend="functional-dependencies"/>) are particularly troublesome.
3548 It is tempting to introduce type variables in the context that do not appear in
3549 the head, something that is excluded by the normal rules. For example:
3551 class HasConverter a b | a -> b where
3554 data Foo a = MkFoo a
3556 instance (HasConverter a b,Show b) => Show (Foo a) where
3557 show (MkFoo value) = show (convert value)
3559 This is dangerous territory, however. Here, for example, is a program that would make the
3564 instance F [a] [[a]]
3565 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3567 Similarly, it can be tempting to lift the coverage condition:
3569 class Mul a b c | a b -> c where
3570 (.*.) :: a -> b -> c
3572 instance Mul Int Int Int where (.*.) = (*)
3573 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3574 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3576 The third instance declaration does not obey the coverage condition;
3577 and indeed the (somewhat strange) definition:
3579 f = \ b x y -> if b then x .*. [y] else y
3581 makes instance inference go into a loop, because it requires the constraint
3582 <literal>(Mul a [b] b)</literal>.
3585 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3586 the experimental flag <option>-XUndecidableInstances</option>
3587 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3588 both the Paterson Conditions and the Coverage Condition
3589 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3590 fixed-depth recursion stack. If you exceed the stack depth you get a
3591 sort of backtrace, and the opportunity to increase the stack depth
3592 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3598 <sect3 id="instance-overlap">
3599 <title>Overlapping instances</title>
3601 In general, <emphasis>GHC requires that that it be unambiguous which instance
3603 should be used to resolve a type-class constraint</emphasis>. This behaviour
3604 can be modified by two flags: <option>-XOverlappingInstances</option>
3605 <indexterm><primary>-XOverlappingInstances
3606 </primary></indexterm>
3607 and <option>-XIncoherentInstances</option>
3608 <indexterm><primary>-XIncoherentInstances
3609 </primary></indexterm>, as this section discusses. Both these
3610 flags are dynamic flags, and can be set on a per-module basis, using
3611 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3613 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3614 it tries to match every instance declaration against the
3616 by instantiating the head of the instance declaration. For example, consider
3619 instance context1 => C Int a where ... -- (A)
3620 instance context2 => C a Bool where ... -- (B)
3621 instance context3 => C Int [a] where ... -- (C)
3622 instance context4 => C Int [Int] where ... -- (D)
3624 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3625 but (C) and (D) do not. When matching, GHC takes
3626 no account of the context of the instance declaration
3627 (<literal>context1</literal> etc).
3628 GHC's default behaviour is that <emphasis>exactly one instance must match the
3629 constraint it is trying to resolve</emphasis>.
3630 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3631 including both declarations (A) and (B), say); an error is only reported if a
3632 particular constraint matches more than one.
3636 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3637 more than one instance to match, provided there is a most specific one. For
3638 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3639 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3640 most-specific match, the program is rejected.
3643 However, GHC is conservative about committing to an overlapping instance. For example:
3648 Suppose that from the RHS of <literal>f</literal> we get the constraint
3649 <literal>C Int [b]</literal>. But
3650 GHC does not commit to instance (C), because in a particular
3651 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3652 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3653 So GHC rejects the program.
3654 (If you add the flag <option>-XIncoherentInstances</option>,
3655 GHC will instead pick (C), without complaining about
3656 the problem of subsequent instantiations.)
3659 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3660 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3661 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3662 it instead. In this case, GHC will refrain from
3663 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3664 as before) but, rather than rejecting the program, it will infer the type
3666 f :: C Int [b] => [b] -> [b]
3668 That postpones the question of which instance to pick to the
3669 call site for <literal>f</literal>
3670 by which time more is known about the type <literal>b</literal>.
3671 You can write this type signature yourself if you use the
3672 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3676 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3680 instance Foo [b] where
3683 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3684 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3685 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3686 declaration. The solution is to postpone the choice by adding the constraint to the context
3687 of the instance declaration, thus:
3689 instance C Int [b] => Foo [b] where
3692 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3695 The willingness to be overlapped or incoherent is a property of
3696 the <emphasis>instance declaration</emphasis> itself, controlled by the
3697 presence or otherwise of the <option>-XOverlappingInstances</option>
3698 and <option>-XIncoherentInstances</option> flags when that module is
3699 being defined. Neither flag is required in a module that imports and uses the
3700 instance declaration. Specifically, during the lookup process:
3703 An instance declaration is ignored during the lookup process if (a) a more specific
3704 match is found, and (b) the instance declaration was compiled with
3705 <option>-XOverlappingInstances</option>. The flag setting for the
3706 more-specific instance does not matter.
3709 Suppose an instance declaration does not match the constraint being looked up, but
3710 does unify with it, so that it might match when the constraint is further
3711 instantiated. Usually GHC will regard this as a reason for not committing to
3712 some other constraint. But if the instance declaration was compiled with
3713 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3714 check for that declaration.
3717 These rules make it possible for a library author to design a library that relies on
3718 overlapping instances without the library client having to know.
3721 If an instance declaration is compiled without
3722 <option>-XOverlappingInstances</option>,
3723 then that instance can never be overlapped. This could perhaps be
3724 inconvenient. Perhaps the rule should instead say that the
3725 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3726 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3727 at a usage site should be permitted regardless of how the instance declarations
3728 are compiled, if the <option>-XOverlappingInstances</option> flag is
3729 used at the usage site. (Mind you, the exact usage site can occasionally be
3730 hard to pin down.) We are interested to receive feedback on these points.
3732 <para>The <option>-XIncoherentInstances</option> flag implies the
3733 <option>-XOverlappingInstances</option> flag, but not vice versa.
3741 <sect2 id="overloaded-strings">
3742 <title>Overloaded string literals
3746 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3747 string literal has type <literal>String</literal>, but with overloaded string
3748 literals enabled (with <literal>-XOverloadedStrings</literal>)
3749 a string literal has type <literal>(IsString a) => a</literal>.
3752 This means that the usual string syntax can be used, e.g., for packed strings
3753 and other variations of string like types. String literals behave very much
3754 like integer literals, i.e., they can be used in both expressions and patterns.
3755 If used in a pattern the literal with be replaced by an equality test, in the same
3756 way as an integer literal is.
3759 The class <literal>IsString</literal> is defined as:
3761 class IsString a where
3762 fromString :: String -> a
3764 The only predefined instance is the obvious one to make strings work as usual:
3766 instance IsString [Char] where
3769 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3770 it explicitly (for example, to give an instance declaration for it), you can import it
3771 from module <literal>GHC.Exts</literal>.
3774 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3778 Each type in a default declaration must be an
3779 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3783 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3784 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3785 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3786 <emphasis>or</emphasis> <literal>IsString</literal>.
3795 import GHC.Exts( IsString(..) )
3797 newtype MyString = MyString String deriving (Eq, Show)
3798 instance IsString MyString where
3799 fromString = MyString
3801 greet :: MyString -> MyString
3802 greet "hello" = "world"
3806 print $ greet "hello"
3807 print $ greet "fool"
3811 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3812 to work since it gets translated into an equality comparison.
3818 <sect1 id="type-families">
3819 <title>Type families</title>
3822 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3823 facilitate type-level
3824 programming. Type families are a generalisation of <firstterm>associated
3825 data types</firstterm>
3826 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3827 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3828 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3829 Symposium on Principles of Programming Languages (POPL'05)”, pages
3830 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3831 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3832 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3834 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3835 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3836 themselves are described in the paper “<ulink
3837 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3838 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3840 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3841 13th ACM SIGPLAN International Conference on Functional
3842 Programming”, ACM Press, pages 51-62, 2008. Type families
3843 essentially provide type-indexed data types and named functions on types,
3844 which are useful for generic programming and highly parameterised library
3845 interfaces as well as interfaces with enhanced static information, much like
3846 dependent types. They might also be regarded as an alternative to functional
3847 dependencies, but provide a more functional style of type-level programming
3848 than the relational style of functional dependencies.
3851 Indexed type families, or type families for short, are type constructors that
3852 represent sets of types. Set members are denoted by supplying the type family
3853 constructor with type parameters, which are called <firstterm>type
3854 indices</firstterm>. The
3855 difference between vanilla parametrised type constructors and family
3856 constructors is much like between parametrically polymorphic functions and
3857 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3858 behave the same at all type instances, whereas class methods can change their
3859 behaviour in dependence on the class type parameters. Similarly, vanilla type
3860 constructors imply the same data representation for all type instances, but
3861 family constructors can have varying representation types for varying type
3865 Indexed type families come in two flavours: <firstterm>data
3866 families</firstterm> and <firstterm>type synonym
3867 families</firstterm>. They are the indexed family variants of algebraic
3868 data types and type synonyms, respectively. The instances of data families
3869 can be data types and newtypes.
3872 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3873 Additional information on the use of type families in GHC is available on
3874 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3875 Haskell wiki page on type families</ulink>.
3878 <sect2 id="data-families">
3879 <title>Data families</title>
3882 Data families appear in two flavours: (1) they can be defined on the
3884 or (2) they can appear inside type classes (in which case they are known as
3885 associated types). The former is the more general variant, as it lacks the
3886 requirement for the type-indexes to coincide with the class
3887 parameters. However, the latter can lead to more clearly structured code and
3888 compiler warnings if some type instances were - possibly accidentally -
3889 omitted. In the following, we always discuss the general toplevel form first
3890 and then cover the additional constraints placed on associated types.
3893 <sect3 id="data-family-declarations">
3894 <title>Data family declarations</title>
3897 Indexed data families are introduced by a signature, such as
3899 data family GMap k :: * -> *
3901 The special <literal>family</literal> distinguishes family from standard
3902 data declarations. The result kind annotation is optional and, as
3903 usual, defaults to <literal>*</literal> if omitted. An example is
3907 Named arguments can also be given explicit kind signatures if needed.
3909 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3910 declarations] named arguments are entirely optional, so that we can
3911 declare <literal>Array</literal> alternatively with
3913 data family Array :: * -> *
3917 <sect4 id="assoc-data-family-decl">
3918 <title>Associated data family declarations</title>
3920 When a data family is declared as part of a type class, we drop
3921 the <literal>family</literal> special. The <literal>GMap</literal>
3922 declaration takes the following form
3924 class GMapKey k where
3925 data GMap k :: * -> *
3928 In contrast to toplevel declarations, named arguments must be used for
3929 all type parameters that are to be used as type-indexes. Moreover,
3930 the argument names must be class parameters. Each class parameter may
3931 only be used at most once per associated type, but some may be omitted
3932 and they may be in an order other than in the class head. Hence, the
3933 following contrived example is admissible:
3942 <sect3 id="data-instance-declarations">
3943 <title>Data instance declarations</title>
3946 Instance declarations of data and newtype families are very similar to
3947 standard data and newtype declarations. The only two differences are
3948 that the keyword <literal>data</literal> or <literal>newtype</literal>
3949 is followed by <literal>instance</literal> and that some or all of the
3950 type arguments can be non-variable types, but may not contain forall
3951 types or type synonym families. However, data families are generally
3952 allowed in type parameters, and type synonyms are allowed as long as
3953 they are fully applied and expand to a type that is itself admissible -
3954 exactly as this is required for occurrences of type synonyms in class
3955 instance parameters. For example, the <literal>Either</literal>
3956 instance for <literal>GMap</literal> is
3958 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3960 In this example, the declaration has only one variant. In general, it
3964 Data and newtype instance declarations are only permitted when an
3965 appropriate family declaration is in scope - just as a class instance declaratoin
3966 requires the class declaration to be visible. Moreover, each instance
3967 declaration has to conform to the kind determined by its family
3968 declaration. This implies that the number of parameters of an instance
3969 declaration matches the arity determined by the kind of the family.
3972 A data family instance declaration can use the full exprssiveness of
3973 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
3975 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
3976 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
3977 use either <literal>data</literal> or <literal>newtype</literal>. For example:
3980 data instance T Int = T1 Int | T2 Bool
3981 newtype instance T Char = TC Bool
3984 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
3985 and indeed can define a GADT. For example:
3988 data instance G [a] b where
3989 G1 :: c -> G [Int] b
3993 <listitem><para> You can use a <literal>deriving</literal> clause on a
3994 <literal>data instance</literal> or <literal>newtype instance</literal>
4001 Even if type families are defined as toplevel declarations, functions
4002 that perform different computations for different family instances may still
4003 need to be defined as methods of type classes. In particular, the
4004 following is not possible:
4007 data instance T Int = A
4008 data instance T Char = B
4010 foo A = 1 -- WRONG: These two equations together...
4011 foo B = 2 -- ...will produce a type error.
4013 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4017 instance Foo Int where
4019 instance Foo Char where
4022 (Given the functionality provided by GADTs (Generalised Algebraic Data
4023 Types), it might seem as if a definition, such as the above, should be
4024 feasible. However, type families are - in contrast to GADTs - are
4025 <emphasis>open;</emphasis> i.e., new instances can always be added,
4027 modules. Supporting pattern matching across different data instances
4028 would require a form of extensible case construct.)
4031 <sect4 id="assoc-data-inst">
4032 <title>Associated data instances</title>
4034 When an associated data family instance is declared within a type
4035 class instance, we drop the <literal>instance</literal> keyword in the
4036 family instance. So, the <literal>Either</literal> instance
4037 for <literal>GMap</literal> becomes:
4039 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4040 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4043 The most important point about associated family instances is that the
4044 type indexes corresponding to class parameters must be identical to
4045 the type given in the instance head; here this is the first argument
4046 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4047 which coincides with the only class parameter. Any parameters to the
4048 family constructor that do not correspond to class parameters, need to
4049 be variables in every instance; here this is the
4050 variable <literal>v</literal>.
4053 Instances for an associated family can only appear as part of
4054 instances declarations of the class in which the family was declared -
4055 just as with the equations of the methods of a class. Also in
4056 correspondence to how methods are handled, declarations of associated
4057 types can be omitted in class instances. If an associated family
4058 instance is omitted, the corresponding instance type is not inhabited;
4059 i.e., only diverging expressions, such
4060 as <literal>undefined</literal>, can assume the type.
4064 <sect4 id="scoping-class-params">
4065 <title>Scoping of class parameters</title>
4067 In the case of multi-parameter type classes, the visibility of class
4068 parameters in the right-hand side of associated family instances
4069 depends <emphasis>solely</emphasis> on the parameters of the data
4070 family. As an example, consider the simple class declaration
4075 Only one of the two class parameters is a parameter to the data
4076 family. Hence, the following instance declaration is invalid:
4078 instance C [c] d where
4079 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4081 Here, the right-hand side of the data instance mentions the type
4082 variable <literal>d</literal> that does not occur in its left-hand
4083 side. We cannot admit such data instances as they would compromise
4088 <sect4 id="family-class-inst">
4089 <title>Type class instances of family instances</title>
4091 Type class instances of instances of data families can be defined as
4092 usual, and in particular data instance declarations can
4093 have <literal>deriving</literal> clauses. For example, we can write
4095 data GMap () v = GMapUnit (Maybe v)
4098 which implicitly defines an instance of the form
4100 instance Show v => Show (GMap () v) where ...
4104 Note that class instances are always for
4105 particular <emphasis>instances</emphasis> of a data family and never
4106 for an entire family as a whole. This is for essentially the same
4107 reasons that we cannot define a toplevel function that performs
4108 pattern matching on the data constructors
4109 of <emphasis>different</emphasis> instances of a single type family.
4110 It would require a form of extensible case construct.
4114 <sect4 id="data-family-overlap">
4115 <title>Overlap of data instances</title>
4117 The instance declarations of a data family used in a single program
4118 may not overlap at all, independent of whether they are associated or
4119 not. In contrast to type class instances, this is not only a matter
4120 of consistency, but one of type safety.
4126 <sect3 id="data-family-import-export">
4127 <title>Import and export</title>
4130 The association of data constructors with type families is more dynamic
4131 than that is the case with standard data and newtype declarations. In
4132 the standard case, the notation <literal>T(..)</literal> in an import or
4133 export list denotes the type constructor and all the data constructors
4134 introduced in its declaration. However, a family declaration never
4135 introduces any data constructors; instead, data constructors are
4136 introduced by family instances. As a result, which data constructors
4137 are associated with a type family depends on the currently visible
4138 instance declarations for that family. Consequently, an import or
4139 export item of the form <literal>T(..)</literal> denotes the family
4140 constructor and all currently visible data constructors - in the case of
4141 an export item, these may be either imported or defined in the current
4142 module. The treatment of import and export items that explicitly list
4143 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4147 <sect4 id="data-family-impexp-assoc">
4148 <title>Associated families</title>
4150 As expected, an import or export item of the
4151 form <literal>C(..)</literal> denotes all of the class' methods and
4152 associated types. However, when associated types are explicitly
4153 listed as subitems of a class, we need some new syntax, as uppercase
4154 identifiers as subitems are usually data constructors, not type
4155 constructors. To clarify that we denote types here, each associated
4156 type name needs to be prefixed by the keyword <literal>type</literal>.
4157 So for example, when explicitly listing the components of
4158 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4159 GMap, empty, lookup, insert)</literal>.
4163 <sect4 id="data-family-impexp-examples">
4164 <title>Examples</title>
4166 Assuming our running <literal>GMapKey</literal> class example, let us
4167 look at some export lists and their meaning:
4170 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4171 just the class name.</para>
4174 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4175 Exports the class, the associated type <literal>GMap</literal>
4177 functions <literal>empty</literal>, <literal>lookup</literal>,
4178 and <literal>insert</literal>. None of the data constructors is
4182 <para><literal>module GMap (GMapKey(..), GMap(..))
4183 where...</literal>: As before, but also exports all the data
4184 constructors <literal>GMapInt</literal>,
4185 <literal>GMapChar</literal>,
4186 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4187 and <literal>GMapUnit</literal>.</para>
4190 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4191 GMap(..)) where...</literal>: As before.</para>
4194 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4195 where...</literal>: As before.</para>
4200 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4201 both the class <literal>GMapKey</literal> as well as its associated
4202 type <literal>GMap</literal>. However, you cannot
4203 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4204 sub-component specifications cannot be nested. To
4205 specify <literal>GMap</literal>'s data constructors, you have to list
4210 <sect4 id="data-family-impexp-instances">
4211 <title>Instances</title>
4213 Family instances are implicitly exported, just like class instances.
4214 However, this applies only to the heads of instances, not to the data
4215 constructors an instance defines.
4223 <sect2 id="synonym-families">
4224 <title>Synonym families</title>
4227 Type families appear in two flavours: (1) they can be defined on the
4228 toplevel or (2) they can appear inside type classes (in which case they
4229 are known as associated type synonyms). The former is the more general
4230 variant, as it lacks the requirement for the type-indexes to coincide with
4231 the class parameters. However, the latter can lead to more clearly
4232 structured code and compiler warnings if some type instances were -
4233 possibly accidentally - omitted. In the following, we always discuss the
4234 general toplevel form first and then cover the additional constraints
4235 placed on associated types.
4238 <sect3 id="type-family-declarations">
4239 <title>Type family declarations</title>
4242 Indexed type families are introduced by a signature, such as
4244 type family Elem c :: *
4246 The special <literal>family</literal> distinguishes family from standard
4247 type declarations. The result kind annotation is optional and, as
4248 usual, defaults to <literal>*</literal> if omitted. An example is
4252 Parameters can also be given explicit kind signatures if needed. We
4253 call the number of parameters in a type family declaration, the family's
4254 arity, and all applications of a type family must be fully saturated
4255 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4256 and it implies that the kind of a type family is not sufficient to
4257 determine a family's arity, and hence in general, also insufficient to
4258 determine whether a type family application is well formed. As an
4259 example, consider the following declaration:
4261 type family F a b :: * -> * -- F's arity is 2,
4262 -- although it's overall kind is * -> * -> * -> *
4264 Given this declaration the following are examples of well-formed and
4267 F Char [Int] -- OK! Kind: * -> *
4268 F Char [Int] Bool -- OK! Kind: *
4269 F IO Bool -- WRONG: kind mismatch in the first argument
4270 F Bool -- WRONG: unsaturated application
4274 <sect4 id="assoc-type-family-decl">
4275 <title>Associated type family declarations</title>
4277 When a type family is declared as part of a type class, we drop
4278 the <literal>family</literal> special. The <literal>Elem</literal>
4279 declaration takes the following form
4281 class Collects ce where
4285 The argument names of the type family must be class parameters. Each
4286 class parameter may only be used at most once per associated type, but
4287 some may be omitted and they may be in an order other than in the
4288 class head. Hence, the following contrived example is admissible:
4293 These rules are exactly as for associated data families.
4298 <sect3 id="type-instance-declarations">
4299 <title>Type instance declarations</title>
4301 Instance declarations of type families are very similar to standard type
4302 synonym declarations. The only two differences are that the
4303 keyword <literal>type</literal> is followed
4304 by <literal>instance</literal> and that some or all of the type
4305 arguments can be non-variable types, but may not contain forall types or
4306 type synonym families. However, data families are generally allowed, and
4307 type synonyms are allowed as long as they are fully applied and expand
4308 to a type that is admissible - these are the exact same requirements as
4309 for data instances. For example, the <literal>[e]</literal> instance
4310 for <literal>Elem</literal> is
4312 type instance Elem [e] = e
4316 Type family instance declarations are only legitimate when an
4317 appropriate family declaration is in scope - just like class instances
4318 require the class declaration to be visible. Moreover, each instance
4319 declaration has to conform to the kind determined by its family
4320 declaration, and the number of type parameters in an instance
4321 declaration must match the number of type parameters in the family
4322 declaration. Finally, the right-hand side of a type instance must be a
4323 monotype (i.e., it may not include foralls) and after the expansion of
4324 all saturated vanilla type synonyms, no synonyms, except family synonyms
4325 may remain. Here are some examples of admissible and illegal type
4328 type family F a :: *
4329 type instance F [Int] = Int -- OK!
4330 type instance F String = Char -- OK!
4331 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4332 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4333 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4335 type family G a b :: * -> *
4336 type instance G Int = (,) -- WRONG: must be two type parameters
4337 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4341 <sect4 id="assoc-type-instance">
4342 <title>Associated type instance declarations</title>
4344 When an associated family instance is declared within a type class
4345 instance, we drop the <literal>instance</literal> keyword in the family
4346 instance. So, the <literal>[e]</literal> instance
4347 for <literal>Elem</literal> becomes:
4349 instance (Eq (Elem [e])) => Collects ([e]) where
4353 The most important point about associated family instances is that the
4354 type indexes corresponding to class parameters must be identical to the
4355 type given in the instance head; here this is <literal>[e]</literal>,
4356 which coincides with the only class parameter.
4359 Instances for an associated family can only appear as part of instances
4360 declarations of the class in which the family was declared - just as
4361 with the equations of the methods of a class. Also in correspondence to
4362 how methods are handled, declarations of associated types can be omitted
4363 in class instances. If an associated family instance is omitted, the
4364 corresponding instance type is not inhabited; i.e., only diverging
4365 expressions, such as <literal>undefined</literal>, can assume the type.
4369 <sect4 id="type-family-overlap">
4370 <title>Overlap of type synonym instances</title>
4372 The instance declarations of a type family used in a single program
4373 may only overlap if the right-hand sides of the overlapping instances
4374 coincide for the overlapping types. More formally, two instance
4375 declarations overlap if there is a substitution that makes the
4376 left-hand sides of the instances syntactically the same. Whenever
4377 that is the case, the right-hand sides of the instances must also be
4378 syntactically equal under the same substitution. This condition is
4379 independent of whether the type family is associated or not, and it is
4380 not only a matter of consistency, but one of type safety.
4383 Here are two example to illustrate the condition under which overlap
4386 type instance F (a, Int) = [a]
4387 type instance F (Int, b) = [b] -- overlap permitted
4389 type instance G (a, Int) = [a]
4390 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4395 <sect4 id="type-family-decidability">
4396 <title>Decidability of type synonym instances</title>
4398 In order to guarantee that type inference in the presence of type
4399 families decidable, we need to place a number of additional
4400 restrictions on the formation of type instance declarations (c.f.,
4401 Definition 5 (Relaxed Conditions) of “<ulink
4402 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4403 Checking with Open Type Functions</ulink>”). Instance
4404 declarations have the general form
4406 type instance F t1 .. tn = t
4408 where we require that for every type family application <literal>(G s1
4409 .. sm)</literal> in <literal>t</literal>,
4412 <para><literal>s1 .. sm</literal> do not contain any type family
4413 constructors,</para>
4416 <para>the total number of symbols (data type constructors and type
4417 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4418 in <literal>t1 .. tn</literal>, and</para>
4421 <para>for every type
4422 variable <literal>a</literal>, <literal>a</literal> occurs
4423 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4424 .. tn</literal>.</para>
4427 These restrictions are easily verified and ensure termination of type
4428 inference. However, they are not sufficient to guarantee completeness
4429 of type inference in the presence of, so called, ''loopy equalities'',
4430 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4431 a type variable is underneath a family application and data
4432 constructor application - see the above mentioned paper for details.
4435 If the option <option>-XUndecidableInstances</option> is passed to the
4436 compiler, the above restrictions are not enforced and it is on the
4437 programmer to ensure termination of the normalisation of type families
4438 during type inference.
4443 <sect3 id-="equality-constraints">
4444 <title>Equality constraints</title>
4446 Type context can include equality constraints of the form <literal>t1 ~
4447 t2</literal>, which denote that the types <literal>t1</literal>
4448 and <literal>t2</literal> need to be the same. In the presence of type
4449 families, whether two types are equal cannot generally be decided
4450 locally. Hence, the contexts of function signatures may include
4451 equality constraints, as in the following example:
4453 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4455 where we require that the element type of <literal>c1</literal>
4456 and <literal>c2</literal> are the same. In general, the
4457 types <literal>t1</literal> and <literal>t2</literal> of an equality
4458 constraint may be arbitrary monotypes; i.e., they may not contain any
4459 quantifiers, independent of whether higher-rank types are otherwise
4463 Equality constraints can also appear in class and instance contexts.
4464 The former enable a simple translation of programs using functional
4465 dependencies into programs using family synonyms instead. The general
4466 idea is to rewrite a class declaration of the form
4468 class C a b | a -> b
4472 class (F a ~ b) => C a b where
4475 That is, we represent every functional dependency (FD) <literal>a1 .. an
4476 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4477 superclass context equality <literal>F a1 .. an ~ b</literal>,
4478 essentially giving a name to the functional dependency. In class
4479 instances, we define the type instances of FD families in accordance
4480 with the class head. Method signatures are not affected by that
4484 NB: Equalities in superclass contexts are not fully implemented in
4489 <sect3 id-="ty-fams-in-instances">
4490 <title>Type families and instance declarations</title>
4491 <para>Type families require us to extend the rules for
4492 the form of instance heads, which are given
4493 in <xref linkend="flexible-instance-head"/>.
4496 <listitem><para>Data type families may appear in an instance head</para></listitem>
4497 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4499 The reason for the latter restriction is that there is no way to check for. Consider
4502 type instance F Bool = Int
4509 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4510 The situation is especially bad because the type instance for <literal>F Bool</literal>
4511 might be in another module, or even in a module that is not yet written.
4518 <sect1 id="other-type-extensions">
4519 <title>Other type system extensions</title>
4521 <sect2 id="type-restrictions">
4522 <title>Type signatures</title>
4524 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4526 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4527 that the type-class constraints in a type signature must have the
4528 form <emphasis>(class type-variable)</emphasis> or
4529 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4530 With <option>-XFlexibleContexts</option>
4531 these type signatures are perfectly OK
4534 g :: Ord (T a ()) => ...
4538 GHC imposes the following restrictions on the constraints in a type signature.
4542 forall tv1..tvn (c1, ...,cn) => type
4545 (Here, we write the "foralls" explicitly, although the Haskell source
4546 language omits them; in Haskell 98, all the free type variables of an
4547 explicit source-language type signature are universally quantified,
4548 except for the class type variables in a class declaration. However,
4549 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4558 <emphasis>Each universally quantified type variable
4559 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4561 A type variable <literal>a</literal> is "reachable" if it appears
4562 in the same constraint as either a type variable free in
4563 <literal>type</literal>, or another reachable type variable.
4564 A value with a type that does not obey
4565 this reachability restriction cannot be used without introducing
4566 ambiguity; that is why the type is rejected.
4567 Here, for example, is an illegal type:
4571 forall a. Eq a => Int
4575 When a value with this type was used, the constraint <literal>Eq tv</literal>
4576 would be introduced where <literal>tv</literal> is a fresh type variable, and
4577 (in the dictionary-translation implementation) the value would be
4578 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4579 can never know which instance of <literal>Eq</literal> to use because we never
4580 get any more information about <literal>tv</literal>.
4584 that the reachability condition is weaker than saying that <literal>a</literal> is
4585 functionally dependent on a type variable free in
4586 <literal>type</literal> (see <xref
4587 linkend="functional-dependencies"/>). The reason for this is there
4588 might be a "hidden" dependency, in a superclass perhaps. So
4589 "reachable" is a conservative approximation to "functionally dependent".
4590 For example, consider:
4592 class C a b | a -> b where ...
4593 class C a b => D a b where ...
4594 f :: forall a b. D a b => a -> a
4596 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4597 but that is not immediately apparent from <literal>f</literal>'s type.
4603 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4604 universally quantified type variables <literal>tvi</literal></emphasis>.
4606 For example, this type is OK because <literal>C a b</literal> mentions the
4607 universally quantified type variable <literal>b</literal>:
4611 forall a. C a b => burble
4615 The next type is illegal because the constraint <literal>Eq b</literal> does not
4616 mention <literal>a</literal>:
4620 forall a. Eq b => burble
4624 The reason for this restriction is milder than the other one. The
4625 excluded types are never useful or necessary (because the offending
4626 context doesn't need to be witnessed at this point; it can be floated
4627 out). Furthermore, floating them out increases sharing. Lastly,
4628 excluding them is a conservative choice; it leaves a patch of
4629 territory free in case we need it later.
4643 <sect2 id="implicit-parameters">
4644 <title>Implicit parameters</title>
4646 <para> Implicit parameters are implemented as described in
4647 "Implicit parameters: dynamic scoping with static types",
4648 J Lewis, MB Shields, E Meijer, J Launchbury,
4649 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4653 <para>(Most of the following, still rather incomplete, documentation is
4654 due to Jeff Lewis.)</para>
4656 <para>Implicit parameter support is enabled with the option
4657 <option>-XImplicitParams</option>.</para>
4660 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4661 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4662 context. In Haskell, all variables are statically bound. Dynamic
4663 binding of variables is a notion that goes back to Lisp, but was later
4664 discarded in more modern incarnations, such as Scheme. Dynamic binding
4665 can be very confusing in an untyped language, and unfortunately, typed
4666 languages, in particular Hindley-Milner typed languages like Haskell,
4667 only support static scoping of variables.
4670 However, by a simple extension to the type class system of Haskell, we
4671 can support dynamic binding. Basically, we express the use of a
4672 dynamically bound variable as a constraint on the type. These
4673 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4674 function uses a dynamically-bound variable <literal>?x</literal>
4675 of type <literal>t'</literal>". For
4676 example, the following expresses the type of a sort function,
4677 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4679 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4681 The dynamic binding constraints are just a new form of predicate in the type class system.
4684 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4685 where <literal>x</literal> is
4686 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4687 Use of this construct also introduces a new
4688 dynamic-binding constraint in the type of the expression.
4689 For example, the following definition
4690 shows how we can define an implicitly parameterized sort function in
4691 terms of an explicitly parameterized <literal>sortBy</literal> function:
4693 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4695 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4701 <title>Implicit-parameter type constraints</title>
4703 Dynamic binding constraints behave just like other type class
4704 constraints in that they are automatically propagated. Thus, when a
4705 function is used, its implicit parameters are inherited by the
4706 function that called it. For example, our <literal>sort</literal> function might be used
4707 to pick out the least value in a list:
4709 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4710 least xs = head (sort xs)
4712 Without lifting a finger, the <literal>?cmp</literal> parameter is
4713 propagated to become a parameter of <literal>least</literal> as well. With explicit
4714 parameters, the default is that parameters must always be explicit
4715 propagated. With implicit parameters, the default is to always
4719 An implicit-parameter type constraint differs from other type class constraints in the
4720 following way: All uses of a particular implicit parameter must have
4721 the same type. This means that the type of <literal>(?x, ?x)</literal>
4722 is <literal>(?x::a) => (a,a)</literal>, and not
4723 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4727 <para> You can't have an implicit parameter in the context of a class or instance
4728 declaration. For example, both these declarations are illegal:
4730 class (?x::Int) => C a where ...
4731 instance (?x::a) => Foo [a] where ...
4733 Reason: exactly which implicit parameter you pick up depends on exactly where
4734 you invoke a function. But the ``invocation'' of instance declarations is done
4735 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4736 Easiest thing is to outlaw the offending types.</para>
4738 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4740 f :: (?x :: [a]) => Int -> Int
4743 g :: (Read a, Show a) => String -> String
4746 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4747 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4748 quite unambiguous, and fixes the type <literal>a</literal>.
4753 <title>Implicit-parameter bindings</title>
4756 An implicit parameter is <emphasis>bound</emphasis> using the standard
4757 <literal>let</literal> or <literal>where</literal> binding forms.
4758 For example, we define the <literal>min</literal> function by binding
4759 <literal>cmp</literal>.
4762 min = let ?cmp = (<=) in least
4766 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4767 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4768 (including in a list comprehension, or do-notation, or pattern guards),
4769 or a <literal>where</literal> clause.
4770 Note the following points:
4773 An implicit-parameter binding group must be a
4774 collection of simple bindings to implicit-style variables (no
4775 function-style bindings, and no type signatures); these bindings are
4776 neither polymorphic or recursive.
4779 You may not mix implicit-parameter bindings with ordinary bindings in a
4780 single <literal>let</literal>
4781 expression; use two nested <literal>let</literal>s instead.
4782 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4786 You may put multiple implicit-parameter bindings in a
4787 single binding group; but they are <emphasis>not</emphasis> treated
4788 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4789 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4790 parameter. The bindings are not nested, and may be re-ordered without changing
4791 the meaning of the program.
4792 For example, consider:
4794 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4796 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4797 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4799 f :: (?x::Int) => Int -> Int
4807 <sect3><title>Implicit parameters and polymorphic recursion</title>
4810 Consider these two definitions:
4813 len1 xs = let ?acc = 0 in len_acc1 xs
4816 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4821 len2 xs = let ?acc = 0 in len_acc2 xs
4823 len_acc2 :: (?acc :: Int) => [a] -> Int
4825 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4827 The only difference between the two groups is that in the second group
4828 <literal>len_acc</literal> is given a type signature.
4829 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4830 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4831 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4832 has a type signature, the recursive call is made to the
4833 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4834 as an implicit parameter. So we get the following results in GHCi:
4841 Adding a type signature dramatically changes the result! This is a rather
4842 counter-intuitive phenomenon, worth watching out for.
4846 <sect3><title>Implicit parameters and monomorphism</title>
4848 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4849 Haskell Report) to implicit parameters. For example, consider:
4857 Since the binding for <literal>y</literal> falls under the Monomorphism
4858 Restriction it is not generalised, so the type of <literal>y</literal> is
4859 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4860 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4861 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4862 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4863 <literal>y</literal> in the body of the <literal>let</literal> will see the
4864 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4865 <literal>14</literal>.
4870 <!-- ======================= COMMENTED OUT ========================
4872 We intend to remove linear implicit parameters, so I'm at least removing
4873 them from the 6.6 user manual
4875 <sect2 id="linear-implicit-parameters">
4876 <title>Linear implicit parameters</title>
4878 Linear implicit parameters are an idea developed by Koen Claessen,
4879 Mark Shields, and Simon PJ. They address the long-standing
4880 problem that monads seem over-kill for certain sorts of problem, notably:
4883 <listitem> <para> distributing a supply of unique names </para> </listitem>
4884 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4885 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4889 Linear implicit parameters are just like ordinary implicit parameters,
4890 except that they are "linear"; that is, they cannot be copied, and
4891 must be explicitly "split" instead. Linear implicit parameters are
4892 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4893 (The '/' in the '%' suggests the split!)
4898 import GHC.Exts( Splittable )
4900 data NameSupply = ...
4902 splitNS :: NameSupply -> (NameSupply, NameSupply)
4903 newName :: NameSupply -> Name
4905 instance Splittable NameSupply where
4909 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4910 f env (Lam x e) = Lam x' (f env e)
4913 env' = extend env x x'
4914 ...more equations for f...
4916 Notice that the implicit parameter %ns is consumed
4918 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4919 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4923 So the translation done by the type checker makes
4924 the parameter explicit:
4926 f :: NameSupply -> Env -> Expr -> Expr
4927 f ns env (Lam x e) = Lam x' (f ns1 env e)
4929 (ns1,ns2) = splitNS ns
4931 env = extend env x x'
4933 Notice the call to 'split' introduced by the type checker.
4934 How did it know to use 'splitNS'? Because what it really did
4935 was to introduce a call to the overloaded function 'split',
4936 defined by the class <literal>Splittable</literal>:
4938 class Splittable a where
4941 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4942 split for name supplies. But we can simply write
4948 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4950 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4951 <literal>GHC.Exts</literal>.
4956 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4957 are entirely distinct implicit parameters: you
4958 can use them together and they won't interfere with each other. </para>
4961 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4963 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4964 in the context of a class or instance declaration. </para></listitem>
4968 <sect3><title>Warnings</title>
4971 The monomorphism restriction is even more important than usual.
4972 Consider the example above:
4974 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4975 f env (Lam x e) = Lam x' (f env e)
4978 env' = extend env x x'
4980 If we replaced the two occurrences of x' by (newName %ns), which is
4981 usually a harmless thing to do, we get:
4983 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4984 f env (Lam x e) = Lam (newName %ns) (f env e)
4986 env' = extend env x (newName %ns)
4988 But now the name supply is consumed in <emphasis>three</emphasis> places
4989 (the two calls to newName,and the recursive call to f), so
4990 the result is utterly different. Urk! We don't even have
4994 Well, this is an experimental change. With implicit
4995 parameters we have already lost beta reduction anyway, and
4996 (as John Launchbury puts it) we can't sensibly reason about
4997 Haskell programs without knowing their typing.
5002 <sect3><title>Recursive functions</title>
5003 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5006 foo :: %x::T => Int -> [Int]
5008 foo n = %x : foo (n-1)
5010 where T is some type in class Splittable.</para>
5012 Do you get a list of all the same T's or all different T's
5013 (assuming that split gives two distinct T's back)?
5015 If you supply the type signature, taking advantage of polymorphic
5016 recursion, you get what you'd probably expect. Here's the
5017 translated term, where the implicit param is made explicit:
5020 foo x n = let (x1,x2) = split x
5021 in x1 : foo x2 (n-1)
5023 But if you don't supply a type signature, GHC uses the Hindley
5024 Milner trick of using a single monomorphic instance of the function
5025 for the recursive calls. That is what makes Hindley Milner type inference
5026 work. So the translation becomes
5030 foom n = x : foom (n-1)
5034 Result: 'x' is not split, and you get a list of identical T's. So the
5035 semantics of the program depends on whether or not foo has a type signature.
5038 You may say that this is a good reason to dislike linear implicit parameters
5039 and you'd be right. That is why they are an experimental feature.
5045 ================ END OF Linear Implicit Parameters commented out -->
5047 <sect2 id="kinding">
5048 <title>Explicitly-kinded quantification</title>
5051 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5052 to give the kind explicitly as (machine-checked) documentation,
5053 just as it is nice to give a type signature for a function. On some occasions,
5054 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5055 John Hughes had to define the data type:
5057 data Set cxt a = Set [a]
5058 | Unused (cxt a -> ())
5060 The only use for the <literal>Unused</literal> constructor was to force the correct
5061 kind for the type variable <literal>cxt</literal>.
5064 GHC now instead allows you to specify the kind of a type variable directly, wherever
5065 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5068 This flag enables kind signatures in the following places:
5070 <listitem><para><literal>data</literal> declarations:
5072 data Set (cxt :: * -> *) a = Set [a]
5073 </screen></para></listitem>
5074 <listitem><para><literal>type</literal> declarations:
5076 type T (f :: * -> *) = f Int
5077 </screen></para></listitem>
5078 <listitem><para><literal>class</literal> declarations:
5080 class (Eq a) => C (f :: * -> *) a where ...
5081 </screen></para></listitem>
5082 <listitem><para><literal>forall</literal>'s in type signatures:
5084 f :: forall (cxt :: * -> *). Set cxt Int
5085 </screen></para></listitem>
5090 The parentheses are required. Some of the spaces are required too, to
5091 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5092 will get a parse error, because "<literal>::*->*</literal>" is a
5093 single lexeme in Haskell.
5097 As part of the same extension, you can put kind annotations in types
5100 f :: (Int :: *) -> Int
5101 g :: forall a. a -> (a :: *)
5105 atype ::= '(' ctype '::' kind ')
5107 The parentheses are required.
5112 <sect2 id="universal-quantification">
5113 <title>Arbitrary-rank polymorphism
5117 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5118 allows us to say exactly what this means. For example:
5126 g :: forall b. (b -> b)
5128 The two are treated identically.
5132 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5133 explicit universal quantification in
5135 For example, all the following types are legal:
5137 f1 :: forall a b. a -> b -> a
5138 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5140 f2 :: (forall a. a->a) -> Int -> Int
5141 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5143 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5145 f4 :: Int -> (forall a. a -> a)
5147 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5148 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5149 The <literal>forall</literal> makes explicit the universal quantification that
5150 is implicitly added by Haskell.
5153 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5154 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5155 shows, the polymorphic type on the left of the function arrow can be overloaded.
5158 The function <literal>f3</literal> has a rank-3 type;
5159 it has rank-2 types on the left of a function arrow.
5162 GHC has three flags to control higher-rank types:
5165 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5168 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5171 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5172 That is, you can nest <literal>forall</literal>s
5173 arbitrarily deep in function arrows.
5174 In particular, a forall-type (also called a "type scheme"),
5175 including an operational type class context, is legal:
5177 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5178 of a function arrow </para> </listitem>
5179 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5180 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5181 field type signatures.</para> </listitem>
5182 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5183 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5187 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5188 a type variable any more!
5197 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5198 the types of the constructor arguments. Here are several examples:
5204 data T a = T1 (forall b. b -> b -> b) a
5206 data MonadT m = MkMonad { return :: forall a. a -> m a,
5207 bind :: forall a b. m a -> (a -> m b) -> m b
5210 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5216 The constructors have rank-2 types:
5222 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5223 MkMonad :: forall m. (forall a. a -> m a)
5224 -> (forall a b. m a -> (a -> m b) -> m b)
5226 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5232 Notice that you don't need to use a <literal>forall</literal> if there's an
5233 explicit context. For example in the first argument of the
5234 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5235 prefixed to the argument type. The implicit <literal>forall</literal>
5236 quantifies all type variables that are not already in scope, and are
5237 mentioned in the type quantified over.
5241 As for type signatures, implicit quantification happens for non-overloaded
5242 types too. So if you write this:
5245 data T a = MkT (Either a b) (b -> b)
5248 it's just as if you had written this:
5251 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5254 That is, since the type variable <literal>b</literal> isn't in scope, it's
5255 implicitly universally quantified. (Arguably, it would be better
5256 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5257 where that is what is wanted. Feedback welcomed.)
5261 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5262 the constructor to suitable values, just as usual. For example,
5273 a3 = MkSwizzle reverse
5276 a4 = let r x = Just x
5283 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5284 mkTs f x y = [T1 f x, T1 f y]
5290 The type of the argument can, as usual, be more general than the type
5291 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5292 does not need the <literal>Ord</literal> constraint.)
5296 When you use pattern matching, the bound variables may now have
5297 polymorphic types. For example:
5303 f :: T a -> a -> (a, Char)
5304 f (T1 w k) x = (w k x, w 'c' 'd')
5306 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5307 g (MkSwizzle s) xs f = s (map f (s xs))
5309 h :: MonadT m -> [m a] -> m [a]
5310 h m [] = return m []
5311 h m (x:xs) = bind m x $ \y ->
5312 bind m (h m xs) $ \ys ->
5319 In the function <function>h</function> we use the record selectors <literal>return</literal>
5320 and <literal>bind</literal> to extract the polymorphic bind and return functions
5321 from the <literal>MonadT</literal> data structure, rather than using pattern
5327 <title>Type inference</title>
5330 In general, type inference for arbitrary-rank types is undecidable.
5331 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5332 to get a decidable algorithm by requiring some help from the programmer.
5333 We do not yet have a formal specification of "some help" but the rule is this:
5336 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5337 provides an explicit polymorphic type for x, or GHC's type inference will assume
5338 that x's type has no foralls in it</emphasis>.
5341 What does it mean to "provide" an explicit type for x? You can do that by
5342 giving a type signature for x directly, using a pattern type signature
5343 (<xref linkend="scoped-type-variables"/>), thus:
5345 \ f :: (forall a. a->a) -> (f True, f 'c')
5347 Alternatively, you can give a type signature to the enclosing
5348 context, which GHC can "push down" to find the type for the variable:
5350 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5352 Here the type signature on the expression can be pushed inwards
5353 to give a type signature for f. Similarly, and more commonly,
5354 one can give a type signature for the function itself:
5356 h :: (forall a. a->a) -> (Bool,Char)
5357 h f = (f True, f 'c')
5359 You don't need to give a type signature if the lambda bound variable
5360 is a constructor argument. Here is an example we saw earlier:
5362 f :: T a -> a -> (a, Char)
5363 f (T1 w k) x = (w k x, w 'c' 'd')
5365 Here we do not need to give a type signature to <literal>w</literal>, because
5366 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5373 <sect3 id="implicit-quant">
5374 <title>Implicit quantification</title>
5377 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5378 user-written types, if and only if there is no explicit <literal>forall</literal>,
5379 GHC finds all the type variables mentioned in the type that are not already
5380 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5384 f :: forall a. a -> a
5391 h :: forall b. a -> b -> b
5397 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5400 f :: (a -> a) -> Int
5402 f :: forall a. (a -> a) -> Int
5404 f :: (forall a. a -> a) -> Int
5407 g :: (Ord a => a -> a) -> Int
5408 -- MEANS the illegal type
5409 g :: forall a. (Ord a => a -> a) -> Int
5411 g :: (forall a. Ord a => a -> a) -> Int
5413 The latter produces an illegal type, which you might think is silly,
5414 but at least the rule is simple. If you want the latter type, you
5415 can write your for-alls explicitly. Indeed, doing so is strongly advised
5422 <sect2 id="impredicative-polymorphism">
5423 <title>Impredicative polymorphism
5425 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5426 enabled with <option>-XImpredicativeTypes</option>.
5428 that you can call a polymorphic function at a polymorphic type, and
5429 parameterise data structures over polymorphic types. For example:
5431 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5432 f (Just g) = Just (g [3], g "hello")
5435 Notice here that the <literal>Maybe</literal> type is parameterised by the
5436 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5439 <para>The technical details of this extension are described in the paper
5440 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5441 type inference for higher-rank types and impredicativity</ulink>,
5442 which appeared at ICFP 2006.
5446 <sect2 id="scoped-type-variables">
5447 <title>Lexically scoped type variables
5451 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5452 which some type signatures are simply impossible to write. For example:
5454 f :: forall a. [a] -> [a]
5460 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5461 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5462 The type variables bound by a <literal>forall</literal> scope over
5463 the entire definition of the accompanying value declaration.
5464 In this example, the type variable <literal>a</literal> scopes over the whole
5465 definition of <literal>f</literal>, including over
5466 the type signature for <varname>ys</varname>.
5467 In Haskell 98 it is not possible to declare
5468 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5469 it becomes possible to do so.
5471 <para>Lexically-scoped type variables are enabled by
5472 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5474 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5475 variables work, compared to earlier releases. Read this section
5479 <title>Overview</title>
5481 <para>The design follows the following principles
5483 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5484 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5485 design.)</para></listitem>
5486 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5487 type variables. This means that every programmer-written type signature
5488 (including one that contains free scoped type variables) denotes a
5489 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5490 checker, and no inference is involved.</para></listitem>
5491 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5492 changing the program.</para></listitem>
5496 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5498 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5499 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5500 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5501 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5505 In Haskell, a programmer-written type signature is implicitly quantified over
5506 its free type variables (<ulink
5507 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5509 of the Haskell Report).
5510 Lexically scoped type variables affect this implicit quantification rules
5511 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5512 quantified. For example, if type variable <literal>a</literal> is in scope,
5515 (e :: a -> a) means (e :: a -> a)
5516 (e :: b -> b) means (e :: forall b. b->b)
5517 (e :: a -> b) means (e :: forall b. a->b)
5525 <sect3 id="decl-type-sigs">
5526 <title>Declaration type signatures</title>
5527 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5528 quantification (using <literal>forall</literal>) brings into scope the
5529 explicitly-quantified
5530 type variables, in the definition of the named function. For example:
5532 f :: forall a. [a] -> [a]
5533 f (x:xs) = xs ++ [ x :: a ]
5535 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5536 the definition of "<literal>f</literal>".
5538 <para>This only happens if:
5540 <listitem><para> The quantification in <literal>f</literal>'s type
5541 signature is explicit. For example:
5544 g (x:xs) = xs ++ [ x :: a ]
5546 This program will be rejected, because "<literal>a</literal>" does not scope
5547 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5548 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5549 quantification rules.
5551 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5552 not a pattern binding.
5555 f1 :: forall a. [a] -> [a]
5556 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5558 f2 :: forall a. [a] -> [a]
5559 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5561 f3 :: forall a. [a] -> [a]
5562 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5564 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5565 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5566 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5567 the type signature brings <literal>a</literal> into scope.
5573 <sect3 id="exp-type-sigs">
5574 <title>Expression type signatures</title>
5576 <para>An expression type signature that has <emphasis>explicit</emphasis>
5577 quantification (using <literal>forall</literal>) brings into scope the
5578 explicitly-quantified
5579 type variables, in the annotated expression. For example:
5581 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5583 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5584 type variable <literal>s</literal> into scope, in the annotated expression
5585 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5590 <sect3 id="pattern-type-sigs">
5591 <title>Pattern type signatures</title>
5593 A type signature may occur in any pattern; this is a <emphasis>pattern type
5594 signature</emphasis>.
5597 -- f and g assume that 'a' is already in scope
5598 f = \(x::Int, y::a) -> x
5600 h ((x,y) :: (Int,Bool)) = (y,x)
5602 In the case where all the type variables in the pattern type signature are
5603 already in scope (i.e. bound by the enclosing context), matters are simple: the
5604 signature simply constrains the type of the pattern in the obvious way.
5607 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5608 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5609 that are already in scope. For example:
5611 f :: forall a. [a] -> (Int, [a])
5614 (ys::[a], n) = (reverse xs, length xs) -- OK
5615 zs::[a] = xs ++ ys -- OK
5617 Just (v::b) = ... -- Not OK; b is not in scope
5619 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5620 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5624 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5625 type signature may mention a type variable that is not in scope; in this case,
5626 <emphasis>the signature brings that type variable into scope</emphasis>.
5627 This is particularly important for existential data constructors. For example:
5629 data T = forall a. MkT [a]
5632 k (MkT [t::a]) = MkT t3
5636 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5637 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5638 because it is bound by the pattern match. GHC's rule is that in this situation
5639 (and only then), a pattern type signature can mention a type variable that is
5640 not already in scope; the effect is to bring it into scope, standing for the
5641 existentially-bound type variable.
5644 When a pattern type signature binds a type variable in this way, GHC insists that the
5645 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5646 This means that any user-written type signature always stands for a completely known type.
5649 If all this seems a little odd, we think so too. But we must have
5650 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5651 could not name existentially-bound type variables in subsequent type signatures.
5654 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5655 signature is allowed to mention a lexical variable that is not already in
5657 For example, both <literal>f</literal> and <literal>g</literal> would be
5658 illegal if <literal>a</literal> was not already in scope.
5664 <!-- ==================== Commented out part about result type signatures
5666 <sect3 id="result-type-sigs">
5667 <title>Result type signatures</title>
5670 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5673 {- f assumes that 'a' is already in scope -}
5674 f x y :: [a] = [x,y,x]
5676 g = \ x :: [Int] -> [3,4]
5678 h :: forall a. [a] -> a
5682 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5683 the result of the function. Similarly, the body of the lambda in the RHS of
5684 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5685 alternative in <literal>h</literal> is <literal>a</literal>.
5687 <para> A result type signature never brings new type variables into scope.</para>
5689 There are a couple of syntactic wrinkles. First, notice that all three
5690 examples would parse quite differently with parentheses:
5692 {- f assumes that 'a' is already in scope -}
5693 f x (y :: [a]) = [x,y,x]
5695 g = \ (x :: [Int]) -> [3,4]
5697 h :: forall a. [a] -> a
5701 Now the signature is on the <emphasis>pattern</emphasis>; and
5702 <literal>h</literal> would certainly be ill-typed (since the pattern
5703 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5705 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5706 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5707 token or a parenthesised type of some sort). To see why,
5708 consider how one would parse this:
5717 <sect3 id="cls-inst-scoped-tyvars">
5718 <title>Class and instance declarations</title>
5721 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5722 scope over the methods defined in the <literal>where</literal> part. For example:
5740 <sect2 id="typing-binds">
5741 <title>Generalised typing of mutually recursive bindings</title>
5744 The Haskell Report specifies that a group of bindings (at top level, or in a
5745 <literal>let</literal> or <literal>where</literal>) should be sorted into
5746 strongly-connected components, and then type-checked in dependency order
5747 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5748 Report, Section 4.5.1</ulink>).
5749 As each group is type-checked, any binders of the group that
5751 an explicit type signature are put in the type environment with the specified
5753 and all others are monomorphic until the group is generalised
5754 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5757 <para>Following a suggestion of Mark Jones, in his paper
5758 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5760 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5762 <emphasis>the dependency analysis ignores references to variables that have an explicit
5763 type signature</emphasis>.
5764 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5765 typecheck. For example, consider:
5767 f :: Eq a => a -> Bool
5768 f x = (x == x) || g True || g "Yes"
5770 g y = (y <= y) || f True
5772 This is rejected by Haskell 98, but under Jones's scheme the definition for
5773 <literal>g</literal> is typechecked first, separately from that for
5774 <literal>f</literal>,
5775 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5776 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5777 type is generalised, to get
5779 g :: Ord a => a -> Bool
5781 Now, the definition for <literal>f</literal> is typechecked, with this type for
5782 <literal>g</literal> in the type environment.
5786 The same refined dependency analysis also allows the type signatures of
5787 mutually-recursive functions to have different contexts, something that is illegal in
5788 Haskell 98 (Section 4.5.2, last sentence). With
5789 <option>-XRelaxedPolyRec</option>
5790 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5791 type signatures; in practice this means that only variables bound by the same
5792 pattern binding must have the same context. For example, this is fine:
5794 f :: Eq a => a -> Bool
5795 f x = (x == x) || g True
5797 g :: Ord a => a -> Bool
5798 g y = (y <= y) || f True
5804 <!-- ==================== End of type system extensions ================= -->
5806 <!-- ====================== TEMPLATE HASKELL ======================= -->
5808 <sect1 id="template-haskell">
5809 <title>Template Haskell</title>
5811 <para>Template Haskell allows you to do compile-time meta-programming in
5814 the main technical innovations is discussed in "<ulink
5815 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5816 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5819 There is a Wiki page about
5820 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5821 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5825 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5826 Haskell library reference material</ulink>
5827 (look for module <literal>Language.Haskell.TH</literal>).
5828 Many changes to the original design are described in
5829 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5830 Notes on Template Haskell version 2</ulink>.
5831 Not all of these changes are in GHC, however.
5834 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5835 as a worked example to help get you started.
5839 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5840 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5845 <title>Syntax</title>
5847 <para> Template Haskell has the following new syntactic
5848 constructions. You need to use the flag
5849 <option>-XTemplateHaskell</option>
5850 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5851 </indexterm>to switch these syntactic extensions on
5852 (<option>-XTemplateHaskell</option> is no longer implied by
5853 <option>-fglasgow-exts</option>).</para>
5857 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5858 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5859 There must be no space between the "$" and the identifier or parenthesis. This use
5860 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5861 of "." as an infix operator. If you want the infix operator, put spaces around it.
5863 <para> A splice can occur in place of
5865 <listitem><para> an expression; the spliced expression must
5866 have type <literal>Q Exp</literal></para></listitem>
5867 <listitem><para> an type; the spliced expression must
5868 have type <literal>Q Typ</literal></para></listitem>
5869 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5872 Inside a splice you can can only call functions defined in imported modules,
5873 not functions defined elsewhere in the same module.</listitem>
5877 A expression quotation is written in Oxford brackets, thus:
5879 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5880 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5881 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5882 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5883 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5884 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5885 </itemizedlist></para></listitem>
5888 A quasi-quotation can appear in either a pattern context or an
5889 expression context and is also written in Oxford brackets:
5891 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5892 where the "..." is an arbitrary string; a full description of the
5893 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5894 </itemizedlist></para></listitem>
5897 A name can be quoted with either one or two prefix single quotes:
5899 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5900 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5901 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5903 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5904 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5907 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5908 may also be given as an argument to the <literal>reify</literal> function.
5914 (Compared to the original paper, there are many differences of detail.
5915 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5916 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5917 Pattern splices and quotations are not implemented.)
5921 <sect2> <title> Using Template Haskell </title>
5925 The data types and monadic constructor functions for Template Haskell are in the library
5926 <literal>Language.Haskell.THSyntax</literal>.
5930 You can only run a function at compile time if it is imported from another module. That is,
5931 you can't define a function in a module, and call it from within a splice in the same module.
5932 (It would make sense to do so, but it's hard to implement.)
5936 You can only run a function at compile time if it is imported
5937 from another module <emphasis>that is not part of a mutually-recursive group of modules
5938 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5939 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5940 splice is to be run.</para>
5942 For example, when compiling module A,
5943 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5944 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5948 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5951 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5952 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5953 compiles and runs a program, and then looks at the result. So it's important that
5954 the program it compiles produces results whose representations are identical to
5955 those of the compiler itself.
5959 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5960 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5965 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5966 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5967 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5974 -- Import our template "pr"
5975 import Printf ( pr )
5977 -- The splice operator $ takes the Haskell source code
5978 -- generated at compile time by "pr" and splices it into
5979 -- the argument of "putStrLn".
5980 main = putStrLn ( $(pr "Hello") )
5986 -- Skeletal printf from the paper.
5987 -- It needs to be in a separate module to the one where
5988 -- you intend to use it.
5990 -- Import some Template Haskell syntax
5991 import Language.Haskell.TH
5993 -- Describe a format string
5994 data Format = D | S | L String
5996 -- Parse a format string. This is left largely to you
5997 -- as we are here interested in building our first ever
5998 -- Template Haskell program and not in building printf.
5999 parse :: String -> [Format]
6002 -- Generate Haskell source code from a parsed representation
6003 -- of the format string. This code will be spliced into
6004 -- the module which calls "pr", at compile time.
6005 gen :: [Format] -> Q Exp
6006 gen [D] = [| \n -> show n |]
6007 gen [S] = [| \s -> s |]
6008 gen [L s] = stringE s
6010 -- Here we generate the Haskell code for the splice
6011 -- from an input format string.
6012 pr :: String -> Q Exp
6013 pr s = gen (parse s)
6016 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6019 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6022 <para>Run "main.exe" and here is your output:</para>
6032 <title>Using Template Haskell with Profiling</title>
6033 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6035 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6036 interpreter to run the splice expressions. The bytecode interpreter
6037 runs the compiled expression on top of the same runtime on which GHC
6038 itself is running; this means that the compiled code referred to by
6039 the interpreted expression must be compatible with this runtime, and
6040 in particular this means that object code that is compiled for
6041 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6042 expression, because profiled object code is only compatible with the
6043 profiling version of the runtime.</para>
6045 <para>This causes difficulties if you have a multi-module program
6046 containing Template Haskell code and you need to compile it for
6047 profiling, because GHC cannot load the profiled object code and use it
6048 when executing the splices. Fortunately GHC provides a workaround.
6049 The basic idea is to compile the program twice:</para>
6053 <para>Compile the program or library first the normal way, without
6054 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6057 <para>Then compile it again with <option>-prof</option>, and
6058 additionally use <option>-osuf
6059 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6060 to name the object files differently (you can choose any suffix
6061 that isn't the normal object suffix here). GHC will automatically
6062 load the object files built in the first step when executing splice
6063 expressions. If you omit the <option>-osuf</option> flag when
6064 building with <option>-prof</option> and Template Haskell is used,
6065 GHC will emit an error message. </para>
6070 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6071 <para>Quasi-quotation allows patterns and expressions to be written using
6072 programmer-defined concrete syntax; the motivation behind the extension and
6073 several examples are documented in
6074 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6075 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6076 2007). The example below shows how to write a quasiquoter for a simple
6077 expression language.</para>
6080 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6081 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6082 functions for quoting expressions and patterns, respectively. The first argument
6083 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6084 context of the quasi-quotation statement determines which of the two parsers is
6085 called: if the quasi-quotation occurs in an expression context, the expression
6086 parser is called, and if it occurs in a pattern context, the pattern parser is
6090 Note that in the example we make use of an antiquoted
6091 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6092 (this syntax for anti-quotation was defined by the parser's
6093 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6094 integer value argument of the constructor <literal>IntExpr</literal> when
6095 pattern matching. Please see the referenced paper for further details regarding
6096 anti-quotation as well as the description of a technique that uses SYB to
6097 leverage a single parser of type <literal>String -> a</literal> to generate both
6098 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6099 pattern parser that returns a value of type <literal>Q Pat</literal>.
6102 <para>In general, a quasi-quote has the form
6103 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6104 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6105 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6106 can be arbitrary, and may contain newlines.
6109 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6110 the example, <literal>expr</literal> cannot be defined
6111 in <literal>Main.hs</literal> where it is used, but must be imported.
6122 main = do { print $ eval [$expr|1 + 2|]
6124 { [$expr|'int:n|] -> print n
6133 import qualified Language.Haskell.TH as TH
6134 import Language.Haskell.TH.Quote
6136 data Expr = IntExpr Integer
6137 | AntiIntExpr String
6138 | BinopExpr BinOp Expr Expr
6140 deriving(Show, Typeable, Data)
6146 deriving(Show, Typeable, Data)
6148 eval :: Expr -> Integer
6149 eval (IntExpr n) = n
6150 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6157 expr = QuasiQuoter parseExprExp parseExprPat
6159 -- Parse an Expr, returning its representation as
6160 -- either a Q Exp or a Q Pat. See the referenced paper
6161 -- for how to use SYB to do this by writing a single
6162 -- parser of type String -> Expr instead of two
6163 -- separate parsers.
6165 parseExprExp :: String -> Q Exp
6168 parseExprPat :: String -> Q Pat
6172 <para>Now run the compiler:
6175 $ ghc --make -XQuasiQuotes Main.hs -o main
6178 <para>Run "main" and here is your output:</para>
6190 <!-- ===================== Arrow notation =================== -->
6192 <sect1 id="arrow-notation">
6193 <title>Arrow notation
6196 <para>Arrows are a generalization of monads introduced by John Hughes.
6197 For more details, see
6202 “Generalising Monads to Arrows”,
6203 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6204 pp67–111, May 2000.
6205 The paper that introduced arrows: a friendly introduction, motivated with
6206 programming examples.
6212 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6213 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6214 Introduced the notation described here.
6220 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6221 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6228 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6229 John Hughes, in <citetitle>5th International Summer School on
6230 Advanced Functional Programming</citetitle>,
6231 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6233 This paper includes another introduction to the notation,
6234 with practical examples.
6240 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6241 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6242 A terse enumeration of the formal rules used
6243 (extracted from comments in the source code).
6249 The arrows web page at
6250 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6255 With the <option>-XArrows</option> flag, GHC supports the arrow
6256 notation described in the second of these papers,
6257 translating it using combinators from the
6258 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6260 What follows is a brief introduction to the notation;
6261 it won't make much sense unless you've read Hughes's paper.
6264 <para>The extension adds a new kind of expression for defining arrows:
6266 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6267 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6269 where <literal>proc</literal> is a new keyword.
6270 The variables of the pattern are bound in the body of the
6271 <literal>proc</literal>-expression,
6272 which is a new sort of thing called a <firstterm>command</firstterm>.
6273 The syntax of commands is as follows:
6275 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6276 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6277 | <replaceable>cmd</replaceable><superscript>0</superscript>
6279 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6280 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6281 infix operators as for expressions, and
6283 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6284 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6285 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6286 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6287 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6288 | <replaceable>fcmd</replaceable>
6290 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6291 | ( <replaceable>cmd</replaceable> )
6292 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6294 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6295 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6296 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6297 | <replaceable>cmd</replaceable>
6299 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6300 except that the bodies are commands instead of expressions.
6304 Commands produce values, but (like monadic computations)
6305 may yield more than one value,
6306 or none, and may do other things as well.
6307 For the most part, familiarity with monadic notation is a good guide to
6309 However the values of expressions, even monadic ones,
6310 are determined by the values of the variables they contain;
6311 this is not necessarily the case for commands.
6315 A simple example of the new notation is the expression
6317 proc x -> f -< x+1
6319 We call this a <firstterm>procedure</firstterm> or
6320 <firstterm>arrow abstraction</firstterm>.
6321 As with a lambda expression, the variable <literal>x</literal>
6322 is a new variable bound within the <literal>proc</literal>-expression.
6323 It refers to the input to the arrow.
6324 In the above example, <literal>-<</literal> is not an identifier but an
6325 new reserved symbol used for building commands from an expression of arrow
6326 type and an expression to be fed as input to that arrow.
6327 (The weird look will make more sense later.)
6328 It may be read as analogue of application for arrows.
6329 The above example is equivalent to the Haskell expression
6331 arr (\ x -> x+1) >>> f
6333 That would make no sense if the expression to the left of
6334 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6335 More generally, the expression to the left of <literal>-<</literal>
6336 may not involve any <firstterm>local variable</firstterm>,
6337 i.e. a variable bound in the current arrow abstraction.
6338 For such a situation there is a variant <literal>-<<</literal>, as in
6340 proc x -> f x -<< x+1
6342 which is equivalent to
6344 arr (\ x -> (f x, x+1)) >>> app
6346 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6348 Such an arrow is equivalent to a monad, so if you're using this form
6349 you may find a monadic formulation more convenient.
6353 <title>do-notation for commands</title>
6356 Another form of command is a form of <literal>do</literal>-notation.
6357 For example, you can write
6366 You can read this much like ordinary <literal>do</literal>-notation,
6367 but with commands in place of monadic expressions.
6368 The first line sends the value of <literal>x+1</literal> as an input to
6369 the arrow <literal>f</literal>, and matches its output against
6370 <literal>y</literal>.
6371 In the next line, the output is discarded.
6372 The arrow <function>returnA</function> is defined in the
6373 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6374 module as <literal>arr id</literal>.
6375 The above example is treated as an abbreviation for
6377 arr (\ x -> (x, x)) >>>
6378 first (arr (\ x -> x+1) >>> f) >>>
6379 arr (\ (y, x) -> (y, (x, y))) >>>
6380 first (arr (\ y -> 2*y) >>> g) >>>
6382 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6383 first (arr (\ (x, z) -> x*z) >>> h) >>>
6384 arr (\ (t, z) -> t+z) >>>
6387 Note that variables not used later in the composition are projected out.
6388 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6390 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6391 module, this reduces to
6393 arr (\ x -> (x+1, x)) >>>
6395 arr (\ (y, x) -> (2*y, (x, y))) >>>
6397 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6399 arr (\ (t, z) -> t+z)
6401 which is what you might have written by hand.
6402 With arrow notation, GHC keeps track of all those tuples of variables for you.
6406 Note that although the above translation suggests that
6407 <literal>let</literal>-bound variables like <literal>z</literal> must be
6408 monomorphic, the actual translation produces Core,
6409 so polymorphic variables are allowed.
6413 It's also possible to have mutually recursive bindings,
6414 using the new <literal>rec</literal> keyword, as in the following example:
6416 counter :: ArrowCircuit a => a Bool Int
6417 counter = proc reset -> do
6418 rec output <- returnA -< if reset then 0 else next
6419 next <- delay 0 -< output+1
6420 returnA -< output
6422 The translation of such forms uses the <function>loop</function> combinator,
6423 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6429 <title>Conditional commands</title>
6432 In the previous example, we used a conditional expression to construct the
6434 Sometimes we want to conditionally execute different commands, as in
6441 which is translated to
6443 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6444 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6446 Since the translation uses <function>|||</function>,
6447 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6451 There are also <literal>case</literal> commands, like
6457 y <- h -< (x1, x2)
6461 The syntax is the same as for <literal>case</literal> expressions,
6462 except that the bodies of the alternatives are commands rather than expressions.
6463 The translation is similar to that of <literal>if</literal> commands.
6469 <title>Defining your own control structures</title>
6472 As we're seen, arrow notation provides constructs,
6473 modelled on those for expressions,
6474 for sequencing, value recursion and conditionals.
6475 But suitable combinators,
6476 which you can define in ordinary Haskell,
6477 may also be used to build new commands out of existing ones.
6478 The basic idea is that a command defines an arrow from environments to values.
6479 These environments assign values to the free local variables of the command.
6480 Thus combinators that produce arrows from arrows
6481 may also be used to build commands from commands.
6482 For example, the <literal>ArrowChoice</literal> class includes a combinator
6484 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6486 so we can use it to build commands:
6488 expr' = proc x -> do
6491 symbol Plus -< ()
6492 y <- term -< ()
6495 symbol Minus -< ()
6496 y <- term -< ()
6499 (The <literal>do</literal> on the first line is needed to prevent the first
6500 <literal><+> ...</literal> from being interpreted as part of the
6501 expression on the previous line.)
6502 This is equivalent to
6504 expr' = (proc x -> returnA -< x)
6505 <+> (proc x -> do
6506 symbol Plus -< ()
6507 y <- term -< ()
6509 <+> (proc x -> do
6510 symbol Minus -< ()
6511 y <- term -< ()
6514 It is essential that this operator be polymorphic in <literal>e</literal>
6515 (representing the environment input to the command
6516 and thence to its subcommands)
6517 and satisfy the corresponding naturality property
6519 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6521 at least for strict <literal>k</literal>.
6522 (This should be automatic if you're not using <function>seq</function>.)
6523 This ensures that environments seen by the subcommands are environments
6524 of the whole command,
6525 and also allows the translation to safely trim these environments.
6526 The operator must also not use any variable defined within the current
6531 We could define our own operator
6533 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6534 untilA body cond = proc x ->
6535 b <- cond -< x
6536 if b then returnA -< ()
6539 untilA body cond -< x
6541 and use it in the same way.
6542 Of course this infix syntax only makes sense for binary operators;
6543 there is also a more general syntax involving special brackets:
6547 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6554 <title>Primitive constructs</title>
6557 Some operators will need to pass additional inputs to their subcommands.
6558 For example, in an arrow type supporting exceptions,
6559 the operator that attaches an exception handler will wish to pass the
6560 exception that occurred to the handler.
6561 Such an operator might have a type
6563 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6565 where <literal>Ex</literal> is the type of exceptions handled.
6566 You could then use this with arrow notation by writing a command
6568 body `handleA` \ ex -> handler
6570 so that if an exception is raised in the command <literal>body</literal>,
6571 the variable <literal>ex</literal> is bound to the value of the exception
6572 and the command <literal>handler</literal>,
6573 which typically refers to <literal>ex</literal>, is entered.
6574 Though the syntax here looks like a functional lambda,
6575 we are talking about commands, and something different is going on.
6576 The input to the arrow represented by a command consists of values for
6577 the free local variables in the command, plus a stack of anonymous values.
6578 In all the prior examples, this stack was empty.
6579 In the second argument to <function>handleA</function>,
6580 this stack consists of one value, the value of the exception.
6581 The command form of lambda merely gives this value a name.
6586 the values on the stack are paired to the right of the environment.
6587 So operators like <function>handleA</function> that pass
6588 extra inputs to their subcommands can be designed for use with the notation
6589 by pairing the values with the environment in this way.
6590 More precisely, the type of each argument of the operator (and its result)
6591 should have the form
6593 a (...(e,t1), ... tn) t
6595 where <replaceable>e</replaceable> is a polymorphic variable
6596 (representing the environment)
6597 and <replaceable>ti</replaceable> are the types of the values on the stack,
6598 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6599 The polymorphic variable <replaceable>e</replaceable> must not occur in
6600 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6601 <replaceable>t</replaceable>.
6602 However the arrows involved need not be the same.
6603 Here are some more examples of suitable operators:
6605 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6606 runReader :: ... => a e c -> a' (e,State) c
6607 runState :: ... => a e c -> a' (e,State) (c,State)
6609 We can supply the extra input required by commands built with the last two
6610 by applying them to ordinary expressions, as in
6614 (|runReader (do { ... })|) s
6616 which adds <literal>s</literal> to the stack of inputs to the command
6617 built using <function>runReader</function>.
6621 The command versions of lambda abstraction and application are analogous to
6622 the expression versions.
6623 In particular, the beta and eta rules describe equivalences of commands.
6624 These three features (operators, lambda abstraction and application)
6625 are the core of the notation; everything else can be built using them,
6626 though the results would be somewhat clumsy.
6627 For example, we could simulate <literal>do</literal>-notation by defining
6629 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6630 u `bind` f = returnA &&& u >>> f
6632 bind_ :: Arrow a => a e b -> a e c -> a e c
6633 u `bind_` f = u `bind` (arr fst >>> f)
6635 We could simulate <literal>if</literal> by defining
6637 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6638 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6645 <title>Differences with the paper</title>
6650 <para>Instead of a single form of arrow application (arrow tail) with two
6651 translations, the implementation provides two forms
6652 <quote><literal>-<</literal></quote> (first-order)
6653 and <quote><literal>-<<</literal></quote> (higher-order).
6658 <para>User-defined operators are flagged with banana brackets instead of
6659 a new <literal>form</literal> keyword.
6668 <title>Portability</title>
6671 Although only GHC implements arrow notation directly,
6672 there is also a preprocessor
6674 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6675 that translates arrow notation into Haskell 98
6676 for use with other Haskell systems.
6677 You would still want to check arrow programs with GHC;
6678 tracing type errors in the preprocessor output is not easy.
6679 Modules intended for both GHC and the preprocessor must observe some
6680 additional restrictions:
6685 The module must import
6686 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6692 The preprocessor cannot cope with other Haskell extensions.
6693 These would have to go in separate modules.
6699 Because the preprocessor targets Haskell (rather than Core),
6700 <literal>let</literal>-bound variables are monomorphic.
6711 <!-- ==================== BANG PATTERNS ================= -->
6713 <sect1 id="bang-patterns">
6714 <title>Bang patterns
6715 <indexterm><primary>Bang patterns</primary></indexterm>
6717 <para>GHC supports an extension of pattern matching called <emphasis>bang
6718 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6719 Bang patterns are under consideration for Haskell Prime.
6721 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6722 prime feature description</ulink> contains more discussion and examples
6723 than the material below.
6726 The key change is the addition of a new rule to the
6727 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6728 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6729 against a value <replaceable>v</replaceable> behaves as follows:
6731 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6732 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6736 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6739 <sect2 id="bang-patterns-informal">
6740 <title>Informal description of bang patterns
6743 The main idea is to add a single new production to the syntax of patterns:
6747 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6748 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6753 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6754 whereas without the bang it would be lazy.
6755 Bang patterns can be nested of course:
6759 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6760 <literal>y</literal>.
6761 A bang only really has an effect if it precedes a variable or wild-card pattern:
6766 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6767 putting a bang before a pattern that
6768 forces evaluation anyway does nothing.
6771 There is one (apparent) exception to this general rule that a bang only
6772 makes a difference when it precedes a variable or wild-card: a bang at the
6773 top level of a <literal>let</literal> or <literal>where</literal>
6774 binding makes the binding strict, regardless of the pattern. For example:
6778 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6779 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6780 (We say "apparent" exception because the Right Way to think of it is that the bang
6781 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6782 is part of the syntax of the <emphasis>binding</emphasis>.)
6783 Nested bangs in a pattern binding behave uniformly with all other forms of
6784 pattern matching. For example
6786 let (!x,[y]) = e in b
6788 is equivalent to this:
6790 let { t = case e of (x,[y]) -> x `seq` (x,y)
6795 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6796 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6797 evaluation of <literal>x</literal>.
6800 Bang patterns work in <literal>case</literal> expressions too, of course:
6802 g5 x = let y = f x in body
6803 g6 x = case f x of { y -> body }
6804 g7 x = case f x of { !y -> body }
6806 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6807 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6808 result, and then evaluates <literal>body</literal>.
6813 <sect2 id="bang-patterns-sem">
6814 <title>Syntax and semantics
6818 We add a single new production to the syntax of patterns:
6822 There is one problem with syntactic ambiguity. Consider:
6826 Is this a definition of the infix function "<literal>(!)</literal>",
6827 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6828 ambiguity in favour of the latter. If you want to define
6829 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6834 The semantics of Haskell pattern matching is described in <ulink
6835 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6836 Section 3.17.2</ulink> of the Haskell Report. To this description add
6837 one extra item 10, saying:
6838 <itemizedlist><listitem><para>Matching
6839 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6840 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6841 <listitem><para>otherwise, <literal>pat</literal> is matched against
6842 <literal>v</literal></para></listitem>
6844 </para></listitem></itemizedlist>
6845 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6846 Section 3.17.3</ulink>, add a new case (t):
6848 case v of { !pat -> e; _ -> e' }
6849 = v `seq` case v of { pat -> e; _ -> e' }
6852 That leaves let expressions, whose translation is given in
6853 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6855 of the Haskell Report.
6856 In the translation box, first apply
6857 the following transformation: for each pattern <literal>pi</literal> that is of
6858 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6859 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6860 have a bang at the top, apply the rules in the existing box.
6862 <para>The effect of the let rule is to force complete matching of the pattern
6863 <literal>qi</literal> before evaluation of the body is begun. The bang is
6864 retained in the translated form in case <literal>qi</literal> is a variable,
6872 The let-binding can be recursive. However, it is much more common for
6873 the let-binding to be non-recursive, in which case the following law holds:
6874 <literal>(let !p = rhs in body)</literal>
6876 <literal>(case rhs of !p -> body)</literal>
6879 A pattern with a bang at the outermost level is not allowed at the top level of
6885 <!-- ==================== ASSERTIONS ================= -->
6887 <sect1 id="assertions">
6889 <indexterm><primary>Assertions</primary></indexterm>
6893 If you want to make use of assertions in your standard Haskell code, you
6894 could define a function like the following:
6900 assert :: Bool -> a -> a
6901 assert False x = error "assertion failed!"
6908 which works, but gives you back a less than useful error message --
6909 an assertion failed, but which and where?
6913 One way out is to define an extended <function>assert</function> function which also
6914 takes a descriptive string to include in the error message and
6915 perhaps combine this with the use of a pre-processor which inserts
6916 the source location where <function>assert</function> was used.
6920 Ghc offers a helping hand here, doing all of this for you. For every
6921 use of <function>assert</function> in the user's source:
6927 kelvinToC :: Double -> Double
6928 kelvinToC k = assert (k >= 0.0) (k+273.15)
6934 Ghc will rewrite this to also include the source location where the
6941 assert pred val ==> assertError "Main.hs|15" pred val
6947 The rewrite is only performed by the compiler when it spots
6948 applications of <function>Control.Exception.assert</function>, so you
6949 can still define and use your own versions of
6950 <function>assert</function>, should you so wish. If not, import
6951 <literal>Control.Exception</literal> to make use
6952 <function>assert</function> in your code.
6956 GHC ignores assertions when optimisation is turned on with the
6957 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6958 <literal>assert pred e</literal> will be rewritten to
6959 <literal>e</literal>. You can also disable assertions using the
6960 <option>-fignore-asserts</option>
6961 option<indexterm><primary><option>-fignore-asserts</option></primary>
6962 </indexterm>.</para>
6965 Assertion failures can be caught, see the documentation for the
6966 <literal>Control.Exception</literal> library for the details.
6972 <!-- =============================== PRAGMAS =========================== -->
6974 <sect1 id="pragmas">
6975 <title>Pragmas</title>
6977 <indexterm><primary>pragma</primary></indexterm>
6979 <para>GHC supports several pragmas, or instructions to the
6980 compiler placed in the source code. Pragmas don't normally affect
6981 the meaning of the program, but they might affect the efficiency
6982 of the generated code.</para>
6984 <para>Pragmas all take the form
6986 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6988 where <replaceable>word</replaceable> indicates the type of
6989 pragma, and is followed optionally by information specific to that
6990 type of pragma. Case is ignored in
6991 <replaceable>word</replaceable>. The various values for
6992 <replaceable>word</replaceable> that GHC understands are described
6993 in the following sections; any pragma encountered with an
6994 unrecognised <replaceable>word</replaceable> is
6995 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6996 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6998 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7002 pragma must precede the <literal>module</literal> keyword in the file.
7005 There can be as many file-header pragmas as you please, and they can be
7006 preceded or followed by comments.
7009 File-header pragmas are read once only, before
7010 pre-processing the file (e.g. with cpp).
7013 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7014 <literal>{-# OPTIONS_GHC #-}</literal>, and
7015 <literal>{-# INCLUDE #-}</literal>.
7020 <sect2 id="language-pragma">
7021 <title>LANGUAGE pragma</title>
7023 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7024 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7026 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7028 It is the intention that all Haskell compilers support the
7029 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7030 all extensions are supported by all compilers, of
7031 course. The <literal>LANGUAGE</literal> pragma should be used instead
7032 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7034 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7036 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7038 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7040 <para>Every language extension can also be turned into a command-line flag
7041 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7042 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7045 <para>A list of all supported language extensions can be obtained by invoking
7046 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7048 <para>Any extension from the <literal>Extension</literal> type defined in
7050 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7051 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7055 <sect2 id="options-pragma">
7056 <title>OPTIONS_GHC pragma</title>
7057 <indexterm><primary>OPTIONS_GHC</primary>
7059 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7062 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7063 additional options that are given to the compiler when compiling
7064 this source file. See <xref linkend="source-file-options"/> for
7067 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7068 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7071 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7073 <sect2 id="include-pragma">
7074 <title>INCLUDE pragma</title>
7076 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
7077 of C header files that should be <literal>#include</literal>'d into
7078 the C source code generated by the compiler for the current module (if
7079 compiling via C). For example:</para>
7082 {-# INCLUDE "foo.h" #-}
7083 {-# INCLUDE <stdio.h> #-}</programlisting>
7085 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7087 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
7088 to the <option>-#include</option> option (<xref
7089 linkend="options-C-compiler" />), because the
7090 <literal>INCLUDE</literal> pragma is understood by other
7091 compilers. Yet another alternative is to add the include file to each
7092 <literal>foreign import</literal> declaration in your code, but we
7093 don't recommend using this approach with GHC.</para>
7096 <sect2 id="warning-deprecated-pragma">
7097 <title>WARNING and DEPRECATED pragmas</title>
7098 <indexterm><primary>WARNING</primary></indexterm>
7099 <indexterm><primary>DEPRECATED</primary></indexterm>
7101 <para>The WARNING pragma allows you to attach an arbitrary warning
7102 to a particular function, class, or type.
7103 A DEPRECATED pragma lets you specify that
7104 a particular function, class, or type is deprecated.
7105 There are two ways of using these pragmas.
7109 <para>You can work on an entire module thus:</para>
7111 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7116 module Wibble {-# WARNING "This is an unstable interface." #-} where
7119 <para>When you compile any module that import
7120 <literal>Wibble</literal>, GHC will print the specified
7125 <para>You can attach a warning to a function, class, type, or data constructor, with the
7126 following top-level declarations:</para>
7128 {-# DEPRECATED f, C, T "Don't use these" #-}
7129 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7131 <para>When you compile any module that imports and uses any
7132 of the specified entities, GHC will print the specified
7134 <para> You can only attach to entities declared at top level in the module
7135 being compiled, and you can only use unqualified names in the list of
7136 entities. A capitalised name, such as <literal>T</literal>
7137 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7138 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7139 both are in scope. If both are in scope, there is currently no way to
7140 specify one without the other (c.f. fixities
7141 <xref linkend="infix-tycons"/>).</para>
7144 Warnings and deprecations are not reported for
7145 (a) uses within the defining module, and
7146 (b) uses in an export list.
7147 The latter reduces spurious complaints within a library
7148 in which one module gathers together and re-exports
7149 the exports of several others.
7151 <para>You can suppress the warnings with the flag
7152 <option>-fno-warn-warnings-deprecations</option>.</para>
7155 <sect2 id="inline-noinline-pragma">
7156 <title>INLINE and NOINLINE pragmas</title>
7158 <para>These pragmas control the inlining of function
7161 <sect3 id="inline-pragma">
7162 <title>INLINE pragma</title>
7163 <indexterm><primary>INLINE</primary></indexterm>
7165 <para>GHC (with <option>-O</option>, as always) tries to
7166 inline (or “unfold”) functions/values that are
7167 “small enough,” thus avoiding the call overhead
7168 and possibly exposing other more-wonderful optimisations.
7169 Normally, if GHC decides a function is “too
7170 expensive” to inline, it will not do so, nor will it
7171 export that unfolding for other modules to use.</para>
7173 <para>The sledgehammer you can bring to bear is the
7174 <literal>INLINE</literal><indexterm><primary>INLINE
7175 pragma</primary></indexterm> pragma, used thusly:</para>
7178 key_function :: Int -> String -> (Bool, Double)
7179 {-# INLINE key_function #-}
7182 <para>The major effect of an <literal>INLINE</literal> pragma
7183 is to declare a function's “cost” to be very low.
7184 The normal unfolding machinery will then be very keen to
7185 inline it. However, an <literal>INLINE</literal> pragma for a
7186 function "<literal>f</literal>" has a number of other effects:
7189 No functions are inlined into <literal>f</literal>. Otherwise
7190 GHC might inline a big function into <literal>f</literal>'s right hand side,
7191 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7194 The float-in, float-out, and common-sub-expression transformations are not
7195 applied to the body of <literal>f</literal>.
7198 An INLINE function is not worker/wrappered by strictness analysis.
7199 It's going to be inlined wholesale instead.
7202 All of these effects are aimed at ensuring that what gets inlined is
7203 exactly what you asked for, no more and no less.
7205 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7206 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7207 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7208 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7209 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7210 when there is no choice even an INLINE function can be selected, in which case
7211 the INLINE pragma is ignored.
7212 For example, for a self-recursive function, the loop breaker can only be the function
7213 itself, so an INLINE pragma is always ignored.</para>
7215 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7216 function can be put anywhere its type signature could be
7219 <para><literal>INLINE</literal> pragmas are a particularly
7221 <literal>then</literal>/<literal>return</literal> (or
7222 <literal>bind</literal>/<literal>unit</literal>) functions in
7223 a monad. For example, in GHC's own
7224 <literal>UniqueSupply</literal> monad code, we have:</para>
7227 {-# INLINE thenUs #-}
7228 {-# INLINE returnUs #-}
7231 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7232 linkend="noinline-pragma"/>).</para>
7234 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7235 so if you want your code to be HBC-compatible you'll have to surround
7236 the pragma with C pre-processor directives
7237 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7241 <sect3 id="noinline-pragma">
7242 <title>NOINLINE pragma</title>
7244 <indexterm><primary>NOINLINE</primary></indexterm>
7245 <indexterm><primary>NOTINLINE</primary></indexterm>
7247 <para>The <literal>NOINLINE</literal> pragma does exactly what
7248 you'd expect: it stops the named function from being inlined
7249 by the compiler. You shouldn't ever need to do this, unless
7250 you're very cautious about code size.</para>
7252 <para><literal>NOTINLINE</literal> is a synonym for
7253 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7254 specified by Haskell 98 as the standard way to disable
7255 inlining, so it should be used if you want your code to be
7259 <sect3 id="phase-control">
7260 <title>Phase control</title>
7262 <para> Sometimes you want to control exactly when in GHC's
7263 pipeline the INLINE pragma is switched on. Inlining happens
7264 only during runs of the <emphasis>simplifier</emphasis>. Each
7265 run of the simplifier has a different <emphasis>phase
7266 number</emphasis>; the phase number decreases towards zero.
7267 If you use <option>-dverbose-core2core</option> you'll see the
7268 sequence of phase numbers for successive runs of the
7269 simplifier. In an INLINE pragma you can optionally specify a
7273 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7274 <literal>f</literal>
7275 until phase <literal>k</literal>, but from phase
7276 <literal>k</literal> onwards be very keen to inline it.
7279 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7280 <literal>f</literal>
7281 until phase <literal>k</literal>, but from phase
7282 <literal>k</literal> onwards do not inline it.
7285 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7286 <literal>f</literal>
7287 until phase <literal>k</literal>, but from phase
7288 <literal>k</literal> onwards be willing to inline it (as if
7289 there was no pragma).
7292 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7293 <literal>f</literal>
7294 until phase <literal>k</literal>, but from phase
7295 <literal>k</literal> onwards do not inline it.
7298 The same information is summarised here:
7300 -- Before phase 2 Phase 2 and later
7301 {-# INLINE [2] f #-} -- No Yes
7302 {-# INLINE [~2] f #-} -- Yes No
7303 {-# NOINLINE [2] f #-} -- No Maybe
7304 {-# NOINLINE [~2] f #-} -- Maybe No
7306 {-# INLINE f #-} -- Yes Yes
7307 {-# NOINLINE f #-} -- No No
7309 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7310 function body is small, or it is applied to interesting-looking arguments etc).
7311 Another way to understand the semantics is this:
7313 <listitem><para>For both INLINE and NOINLINE, the phase number says
7314 when inlining is allowed at all.</para></listitem>
7315 <listitem><para>The INLINE pragma has the additional effect of making the
7316 function body look small, so that when inlining is allowed it is very likely to
7321 <para>The same phase-numbering control is available for RULES
7322 (<xref linkend="rewrite-rules"/>).</para>
7326 <sect2 id="annotation-pragmas">
7327 <title>ANN pragmas</title>
7329 <para>GHC offers the ability to annotate various code constructs with additional
7330 data by using three pragmas. This data can then be inspected at a later date by
7331 using GHC-as-a-library.</para>
7333 <sect3 id="ann-pragma">
7334 <title>Annotating values</title>
7336 <indexterm><primary>ANN</primary></indexterm>
7338 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7339 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7340 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7341 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7342 you would do this:</para>
7345 {-# ANN foo (Just "Hello") #-}
7350 A number of restrictions apply to use of annotations:
7352 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7353 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7354 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7355 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7356 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7358 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7359 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7362 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7363 please give the GHC team a shout</ulink>.
7366 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7367 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7370 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7375 <sect3 id="typeann-pragma">
7376 <title>Annotating types</title>
7378 <indexterm><primary>ANN type</primary></indexterm>
7379 <indexterm><primary>ANN</primary></indexterm>
7381 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7384 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7389 <sect3 id="modann-pragma">
7390 <title>Annotating modules</title>
7392 <indexterm><primary>ANN module</primary></indexterm>
7393 <indexterm><primary>ANN</primary></indexterm>
7395 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7398 {-# ANN module (Just "A `Maybe String' annotation") #-}
7403 <sect2 id="line-pragma">
7404 <title>LINE pragma</title>
7406 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7407 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7408 <para>This pragma is similar to C's <literal>#line</literal>
7409 pragma, and is mainly for use in automatically generated Haskell
7410 code. It lets you specify the line number and filename of the
7411 original code; for example</para>
7413 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7415 <para>if you'd generated the current file from something called
7416 <filename>Foo.vhs</filename> and this line corresponds to line
7417 42 in the original. GHC will adjust its error messages to refer
7418 to the line/file named in the <literal>LINE</literal>
7423 <title>RULES pragma</title>
7425 <para>The RULES pragma lets you specify rewrite rules. It is
7426 described in <xref linkend="rewrite-rules"/>.</para>
7429 <sect2 id="specialize-pragma">
7430 <title>SPECIALIZE pragma</title>
7432 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7433 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7434 <indexterm><primary>overloading, death to</primary></indexterm>
7436 <para>(UK spelling also accepted.) For key overloaded
7437 functions, you can create extra versions (NB: more code space)
7438 specialised to particular types. Thus, if you have an
7439 overloaded function:</para>
7442 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7445 <para>If it is heavily used on lists with
7446 <literal>Widget</literal> keys, you could specialise it as
7450 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7453 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7454 be put anywhere its type signature could be put.</para>
7456 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7457 (a) a specialised version of the function and (b) a rewrite rule
7458 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7459 un-specialised function into a call to the specialised one.</para>
7461 <para>The type in a SPECIALIZE pragma can be any type that is less
7462 polymorphic than the type of the original function. In concrete terms,
7463 if the original function is <literal>f</literal> then the pragma
7465 {-# SPECIALIZE f :: <type> #-}
7467 is valid if and only if the definition
7469 f_spec :: <type>
7472 is valid. Here are some examples (where we only give the type signature
7473 for the original function, not its code):
7475 f :: Eq a => a -> b -> b
7476 {-# SPECIALISE f :: Int -> b -> b #-}
7478 g :: (Eq a, Ix b) => a -> b -> b
7479 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7481 h :: Eq a => a -> a -> a
7482 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7484 The last of these examples will generate a
7485 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7486 well. If you use this kind of specialisation, let us know how well it works.
7489 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7490 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7491 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7492 The <literal>INLINE</literal> pragma affects the specialised version of the
7493 function (only), and applies even if the function is recursive. The motivating
7496 -- A GADT for arrays with type-indexed representation
7498 ArrInt :: !Int -> ByteArray# -> Arr Int
7499 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7501 (!:) :: Arr e -> Int -> e
7502 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7503 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7504 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7505 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7507 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7508 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7509 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7510 the specialised function will be inlined. It has two calls to
7511 <literal>(!:)</literal>,
7512 both at type <literal>Int</literal>. Both these calls fire the first
7513 specialisation, whose body is also inlined. The result is a type-based
7514 unrolling of the indexing function.</para>
7515 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7516 on an ordinarily-recursive function.</para>
7518 <para>Note: In earlier versions of GHC, it was possible to provide your own
7519 specialised function for a given type:
7522 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7525 This feature has been removed, as it is now subsumed by the
7526 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7530 <sect2 id="specialize-instance-pragma">
7531 <title>SPECIALIZE instance pragma
7535 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7536 <indexterm><primary>overloading, death to</primary></indexterm>
7537 Same idea, except for instance declarations. For example:
7540 instance (Eq a) => Eq (Foo a) where {
7541 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7545 The pragma must occur inside the <literal>where</literal> part
7546 of the instance declaration.
7549 Compatible with HBC, by the way, except perhaps in the placement
7555 <sect2 id="unpack-pragma">
7556 <title>UNPACK pragma</title>
7558 <indexterm><primary>UNPACK</primary></indexterm>
7560 <para>The <literal>UNPACK</literal> indicates to the compiler
7561 that it should unpack the contents of a constructor field into
7562 the constructor itself, removing a level of indirection. For
7566 data T = T {-# UNPACK #-} !Float
7567 {-# UNPACK #-} !Float
7570 <para>will create a constructor <literal>T</literal> containing
7571 two unboxed floats. This may not always be an optimisation: if
7572 the <function>T</function> constructor is scrutinised and the
7573 floats passed to a non-strict function for example, they will
7574 have to be reboxed (this is done automatically by the
7577 <para>Unpacking constructor fields should only be used in
7578 conjunction with <option>-O</option>, in order to expose
7579 unfoldings to the compiler so the reboxing can be removed as
7580 often as possible. For example:</para>
7584 f (T f1 f2) = f1 + f2
7587 <para>The compiler will avoid reboxing <function>f1</function>
7588 and <function>f2</function> by inlining <function>+</function>
7589 on floats, but only when <option>-O</option> is on.</para>
7591 <para>Any single-constructor data is eligible for unpacking; for
7595 data T = T {-# UNPACK #-} !(Int,Int)
7598 <para>will store the two <literal>Int</literal>s directly in the
7599 <function>T</function> constructor, by flattening the pair.
7600 Multi-level unpacking is also supported:
7603 data T = T {-# UNPACK #-} !S
7604 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7607 will store two unboxed <literal>Int#</literal>s
7608 directly in the <function>T</function> constructor. The
7609 unpacker can see through newtypes, too.</para>
7611 <para>If a field cannot be unpacked, you will not get a warning,
7612 so it might be an idea to check the generated code with
7613 <option>-ddump-simpl</option>.</para>
7615 <para>See also the <option>-funbox-strict-fields</option> flag,
7616 which essentially has the effect of adding
7617 <literal>{-# UNPACK #-}</literal> to every strict
7618 constructor field.</para>
7621 <sect2 id="source-pragma">
7622 <title>SOURCE pragma</title>
7624 <indexterm><primary>SOURCE</primary></indexterm>
7625 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7626 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7632 <!-- ======================= REWRITE RULES ======================== -->
7634 <sect1 id="rewrite-rules">
7635 <title>Rewrite rules
7637 <indexterm><primary>RULES pragma</primary></indexterm>
7638 <indexterm><primary>pragma, RULES</primary></indexterm>
7639 <indexterm><primary>rewrite rules</primary></indexterm></title>
7642 The programmer can specify rewrite rules as part of the source program
7648 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7653 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7654 If you need more information, then <option>-ddump-rule-firings</option> shows you
7655 each individual rule firing in detail.
7659 <title>Syntax</title>
7662 From a syntactic point of view:
7668 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7669 may be generated by the layout rule).
7675 The layout rule applies in a pragma.
7676 Currently no new indentation level
7677 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7678 you must lay out the starting in the same column as the enclosing definitions.
7681 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7682 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7685 Furthermore, the closing <literal>#-}</literal>
7686 should start in a column to the right of the opening <literal>{-#</literal>.
7692 Each rule has a name, enclosed in double quotes. The name itself has
7693 no significance at all. It is only used when reporting how many times the rule fired.
7699 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7700 immediately after the name of the rule. Thus:
7703 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7706 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7707 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7716 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7717 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7718 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7719 by spaces, just like in a type <literal>forall</literal>.
7725 A pattern variable may optionally have a type signature.
7726 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7727 For example, here is the <literal>foldr/build</literal> rule:
7730 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7731 foldr k z (build g) = g k z
7734 Since <function>g</function> has a polymorphic type, it must have a type signature.
7741 The left hand side of a rule must consist of a top-level variable applied
7742 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7745 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7746 "wrong2" forall f. f True = True
7749 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7756 A rule does not need to be in the same module as (any of) the
7757 variables it mentions, though of course they need to be in scope.
7763 All rules are implicitly exported from the module, and are therefore
7764 in force in any module that imports the module that defined the rule, directly
7765 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7766 in force when compiling A.) The situation is very similar to that for instance
7774 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7775 any other flag settings. Furthermore, inside a RULE, the language extension
7776 <option>-XScopedTypeVariables</option> is automatically enabled; see
7777 <xref linkend="scoped-type-variables"/>.
7783 Like other pragmas, RULE pragmas are always checked for scope errors, and
7784 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7785 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7786 if the <option>-fenable-rewrite-rules</option> flag is
7787 on (see <xref linkend="rule-semantics"/>).
7796 <sect2 id="rule-semantics">
7797 <title>Semantics</title>
7800 From a semantic point of view:
7805 Rules are enabled (that is, used during optimisation)
7806 by the <option>-fenable-rewrite-rules</option> flag.
7807 This flag is implied by <option>-O</option>, and may be switched
7808 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7809 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7810 may not do what you expect, though, because without <option>-O</option> GHC
7811 ignores all optimisation information in interface files;
7812 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7813 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7814 has no effect on parsing or typechecking.
7820 Rules are regarded as left-to-right rewrite rules.
7821 When GHC finds an expression that is a substitution instance of the LHS
7822 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7823 By "a substitution instance" we mean that the LHS can be made equal to the
7824 expression by substituting for the pattern variables.
7831 GHC makes absolutely no attempt to verify that the LHS and RHS
7832 of a rule have the same meaning. That is undecidable in general, and
7833 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7840 GHC makes no attempt to make sure that the rules are confluent or
7841 terminating. For example:
7844 "loop" forall x y. f x y = f y x
7847 This rule will cause the compiler to go into an infinite loop.
7854 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7860 GHC currently uses a very simple, syntactic, matching algorithm
7861 for matching a rule LHS with an expression. It seeks a substitution
7862 which makes the LHS and expression syntactically equal modulo alpha
7863 conversion. The pattern (rule), but not the expression, is eta-expanded if
7864 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7865 But not beta conversion (that's called higher-order matching).
7869 Matching is carried out on GHC's intermediate language, which includes
7870 type abstractions and applications. So a rule only matches if the
7871 types match too. See <xref linkend="rule-spec"/> below.
7877 GHC keeps trying to apply the rules as it optimises the program.
7878 For example, consider:
7887 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7888 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7889 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7890 not be substituted, and the rule would not fire.
7897 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7898 results. Consider this (artificial) example
7901 {-# RULES "f" f True = False #-}
7907 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7912 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7914 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7915 would have been a better chance that <literal>f</literal>'s RULE might fire.
7918 The way to get predictable behaviour is to use a NOINLINE
7919 pragma on <literal>f</literal>, to ensure
7920 that it is not inlined until its RULEs have had a chance to fire.
7930 <title>List fusion</title>
7933 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7934 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7935 intermediate list should be eliminated entirely.
7939 The following are good producers:
7951 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7957 Explicit lists (e.g. <literal>[True, False]</literal>)
7963 The cons constructor (e.g <literal>3:4:[]</literal>)
7969 <function>++</function>
7975 <function>map</function>
7981 <function>take</function>, <function>filter</function>
7987 <function>iterate</function>, <function>repeat</function>
7993 <function>zip</function>, <function>zipWith</function>
8002 The following are good consumers:
8014 <function>array</function> (on its second argument)
8020 <function>++</function> (on its first argument)
8026 <function>foldr</function>
8032 <function>map</function>
8038 <function>take</function>, <function>filter</function>
8044 <function>concat</function>
8050 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8056 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8057 will fuse with one but not the other)
8063 <function>partition</function>
8069 <function>head</function>
8075 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8081 <function>sequence_</function>
8087 <function>msum</function>
8093 <function>sortBy</function>
8102 So, for example, the following should generate no intermediate lists:
8105 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8111 This list could readily be extended; if there are Prelude functions that you use
8112 a lot which are not included, please tell us.
8116 If you want to write your own good consumers or producers, look at the
8117 Prelude definitions of the above functions to see how to do so.
8122 <sect2 id="rule-spec">
8123 <title>Specialisation
8127 Rewrite rules can be used to get the same effect as a feature
8128 present in earlier versions of GHC.
8129 For example, suppose that:
8132 genericLookup :: Ord a => Table a b -> a -> b
8133 intLookup :: Table Int b -> Int -> b
8136 where <function>intLookup</function> is an implementation of
8137 <function>genericLookup</function> that works very fast for
8138 keys of type <literal>Int</literal>. You might wish
8139 to tell GHC to use <function>intLookup</function> instead of
8140 <function>genericLookup</function> whenever the latter was called with
8141 type <literal>Table Int b -> Int -> b</literal>.
8142 It used to be possible to write
8145 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8148 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8151 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8154 This slightly odd-looking rule instructs GHC to replace
8155 <function>genericLookup</function> by <function>intLookup</function>
8156 <emphasis>whenever the types match</emphasis>.
8157 What is more, this rule does not need to be in the same
8158 file as <function>genericLookup</function>, unlike the
8159 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8160 have an original definition available to specialise).
8163 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8164 <function>intLookup</function> really behaves as a specialised version
8165 of <function>genericLookup</function>!!!</para>
8167 <para>An example in which using <literal>RULES</literal> for
8168 specialisation will Win Big:
8171 toDouble :: Real a => a -> Double
8172 toDouble = fromRational . toRational
8174 {-# RULES "toDouble/Int" toDouble = i2d #-}
8175 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8178 The <function>i2d</function> function is virtually one machine
8179 instruction; the default conversion—via an intermediate
8180 <literal>Rational</literal>—is obscenely expensive by
8187 <title>Controlling what's going on</title>
8195 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8201 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8202 If you add <option>-dppr-debug</option> you get a more detailed listing.
8208 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8211 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8212 {-# INLINE build #-}
8216 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8217 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8218 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8219 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8226 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8227 see how to write rules that will do fusion and yet give an efficient
8228 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8238 <sect2 id="core-pragma">
8239 <title>CORE pragma</title>
8241 <indexterm><primary>CORE pragma</primary></indexterm>
8242 <indexterm><primary>pragma, CORE</primary></indexterm>
8243 <indexterm><primary>core, annotation</primary></indexterm>
8246 The external core format supports <quote>Note</quote> annotations;
8247 the <literal>CORE</literal> pragma gives a way to specify what these
8248 should be in your Haskell source code. Syntactically, core
8249 annotations are attached to expressions and take a Haskell string
8250 literal as an argument. The following function definition shows an
8254 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8257 Semantically, this is equivalent to:
8265 However, when external core is generated (via
8266 <option>-fext-core</option>), there will be Notes attached to the
8267 expressions <function>show</function> and <varname>x</varname>.
8268 The core function declaration for <function>f</function> is:
8272 f :: %forall a . GHCziShow.ZCTShow a ->
8273 a -> GHCziBase.ZMZN GHCziBase.Char =
8274 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8276 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8278 (tpl1::GHCziBase.Int ->
8280 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8282 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8283 (tpl3::GHCziBase.ZMZN a ->
8284 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8292 Here, we can see that the function <function>show</function> (which
8293 has been expanded out to a case expression over the Show dictionary)
8294 has a <literal>%note</literal> attached to it, as does the
8295 expression <varname>eta</varname> (which used to be called
8296 <varname>x</varname>).
8303 <sect1 id="special-ids">
8304 <title>Special built-in functions</title>
8305 <para>GHC has a few built-in functions with special behaviour. These
8306 are now described in the module <ulink
8307 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8308 in the library documentation.</para>
8312 <sect1 id="generic-classes">
8313 <title>Generic classes</title>
8316 The ideas behind this extension are described in detail in "Derivable type classes",
8317 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8318 An example will give the idea:
8326 fromBin :: [Int] -> (a, [Int])
8328 toBin {| Unit |} Unit = []
8329 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8330 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8331 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8333 fromBin {| Unit |} bs = (Unit, bs)
8334 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8335 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8336 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8337 (y,bs'') = fromBin bs'
8340 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8341 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8342 which are defined thus in the library module <literal>Generics</literal>:
8346 data a :+: b = Inl a | Inr b
8347 data a :*: b = a :*: b
8350 Now you can make a data type into an instance of Bin like this:
8352 instance (Bin a, Bin b) => Bin (a,b)
8353 instance Bin a => Bin [a]
8355 That is, just leave off the "where" clause. Of course, you can put in the
8356 where clause and over-ride whichever methods you please.
8360 <title> Using generics </title>
8361 <para>To use generics you need to</para>
8364 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8365 <option>-XGenerics</option> (to generate extra per-data-type code),
8366 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8370 <para>Import the module <literal>Generics</literal> from the
8371 <literal>lang</literal> package. This import brings into
8372 scope the data types <literal>Unit</literal>,
8373 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8374 don't need this import if you don't mention these types
8375 explicitly; for example, if you are simply giving instance
8376 declarations.)</para>
8381 <sect2> <title> Changes wrt the paper </title>
8383 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8384 can be written infix (indeed, you can now use
8385 any operator starting in a colon as an infix type constructor). Also note that
8386 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8387 Finally, note that the syntax of the type patterns in the class declaration
8388 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8389 alone would ambiguous when they appear on right hand sides (an extension we
8390 anticipate wanting).
8394 <sect2> <title>Terminology and restrictions</title>
8396 Terminology. A "generic default method" in a class declaration
8397 is one that is defined using type patterns as above.
8398 A "polymorphic default method" is a default method defined as in Haskell 98.
8399 A "generic class declaration" is a class declaration with at least one
8400 generic default method.
8408 Alas, we do not yet implement the stuff about constructor names and
8415 A generic class can have only one parameter; you can't have a generic
8416 multi-parameter class.
8422 A default method must be defined entirely using type patterns, or entirely
8423 without. So this is illegal:
8426 op :: a -> (a, Bool)
8427 op {| Unit |} Unit = (Unit, True)
8430 However it is perfectly OK for some methods of a generic class to have
8431 generic default methods and others to have polymorphic default methods.
8437 The type variable(s) in the type pattern for a generic method declaration
8438 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:
8442 op {| p :*: q |} (x :*: y) = op (x :: p)
8450 The type patterns in a generic default method must take one of the forms:
8456 where "a" and "b" are type variables. Furthermore, all the type patterns for
8457 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8458 must use the same type variables. So this is illegal:
8462 op {| a :+: b |} (Inl x) = True
8463 op {| p :+: q |} (Inr y) = False
8465 The type patterns must be identical, even in equations for different methods of the class.
8466 So this too is illegal:
8470 op1 {| a :*: b |} (x :*: y) = True
8473 op2 {| p :*: q |} (x :*: y) = False
8475 (The reason for this restriction is that we gather all the equations for a particular type constructor
8476 into a single generic instance declaration.)
8482 A generic method declaration must give a case for each of the three type constructors.
8488 The type for a generic method can be built only from:
8490 <listitem> <para> Function arrows </para> </listitem>
8491 <listitem> <para> Type variables </para> </listitem>
8492 <listitem> <para> Tuples </para> </listitem>
8493 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8495 Here are some example type signatures for generic methods:
8498 op2 :: Bool -> (a,Bool)
8499 op3 :: [Int] -> a -> a
8502 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8506 This restriction is an implementation restriction: we just haven't got around to
8507 implementing the necessary bidirectional maps over arbitrary type constructors.
8508 It would be relatively easy to add specific type constructors, such as Maybe and list,
8509 to the ones that are allowed.</para>
8514 In an instance declaration for a generic class, the idea is that the compiler
8515 will fill in the methods for you, based on the generic templates. However it can only
8520 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8525 No constructor of the instance type has unboxed fields.
8529 (Of course, these things can only arise if you are already using GHC extensions.)
8530 However, you can still give an instance declarations for types which break these rules,
8531 provided you give explicit code to override any generic default methods.
8539 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8540 what the compiler does with generic declarations.
8545 <sect2> <title> Another example </title>
8547 Just to finish with, here's another example I rather like:
8551 nCons {| Unit |} _ = 1
8552 nCons {| a :*: b |} _ = 1
8553 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8556 tag {| Unit |} _ = 1
8557 tag {| a :*: b |} _ = 1
8558 tag {| a :+: b |} (Inl x) = tag x
8559 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8565 <sect1 id="monomorphism">
8566 <title>Control over monomorphism</title>
8568 <para>GHC supports two flags that control the way in which generalisation is
8569 carried out at let and where bindings.
8573 <title>Switching off the dreaded Monomorphism Restriction</title>
8574 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8576 <para>Haskell's monomorphism restriction (see
8577 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8579 of the Haskell Report)
8580 can be completely switched off by
8581 <option>-XNoMonomorphismRestriction</option>.
8586 <title>Monomorphic pattern bindings</title>
8587 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8588 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8590 <para> As an experimental change, we are exploring the possibility of
8591 making pattern bindings monomorphic; that is, not generalised at all.
8592 A pattern binding is a binding whose LHS has no function arguments,
8593 and is not a simple variable. For example:
8595 f x = x -- Not a pattern binding
8596 f = \x -> x -- Not a pattern binding
8597 f :: Int -> Int = \x -> x -- Not a pattern binding
8599 (g,h) = e -- A pattern binding
8600 (f) = e -- A pattern binding
8601 [x] = e -- A pattern binding
8603 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8604 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8613 ;;; Local Variables: ***
8615 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8616 ;;; ispell-local-dictionary: "british" ***
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