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>Here is an example:
1013 employees = [ ("Simon", "MS", 80)
1014 , ("Erik", "MS", 100)
1015 , ("Phil", "Ed", 40)
1016 , ("Gordon", "Ed", 45)
1017 , ("Paul", "Yale", 60)]
1019 output = [ (the dept, sum salary)
1020 | (name, dept, salary) <- employees
1021 , then group by dept
1022 , then sortWith by (sum salary)
1025 In this example, the list <literal>output</literal> would take on
1029 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1032 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1033 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1034 function that is exported by <literal>GHC.Exts</literal>.)</para>
1036 <para>There are five new forms of comprehension qualifier,
1037 all introduced by the (existing) keyword <literal>then</literal>:
1045 This statement requires that <literal>f</literal> have the type <literal>
1046 forall a. [a] -> [a]</literal>. You can see an example of it's use in the
1047 motivating example, as this form is used to apply <literal>take 5</literal>.
1058 This form is similar to the previous one, but allows you to create a function
1059 which will be passed as the first argument to f. As a consequence f must have
1060 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1061 from the type, this function lets f "project out" some information
1062 from the elements of the list it is transforming.</para>
1064 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1065 is supplied with a function that lets it find out the <literal>sum salary</literal>
1066 for any item in the list comprehension it transforms.</para>
1074 then group by e using f
1077 <para>This is the most general of the grouping-type statements. In this form,
1078 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1079 As with the <literal>then f by e</literal> case above, the first argument
1080 is a function supplied to f by the compiler which lets it compute e on every
1081 element of the list being transformed. However, unlike the non-grouping case,
1082 f additionally partitions the list into a number of sublists: this means that
1083 at every point after this statement, binders occurring before it in the comprehension
1084 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1085 this, let's look at an example:</para>
1088 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1089 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1090 groupRuns f = groupBy (\x y -> f x == f y)
1092 output = [ (the x, y)
1093 | x <- ([1..3] ++ [1..2])
1095 , then group by x using groupRuns ]
1098 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1101 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1104 <para>Note that we have used the <literal>the</literal> function to change the type
1105 of x from a list to its original numeric type. The variable y, in contrast, is left
1106 unchanged from the list form introduced by the grouping.</para>
1116 <para>This form of grouping is essentially the same as the one described above. However,
1117 since no function to use for the grouping has been supplied it will fall back on the
1118 <literal>groupWith</literal> function defined in
1119 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1120 is the form of the group statement that we made use of in the opening example.</para>
1131 <para>With this form of the group statement, f is required to simply have the type
1132 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1133 comprehension so far directly. An example of this form is as follows:</para>
1139 , then group using inits]
1142 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1145 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1153 <!-- ===================== REBINDABLE SYNTAX =================== -->
1155 <sect2 id="rebindable-syntax">
1156 <title>Rebindable syntax and the implicit Prelude import</title>
1158 <para><indexterm><primary>-XNoImplicitPrelude
1159 option</primary></indexterm> GHC normally imports
1160 <filename>Prelude.hi</filename> files for you. If you'd
1161 rather it didn't, then give it a
1162 <option>-XNoImplicitPrelude</option> option. The idea is
1163 that you can then import a Prelude of your own. (But don't
1164 call it <literal>Prelude</literal>; the Haskell module
1165 namespace is flat, and you must not conflict with any
1166 Prelude module.)</para>
1168 <para>Suppose you are importing a Prelude of your own
1169 in order to define your own numeric class
1170 hierarchy. It completely defeats that purpose if the
1171 literal "1" means "<literal>Prelude.fromInteger
1172 1</literal>", which is what the Haskell Report specifies.
1173 So the <option>-XNoImplicitPrelude</option>
1174 flag <emphasis>also</emphasis> causes
1175 the following pieces of built-in syntax to refer to
1176 <emphasis>whatever is in scope</emphasis>, not the Prelude
1180 <para>An integer literal <literal>368</literal> means
1181 "<literal>fromInteger (368::Integer)</literal>", rather than
1182 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1185 <listitem><para>Fractional literals are handed in just the same way,
1186 except that the translation is
1187 <literal>fromRational (3.68::Rational)</literal>.
1190 <listitem><para>The equality test in an overloaded numeric pattern
1191 uses whatever <literal>(==)</literal> is in scope.
1194 <listitem><para>The subtraction operation, and the
1195 greater-than-or-equal test, in <literal>n+k</literal> patterns
1196 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1200 <para>Negation (e.g. "<literal>- (f x)</literal>")
1201 means "<literal>negate (f x)</literal>", both in numeric
1202 patterns, and expressions.
1206 <para>"Do" notation is translated using whatever
1207 functions <literal>(>>=)</literal>,
1208 <literal>(>>)</literal>, and <literal>fail</literal>,
1209 are in scope (not the Prelude
1210 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1211 comprehensions, are unaffected. </para></listitem>
1215 notation (see <xref linkend="arrow-notation"/>)
1216 uses whatever <literal>arr</literal>,
1217 <literal>(>>>)</literal>, <literal>first</literal>,
1218 <literal>app</literal>, <literal>(|||)</literal> and
1219 <literal>loop</literal> functions are in scope. But unlike the
1220 other constructs, the types of these functions must match the
1221 Prelude types very closely. Details are in flux; if you want
1225 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1226 even if that is a little unexpected. For example, the
1227 static semantics of the literal <literal>368</literal>
1228 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1229 <literal>fromInteger</literal> to have any of the types:
1231 fromInteger :: Integer -> Integer
1232 fromInteger :: forall a. Foo a => Integer -> a
1233 fromInteger :: Num a => a -> Integer
1234 fromInteger :: Integer -> Bool -> Bool
1238 <para>Be warned: this is an experimental facility, with
1239 fewer checks than usual. Use <literal>-dcore-lint</literal>
1240 to typecheck the desugared program. If Core Lint is happy
1241 you should be all right.</para>
1245 <sect2 id="postfix-operators">
1246 <title>Postfix operators</title>
1249 The <option>-XPostfixOperators</option> flag enables a small
1250 extension to the syntax of left operator sections, which allows you to
1251 define postfix operators. The extension is this: the left section
1255 is equivalent (from the point of view of both type checking and execution) to the expression
1259 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1260 The strict Haskell 98 interpretation is that the section is equivalent to
1264 That is, the operator must be a function of two arguments. GHC allows it to
1265 take only one argument, and that in turn allows you to write the function
1268 <para>The extension does not extend to the left-hand side of function
1269 definitions; you must define such a function in prefix form.</para>
1273 <sect2 id="disambiguate-fields">
1274 <title>Record field disambiguation</title>
1276 In record construction and record pattern matching
1277 it is entirely unambiguous which field is referred to, even if there are two different
1278 data types in scope with a common field name. For example:
1281 data S = MkS { x :: Int, y :: Bool }
1286 data T = MkT { x :: Int }
1288 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1290 ok2 n = MkT { x = n+1 } -- Unambiguous
1292 bad1 k = k { x = 3 } -- Ambiguous
1293 bad2 k = x k -- Ambiguous
1295 Even though there are two <literal>x</literal>'s in scope,
1296 it is clear that the <literal>x</literal> in the pattern in the
1297 definition of <literal>ok1</literal> can only mean the field
1298 <literal>x</literal> from type <literal>S</literal>. Similarly for
1299 the function <literal>ok2</literal>. However, in the record update
1300 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1301 it is not clear which of the two types is intended.
1304 Haskell 98 regards all four as ambiguous, but with the
1305 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1306 the former two. The rules are precisely the same as those for instance
1307 declarations in Haskell 98, where the method names on the left-hand side
1308 of the method bindings in an instance declaration refer unambiguously
1309 to the method of that class (provided they are in scope at all), even
1310 if there are other variables in scope with the same name.
1311 This reduces the clutter of qualified names when you import two
1312 records from different modules that use the same field name.
1316 <!-- ===================== Record puns =================== -->
1318 <sect2 id="record-puns">
1323 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1327 When using records, it is common to write a pattern that binds a
1328 variable with the same name as a record field, such as:
1331 data C = C {a :: Int}
1337 Record punning permits the variable name to be elided, so one can simply
1344 to mean the same pattern as above. That is, in a record pattern, the
1345 pattern <literal>a</literal> expands into the pattern <literal>a =
1346 a</literal> for the same name <literal>a</literal>.
1350 Note that puns and other patterns can be mixed in the same record:
1352 data C = C {a :: Int, b :: Int}
1353 f (C {a, b = 4}) = a
1355 and that puns can be used wherever record patterns occur (e.g. in
1356 <literal>let</literal> bindings or at the top-level).
1360 Record punning can also be used in an expression, writing, for example,
1366 let a = 1 in C {a = a}
1369 Note that this expansion is purely syntactic, so the record pun
1370 expression refers to the nearest enclosing variable that is spelled the
1371 same as the field name.
1376 <!-- ===================== Record wildcards =================== -->
1378 <sect2 id="record-wildcards">
1379 <title>Record wildcards
1383 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1387 For records with many fields, it can be tiresome to write out each field
1388 individually in a record pattern, as in
1390 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1391 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1396 Record wildcard syntax permits a (<literal>..</literal>) in a record
1397 pattern, where each elided field <literal>f</literal> is replaced by the
1398 pattern <literal>f = f</literal>. For example, the above pattern can be
1401 f (C {a = 1, ..}) = b + c + d
1406 Note that wildcards can be mixed with other patterns, including puns
1407 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1408 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1409 wherever record patterns occur, including in <literal>let</literal>
1410 bindings and at the top-level. For example, the top-level binding
1414 defines <literal>b</literal>, <literal>c</literal>, and
1415 <literal>d</literal>.
1419 Record wildcards can also be used in expressions, writing, for example,
1422 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1428 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1431 Note that this expansion is purely syntactic, so the record wildcard
1432 expression refers to the nearest enclosing variables that are spelled
1433 the same as the omitted field names.
1438 <!-- ===================== Local fixity declarations =================== -->
1440 <sect2 id="local-fixity-declarations">
1441 <title>Local Fixity Declarations
1444 <para>A careful reading of the Haskell 98 Report reveals that fixity
1445 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1446 <literal>infixr</literal>) are permitted to appear inside local bindings
1447 such those introduced by <literal>let</literal> and
1448 <literal>where</literal>. However, the Haskell Report does not specify
1449 the semantics of such bindings very precisely.
1452 <para>In GHC, a fixity declaration may accompany a local binding:
1459 and the fixity declaration applies wherever the binding is in scope.
1460 For example, in a <literal>let</literal>, it applies in the right-hand
1461 sides of other <literal>let</literal>-bindings and the body of the
1462 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1463 expressions (<xref linkend="mdo-notation"/>), the local fixity
1464 declarations of a <literal>let</literal> statement scope over other
1465 statements in the group, just as the bound name does.
1469 Moreover, a local fixity declaration *must* accompany a local binding of
1470 that name: it is not possible to revise the fixity of name bound
1473 let infixr 9 $ in ...
1476 Because local fixity declarations are technically Haskell 98, no flag is
1477 necessary to enable them.
1481 <sect2 id="package-imports">
1482 <title>Package-qualified imports</title>
1484 <para>With the <option>-XPackageImports</option> flag, GHC allows
1485 import declarations to be qualified by the package name that the
1486 module is intended to be imported from. For example:</para>
1489 import "network" Network.Socket
1492 <para>would import the module <literal>Network.Socket</literal> from
1493 the package <literal>network</literal> (any version). This may
1494 be used to disambiguate an import when the same module is
1495 available from multiple packages, or is present in both the
1496 current package being built and an external package.</para>
1498 <para>Note: you probably don't need to use this feature, it was
1499 added mainly so that we can build backwards-compatible versions of
1500 packages when APIs change. It can lead to fragile dependencies in
1501 the common case: modules occasionally move from one package to
1502 another, rendering any package-qualified imports broken.</para>
1505 <sect2 id="syntax-stolen">
1506 <title>Summary of stolen syntax</title>
1508 <para>Turning on an option that enables special syntax
1509 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1510 to compile, perhaps because it uses a variable name which has
1511 become a reserved word. This section lists the syntax that is
1512 "stolen" by language extensions.
1514 notation and nonterminal names from the Haskell 98 lexical syntax
1515 (see the Haskell 98 Report).
1516 We only list syntax changes here that might affect
1517 existing working programs (i.e. "stolen" syntax). Many of these
1518 extensions will also enable new context-free syntax, but in all
1519 cases programs written to use the new syntax would not be
1520 compilable without the option enabled.</para>
1522 <para>There are two classes of special
1527 <para>New reserved words and symbols: character sequences
1528 which are no longer available for use as identifiers in the
1532 <para>Other special syntax: sequences of characters that have
1533 a different meaning when this particular option is turned
1538 The following syntax is stolen:
1543 <literal>forall</literal>
1544 <indexterm><primary><literal>forall</literal></primary></indexterm>
1547 Stolen (in types) by: <option>-XScopedTypeVariables</option>,
1548 <option>-XLiberalTypeSynonyms</option>,
1549 <option>-XRank2Types</option>,
1550 <option>-XRankNTypes</option>,
1551 <option>-XPolymorphicComponents</option>,
1552 <option>-XExistentialQuantification</option>
1558 <literal>mdo</literal>
1559 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1562 Stolen by: <option>-XRecursiveDo</option>,
1568 <literal>foreign</literal>
1569 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1572 Stolen by: <option>-XForeignFunctionInterface</option>,
1578 <literal>rec</literal>,
1579 <literal>proc</literal>, <literal>-<</literal>,
1580 <literal>>-</literal>, <literal>-<<</literal>,
1581 <literal>>>-</literal>, and <literal>(|</literal>,
1582 <literal>|)</literal> brackets
1583 <indexterm><primary><literal>proc</literal></primary></indexterm>
1586 Stolen by: <option>-XArrows</option>,
1592 <literal>?<replaceable>varid</replaceable></literal>,
1593 <literal>%<replaceable>varid</replaceable></literal>
1594 <indexterm><primary>implicit parameters</primary></indexterm>
1597 Stolen by: <option>-XImplicitParams</option>,
1603 <literal>[|</literal>,
1604 <literal>[e|</literal>, <literal>[p|</literal>,
1605 <literal>[d|</literal>, <literal>[t|</literal>,
1606 <literal>$(</literal>,
1607 <literal>$<replaceable>varid</replaceable></literal>
1608 <indexterm><primary>Template Haskell</primary></indexterm>
1611 Stolen by: <option>-XTemplateHaskell</option>,
1617 <literal>[:<replaceable>varid</replaceable>|</literal>
1618 <indexterm><primary>quasi-quotation</primary></indexterm>
1621 Stolen by: <option>-XQuasiQuotes</option>,
1627 <replaceable>varid</replaceable>{<literal>#</literal>},
1628 <replaceable>char</replaceable><literal>#</literal>,
1629 <replaceable>string</replaceable><literal>#</literal>,
1630 <replaceable>integer</replaceable><literal>#</literal>,
1631 <replaceable>float</replaceable><literal>#</literal>,
1632 <replaceable>float</replaceable><literal>##</literal>,
1633 <literal>(#</literal>, <literal>#)</literal>,
1636 Stolen by: <option>-XMagicHash</option>,
1645 <!-- TYPE SYSTEM EXTENSIONS -->
1646 <sect1 id="data-type-extensions">
1647 <title>Extensions to data types and type synonyms</title>
1649 <sect2 id="nullary-types">
1650 <title>Data types with no constructors</title>
1652 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1653 a data type with no constructors. For example:</para>
1657 data T a -- T :: * -> *
1660 <para>Syntactically, the declaration lacks the "= constrs" part. The
1661 type can be parameterised over types of any kind, but if the kind is
1662 not <literal>*</literal> then an explicit kind annotation must be used
1663 (see <xref linkend="kinding"/>).</para>
1665 <para>Such data types have only one value, namely bottom.
1666 Nevertheless, they can be useful when defining "phantom types".</para>
1669 <sect2 id="infix-tycons">
1670 <title>Infix type constructors, classes, and type variables</title>
1673 GHC allows type constructors, classes, and type variables to be operators, and
1674 to be written infix, very much like expressions. More specifically:
1677 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1678 The lexical syntax is the same as that for data constructors.
1681 Data type and type-synonym declarations can be written infix, parenthesised
1682 if you want further arguments. E.g.
1684 data a :*: b = Foo a b
1685 type a :+: b = Either a b
1686 class a :=: b where ...
1688 data (a :**: b) x = Baz a b x
1689 type (a :++: b) y = Either (a,b) y
1693 Types, and class constraints, can be written infix. For example
1696 f :: (a :=: b) => a -> b
1700 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1701 The lexical syntax is the same as that for variable operators, excluding "(.)",
1702 "(!)", and "(*)". In a binding position, the operator must be
1703 parenthesised. For example:
1705 type T (+) = Int + Int
1709 liftA2 :: Arrow (~>)
1710 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1716 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1717 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1720 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1721 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1722 sets the fixity for a data constructor and the corresponding type constructor. For example:
1726 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1727 and similarly for <literal>:*:</literal>.
1728 <literal>Int `a` Bool</literal>.
1731 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1738 <sect2 id="type-synonyms">
1739 <title>Liberalised type synonyms</title>
1742 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1743 on individual synonym declarations.
1744 With the <option>-XLiberalTypeSynonyms</option> extension,
1745 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1746 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1749 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1750 in a type synonym, thus:
1752 type Discard a = forall b. Show b => a -> b -> (a, String)
1757 g :: Discard Int -> (Int,String) -- A rank-2 type
1764 If you also use <option>-XUnboxedTuples</option>,
1765 you can write an unboxed tuple in a type synonym:
1767 type Pr = (# Int, Int #)
1775 You can apply a type synonym to a forall type:
1777 type Foo a = a -> a -> Bool
1779 f :: Foo (forall b. b->b)
1781 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1783 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1788 You can apply a type synonym to a partially applied type synonym:
1790 type Generic i o = forall x. i x -> o x
1793 foo :: Generic Id []
1795 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1797 foo :: forall x. x -> [x]
1805 GHC currently does kind checking before expanding synonyms (though even that
1809 After expanding type synonyms, GHC does validity checking on types, looking for
1810 the following mal-formedness which isn't detected simply by kind checking:
1813 Type constructor applied to a type involving for-alls.
1816 Unboxed tuple on left of an arrow.
1819 Partially-applied type synonym.
1823 this will be rejected:
1825 type Pr = (# Int, Int #)
1830 because GHC does not allow unboxed tuples on the left of a function arrow.
1835 <sect2 id="existential-quantification">
1836 <title>Existentially quantified data constructors
1840 The idea of using existential quantification in data type declarations
1841 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1842 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1843 London, 1991). It was later formalised by Laufer and Odersky
1844 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1845 TOPLAS, 16(5), pp1411-1430, 1994).
1846 It's been in Lennart
1847 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1848 proved very useful. Here's the idea. Consider the declaration:
1854 data Foo = forall a. MkFoo a (a -> Bool)
1861 The data type <literal>Foo</literal> has two constructors with types:
1867 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1874 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1875 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1876 For example, the following expression is fine:
1882 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1888 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1889 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1890 isUpper</function> packages a character with a compatible function. These
1891 two things are each of type <literal>Foo</literal> and can be put in a list.
1895 What can we do with a value of type <literal>Foo</literal>?. In particular,
1896 what happens when we pattern-match on <function>MkFoo</function>?
1902 f (MkFoo val fn) = ???
1908 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1909 are compatible, the only (useful) thing we can do with them is to
1910 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1917 f (MkFoo val fn) = fn val
1923 What this allows us to do is to package heterogeneous values
1924 together with a bunch of functions that manipulate them, and then treat
1925 that collection of packages in a uniform manner. You can express
1926 quite a bit of object-oriented-like programming this way.
1929 <sect3 id="existential">
1930 <title>Why existential?
1934 What has this to do with <emphasis>existential</emphasis> quantification?
1935 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1941 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1947 But Haskell programmers can safely think of the ordinary
1948 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1949 adding a new existential quantification construct.
1954 <sect3 id="existential-with-context">
1955 <title>Existentials and type classes</title>
1958 An easy extension is to allow
1959 arbitrary contexts before the constructor. For example:
1965 data Baz = forall a. Eq a => Baz1 a a
1966 | forall b. Show b => Baz2 b (b -> b)
1972 The two constructors have the types you'd expect:
1978 Baz1 :: forall a. Eq a => a -> a -> Baz
1979 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1985 But when pattern matching on <function>Baz1</function> the matched values can be compared
1986 for equality, and when pattern matching on <function>Baz2</function> the first matched
1987 value can be converted to a string (as well as applying the function to it).
1988 So this program is legal:
1995 f (Baz1 p q) | p == q = "Yes"
1997 f (Baz2 v fn) = show (fn v)
2003 Operationally, in a dictionary-passing implementation, the
2004 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2005 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2006 extract it on pattern matching.
2011 <sect3 id="existential-records">
2012 <title>Record Constructors</title>
2015 GHC allows existentials to be used with records syntax as well. For example:
2018 data Counter a = forall self. NewCounter
2020 , _inc :: self -> self
2021 , _display :: self -> IO ()
2025 Here <literal>tag</literal> is a public field, with a well-typed selector
2026 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2027 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2028 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2029 compile-time error. In other words, <emphasis>GHC defines a record selector function
2030 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2031 (This example used an underscore in the fields for which record selectors
2032 will not be defined, but that is only programming style; GHC ignores them.)
2036 To make use of these hidden fields, we need to create some helper functions:
2039 inc :: Counter a -> Counter a
2040 inc (NewCounter x i d t) = NewCounter
2041 { _this = i x, _inc = i, _display = d, tag = t }
2043 display :: Counter a -> IO ()
2044 display NewCounter{ _this = x, _display = d } = d x
2047 Now we can define counters with different underlying implementations:
2050 counterA :: Counter String
2051 counterA = NewCounter
2052 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2054 counterB :: Counter String
2055 counterB = NewCounter
2056 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2059 display (inc counterA) -- prints "1"
2060 display (inc (inc counterB)) -- prints "##"
2063 Record update syntax is supported for existentials (and GADTs):
2065 setTag :: Counter a -> a -> Counter a
2066 setTag obj t = obj{ tag = t }
2068 The rule for record update is this: <emphasis>
2069 the types of the updated fields may
2070 mention only the universally-quantified type variables
2071 of the data constructor. For GADTs, the field may mention only types
2072 that appear as a simple type-variable argument in the constructor's result
2073 type</emphasis>. For example:
2075 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2076 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2077 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2078 -- existentially quantified)
2080 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2081 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2082 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2083 -- type-variable argument in G1's result type)
2091 <title>Restrictions</title>
2094 There are several restrictions on the ways in which existentially-quantified
2095 constructors can be use.
2104 When pattern matching, each pattern match introduces a new,
2105 distinct, type for each existential type variable. These types cannot
2106 be unified with any other type, nor can they escape from the scope of
2107 the pattern match. For example, these fragments are incorrect:
2115 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2116 is the result of <function>f1</function>. One way to see why this is wrong is to
2117 ask what type <function>f1</function> has:
2121 f1 :: Foo -> a -- Weird!
2125 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2130 f1 :: forall a. Foo -> a -- Wrong!
2134 The original program is just plain wrong. Here's another sort of error
2138 f2 (Baz1 a b) (Baz1 p q) = a==q
2142 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2143 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2144 from the two <function>Baz1</function> constructors.
2152 You can't pattern-match on an existentially quantified
2153 constructor in a <literal>let</literal> or <literal>where</literal> group of
2154 bindings. So this is illegal:
2158 f3 x = a==b where { Baz1 a b = x }
2161 Instead, use a <literal>case</literal> expression:
2164 f3 x = case x of Baz1 a b -> a==b
2167 In general, you can only pattern-match
2168 on an existentially-quantified constructor in a <literal>case</literal> expression or
2169 in the patterns of a function definition.
2171 The reason for this restriction is really an implementation one.
2172 Type-checking binding groups is already a nightmare without
2173 existentials complicating the picture. Also an existential pattern
2174 binding at the top level of a module doesn't make sense, because it's
2175 not clear how to prevent the existentially-quantified type "escaping".
2176 So for now, there's a simple-to-state restriction. We'll see how
2184 You can't use existential quantification for <literal>newtype</literal>
2185 declarations. So this is illegal:
2189 newtype T = forall a. Ord a => MkT a
2193 Reason: a value of type <literal>T</literal> must be represented as a
2194 pair of a dictionary for <literal>Ord t</literal> and a value of type
2195 <literal>t</literal>. That contradicts the idea that
2196 <literal>newtype</literal> should have no concrete representation.
2197 You can get just the same efficiency and effect by using
2198 <literal>data</literal> instead of <literal>newtype</literal>. If
2199 there is no overloading involved, then there is more of a case for
2200 allowing an existentially-quantified <literal>newtype</literal>,
2201 because the <literal>data</literal> version does carry an
2202 implementation cost, but single-field existentially quantified
2203 constructors aren't much use. So the simple restriction (no
2204 existential stuff on <literal>newtype</literal>) stands, unless there
2205 are convincing reasons to change it.
2213 You can't use <literal>deriving</literal> to define instances of a
2214 data type with existentially quantified data constructors.
2216 Reason: in most cases it would not make sense. For example:;
2219 data T = forall a. MkT [a] deriving( Eq )
2222 To derive <literal>Eq</literal> in the standard way we would need to have equality
2223 between the single component of two <function>MkT</function> constructors:
2227 (MkT a) == (MkT b) = ???
2230 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2231 It's just about possible to imagine examples in which the derived instance
2232 would make sense, but it seems altogether simpler simply to prohibit such
2233 declarations. Define your own instances!
2244 <!-- ====================== Generalised algebraic data types ======================= -->
2246 <sect2 id="gadt-style">
2247 <title>Declaring data types with explicit constructor signatures</title>
2249 <para>GHC allows you to declare an algebraic data type by
2250 giving the type signatures of constructors explicitly. For example:
2254 Just :: a -> Maybe a
2256 The form is called a "GADT-style declaration"
2257 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2258 can only be declared using this form.</para>
2259 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2260 For example, these two declarations are equivalent:
2262 data Foo = forall a. MkFoo a (a -> Bool)
2263 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2266 <para>Any data type that can be declared in standard Haskell-98 syntax
2267 can also be declared using GADT-style syntax.
2268 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2269 they treat class constraints on the data constructors differently.
2270 Specifically, if the constructor is given a type-class context, that
2271 context is made available by pattern matching. For example:
2274 MkSet :: Eq a => [a] -> Set a
2276 makeSet :: Eq a => [a] -> Set a
2277 makeSet xs = MkSet (nub xs)
2279 insert :: a -> Set a -> Set a
2280 insert a (MkSet as) | a `elem` as = MkSet as
2281 | otherwise = MkSet (a:as)
2283 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2284 gives rise to a <literal>(Eq a)</literal>
2285 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2286 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2287 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2288 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2289 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2290 In the example, the equality dictionary is used to satisfy the equality constraint
2291 generated by the call to <literal>elem</literal>, so that the type of
2292 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2295 For example, one possible application is to reify dictionaries:
2297 data NumInst a where
2298 MkNumInst :: Num a => NumInst a
2300 intInst :: NumInst Int
2303 plus :: NumInst a -> a -> a -> a
2304 plus MkNumInst p q = p + q
2306 Here, a value of type <literal>NumInst a</literal> is equivalent
2307 to an explicit <literal>(Num a)</literal> dictionary.
2310 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2311 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2315 = Num a => MkNumInst (NumInst a)
2317 Notice that, unlike the situation when declaring an existential, there is
2318 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2319 data type's universally quantified type variable <literal>a</literal>.
2320 A constructor may have both universal and existential type variables: for example,
2321 the following two declarations are equivalent:
2324 = forall b. (Num a, Eq b) => MkT1 a b
2326 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2329 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2330 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2331 In Haskell 98 the definition
2333 data Eq a => Set' a = MkSet' [a]
2335 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2336 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2337 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2338 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2339 GHC's behaviour is much more useful, as well as much more intuitive.
2343 The rest of this section gives further details about GADT-style data
2348 The result type of each data constructor must begin with the type constructor being defined.
2349 If the result type of all constructors
2350 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2351 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2352 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2356 As with other type signatures, you can give a single signature for several data constructors.
2357 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2366 The type signature of
2367 each constructor is independent, and is implicitly universally quantified as usual.
2368 Different constructors may have different universally-quantified type variables
2369 and different type-class constraints.
2370 For example, this is fine:
2373 T1 :: Eq b => b -> T b
2374 T2 :: (Show c, Ix c) => c -> [c] -> T c
2379 Unlike a Haskell-98-style
2380 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2381 have no scope. Indeed, one can write a kind signature instead:
2383 data Set :: * -> * where ...
2385 or even a mixture of the two:
2387 data Foo a :: (* -> *) -> * where ...
2389 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2392 data Foo a (b :: * -> *) where ...
2398 You can use strictness annotations, in the obvious places
2399 in the constructor type:
2402 Lit :: !Int -> Term Int
2403 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2404 Pair :: Term a -> Term b -> Term (a,b)
2409 You can use a <literal>deriving</literal> clause on a GADT-style data type
2410 declaration. For example, these two declarations are equivalent
2412 data Maybe1 a where {
2413 Nothing1 :: Maybe1 a ;
2414 Just1 :: a -> Maybe1 a
2415 } deriving( Eq, Ord )
2417 data Maybe2 a = Nothing2 | Just2 a
2423 You can use record syntax on a GADT-style data type declaration:
2427 Adult { name :: String, children :: [Person] } :: Person
2428 Child { name :: String } :: Person
2430 As usual, for every constructor that has a field <literal>f</literal>, the type of
2431 field <literal>f</literal> must be the same (modulo alpha conversion).
2434 At the moment, record updates are not yet possible with GADT-style declarations,
2435 so support is limited to record construction, selection and pattern matching.
2438 aPerson = Adult { name = "Fred", children = [] }
2440 shortName :: Person -> Bool
2441 hasChildren (Adult { children = kids }) = not (null kids)
2442 hasChildren (Child {}) = False
2447 As in the case of existentials declared using the Haskell-98-like record syntax
2448 (<xref linkend="existential-records"/>),
2449 record-selector functions are generated only for those fields that have well-typed
2451 Here is the example of that section, in GADT-style syntax:
2453 data Counter a where
2454 NewCounter { _this :: self
2455 , _inc :: self -> self
2456 , _display :: self -> IO ()
2461 As before, only one selector function is generated here, that for <literal>tag</literal>.
2462 Nevertheless, you can still use all the field names in pattern matching and record construction.
2464 </itemizedlist></para>
2468 <title>Generalised Algebraic Data Types (GADTs)</title>
2470 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2471 by allowing constructors to have richer return types. Here is an example:
2474 Lit :: Int -> Term Int
2475 Succ :: Term Int -> Term Int
2476 IsZero :: Term Int -> Term Bool
2477 If :: Term Bool -> Term a -> Term a -> Term a
2478 Pair :: Term a -> Term b -> Term (a,b)
2480 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2481 case with ordinary data types. This generality allows us to
2482 write a well-typed <literal>eval</literal> function
2483 for these <literal>Terms</literal>:
2487 eval (Succ t) = 1 + eval t
2488 eval (IsZero t) = eval t == 0
2489 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2490 eval (Pair e1 e2) = (eval e1, eval e2)
2492 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2493 For example, in the right hand side of the equation
2498 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2499 A precise specification of the type rules is beyond what this user manual aspires to,
2500 but the design closely follows that described in
2502 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2503 unification-based type inference for GADTs</ulink>,
2505 The general principle is this: <emphasis>type refinement is only carried out
2506 based on user-supplied type annotations</emphasis>.
2507 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2508 and lots of obscure error messages will
2509 occur. However, the refinement is quite general. For example, if we had:
2511 eval :: Term a -> a -> a
2512 eval (Lit i) j = i+j
2514 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2515 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2516 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2519 These and many other examples are given in papers by Hongwei Xi, and
2520 Tim Sheard. There is a longer introduction
2521 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2523 <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
2524 may use different notation to that implemented in GHC.
2527 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2528 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2531 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2532 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2533 The result type of each constructor must begin with the type constructor being defined,
2534 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2535 For example, in the <literal>Term</literal> data
2536 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2537 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2542 It's is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2543 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2544 whose result type is not just <literal>T a b</literal>.
2548 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2549 an ordinary data type.
2553 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2557 Lit { val :: Int } :: Term Int
2558 Succ { num :: Term Int } :: Term Int
2559 Pred { num :: Term Int } :: Term Int
2560 IsZero { arg :: Term Int } :: Term Bool
2561 Pair { arg1 :: Term a
2564 If { cnd :: Term Bool
2569 However, for GADTs there is the following additional constraint:
2570 every constructor that has a field <literal>f</literal> must have
2571 the same result type (modulo alpha conversion)
2572 Hence, in the above example, we cannot merge the <literal>num</literal>
2573 and <literal>arg</literal> fields above into a
2574 single name. Although their field types are both <literal>Term Int</literal>,
2575 their selector functions actually have different types:
2578 num :: Term Int -> Term Int
2579 arg :: Term Bool -> Term Int
2584 When pattern-matching against data constructors drawn from a GADT,
2585 for example in a <literal>case</literal> expression, the following rules apply:
2587 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2588 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2589 <listitem><para>The type of any free variable mentioned in any of
2590 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2592 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2593 way to ensure that a variable a rigid type is to give it a type signature.
2594 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2595 Simple unification-based type inference for GADTs
2596 </ulink>. The criteria implemented by GHC are given in the Appendix.
2606 <!-- ====================== End of Generalised algebraic data types ======================= -->
2608 <sect1 id="deriving">
2609 <title>Extensions to the "deriving" mechanism</title>
2611 <sect2 id="deriving-inferred">
2612 <title>Inferred context for deriving clauses</title>
2615 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2618 data T0 f a = MkT0 a deriving( Eq )
2619 data T1 f a = MkT1 (f a) deriving( Eq )
2620 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2622 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2624 instance Eq a => Eq (T0 f a) where ...
2625 instance Eq (f a) => Eq (T1 f a) where ...
2626 instance Eq (f (f a)) => Eq (T2 f a) where ...
2628 The first of these is obviously fine. The second is still fine, although less obviously.
2629 The third is not Haskell 98, and risks losing termination of instances.
2632 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2633 each constraint in the inferred instance context must consist only of type variables,
2634 with no repetitions.
2637 This rule is applied regardless of flags. If you want a more exotic context, you can write
2638 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2642 <sect2 id="stand-alone-deriving">
2643 <title>Stand-alone deriving declarations</title>
2646 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2648 data Foo a = Bar a | Baz String
2650 deriving instance Eq a => Eq (Foo a)
2652 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2653 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2654 You must supply a context (in the example the context is <literal>(Eq a)</literal>),
2655 exactly as you would in an ordinary instance declaration.
2656 (In contrast the context is inferred in a <literal>deriving</literal> clause
2657 attached to a data type declaration.)
2659 A <literal>deriving instance</literal> declaration
2660 must obey the same rules concerning form and termination as ordinary instance declarations,
2661 controlled by the same flags; see <xref linkend="instance-decls"/>.
2664 Unlike a <literal>deriving</literal>
2665 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2666 than the data type (assuming you also use
2667 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2670 data Foo a = Bar a | Baz String
2672 deriving instance Eq a => Eq (Foo [a])
2673 deriving instance Eq a => Eq (Foo (Maybe a))
2675 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2676 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2679 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2680 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2683 newtype Foo a = MkFoo (State Int a)
2685 deriving instance MonadState Int Foo
2687 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2688 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2694 <sect2 id="deriving-typeable">
2695 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2698 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2699 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2700 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2701 classes <literal>Eq</literal>, <literal>Ord</literal>,
2702 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2705 GHC extends this list with several more classes that may be automatically derived:
2707 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2708 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2709 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2711 <para>An instance of <literal>Typeable</literal> can only be derived if the
2712 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2713 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2715 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2716 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2718 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2719 are used, and only <literal>Typeable1</literal> up to
2720 <literal>Typeable7</literal> are provided in the library.)
2721 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2722 class, whose kind suits that of the data type constructor, and
2723 then writing the data type instance by hand.
2727 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2728 the class <literal>Functor</literal>,
2729 defined in <literal>GHC.Base</literal>.
2732 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2733 the class <literal>Foldable</literal>,
2734 defined in <literal>Data.Foldable</literal>.
2737 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2738 the class <literal>Traversable</literal>,
2739 defined in <literal>Data.Traversable</literal>.
2742 In each case the appropriate class must be in scope before it
2743 can be mentioned in the <literal>deriving</literal> clause.
2747 <sect2 id="newtype-deriving">
2748 <title>Generalised derived instances for newtypes</title>
2751 When you define an abstract type using <literal>newtype</literal>, you may want
2752 the new type to inherit some instances from its representation. In
2753 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2754 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2755 other classes you have to write an explicit instance declaration. For
2756 example, if you define
2759 newtype Dollars = Dollars Int
2762 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2763 explicitly define an instance of <literal>Num</literal>:
2766 instance Num Dollars where
2767 Dollars a + Dollars b = Dollars (a+b)
2770 All the instance does is apply and remove the <literal>newtype</literal>
2771 constructor. It is particularly galling that, since the constructor
2772 doesn't appear at run-time, this instance declaration defines a
2773 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2774 dictionary, only slower!
2778 <sect3> <title> Generalising the deriving clause </title>
2780 GHC now permits such instances to be derived instead,
2781 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2784 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2787 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2788 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2789 derives an instance declaration of the form
2792 instance Num Int => Num Dollars
2795 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2799 We can also derive instances of constructor classes in a similar
2800 way. For example, suppose we have implemented state and failure monad
2801 transformers, such that
2804 instance Monad m => Monad (State s m)
2805 instance Monad m => Monad (Failure m)
2807 In Haskell 98, we can define a parsing monad by
2809 type Parser tok m a = State [tok] (Failure m) a
2812 which is automatically a monad thanks to the instance declarations
2813 above. With the extension, we can make the parser type abstract,
2814 without needing to write an instance of class <literal>Monad</literal>, via
2817 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2820 In this case the derived instance declaration is of the form
2822 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2825 Notice that, since <literal>Monad</literal> is a constructor class, the
2826 instance is a <emphasis>partial application</emphasis> of the new type, not the
2827 entire left hand side. We can imagine that the type declaration is
2828 "eta-converted" to generate the context of the instance
2833 We can even derive instances of multi-parameter classes, provided the
2834 newtype is the last class parameter. In this case, a ``partial
2835 application'' of the class appears in the <literal>deriving</literal>
2836 clause. For example, given the class
2839 class StateMonad s m | m -> s where ...
2840 instance Monad m => StateMonad s (State s m) where ...
2842 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2844 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2845 deriving (Monad, StateMonad [tok])
2848 The derived instance is obtained by completing the application of the
2849 class to the new type:
2852 instance StateMonad [tok] (State [tok] (Failure m)) =>
2853 StateMonad [tok] (Parser tok m)
2858 As a result of this extension, all derived instances in newtype
2859 declarations are treated uniformly (and implemented just by reusing
2860 the dictionary for the representation type), <emphasis>except</emphasis>
2861 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2862 the newtype and its representation.
2866 <sect3> <title> A more precise specification </title>
2868 Derived instance declarations are constructed as follows. Consider the
2869 declaration (after expansion of any type synonyms)
2872 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
2878 The <literal>ci</literal> are partial applications of
2879 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
2880 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
2883 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
2886 The type <literal>t</literal> is an arbitrary type.
2889 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
2890 nor in the <literal>ci</literal>, and
2893 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
2894 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
2895 should not "look through" the type or its constructor. You can still
2896 derive these classes for a newtype, but it happens in the usual way, not
2897 via this new mechanism.
2900 Then, for each <literal>ci</literal>, the derived instance
2903 instance ci t => ci (T v1...vk)
2905 As an example which does <emphasis>not</emphasis> work, consider
2907 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2909 Here we cannot derive the instance
2911 instance Monad (State s m) => Monad (NonMonad m)
2914 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2915 and so cannot be "eta-converted" away. It is a good thing that this
2916 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2917 not, in fact, a monad --- for the same reason. Try defining
2918 <literal>>>=</literal> with the correct type: you won't be able to.
2922 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2923 important, since we can only derive instances for the last one. If the
2924 <literal>StateMonad</literal> class above were instead defined as
2927 class StateMonad m s | m -> s where ...
2930 then we would not have been able to derive an instance for the
2931 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2932 classes usually have one "main" parameter for which deriving new
2933 instances is most interesting.
2935 <para>Lastly, all of this applies only for classes other than
2936 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
2937 and <literal>Data</literal>, for which the built-in derivation applies (section
2938 4.3.3. of the Haskell Report).
2939 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
2940 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
2941 the standard method is used or the one described here.)
2948 <!-- TYPE SYSTEM EXTENSIONS -->
2949 <sect1 id="type-class-extensions">
2950 <title>Class and instances declarations</title>
2952 <sect2 id="multi-param-type-classes">
2953 <title>Class declarations</title>
2956 This section, and the next one, documents GHC's type-class extensions.
2957 There's lots of background in the paper <ulink
2958 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
2959 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
2960 Jones, Erik Meijer).
2963 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
2967 <title>Multi-parameter type classes</title>
2969 Multi-parameter type classes are permitted. For example:
2973 class Collection c a where
2974 union :: c a -> c a -> c a
2982 <title>The superclasses of a class declaration</title>
2985 There are no restrictions on the context in a class declaration
2986 (which introduces superclasses), except that the class hierarchy must
2987 be acyclic. So these class declarations are OK:
2991 class Functor (m k) => FiniteMap m k where
2994 class (Monad m, Monad (t m)) => Transform t m where
2995 lift :: m a -> (t m) a
3001 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3002 of "acyclic" involves only the superclass relationships. For example,
3008 op :: D b => a -> b -> b
3011 class C a => D a where { ... }
3015 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3016 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3017 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3024 <sect3 id="class-method-types">
3025 <title>Class method types</title>
3028 Haskell 98 prohibits class method types to mention constraints on the
3029 class type variable, thus:
3032 fromList :: [a] -> s a
3033 elem :: Eq a => a -> s a -> Bool
3035 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3036 contains the constraint <literal>Eq a</literal>, constrains only the
3037 class type variable (in this case <literal>a</literal>).
3038 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3045 <sect2 id="functional-dependencies">
3046 <title>Functional dependencies
3049 <para> Functional dependencies are implemented as described by Mark Jones
3050 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3051 In Proceedings of the 9th European Symposium on Programming,
3052 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3056 Functional dependencies are introduced by a vertical bar in the syntax of a
3057 class declaration; e.g.
3059 class (Monad m) => MonadState s m | m -> s where ...
3061 class Foo a b c | a b -> c where ...
3063 There should be more documentation, but there isn't (yet). Yell if you need it.
3066 <sect3><title>Rules for functional dependencies </title>
3068 In a class declaration, all of the class type variables must be reachable (in the sense
3069 mentioned in <xref linkend="type-restrictions"/>)
3070 from the free variables of each method type.
3074 class Coll s a where
3076 insert :: s -> a -> s
3079 is not OK, because the type of <literal>empty</literal> doesn't mention
3080 <literal>a</literal>. Functional dependencies can make the type variable
3083 class Coll s a | s -> a where
3085 insert :: s -> a -> s
3088 Alternatively <literal>Coll</literal> might be rewritten
3091 class Coll s a where
3093 insert :: s a -> a -> s a
3097 which makes the connection between the type of a collection of
3098 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3099 Occasionally this really doesn't work, in which case you can split the
3107 class CollE s => Coll s a where
3108 insert :: s -> a -> s
3115 <title>Background on functional dependencies</title>
3117 <para>The following description of the motivation and use of functional dependencies is taken
3118 from the Hugs user manual, reproduced here (with minor changes) by kind
3119 permission of Mark Jones.
3122 Consider the following class, intended as part of a
3123 library for collection types:
3125 class Collects e ce where
3127 insert :: e -> ce -> ce
3128 member :: e -> ce -> Bool
3130 The type variable e used here represents the element type, while ce is the type
3131 of the container itself. Within this framework, we might want to define
3132 instances of this class for lists or characteristic functions (both of which
3133 can be used to represent collections of any equality type), bit sets (which can
3134 be used to represent collections of characters), or hash tables (which can be
3135 used to represent any collection whose elements have a hash function). Omitting
3136 standard implementation details, this would lead to the following declarations:
3138 instance Eq e => Collects e [e] where ...
3139 instance Eq e => Collects e (e -> Bool) where ...
3140 instance Collects Char BitSet where ...
3141 instance (Hashable e, Collects a ce)
3142 => Collects e (Array Int ce) where ...
3144 All this looks quite promising; we have a class and a range of interesting
3145 implementations. Unfortunately, there are some serious problems with the class
3146 declaration. First, the empty function has an ambiguous type:
3148 empty :: Collects e ce => ce
3150 By "ambiguous" we mean that there is a type variable e that appears on the left
3151 of the <literal>=></literal> symbol, but not on the right. The problem with
3152 this is that, according to the theoretical foundations of Haskell overloading,
3153 we cannot guarantee a well-defined semantics for any term with an ambiguous
3157 We can sidestep this specific problem by removing the empty member from the
3158 class declaration. However, although the remaining members, insert and member,
3159 do not have ambiguous types, we still run into problems when we try to use
3160 them. For example, consider the following two functions:
3162 f x y = insert x . insert y
3165 for which GHC infers the following types:
3167 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3168 g :: (Collects Bool c, Collects Char c) => c -> c
3170 Notice that the type for f allows the two parameters x and y to be assigned
3171 different types, even though it attempts to insert each of the two values, one
3172 after the other, into the same collection. If we're trying to model collections
3173 that contain only one type of value, then this is clearly an inaccurate
3174 type. Worse still, the definition for g is accepted, without causing a type
3175 error. As a result, the error in this code will not be flagged at the point
3176 where it appears. Instead, it will show up only when we try to use g, which
3177 might even be in a different module.
3180 <sect4><title>An attempt to use constructor classes</title>
3183 Faced with the problems described above, some Haskell programmers might be
3184 tempted to use something like the following version of the class declaration:
3186 class Collects e c where
3188 insert :: e -> c e -> c e
3189 member :: e -> c e -> Bool
3191 The key difference here is that we abstract over the type constructor c that is
3192 used to form the collection type c e, and not over that collection type itself,
3193 represented by ce in the original class declaration. This avoids the immediate
3194 problems that we mentioned above: empty has type <literal>Collects e c => c
3195 e</literal>, which is not ambiguous.
3198 The function f from the previous section has a more accurate type:
3200 f :: (Collects e c) => e -> e -> c e -> c e
3202 The function g from the previous section is now rejected with a type error as
3203 we would hope because the type of f does not allow the two arguments to have
3205 This, then, is an example of a multiple parameter class that does actually work
3206 quite well in practice, without ambiguity problems.
3207 There is, however, a catch. This version of the Collects class is nowhere near
3208 as general as the original class seemed to be: only one of the four instances
3209 for <literal>Collects</literal>
3210 given above can be used with this version of Collects because only one of
3211 them---the instance for lists---has a collection type that can be written in
3212 the form c e, for some type constructor c, and element type e.
3216 <sect4><title>Adding functional dependencies</title>
3219 To get a more useful version of the Collects class, Hugs provides a mechanism
3220 that allows programmers to specify dependencies between the parameters of a
3221 multiple parameter class (For readers with an interest in theoretical
3222 foundations and previous work: The use of dependency information can be seen
3223 both as a generalization of the proposal for `parametric type classes' that was
3224 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3225 later framework for "improvement" of qualified types. The
3226 underlying ideas are also discussed in a more theoretical and abstract setting
3227 in a manuscript [implparam], where they are identified as one point in a
3228 general design space for systems of implicit parameterization.).
3230 To start with an abstract example, consider a declaration such as:
3232 class C a b where ...
3234 which tells us simply that C can be thought of as a binary relation on types
3235 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3236 included in the definition of classes to add information about dependencies
3237 between parameters, as in the following examples:
3239 class D a b | a -> b where ...
3240 class E a b | a -> b, b -> a where ...
3242 The notation <literal>a -> b</literal> used here between the | and where
3243 symbols --- not to be
3244 confused with a function type --- indicates that the a parameter uniquely
3245 determines the b parameter, and might be read as "a determines b." Thus D is
3246 not just a relation, but actually a (partial) function. Similarly, from the two
3247 dependencies that are included in the definition of E, we can see that E
3248 represents a (partial) one-one mapping between types.
3251 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3252 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3253 m>=0, meaning that the y parameters are uniquely determined by the x
3254 parameters. Spaces can be used as separators if more than one variable appears
3255 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3256 annotated with multiple dependencies using commas as separators, as in the
3257 definition of E above. Some dependencies that we can write in this notation are
3258 redundant, and will be rejected because they don't serve any useful
3259 purpose, and may instead indicate an error in the program. Examples of
3260 dependencies like this include <literal>a -> a </literal>,
3261 <literal>a -> a a </literal>,
3262 <literal>a -> </literal>, etc. There can also be
3263 some redundancy if multiple dependencies are given, as in
3264 <literal>a->b</literal>,
3265 <literal>b->c </literal>, <literal>a->c </literal>, and
3266 in which some subset implies the remaining dependencies. Examples like this are
3267 not treated as errors. Note that dependencies appear only in class
3268 declarations, and not in any other part of the language. In particular, the
3269 syntax for instance declarations, class constraints, and types is completely
3273 By including dependencies in a class declaration, we provide a mechanism for
3274 the programmer to specify each multiple parameter class more precisely. The
3275 compiler, on the other hand, is responsible for ensuring that the set of
3276 instances that are in scope at any given point in the program is consistent
3277 with any declared dependencies. For example, the following pair of instance
3278 declarations cannot appear together in the same scope because they violate the
3279 dependency for D, even though either one on its own would be acceptable:
3281 instance D Bool Int where ...
3282 instance D Bool Char where ...
3284 Note also that the following declaration is not allowed, even by itself:
3286 instance D [a] b where ...
3288 The problem here is that this instance would allow one particular choice of [a]
3289 to be associated with more than one choice for b, which contradicts the
3290 dependency specified in the definition of D. More generally, this means that,
3291 in any instance of the form:
3293 instance D t s where ...
3295 for some particular types t and s, the only variables that can appear in s are
3296 the ones that appear in t, and hence, if the type t is known, then s will be
3297 uniquely determined.
3300 The benefit of including dependency information is that it allows us to define
3301 more general multiple parameter classes, without ambiguity problems, and with
3302 the benefit of more accurate types. To illustrate this, we return to the
3303 collection class example, and annotate the original definition of <literal>Collects</literal>
3304 with a simple dependency:
3306 class Collects e ce | ce -> e where
3308 insert :: e -> ce -> ce
3309 member :: e -> ce -> Bool
3311 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3312 determined by the type of the collection ce. Note that both parameters of
3313 Collects are of kind *; there are no constructor classes here. Note too that
3314 all of the instances of Collects that we gave earlier can be used
3315 together with this new definition.
3318 What about the ambiguity problems that we encountered with the original
3319 definition? The empty function still has type Collects e ce => ce, but it is no
3320 longer necessary to regard that as an ambiguous type: Although the variable e
3321 does not appear on the right of the => symbol, the dependency for class
3322 Collects tells us that it is uniquely determined by ce, which does appear on
3323 the right of the => symbol. Hence the context in which empty is used can still
3324 give enough information to determine types for both ce and e, without
3325 ambiguity. More generally, we need only regard a type as ambiguous if it
3326 contains a variable on the left of the => that is not uniquely determined
3327 (either directly or indirectly) by the variables on the right.
3330 Dependencies also help to produce more accurate types for user defined
3331 functions, and hence to provide earlier detection of errors, and less cluttered
3332 types for programmers to work with. Recall the previous definition for a
3335 f x y = insert x y = insert x . insert y
3337 for which we originally obtained a type:
3339 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3341 Given the dependency information that we have for Collects, however, we can
3342 deduce that a and b must be equal because they both appear as the second
3343 parameter in a Collects constraint with the same first parameter c. Hence we
3344 can infer a shorter and more accurate type for f:
3346 f :: (Collects a c) => a -> a -> c -> c
3348 In a similar way, the earlier definition of g will now be flagged as a type error.
3351 Although we have given only a few examples here, it should be clear that the
3352 addition of dependency information can help to make multiple parameter classes
3353 more useful in practice, avoiding ambiguity problems, and allowing more general
3354 sets of instance declarations.
3360 <sect2 id="instance-decls">
3361 <title>Instance declarations</title>
3363 <para>An instance declaration has the form
3365 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 ...
3367 The part before the "<literal>=></literal>" is the
3368 <emphasis>context</emphasis>, while the part after the
3369 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3372 <sect3 id="flexible-instance-head">
3373 <title>Relaxed rules for the instance head</title>
3376 In Haskell 98 the head of an instance declaration
3377 must be of the form <literal>C (T a1 ... an)</literal>, where
3378 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3379 and the <literal>a1 ... an</literal> are distinct type variables.
3380 GHC relaxes these rules in two ways.
3384 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3385 declaration to mention arbitrary nested types.
3386 For example, this becomes a legal instance declaration
3388 instance C (Maybe Int) where ...
3390 See also the <link linkend="instance-overlap">rules on overlap</link>.
3393 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3394 synonyms. As always, using a type synonym is just shorthand for
3395 writing the RHS of the type synonym definition. For example:
3399 type Point = (Int,Int)
3400 instance C Point where ...
3401 instance C [Point] where ...
3405 is legal. However, if you added
3409 instance C (Int,Int) where ...
3413 as well, then the compiler will complain about the overlapping
3414 (actually, identical) instance declarations. As always, type synonyms
3415 must be fully applied. You cannot, for example, write:
3419 instance Monad P where ...
3427 <sect3 id="instance-rules">
3428 <title>Relaxed rules for instance contexts</title>
3430 <para>In Haskell 98, the assertions in the context of the instance declaration
3431 must be of the form <literal>C a</literal> where <literal>a</literal>
3432 is a type variable that occurs in the head.
3436 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3437 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3438 With this flag the context of the instance declaration can each consist of arbitrary
3439 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3443 The Paterson Conditions: for each assertion in the context
3445 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3446 <listitem><para>The assertion has fewer constructors and variables (taken together
3447 and counting repetitions) than the head</para></listitem>
3451 <listitem><para>The Coverage Condition. For each functional dependency,
3452 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3453 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3454 every type variable in
3455 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3456 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3457 substitution mapping each type variable in the class declaration to the
3458 corresponding type in the instance declaration.
3461 These restrictions ensure that context reduction terminates: each reduction
3462 step makes the problem smaller by at least one
3463 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3464 if you give the <option>-XUndecidableInstances</option>
3465 flag (<xref linkend="undecidable-instances"/>).
3466 You can find lots of background material about the reason for these
3467 restrictions in the paper <ulink
3468 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3469 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3472 For example, these are OK:
3474 instance C Int [a] -- Multiple parameters
3475 instance Eq (S [a]) -- Structured type in head
3477 -- Repeated type variable in head
3478 instance C4 a a => C4 [a] [a]
3479 instance Stateful (ST s) (MutVar s)
3481 -- Head can consist of type variables only
3483 instance (Eq a, Show b) => C2 a b
3485 -- Non-type variables in context
3486 instance Show (s a) => Show (Sized s a)
3487 instance C2 Int a => C3 Bool [a]
3488 instance C2 Int a => C3 [a] b
3492 -- Context assertion no smaller than head
3493 instance C a => C a where ...
3494 -- (C b b) has more more occurrences of b than the head
3495 instance C b b => Foo [b] where ...
3500 The same restrictions apply to instances generated by
3501 <literal>deriving</literal> clauses. Thus the following is accepted:
3503 data MinHeap h a = H a (h a)
3506 because the derived instance
3508 instance (Show a, Show (h a)) => Show (MinHeap h a)
3510 conforms to the above rules.
3514 A useful idiom permitted by the above rules is as follows.
3515 If one allows overlapping instance declarations then it's quite
3516 convenient to have a "default instance" declaration that applies if
3517 something more specific does not:
3525 <sect3 id="undecidable-instances">
3526 <title>Undecidable instances</title>
3529 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3530 For example, sometimes you might want to use the following to get the
3531 effect of a "class synonym":
3533 class (C1 a, C2 a, C3 a) => C a where { }
3535 instance (C1 a, C2 a, C3 a) => C a where { }
3537 This allows you to write shorter signatures:
3543 f :: (C1 a, C2 a, C3 a) => ...
3545 The restrictions on functional dependencies (<xref
3546 linkend="functional-dependencies"/>) are particularly troublesome.
3547 It is tempting to introduce type variables in the context that do not appear in
3548 the head, something that is excluded by the normal rules. For example:
3550 class HasConverter a b | a -> b where
3553 data Foo a = MkFoo a
3555 instance (HasConverter a b,Show b) => Show (Foo a) where
3556 show (MkFoo value) = show (convert value)
3558 This is dangerous territory, however. Here, for example, is a program that would make the
3563 instance F [a] [[a]]
3564 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3566 Similarly, it can be tempting to lift the coverage condition:
3568 class Mul a b c | a b -> c where
3569 (.*.) :: a -> b -> c
3571 instance Mul Int Int Int where (.*.) = (*)
3572 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3573 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3575 The third instance declaration does not obey the coverage condition;
3576 and indeed the (somewhat strange) definition:
3578 f = \ b x y -> if b then x .*. [y] else y
3580 makes instance inference go into a loop, because it requires the constraint
3581 <literal>(Mul a [b] b)</literal>.
3584 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3585 the experimental flag <option>-XUndecidableInstances</option>
3586 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3587 both the Paterson Conditions and the Coverage Condition
3588 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3589 fixed-depth recursion stack. If you exceed the stack depth you get a
3590 sort of backtrace, and the opportunity to increase the stack depth
3591 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3597 <sect3 id="instance-overlap">
3598 <title>Overlapping instances</title>
3600 In general, <emphasis>GHC requires that that it be unambiguous which instance
3602 should be used to resolve a type-class constraint</emphasis>. This behaviour
3603 can be modified by two flags: <option>-XOverlappingInstances</option>
3604 <indexterm><primary>-XOverlappingInstances
3605 </primary></indexterm>
3606 and <option>-XIncoherentInstances</option>
3607 <indexterm><primary>-XIncoherentInstances
3608 </primary></indexterm>, as this section discusses. Both these
3609 flags are dynamic flags, and can be set on a per-module basis, using
3610 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3612 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3613 it tries to match every instance declaration against the
3615 by instantiating the head of the instance declaration. For example, consider
3618 instance context1 => C Int a where ... -- (A)
3619 instance context2 => C a Bool where ... -- (B)
3620 instance context3 => C Int [a] where ... -- (C)
3621 instance context4 => C Int [Int] where ... -- (D)
3623 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3624 but (C) and (D) do not. When matching, GHC takes
3625 no account of the context of the instance declaration
3626 (<literal>context1</literal> etc).
3627 GHC's default behaviour is that <emphasis>exactly one instance must match the
3628 constraint it is trying to resolve</emphasis>.
3629 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3630 including both declarations (A) and (B), say); an error is only reported if a
3631 particular constraint matches more than one.
3635 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3636 more than one instance to match, provided there is a most specific one. For
3637 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3638 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3639 most-specific match, the program is rejected.
3642 However, GHC is conservative about committing to an overlapping instance. For example:
3647 Suppose that from the RHS of <literal>f</literal> we get the constraint
3648 <literal>C Int [b]</literal>. But
3649 GHC does not commit to instance (C), because in a particular
3650 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3651 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3652 So GHC rejects the program.
3653 (If you add the flag <option>-XIncoherentInstances</option>,
3654 GHC will instead pick (C), without complaining about
3655 the problem of subsequent instantiations.)
3658 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3659 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3660 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3661 it instead. In this case, GHC will refrain from
3662 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3663 as before) but, rather than rejecting the program, it will infer the type
3665 f :: C Int [b] => [b] -> [b]
3667 That postpones the question of which instance to pick to the
3668 call site for <literal>f</literal>
3669 by which time more is known about the type <literal>b</literal>.
3670 You can write this type signature yourself if you use the
3671 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3675 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3679 instance Foo [b] where
3682 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3683 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3684 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3685 declaration. The solution is to postpone the choice by adding the constraint to the context
3686 of the instance declaration, thus:
3688 instance C Int [b] => Foo [b] where
3691 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3694 The willingness to be overlapped or incoherent is a property of
3695 the <emphasis>instance declaration</emphasis> itself, controlled by the
3696 presence or otherwise of the <option>-XOverlappingInstances</option>
3697 and <option>-XIncoherentInstances</option> flags when that module is
3698 being defined. Neither flag is required in a module that imports and uses the
3699 instance declaration. Specifically, during the lookup process:
3702 An instance declaration is ignored during the lookup process if (a) a more specific
3703 match is found, and (b) the instance declaration was compiled with
3704 <option>-XOverlappingInstances</option>. The flag setting for the
3705 more-specific instance does not matter.
3708 Suppose an instance declaration does not match the constraint being looked up, but
3709 does unify with it, so that it might match when the constraint is further
3710 instantiated. Usually GHC will regard this as a reason for not committing to
3711 some other constraint. But if the instance declaration was compiled with
3712 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3713 check for that declaration.
3716 These rules make it possible for a library author to design a library that relies on
3717 overlapping instances without the library client having to know.
3720 If an instance declaration is compiled without
3721 <option>-XOverlappingInstances</option>,
3722 then that instance can never be overlapped. This could perhaps be
3723 inconvenient. Perhaps the rule should instead say that the
3724 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3725 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3726 at a usage site should be permitted regardless of how the instance declarations
3727 are compiled, if the <option>-XOverlappingInstances</option> flag is
3728 used at the usage site. (Mind you, the exact usage site can occasionally be
3729 hard to pin down.) We are interested to receive feedback on these points.
3731 <para>The <option>-XIncoherentInstances</option> flag implies the
3732 <option>-XOverlappingInstances</option> flag, but not vice versa.
3740 <sect2 id="overloaded-strings">
3741 <title>Overloaded string literals
3745 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3746 string literal has type <literal>String</literal>, but with overloaded string
3747 literals enabled (with <literal>-XOverloadedStrings</literal>)
3748 a string literal has type <literal>(IsString a) => a</literal>.
3751 This means that the usual string syntax can be used, e.g., for packed strings
3752 and other variations of string like types. String literals behave very much
3753 like integer literals, i.e., they can be used in both expressions and patterns.
3754 If used in a pattern the literal with be replaced by an equality test, in the same
3755 way as an integer literal is.
3758 The class <literal>IsString</literal> is defined as:
3760 class IsString a where
3761 fromString :: String -> a
3763 The only predefined instance is the obvious one to make strings work as usual:
3765 instance IsString [Char] where
3768 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3769 it explicitly (for example, to give an instance declaration for it), you can import it
3770 from module <literal>GHC.Exts</literal>.
3773 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3777 Each type in a default declaration must be an
3778 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3782 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3783 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3784 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3785 <emphasis>or</emphasis> <literal>IsString</literal>.
3794 import GHC.Exts( IsString(..) )
3796 newtype MyString = MyString String deriving (Eq, Show)
3797 instance IsString MyString where
3798 fromString = MyString
3800 greet :: MyString -> MyString
3801 greet "hello" = "world"
3805 print $ greet "hello"
3806 print $ greet "fool"
3810 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
3811 to work since it gets translated into an equality comparison.
3817 <sect1 id="type-families">
3818 <title>Type families</title>
3821 <firstterm>Indexed type families</firstterm> are a new GHC extension to
3822 facilitate type-level
3823 programming. Type families are a generalisation of <firstterm>associated
3824 data types</firstterm>
3825 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
3826 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
3827 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
3828 Symposium on Principles of Programming Languages (POPL'05)”, pages
3829 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
3830 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
3831 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
3833 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
3834 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
3835 themselves are described in the paper “<ulink
3836 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
3837 Checking with Open Type Functions</ulink>”, T. Schrijvers,
3839 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
3840 13th ACM SIGPLAN International Conference on Functional
3841 Programming”, ACM Press, pages 51-62, 2008. Type families
3842 essentially provide type-indexed data types and named functions on types,
3843 which are useful for generic programming and highly parameterised library
3844 interfaces as well as interfaces with enhanced static information, much like
3845 dependent types. They might also be regarded as an alternative to functional
3846 dependencies, but provide a more functional style of type-level programming
3847 than the relational style of functional dependencies.
3850 Indexed type families, or type families for short, are type constructors that
3851 represent sets of types. Set members are denoted by supplying the type family
3852 constructor with type parameters, which are called <firstterm>type
3853 indices</firstterm>. The
3854 difference between vanilla parametrised type constructors and family
3855 constructors is much like between parametrically polymorphic functions and
3856 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
3857 behave the same at all type instances, whereas class methods can change their
3858 behaviour in dependence on the class type parameters. Similarly, vanilla type
3859 constructors imply the same data representation for all type instances, but
3860 family constructors can have varying representation types for varying type
3864 Indexed type families come in two flavours: <firstterm>data
3865 families</firstterm> and <firstterm>type synonym
3866 families</firstterm>. They are the indexed family variants of algebraic
3867 data types and type synonyms, respectively. The instances of data families
3868 can be data types and newtypes.
3871 Type families are enabled by the flag <option>-XTypeFamilies</option>.
3872 Additional information on the use of type families in GHC is available on
3873 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
3874 Haskell wiki page on type families</ulink>.
3877 <sect2 id="data-families">
3878 <title>Data families</title>
3881 Data families appear in two flavours: (1) they can be defined on the
3883 or (2) they can appear inside type classes (in which case they are known as
3884 associated types). The former is the more general variant, as it lacks the
3885 requirement for the type-indexes to coincide with the class
3886 parameters. However, the latter can lead to more clearly structured code and
3887 compiler warnings if some type instances were - possibly accidentally -
3888 omitted. In the following, we always discuss the general toplevel form first
3889 and then cover the additional constraints placed on associated types.
3892 <sect3 id="data-family-declarations">
3893 <title>Data family declarations</title>
3896 Indexed data families are introduced by a signature, such as
3898 data family GMap k :: * -> *
3900 The special <literal>family</literal> distinguishes family from standard
3901 data declarations. The result kind annotation is optional and, as
3902 usual, defaults to <literal>*</literal> if omitted. An example is
3906 Named arguments can also be given explicit kind signatures if needed.
3908 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
3909 declarations] named arguments are entirely optional, so that we can
3910 declare <literal>Array</literal> alternatively with
3912 data family Array :: * -> *
3916 <sect4 id="assoc-data-family-decl">
3917 <title>Associated data family declarations</title>
3919 When a data family is declared as part of a type class, we drop
3920 the <literal>family</literal> special. The <literal>GMap</literal>
3921 declaration takes the following form
3923 class GMapKey k where
3924 data GMap k :: * -> *
3927 In contrast to toplevel declarations, named arguments must be used for
3928 all type parameters that are to be used as type-indexes. Moreover,
3929 the argument names must be class parameters. Each class parameter may
3930 only be used at most once per associated type, but some may be omitted
3931 and they may be in an order other than in the class head. Hence, the
3932 following contrived example is admissible:
3941 <sect3 id="data-instance-declarations">
3942 <title>Data instance declarations</title>
3945 Instance declarations of data and newtype families are very similar to
3946 standard data and newtype declarations. The only two differences are
3947 that the keyword <literal>data</literal> or <literal>newtype</literal>
3948 is followed by <literal>instance</literal> and that some or all of the
3949 type arguments can be non-variable types, but may not contain forall
3950 types or type synonym families. However, data families are generally
3951 allowed in type parameters, and type synonyms are allowed as long as
3952 they are fully applied and expand to a type that is itself admissible -
3953 exactly as this is required for occurrences of type synonyms in class
3954 instance parameters. For example, the <literal>Either</literal>
3955 instance for <literal>GMap</literal> is
3957 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
3959 In this example, the declaration has only one variant. In general, it
3963 Data and newtype instance declarations are only permitted when an
3964 appropriate family declaration is in scope - just as a class instance declaratoin
3965 requires the class declaration to be visible. Moreover, each instance
3966 declaration has to conform to the kind determined by its family
3967 declaration. This implies that the number of parameters of an instance
3968 declaration matches the arity determined by the kind of the family.
3971 A data family instance declaration can use the full exprssiveness of
3972 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
3974 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
3975 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
3976 use either <literal>data</literal> or <literal>newtype</literal>. For example:
3979 data instance T Int = T1 Int | T2 Bool
3980 newtype instance T Char = TC Bool
3983 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
3984 and indeed can define a GADT. For example:
3987 data instance G [a] b where
3988 G1 :: c -> G [Int] b
3992 <listitem><para> You can use a <literal>deriving</literal> clause on a
3993 <literal>data instance</literal> or <literal>newtype instance</literal>
4000 Even if type families are defined as toplevel declarations, functions
4001 that perform different computations for different family instances may still
4002 need to be defined as methods of type classes. In particular, the
4003 following is not possible:
4006 data instance T Int = A
4007 data instance T Char = B
4009 foo A = 1 -- WRONG: These two equations together...
4010 foo B = 2 -- ...will produce a type error.
4012 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4016 instance Foo Int where
4018 instance Foo Char where
4021 (Given the functionality provided by GADTs (Generalised Algebraic Data
4022 Types), it might seem as if a definition, such as the above, should be
4023 feasible. However, type families are - in contrast to GADTs - are
4024 <emphasis>open;</emphasis> i.e., new instances can always be added,
4026 modules. Supporting pattern matching across different data instances
4027 would require a form of extensible case construct.)
4030 <sect4 id="assoc-data-inst">
4031 <title>Associated data instances</title>
4033 When an associated data family instance is declared within a type
4034 class instance, we drop the <literal>instance</literal> keyword in the
4035 family instance. So, the <literal>Either</literal> instance
4036 for <literal>GMap</literal> becomes:
4038 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4039 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4042 The most important point about associated family instances is that the
4043 type indexes corresponding to class parameters must be identical to
4044 the type given in the instance head; here this is the first argument
4045 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4046 which coincides with the only class parameter. Any parameters to the
4047 family constructor that do not correspond to class parameters, need to
4048 be variables in every instance; here this is the
4049 variable <literal>v</literal>.
4052 Instances for an associated family can only appear as part of
4053 instances declarations of the class in which the family was declared -
4054 just as with the equations of the methods of a class. Also in
4055 correspondence to how methods are handled, declarations of associated
4056 types can be omitted in class instances. If an associated family
4057 instance is omitted, the corresponding instance type is not inhabited;
4058 i.e., only diverging expressions, such
4059 as <literal>undefined</literal>, can assume the type.
4063 <sect4 id="scoping-class-params">
4064 <title>Scoping of class parameters</title>
4066 In the case of multi-parameter type classes, the visibility of class
4067 parameters in the right-hand side of associated family instances
4068 depends <emphasis>solely</emphasis> on the parameters of the data
4069 family. As an example, consider the simple class declaration
4074 Only one of the two class parameters is a parameter to the data
4075 family. Hence, the following instance declaration is invalid:
4077 instance C [c] d where
4078 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4080 Here, the right-hand side of the data instance mentions the type
4081 variable <literal>d</literal> that does not occur in its left-hand
4082 side. We cannot admit such data instances as they would compromise
4087 <sect4 id="family-class-inst">
4088 <title>Type class instances of family instances</title>
4090 Type class instances of instances of data families can be defined as
4091 usual, and in particular data instance declarations can
4092 have <literal>deriving</literal> clauses. For example, we can write
4094 data GMap () v = GMapUnit (Maybe v)
4097 which implicitly defines an instance of the form
4099 instance Show v => Show (GMap () v) where ...
4103 Note that class instances are always for
4104 particular <emphasis>instances</emphasis> of a data family and never
4105 for an entire family as a whole. This is for essentially the same
4106 reasons that we cannot define a toplevel function that performs
4107 pattern matching on the data constructors
4108 of <emphasis>different</emphasis> instances of a single type family.
4109 It would require a form of extensible case construct.
4113 <sect4 id="data-family-overlap">
4114 <title>Overlap of data instances</title>
4116 The instance declarations of a data family used in a single program
4117 may not overlap at all, independent of whether they are associated or
4118 not. In contrast to type class instances, this is not only a matter
4119 of consistency, but one of type safety.
4125 <sect3 id="data-family-import-export">
4126 <title>Import and export</title>
4129 The association of data constructors with type families is more dynamic
4130 than that is the case with standard data and newtype declarations. In
4131 the standard case, the notation <literal>T(..)</literal> in an import or
4132 export list denotes the type constructor and all the data constructors
4133 introduced in its declaration. However, a family declaration never
4134 introduces any data constructors; instead, data constructors are
4135 introduced by family instances. As a result, which data constructors
4136 are associated with a type family depends on the currently visible
4137 instance declarations for that family. Consequently, an import or
4138 export item of the form <literal>T(..)</literal> denotes the family
4139 constructor and all currently visible data constructors - in the case of
4140 an export item, these may be either imported or defined in the current
4141 module. The treatment of import and export items that explicitly list
4142 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4146 <sect4 id="data-family-impexp-assoc">
4147 <title>Associated families</title>
4149 As expected, an import or export item of the
4150 form <literal>C(..)</literal> denotes all of the class' methods and
4151 associated types. However, when associated types are explicitly
4152 listed as subitems of a class, we need some new syntax, as uppercase
4153 identifiers as subitems are usually data constructors, not type
4154 constructors. To clarify that we denote types here, each associated
4155 type name needs to be prefixed by the keyword <literal>type</literal>.
4156 So for example, when explicitly listing the components of
4157 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4158 GMap, empty, lookup, insert)</literal>.
4162 <sect4 id="data-family-impexp-examples">
4163 <title>Examples</title>
4165 Assuming our running <literal>GMapKey</literal> class example, let us
4166 look at some export lists and their meaning:
4169 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4170 just the class name.</para>
4173 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4174 Exports the class, the associated type <literal>GMap</literal>
4176 functions <literal>empty</literal>, <literal>lookup</literal>,
4177 and <literal>insert</literal>. None of the data constructors is
4181 <para><literal>module GMap (GMapKey(..), GMap(..))
4182 where...</literal>: As before, but also exports all the data
4183 constructors <literal>GMapInt</literal>,
4184 <literal>GMapChar</literal>,
4185 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4186 and <literal>GMapUnit</literal>.</para>
4189 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4190 GMap(..)) where...</literal>: As before.</para>
4193 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4194 where...</literal>: As before.</para>
4199 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4200 both the class <literal>GMapKey</literal> as well as its associated
4201 type <literal>GMap</literal>. However, you cannot
4202 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4203 sub-component specifications cannot be nested. To
4204 specify <literal>GMap</literal>'s data constructors, you have to list
4209 <sect4 id="data-family-impexp-instances">
4210 <title>Instances</title>
4212 Family instances are implicitly exported, just like class instances.
4213 However, this applies only to the heads of instances, not to the data
4214 constructors an instance defines.
4222 <sect2 id="synonym-families">
4223 <title>Synonym families</title>
4226 Type families appear in two flavours: (1) they can be defined on the
4227 toplevel or (2) they can appear inside type classes (in which case they
4228 are known as associated type synonyms). The former is the more general
4229 variant, as it lacks the requirement for the type-indexes to coincide with
4230 the class parameters. However, the latter can lead to more clearly
4231 structured code and compiler warnings if some type instances were -
4232 possibly accidentally - omitted. In the following, we always discuss the
4233 general toplevel form first and then cover the additional constraints
4234 placed on associated types.
4237 <sect3 id="type-family-declarations">
4238 <title>Type family declarations</title>
4241 Indexed type families are introduced by a signature, such as
4243 type family Elem c :: *
4245 The special <literal>family</literal> distinguishes family from standard
4246 type declarations. The result kind annotation is optional and, as
4247 usual, defaults to <literal>*</literal> if omitted. An example is
4251 Parameters can also be given explicit kind signatures if needed. We
4252 call the number of parameters in a type family declaration, the family's
4253 arity, and all applications of a type family must be fully saturated
4254 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4255 and it implies that the kind of a type family is not sufficient to
4256 determine a family's arity, and hence in general, also insufficient to
4257 determine whether a type family application is well formed. As an
4258 example, consider the following declaration:
4260 type family F a b :: * -> * -- F's arity is 2,
4261 -- although it's overall kind is * -> * -> * -> *
4263 Given this declaration the following are examples of well-formed and
4266 F Char [Int] -- OK! Kind: * -> *
4267 F Char [Int] Bool -- OK! Kind: *
4268 F IO Bool -- WRONG: kind mismatch in the first argument
4269 F Bool -- WRONG: unsaturated application
4273 <sect4 id="assoc-type-family-decl">
4274 <title>Associated type family declarations</title>
4276 When a type family is declared as part of a type class, we drop
4277 the <literal>family</literal> special. The <literal>Elem</literal>
4278 declaration takes the following form
4280 class Collects ce where
4284 The argument names of the type family must be class parameters. Each
4285 class parameter may only be used at most once per associated type, but
4286 some may be omitted and they may be in an order other than in the
4287 class head. Hence, the following contrived example is admissible:
4292 These rules are exactly as for associated data families.
4297 <sect3 id="type-instance-declarations">
4298 <title>Type instance declarations</title>
4300 Instance declarations of type families are very similar to standard type
4301 synonym declarations. The only two differences are that the
4302 keyword <literal>type</literal> is followed
4303 by <literal>instance</literal> and that some or all of the type
4304 arguments can be non-variable types, but may not contain forall types or
4305 type synonym families. However, data families are generally allowed, and
4306 type synonyms are allowed as long as they are fully applied and expand
4307 to a type that is admissible - these are the exact same requirements as
4308 for data instances. For example, the <literal>[e]</literal> instance
4309 for <literal>Elem</literal> is
4311 type instance Elem [e] = e
4315 Type family instance declarations are only legitimate when an
4316 appropriate family declaration is in scope - just like class instances
4317 require the class declaration to be visible. Moreover, each instance
4318 declaration has to conform to the kind determined by its family
4319 declaration, and the number of type parameters in an instance
4320 declaration must match the number of type parameters in the family
4321 declaration. Finally, the right-hand side of a type instance must be a
4322 monotype (i.e., it may not include foralls) and after the expansion of
4323 all saturated vanilla type synonyms, no synonyms, except family synonyms
4324 may remain. Here are some examples of admissible and illegal type
4327 type family F a :: *
4328 type instance F [Int] = Int -- OK!
4329 type instance F String = Char -- OK!
4330 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4331 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4332 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4334 type family G a b :: * -> *
4335 type instance G Int = (,) -- WRONG: must be two type parameters
4336 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4340 <sect4 id="assoc-type-instance">
4341 <title>Associated type instance declarations</title>
4343 When an associated family instance is declared within a type class
4344 instance, we drop the <literal>instance</literal> keyword in the family
4345 instance. So, the <literal>[e]</literal> instance
4346 for <literal>Elem</literal> becomes:
4348 instance (Eq (Elem [e])) => Collects ([e]) where
4352 The most important point about associated family instances is that the
4353 type indexes corresponding to class parameters must be identical to the
4354 type given in the instance head; here this is <literal>[e]</literal>,
4355 which coincides with the only class parameter.
4358 Instances for an associated family can only appear as part of instances
4359 declarations of the class in which the family was declared - just as
4360 with the equations of the methods of a class. Also in correspondence to
4361 how methods are handled, declarations of associated types can be omitted
4362 in class instances. If an associated family instance is omitted, the
4363 corresponding instance type is not inhabited; i.e., only diverging
4364 expressions, such as <literal>undefined</literal>, can assume the type.
4368 <sect4 id="type-family-overlap">
4369 <title>Overlap of type synonym instances</title>
4371 The instance declarations of a type family used in a single program
4372 may only overlap if the right-hand sides of the overlapping instances
4373 coincide for the overlapping types. More formally, two instance
4374 declarations overlap if there is a substitution that makes the
4375 left-hand sides of the instances syntactically the same. Whenever
4376 that is the case, the right-hand sides of the instances must also be
4377 syntactically equal under the same substitution. This condition is
4378 independent of whether the type family is associated or not, and it is
4379 not only a matter of consistency, but one of type safety.
4382 Here are two example to illustrate the condition under which overlap
4385 type instance F (a, Int) = [a]
4386 type instance F (Int, b) = [b] -- overlap permitted
4388 type instance G (a, Int) = [a]
4389 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4394 <sect4 id="type-family-decidability">
4395 <title>Decidability of type synonym instances</title>
4397 In order to guarantee that type inference in the presence of type
4398 families decidable, we need to place a number of additional
4399 restrictions on the formation of type instance declarations (c.f.,
4400 Definition 5 (Relaxed Conditions) of “<ulink
4401 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4402 Checking with Open Type Functions</ulink>”). Instance
4403 declarations have the general form
4405 type instance F t1 .. tn = t
4407 where we require that for every type family application <literal>(G s1
4408 .. sm)</literal> in <literal>t</literal>,
4411 <para><literal>s1 .. sm</literal> do not contain any type family
4412 constructors,</para>
4415 <para>the total number of symbols (data type constructors and type
4416 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4417 in <literal>t1 .. tn</literal>, and</para>
4420 <para>for every type
4421 variable <literal>a</literal>, <literal>a</literal> occurs
4422 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4423 .. tn</literal>.</para>
4426 These restrictions are easily verified and ensure termination of type
4427 inference. However, they are not sufficient to guarantee completeness
4428 of type inference in the presence of, so called, ''loopy equalities'',
4429 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4430 a type variable is underneath a family application and data
4431 constructor application - see the above mentioned paper for details.
4434 If the option <option>-XUndecidableInstances</option> is passed to the
4435 compiler, the above restrictions are not enforced and it is on the
4436 programmer to ensure termination of the normalisation of type families
4437 during type inference.
4442 <sect3 id-="equality-constraints">
4443 <title>Equality constraints</title>
4445 Type context can include equality constraints of the form <literal>t1 ~
4446 t2</literal>, which denote that the types <literal>t1</literal>
4447 and <literal>t2</literal> need to be the same. In the presence of type
4448 families, whether two types are equal cannot generally be decided
4449 locally. Hence, the contexts of function signatures may include
4450 equality constraints, as in the following example:
4452 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4454 where we require that the element type of <literal>c1</literal>
4455 and <literal>c2</literal> are the same. In general, the
4456 types <literal>t1</literal> and <literal>t2</literal> of an equality
4457 constraint may be arbitrary monotypes; i.e., they may not contain any
4458 quantifiers, independent of whether higher-rank types are otherwise
4462 Equality constraints can also appear in class and instance contexts.
4463 The former enable a simple translation of programs using functional
4464 dependencies into programs using family synonyms instead. The general
4465 idea is to rewrite a class declaration of the form
4467 class C a b | a -> b
4471 class (F a ~ b) => C a b where
4474 That is, we represent every functional dependency (FD) <literal>a1 .. an
4475 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4476 superclass context equality <literal>F a1 .. an ~ b</literal>,
4477 essentially giving a name to the functional dependency. In class
4478 instances, we define the type instances of FD families in accordance
4479 with the class head. Method signatures are not affected by that
4483 NB: Equalities in superclass contexts are not fully implemented in
4488 <sect3 id-="ty-fams-in-instances">
4489 <title>Type families and instance declarations</title>
4490 <para>Type families require us to extend the rules for
4491 the form of instance heads, which are given
4492 in <xref linkend="flexible-instance-head"/>.
4495 <listitem><para>Data type families may appear in an instance head</para></listitem>
4496 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4498 The reason for the latter restriction is that there is no way to check for. Consider
4501 type instance F Bool = Int
4508 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4509 The situation is especially bad because the type instance for <literal>F Bool</literal>
4510 might be in another module, or even in a module that is not yet written.
4517 <sect1 id="other-type-extensions">
4518 <title>Other type system extensions</title>
4520 <sect2 id="type-restrictions">
4521 <title>Type signatures</title>
4523 <sect3 id="flexible-contexts"><title>The context of a type signature</title>
4525 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4526 that the type-class constraints in a type signature must have the
4527 form <emphasis>(class type-variable)</emphasis> or
4528 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4529 With <option>-XFlexibleContexts</option>
4530 these type signatures are perfectly OK
4533 g :: Ord (T a ()) => ...
4537 GHC imposes the following restrictions on the constraints in a type signature.
4541 forall tv1..tvn (c1, ...,cn) => type
4544 (Here, we write the "foralls" explicitly, although the Haskell source
4545 language omits them; in Haskell 98, all the free type variables of an
4546 explicit source-language type signature are universally quantified,
4547 except for the class type variables in a class declaration. However,
4548 in GHC, you can give the foralls if you want. See <xref linkend="universal-quantification"/>).
4557 <emphasis>Each universally quantified type variable
4558 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4560 A type variable <literal>a</literal> is "reachable" if it appears
4561 in the same constraint as either a type variable free in
4562 <literal>type</literal>, or another reachable type variable.
4563 A value with a type that does not obey
4564 this reachability restriction cannot be used without introducing
4565 ambiguity; that is why the type is rejected.
4566 Here, for example, is an illegal type:
4570 forall a. Eq a => Int
4574 When a value with this type was used, the constraint <literal>Eq tv</literal>
4575 would be introduced where <literal>tv</literal> is a fresh type variable, and
4576 (in the dictionary-translation implementation) the value would be
4577 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4578 can never know which instance of <literal>Eq</literal> to use because we never
4579 get any more information about <literal>tv</literal>.
4583 that the reachability condition is weaker than saying that <literal>a</literal> is
4584 functionally dependent on a type variable free in
4585 <literal>type</literal> (see <xref
4586 linkend="functional-dependencies"/>). The reason for this is there
4587 might be a "hidden" dependency, in a superclass perhaps. So
4588 "reachable" is a conservative approximation to "functionally dependent".
4589 For example, consider:
4591 class C a b | a -> b where ...
4592 class C a b => D a b where ...
4593 f :: forall a b. D a b => a -> a
4595 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4596 but that is not immediately apparent from <literal>f</literal>'s type.
4602 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4603 universally quantified type variables <literal>tvi</literal></emphasis>.
4605 For example, this type is OK because <literal>C a b</literal> mentions the
4606 universally quantified type variable <literal>b</literal>:
4610 forall a. C a b => burble
4614 The next type is illegal because the constraint <literal>Eq b</literal> does not
4615 mention <literal>a</literal>:
4619 forall a. Eq b => burble
4623 The reason for this restriction is milder than the other one. The
4624 excluded types are never useful or necessary (because the offending
4625 context doesn't need to be witnessed at this point; it can be floated
4626 out). Furthermore, floating them out increases sharing. Lastly,
4627 excluding them is a conservative choice; it leaves a patch of
4628 territory free in case we need it later.
4642 <sect2 id="implicit-parameters">
4643 <title>Implicit parameters</title>
4645 <para> Implicit parameters are implemented as described in
4646 "Implicit parameters: dynamic scoping with static types",
4647 J Lewis, MB Shields, E Meijer, J Launchbury,
4648 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4652 <para>(Most of the following, still rather incomplete, documentation is
4653 due to Jeff Lewis.)</para>
4655 <para>Implicit parameter support is enabled with the option
4656 <option>-XImplicitParams</option>.</para>
4659 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4660 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4661 context. In Haskell, all variables are statically bound. Dynamic
4662 binding of variables is a notion that goes back to Lisp, but was later
4663 discarded in more modern incarnations, such as Scheme. Dynamic binding
4664 can be very confusing in an untyped language, and unfortunately, typed
4665 languages, in particular Hindley-Milner typed languages like Haskell,
4666 only support static scoping of variables.
4669 However, by a simple extension to the type class system of Haskell, we
4670 can support dynamic binding. Basically, we express the use of a
4671 dynamically bound variable as a constraint on the type. These
4672 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4673 function uses a dynamically-bound variable <literal>?x</literal>
4674 of type <literal>t'</literal>". For
4675 example, the following expresses the type of a sort function,
4676 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4678 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4680 The dynamic binding constraints are just a new form of predicate in the type class system.
4683 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4684 where <literal>x</literal> is
4685 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4686 Use of this construct also introduces a new
4687 dynamic-binding constraint in the type of the expression.
4688 For example, the following definition
4689 shows how we can define an implicitly parameterized sort function in
4690 terms of an explicitly parameterized <literal>sortBy</literal> function:
4692 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4694 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4700 <title>Implicit-parameter type constraints</title>
4702 Dynamic binding constraints behave just like other type class
4703 constraints in that they are automatically propagated. Thus, when a
4704 function is used, its implicit parameters are inherited by the
4705 function that called it. For example, our <literal>sort</literal> function might be used
4706 to pick out the least value in a list:
4708 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4709 least xs = head (sort xs)
4711 Without lifting a finger, the <literal>?cmp</literal> parameter is
4712 propagated to become a parameter of <literal>least</literal> as well. With explicit
4713 parameters, the default is that parameters must always be explicit
4714 propagated. With implicit parameters, the default is to always
4718 An implicit-parameter type constraint differs from other type class constraints in the
4719 following way: All uses of a particular implicit parameter must have
4720 the same type. This means that the type of <literal>(?x, ?x)</literal>
4721 is <literal>(?x::a) => (a,a)</literal>, and not
4722 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4726 <para> You can't have an implicit parameter in the context of a class or instance
4727 declaration. For example, both these declarations are illegal:
4729 class (?x::Int) => C a where ...
4730 instance (?x::a) => Foo [a] where ...
4732 Reason: exactly which implicit parameter you pick up depends on exactly where
4733 you invoke a function. But the ``invocation'' of instance declarations is done
4734 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4735 Easiest thing is to outlaw the offending types.</para>
4737 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4739 f :: (?x :: [a]) => Int -> Int
4742 g :: (Read a, Show a) => String -> String
4745 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4746 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4747 quite unambiguous, and fixes the type <literal>a</literal>.
4752 <title>Implicit-parameter bindings</title>
4755 An implicit parameter is <emphasis>bound</emphasis> using the standard
4756 <literal>let</literal> or <literal>where</literal> binding forms.
4757 For example, we define the <literal>min</literal> function by binding
4758 <literal>cmp</literal>.
4761 min = let ?cmp = (<=) in least
4765 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
4766 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
4767 (including in a list comprehension, or do-notation, or pattern guards),
4768 or a <literal>where</literal> clause.
4769 Note the following points:
4772 An implicit-parameter binding group must be a
4773 collection of simple bindings to implicit-style variables (no
4774 function-style bindings, and no type signatures); these bindings are
4775 neither polymorphic or recursive.
4778 You may not mix implicit-parameter bindings with ordinary bindings in a
4779 single <literal>let</literal>
4780 expression; use two nested <literal>let</literal>s instead.
4781 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
4785 You may put multiple implicit-parameter bindings in a
4786 single binding group; but they are <emphasis>not</emphasis> treated
4787 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
4788 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
4789 parameter. The bindings are not nested, and may be re-ordered without changing
4790 the meaning of the program.
4791 For example, consider:
4793 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
4795 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
4796 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
4798 f :: (?x::Int) => Int -> Int
4806 <sect3><title>Implicit parameters and polymorphic recursion</title>
4809 Consider these two definitions:
4812 len1 xs = let ?acc = 0 in len_acc1 xs
4815 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
4820 len2 xs = let ?acc = 0 in len_acc2 xs
4822 len_acc2 :: (?acc :: Int) => [a] -> Int
4824 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
4826 The only difference between the two groups is that in the second group
4827 <literal>len_acc</literal> is given a type signature.
4828 In the former case, <literal>len_acc1</literal> is monomorphic in its own
4829 right-hand side, so the implicit parameter <literal>?acc</literal> is not
4830 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
4831 has a type signature, the recursive call is made to the
4832 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
4833 as an implicit parameter. So we get the following results in GHCi:
4840 Adding a type signature dramatically changes the result! This is a rather
4841 counter-intuitive phenomenon, worth watching out for.
4845 <sect3><title>Implicit parameters and monomorphism</title>
4847 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
4848 Haskell Report) to implicit parameters. For example, consider:
4856 Since the binding for <literal>y</literal> falls under the Monomorphism
4857 Restriction it is not generalised, so the type of <literal>y</literal> is
4858 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
4859 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
4860 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
4861 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
4862 <literal>y</literal> in the body of the <literal>let</literal> will see the
4863 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
4864 <literal>14</literal>.
4869 <!-- ======================= COMMENTED OUT ========================
4871 We intend to remove linear implicit parameters, so I'm at least removing
4872 them from the 6.6 user manual
4874 <sect2 id="linear-implicit-parameters">
4875 <title>Linear implicit parameters</title>
4877 Linear implicit parameters are an idea developed by Koen Claessen,
4878 Mark Shields, and Simon PJ. They address the long-standing
4879 problem that monads seem over-kill for certain sorts of problem, notably:
4882 <listitem> <para> distributing a supply of unique names </para> </listitem>
4883 <listitem> <para> distributing a supply of random numbers </para> </listitem>
4884 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
4888 Linear implicit parameters are just like ordinary implicit parameters,
4889 except that they are "linear"; that is, they cannot be copied, and
4890 must be explicitly "split" instead. Linear implicit parameters are
4891 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
4892 (The '/' in the '%' suggests the split!)
4897 import GHC.Exts( Splittable )
4899 data NameSupply = ...
4901 splitNS :: NameSupply -> (NameSupply, NameSupply)
4902 newName :: NameSupply -> Name
4904 instance Splittable NameSupply where
4908 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4909 f env (Lam x e) = Lam x' (f env e)
4912 env' = extend env x x'
4913 ...more equations for f...
4915 Notice that the implicit parameter %ns is consumed
4917 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
4918 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
4922 So the translation done by the type checker makes
4923 the parameter explicit:
4925 f :: NameSupply -> Env -> Expr -> Expr
4926 f ns env (Lam x e) = Lam x' (f ns1 env e)
4928 (ns1,ns2) = splitNS ns
4930 env = extend env x x'
4932 Notice the call to 'split' introduced by the type checker.
4933 How did it know to use 'splitNS'? Because what it really did
4934 was to introduce a call to the overloaded function 'split',
4935 defined by the class <literal>Splittable</literal>:
4937 class Splittable a where
4940 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
4941 split for name supplies. But we can simply write
4947 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
4949 The <literal>Splittable</literal> class is built into GHC. It's exported by module
4950 <literal>GHC.Exts</literal>.
4955 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
4956 are entirely distinct implicit parameters: you
4957 can use them together and they won't interfere with each other. </para>
4960 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
4962 <listitem> <para>You cannot have implicit parameters (whether linear or not)
4963 in the context of a class or instance declaration. </para></listitem>
4967 <sect3><title>Warnings</title>
4970 The monomorphism restriction is even more important than usual.
4971 Consider the example above:
4973 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4974 f env (Lam x e) = Lam x' (f env e)
4977 env' = extend env x x'
4979 If we replaced the two occurrences of x' by (newName %ns), which is
4980 usually a harmless thing to do, we get:
4982 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
4983 f env (Lam x e) = Lam (newName %ns) (f env e)
4985 env' = extend env x (newName %ns)
4987 But now the name supply is consumed in <emphasis>three</emphasis> places
4988 (the two calls to newName,and the recursive call to f), so
4989 the result is utterly different. Urk! We don't even have
4993 Well, this is an experimental change. With implicit
4994 parameters we have already lost beta reduction anyway, and
4995 (as John Launchbury puts it) we can't sensibly reason about
4996 Haskell programs without knowing their typing.
5001 <sect3><title>Recursive functions</title>
5002 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5005 foo :: %x::T => Int -> [Int]
5007 foo n = %x : foo (n-1)
5009 where T is some type in class Splittable.</para>
5011 Do you get a list of all the same T's or all different T's
5012 (assuming that split gives two distinct T's back)?
5014 If you supply the type signature, taking advantage of polymorphic
5015 recursion, you get what you'd probably expect. Here's the
5016 translated term, where the implicit param is made explicit:
5019 foo x n = let (x1,x2) = split x
5020 in x1 : foo x2 (n-1)
5022 But if you don't supply a type signature, GHC uses the Hindley
5023 Milner trick of using a single monomorphic instance of the function
5024 for the recursive calls. That is what makes Hindley Milner type inference
5025 work. So the translation becomes
5029 foom n = x : foom (n-1)
5033 Result: 'x' is not split, and you get a list of identical T's. So the
5034 semantics of the program depends on whether or not foo has a type signature.
5037 You may say that this is a good reason to dislike linear implicit parameters
5038 and you'd be right. That is why they are an experimental feature.
5044 ================ END OF Linear Implicit Parameters commented out -->
5046 <sect2 id="kinding">
5047 <title>Explicitly-kinded quantification</title>
5050 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5051 to give the kind explicitly as (machine-checked) documentation,
5052 just as it is nice to give a type signature for a function. On some occasions,
5053 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5054 John Hughes had to define the data type:
5056 data Set cxt a = Set [a]
5057 | Unused (cxt a -> ())
5059 The only use for the <literal>Unused</literal> constructor was to force the correct
5060 kind for the type variable <literal>cxt</literal>.
5063 GHC now instead allows you to specify the kind of a type variable directly, wherever
5064 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5067 This flag enables kind signatures in the following places:
5069 <listitem><para><literal>data</literal> declarations:
5071 data Set (cxt :: * -> *) a = Set [a]
5072 </screen></para></listitem>
5073 <listitem><para><literal>type</literal> declarations:
5075 type T (f :: * -> *) = f Int
5076 </screen></para></listitem>
5077 <listitem><para><literal>class</literal> declarations:
5079 class (Eq a) => C (f :: * -> *) a where ...
5080 </screen></para></listitem>
5081 <listitem><para><literal>forall</literal>'s in type signatures:
5083 f :: forall (cxt :: * -> *). Set cxt Int
5084 </screen></para></listitem>
5089 The parentheses are required. Some of the spaces are required too, to
5090 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5091 will get a parse error, because "<literal>::*->*</literal>" is a
5092 single lexeme in Haskell.
5096 As part of the same extension, you can put kind annotations in types
5099 f :: (Int :: *) -> Int
5100 g :: forall a. a -> (a :: *)
5104 atype ::= '(' ctype '::' kind ')
5106 The parentheses are required.
5111 <sect2 id="universal-quantification">
5112 <title>Arbitrary-rank polymorphism
5116 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
5117 allows us to say exactly what this means. For example:
5125 g :: forall b. (b -> b)
5127 The two are treated identically.
5131 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5132 explicit universal quantification in
5134 For example, all the following types are legal:
5136 f1 :: forall a b. a -> b -> a
5137 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5139 f2 :: (forall a. a->a) -> Int -> Int
5140 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5142 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5144 f4 :: Int -> (forall a. a -> a)
5146 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5147 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5148 The <literal>forall</literal> makes explicit the universal quantification that
5149 is implicitly added by Haskell.
5152 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5153 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5154 shows, the polymorphic type on the left of the function arrow can be overloaded.
5157 The function <literal>f3</literal> has a rank-3 type;
5158 it has rank-2 types on the left of a function arrow.
5161 GHC has three flags to control higher-rank types:
5164 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5167 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5170 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5171 That is, you can nest <literal>forall</literal>s
5172 arbitrarily deep in function arrows.
5173 In particular, a forall-type (also called a "type scheme"),
5174 including an operational type class context, is legal:
5176 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5177 of a function arrow </para> </listitem>
5178 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5179 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5180 field type signatures.</para> </listitem>
5181 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5182 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5186 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
5187 a type variable any more!
5196 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5197 the types of the constructor arguments. Here are several examples:
5203 data T a = T1 (forall b. b -> b -> b) a
5205 data MonadT m = MkMonad { return :: forall a. a -> m a,
5206 bind :: forall a b. m a -> (a -> m b) -> m b
5209 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5215 The constructors have rank-2 types:
5221 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5222 MkMonad :: forall m. (forall a. a -> m a)
5223 -> (forall a b. m a -> (a -> m b) -> m b)
5225 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5231 Notice that you don't need to use a <literal>forall</literal> if there's an
5232 explicit context. For example in the first argument of the
5233 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5234 prefixed to the argument type. The implicit <literal>forall</literal>
5235 quantifies all type variables that are not already in scope, and are
5236 mentioned in the type quantified over.
5240 As for type signatures, implicit quantification happens for non-overloaded
5241 types too. So if you write this:
5244 data T a = MkT (Either a b) (b -> b)
5247 it's just as if you had written this:
5250 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5253 That is, since the type variable <literal>b</literal> isn't in scope, it's
5254 implicitly universally quantified. (Arguably, it would be better
5255 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5256 where that is what is wanted. Feedback welcomed.)
5260 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5261 the constructor to suitable values, just as usual. For example,
5272 a3 = MkSwizzle reverse
5275 a4 = let r x = Just x
5282 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5283 mkTs f x y = [T1 f x, T1 f y]
5289 The type of the argument can, as usual, be more general than the type
5290 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5291 does not need the <literal>Ord</literal> constraint.)
5295 When you use pattern matching, the bound variables may now have
5296 polymorphic types. For example:
5302 f :: T a -> a -> (a, Char)
5303 f (T1 w k) x = (w k x, w 'c' 'd')
5305 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5306 g (MkSwizzle s) xs f = s (map f (s xs))
5308 h :: MonadT m -> [m a] -> m [a]
5309 h m [] = return m []
5310 h m (x:xs) = bind m x $ \y ->
5311 bind m (h m xs) $ \ys ->
5318 In the function <function>h</function> we use the record selectors <literal>return</literal>
5319 and <literal>bind</literal> to extract the polymorphic bind and return functions
5320 from the <literal>MonadT</literal> data structure, rather than using pattern
5326 <title>Type inference</title>
5329 In general, type inference for arbitrary-rank types is undecidable.
5330 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5331 to get a decidable algorithm by requiring some help from the programmer.
5332 We do not yet have a formal specification of "some help" but the rule is this:
5335 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5336 provides an explicit polymorphic type for x, or GHC's type inference will assume
5337 that x's type has no foralls in it</emphasis>.
5340 What does it mean to "provide" an explicit type for x? You can do that by
5341 giving a type signature for x directly, using a pattern type signature
5342 (<xref linkend="scoped-type-variables"/>), thus:
5344 \ f :: (forall a. a->a) -> (f True, f 'c')
5346 Alternatively, you can give a type signature to the enclosing
5347 context, which GHC can "push down" to find the type for the variable:
5349 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5351 Here the type signature on the expression can be pushed inwards
5352 to give a type signature for f. Similarly, and more commonly,
5353 one can give a type signature for the function itself:
5355 h :: (forall a. a->a) -> (Bool,Char)
5356 h f = (f True, f 'c')
5358 You don't need to give a type signature if the lambda bound variable
5359 is a constructor argument. Here is an example we saw earlier:
5361 f :: T a -> a -> (a, Char)
5362 f (T1 w k) x = (w k x, w 'c' 'd')
5364 Here we do not need to give a type signature to <literal>w</literal>, because
5365 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5372 <sect3 id="implicit-quant">
5373 <title>Implicit quantification</title>
5376 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5377 user-written types, if and only if there is no explicit <literal>forall</literal>,
5378 GHC finds all the type variables mentioned in the type that are not already
5379 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5383 f :: forall a. a -> a
5390 h :: forall b. a -> b -> b
5396 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5399 f :: (a -> a) -> Int
5401 f :: forall a. (a -> a) -> Int
5403 f :: (forall a. a -> a) -> Int
5406 g :: (Ord a => a -> a) -> Int
5407 -- MEANS the illegal type
5408 g :: forall a. (Ord a => a -> a) -> Int
5410 g :: (forall a. Ord a => a -> a) -> Int
5412 The latter produces an illegal type, which you might think is silly,
5413 but at least the rule is simple. If you want the latter type, you
5414 can write your for-alls explicitly. Indeed, doing so is strongly advised
5421 <sect2 id="impredicative-polymorphism">
5422 <title>Impredicative polymorphism
5424 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5425 enabled with <option>-XImpredicativeTypes</option>.
5427 that you can call a polymorphic function at a polymorphic type, and
5428 parameterise data structures over polymorphic types. For example:
5430 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5431 f (Just g) = Just (g [3], g "hello")
5434 Notice here that the <literal>Maybe</literal> type is parameterised by the
5435 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5438 <para>The technical details of this extension are described in the paper
5439 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5440 type inference for higher-rank types and impredicativity</ulink>,
5441 which appeared at ICFP 2006.
5445 <sect2 id="scoped-type-variables">
5446 <title>Lexically scoped type variables
5450 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5451 which some type signatures are simply impossible to write. For example:
5453 f :: forall a. [a] -> [a]
5459 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5460 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5461 The type variables bound by a <literal>forall</literal> scope over
5462 the entire definition of the accompanying value declaration.
5463 In this example, the type variable <literal>a</literal> scopes over the whole
5464 definition of <literal>f</literal>, including over
5465 the type signature for <varname>ys</varname>.
5466 In Haskell 98 it is not possible to declare
5467 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5468 it becomes possible to do so.
5470 <para>Lexically-scoped type variables are enabled by
5471 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5473 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5474 variables work, compared to earlier releases. Read this section
5478 <title>Overview</title>
5480 <para>The design follows the following principles
5482 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5483 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5484 design.)</para></listitem>
5485 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5486 type variables. This means that every programmer-written type signature
5487 (including one that contains free scoped type variables) denotes a
5488 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5489 checker, and no inference is involved.</para></listitem>
5490 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5491 changing the program.</para></listitem>
5495 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5497 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5498 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5499 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5500 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5504 In Haskell, a programmer-written type signature is implicitly quantified over
5505 its free type variables (<ulink
5506 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5508 of the Haskell Report).
5509 Lexically scoped type variables affect this implicit quantification rules
5510 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5511 quantified. For example, if type variable <literal>a</literal> is in scope,
5514 (e :: a -> a) means (e :: a -> a)
5515 (e :: b -> b) means (e :: forall b. b->b)
5516 (e :: a -> b) means (e :: forall b. a->b)
5524 <sect3 id="decl-type-sigs">
5525 <title>Declaration type signatures</title>
5526 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5527 quantification (using <literal>forall</literal>) brings into scope the
5528 explicitly-quantified
5529 type variables, in the definition of the named function. For example:
5531 f :: forall a. [a] -> [a]
5532 f (x:xs) = xs ++ [ x :: a ]
5534 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5535 the definition of "<literal>f</literal>".
5537 <para>This only happens if:
5539 <listitem><para> The quantification in <literal>f</literal>'s type
5540 signature is explicit. For example:
5543 g (x:xs) = xs ++ [ x :: a ]
5545 This program will be rejected, because "<literal>a</literal>" does not scope
5546 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5547 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5548 quantification rules.
5550 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5551 not a pattern binding.
5554 f1 :: forall a. [a] -> [a]
5555 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5557 f2 :: forall a. [a] -> [a]
5558 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5560 f3 :: forall a. [a] -> [a]
5561 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5563 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5564 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5565 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5566 the type signature brings <literal>a</literal> into scope.
5572 <sect3 id="exp-type-sigs">
5573 <title>Expression type signatures</title>
5575 <para>An expression type signature that has <emphasis>explicit</emphasis>
5576 quantification (using <literal>forall</literal>) brings into scope the
5577 explicitly-quantified
5578 type variables, in the annotated expression. For example:
5580 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5582 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5583 type variable <literal>s</literal> into scope, in the annotated expression
5584 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5589 <sect3 id="pattern-type-sigs">
5590 <title>Pattern type signatures</title>
5592 A type signature may occur in any pattern; this is a <emphasis>pattern type
5593 signature</emphasis>.
5596 -- f and g assume that 'a' is already in scope
5597 f = \(x::Int, y::a) -> x
5599 h ((x,y) :: (Int,Bool)) = (y,x)
5601 In the case where all the type variables in the pattern type signature are
5602 already in scope (i.e. bound by the enclosing context), matters are simple: the
5603 signature simply constrains the type of the pattern in the obvious way.
5606 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5607 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5608 that are already in scope. For example:
5610 f :: forall a. [a] -> (Int, [a])
5613 (ys::[a], n) = (reverse xs, length xs) -- OK
5614 zs::[a] = xs ++ ys -- OK
5616 Just (v::b) = ... -- Not OK; b is not in scope
5618 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5619 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5623 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5624 type signature may mention a type variable that is not in scope; in this case,
5625 <emphasis>the signature brings that type variable into scope</emphasis>.
5626 This is particularly important for existential data constructors. For example:
5628 data T = forall a. MkT [a]
5631 k (MkT [t::a]) = MkT t3
5635 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5636 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5637 because it is bound by the pattern match. GHC's rule is that in this situation
5638 (and only then), a pattern type signature can mention a type variable that is
5639 not already in scope; the effect is to bring it into scope, standing for the
5640 existentially-bound type variable.
5643 When a pattern type signature binds a type variable in this way, GHC insists that the
5644 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5645 This means that any user-written type signature always stands for a completely known type.
5648 If all this seems a little odd, we think so too. But we must have
5649 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5650 could not name existentially-bound type variables in subsequent type signatures.
5653 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5654 signature is allowed to mention a lexical variable that is not already in
5656 For example, both <literal>f</literal> and <literal>g</literal> would be
5657 illegal if <literal>a</literal> was not already in scope.
5663 <!-- ==================== Commented out part about result type signatures
5665 <sect3 id="result-type-sigs">
5666 <title>Result type signatures</title>
5669 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5672 {- f assumes that 'a' is already in scope -}
5673 f x y :: [a] = [x,y,x]
5675 g = \ x :: [Int] -> [3,4]
5677 h :: forall a. [a] -> a
5681 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5682 the result of the function. Similarly, the body of the lambda in the RHS of
5683 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5684 alternative in <literal>h</literal> is <literal>a</literal>.
5686 <para> A result type signature never brings new type variables into scope.</para>
5688 There are a couple of syntactic wrinkles. First, notice that all three
5689 examples would parse quite differently with parentheses:
5691 {- f assumes that 'a' is already in scope -}
5692 f x (y :: [a]) = [x,y,x]
5694 g = \ (x :: [Int]) -> [3,4]
5696 h :: forall a. [a] -> a
5700 Now the signature is on the <emphasis>pattern</emphasis>; and
5701 <literal>h</literal> would certainly be ill-typed (since the pattern
5702 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5704 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5705 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5706 token or a parenthesised type of some sort). To see why,
5707 consider how one would parse this:
5716 <sect3 id="cls-inst-scoped-tyvars">
5717 <title>Class and instance declarations</title>
5720 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5721 scope over the methods defined in the <literal>where</literal> part. For example:
5739 <sect2 id="typing-binds">
5740 <title>Generalised typing of mutually recursive bindings</title>
5743 The Haskell Report specifies that a group of bindings (at top level, or in a
5744 <literal>let</literal> or <literal>where</literal>) should be sorted into
5745 strongly-connected components, and then type-checked in dependency order
5746 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5747 Report, Section 4.5.1</ulink>).
5748 As each group is type-checked, any binders of the group that
5750 an explicit type signature are put in the type environment with the specified
5752 and all others are monomorphic until the group is generalised
5753 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5756 <para>Following a suggestion of Mark Jones, in his paper
5757 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5759 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5761 <emphasis>the dependency analysis ignores references to variables that have an explicit
5762 type signature</emphasis>.
5763 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5764 typecheck. For example, consider:
5766 f :: Eq a => a -> Bool
5767 f x = (x == x) || g True || g "Yes"
5769 g y = (y <= y) || f True
5771 This is rejected by Haskell 98, but under Jones's scheme the definition for
5772 <literal>g</literal> is typechecked first, separately from that for
5773 <literal>f</literal>,
5774 because the reference to <literal>f</literal> in <literal>g</literal>'s right
5775 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
5776 type is generalised, to get
5778 g :: Ord a => a -> Bool
5780 Now, the definition for <literal>f</literal> is typechecked, with this type for
5781 <literal>g</literal> in the type environment.
5785 The same refined dependency analysis also allows the type signatures of
5786 mutually-recursive functions to have different contexts, something that is illegal in
5787 Haskell 98 (Section 4.5.2, last sentence). With
5788 <option>-XRelaxedPolyRec</option>
5789 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
5790 type signatures; in practice this means that only variables bound by the same
5791 pattern binding must have the same context. For example, this is fine:
5793 f :: Eq a => a -> Bool
5794 f x = (x == x) || g True
5796 g :: Ord a => a -> Bool
5797 g y = (y <= y) || f True
5803 <!-- ==================== End of type system extensions ================= -->
5805 <!-- ====================== TEMPLATE HASKELL ======================= -->
5807 <sect1 id="template-haskell">
5808 <title>Template Haskell</title>
5810 <para>Template Haskell allows you to do compile-time meta-programming in
5813 the main technical innovations is discussed in "<ulink
5814 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
5815 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
5818 There is a Wiki page about
5819 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
5820 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
5824 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
5825 Haskell library reference material</ulink>
5826 (look for module <literal>Language.Haskell.TH</literal>).
5827 Many changes to the original design are described in
5828 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
5829 Notes on Template Haskell version 2</ulink>.
5830 Not all of these changes are in GHC, however.
5833 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
5834 as a worked example to help get you started.
5838 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
5839 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
5844 <title>Syntax</title>
5846 <para> Template Haskell has the following new syntactic
5847 constructions. You need to use the flag
5848 <option>-XTemplateHaskell</option>
5849 <indexterm><primary><option>-XTemplateHaskell</option></primary>
5850 </indexterm>to switch these syntactic extensions on
5851 (<option>-XTemplateHaskell</option> is no longer implied by
5852 <option>-fglasgow-exts</option>).</para>
5856 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
5857 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
5858 There must be no space between the "$" and the identifier or parenthesis. This use
5859 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
5860 of "." as an infix operator. If you want the infix operator, put spaces around it.
5862 <para> A splice can occur in place of
5864 <listitem><para> an expression; the spliced expression must
5865 have type <literal>Q Exp</literal></para></listitem>
5866 <listitem><para> an type; the spliced expression must
5867 have type <literal>Q Typ</literal></para></listitem>
5868 <listitem><para> a list of top-level declarations; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
5871 Inside a splice you can can only call functions defined in imported modules,
5872 not functions defined elsewhere in the same module.</listitem>
5876 A expression quotation is written in Oxford brackets, thus:
5878 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
5879 the quotation has type <literal>Q Exp</literal>.</para></listitem>
5880 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
5881 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
5882 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
5883 the quotation has type <literal>Q Typ</literal>.</para></listitem>
5884 </itemizedlist></para></listitem>
5887 A quasi-quotation can appear in either a pattern context or an
5888 expression context and is also written in Oxford brackets:
5890 <listitem><para> <literal>[:<replaceable>varid</replaceable>| ... |]</literal>,
5891 where the "..." is an arbitrary string; a full description of the
5892 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
5893 </itemizedlist></para></listitem>
5896 A name can be quoted with either one or two prefix single quotes:
5898 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
5899 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
5900 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
5902 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
5903 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
5906 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
5907 may also be given as an argument to the <literal>reify</literal> function.
5913 (Compared to the original paper, there are many differences of detail.
5914 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
5915 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
5916 Pattern splices and quotations are not implemented.)
5920 <sect2> <title> Using Template Haskell </title>
5924 The data types and monadic constructor functions for Template Haskell are in the library
5925 <literal>Language.Haskell.THSyntax</literal>.
5929 You can only run a function at compile time if it is imported from another module. That is,
5930 you can't define a function in a module, and call it from within a splice in the same module.
5931 (It would make sense to do so, but it's hard to implement.)
5935 You can only run a function at compile time if it is imported
5936 from another module <emphasis>that is not part of a mutually-recursive group of modules
5937 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
5938 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
5939 splice is to be run.</para>
5941 For example, when compiling module A,
5942 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
5943 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
5947 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
5950 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
5951 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
5952 compiles and runs a program, and then looks at the result. So it's important that
5953 the program it compiles produces results whose representations are identical to
5954 those of the compiler itself.
5958 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
5959 or file-at-a-time). There used to be a restriction to the former two, but that restriction
5964 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
5965 <para>To help you get over the confidence barrier, try out this skeletal worked example.
5966 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
5973 -- Import our template "pr"
5974 import Printf ( pr )
5976 -- The splice operator $ takes the Haskell source code
5977 -- generated at compile time by "pr" and splices it into
5978 -- the argument of "putStrLn".
5979 main = putStrLn ( $(pr "Hello") )
5985 -- Skeletal printf from the paper.
5986 -- It needs to be in a separate module to the one where
5987 -- you intend to use it.
5989 -- Import some Template Haskell syntax
5990 import Language.Haskell.TH
5992 -- Describe a format string
5993 data Format = D | S | L String
5995 -- Parse a format string. This is left largely to you
5996 -- as we are here interested in building our first ever
5997 -- Template Haskell program and not in building printf.
5998 parse :: String -> [Format]
6001 -- Generate Haskell source code from a parsed representation
6002 -- of the format string. This code will be spliced into
6003 -- the module which calls "pr", at compile time.
6004 gen :: [Format] -> Q Exp
6005 gen [D] = [| \n -> show n |]
6006 gen [S] = [| \s -> s |]
6007 gen [L s] = stringE s
6009 -- Here we generate the Haskell code for the splice
6010 -- from an input format string.
6011 pr :: String -> Q Exp
6012 pr s = gen (parse s)
6015 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6018 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6021 <para>Run "main.exe" and here is your output:</para>
6031 <title>Using Template Haskell with Profiling</title>
6032 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6034 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6035 interpreter to run the splice expressions. The bytecode interpreter
6036 runs the compiled expression on top of the same runtime on which GHC
6037 itself is running; this means that the compiled code referred to by
6038 the interpreted expression must be compatible with this runtime, and
6039 in particular this means that object code that is compiled for
6040 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6041 expression, because profiled object code is only compatible with the
6042 profiling version of the runtime.</para>
6044 <para>This causes difficulties if you have a multi-module program
6045 containing Template Haskell code and you need to compile it for
6046 profiling, because GHC cannot load the profiled object code and use it
6047 when executing the splices. Fortunately GHC provides a workaround.
6048 The basic idea is to compile the program twice:</para>
6052 <para>Compile the program or library first the normal way, without
6053 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6056 <para>Then compile it again with <option>-prof</option>, and
6057 additionally use <option>-osuf
6058 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6059 to name the object files differently (you can choose any suffix
6060 that isn't the normal object suffix here). GHC will automatically
6061 load the object files built in the first step when executing splice
6062 expressions. If you omit the <option>-osuf</option> flag when
6063 building with <option>-prof</option> and Template Haskell is used,
6064 GHC will emit an error message. </para>
6069 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6070 <para>Quasi-quotation allows patterns and expressions to be written using
6071 programmer-defined concrete syntax; the motivation behind the extension and
6072 several examples are documented in
6073 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6074 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6075 2007). The example below shows how to write a quasiquoter for a simple
6076 expression language.</para>
6079 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6080 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6081 functions for quoting expressions and patterns, respectively. The first argument
6082 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6083 context of the quasi-quotation statement determines which of the two parsers is
6084 called: if the quasi-quotation occurs in an expression context, the expression
6085 parser is called, and if it occurs in a pattern context, the pattern parser is
6089 Note that in the example we make use of an antiquoted
6090 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6091 (this syntax for anti-quotation was defined by the parser's
6092 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6093 integer value argument of the constructor <literal>IntExpr</literal> when
6094 pattern matching. Please see the referenced paper for further details regarding
6095 anti-quotation as well as the description of a technique that uses SYB to
6096 leverage a single parser of type <literal>String -> a</literal> to generate both
6097 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6098 pattern parser that returns a value of type <literal>Q Pat</literal>.
6101 <para>In general, a quasi-quote has the form
6102 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6103 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6104 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6105 can be arbitrary, and may contain newlines.
6108 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6109 the example, <literal>expr</literal> cannot be defined
6110 in <literal>Main.hs</literal> where it is used, but must be imported.
6121 main = do { print $ eval [$expr|1 + 2|]
6123 { [$expr|'int:n|] -> print n
6132 import qualified Language.Haskell.TH as TH
6133 import Language.Haskell.TH.Quote
6135 data Expr = IntExpr Integer
6136 | AntiIntExpr String
6137 | BinopExpr BinOp Expr Expr
6139 deriving(Show, Typeable, Data)
6145 deriving(Show, Typeable, Data)
6147 eval :: Expr -> Integer
6148 eval (IntExpr n) = n
6149 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6156 expr = QuasiQuoter parseExprExp parseExprPat
6158 -- Parse an Expr, returning its representation as
6159 -- either a Q Exp or a Q Pat. See the referenced paper
6160 -- for how to use SYB to do this by writing a single
6161 -- parser of type String -> Expr instead of two
6162 -- separate parsers.
6164 parseExprExp :: String -> Q Exp
6167 parseExprPat :: String -> Q Pat
6171 <para>Now run the compiler:
6174 $ ghc --make -XQuasiQuotes Main.hs -o main
6177 <para>Run "main" and here is your output:</para>
6189 <!-- ===================== Arrow notation =================== -->
6191 <sect1 id="arrow-notation">
6192 <title>Arrow notation
6195 <para>Arrows are a generalization of monads introduced by John Hughes.
6196 For more details, see
6201 “Generalising Monads to Arrows”,
6202 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6203 pp67–111, May 2000.
6204 The paper that introduced arrows: a friendly introduction, motivated with
6205 programming examples.
6211 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6212 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6213 Introduced the notation described here.
6219 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6220 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6227 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6228 John Hughes, in <citetitle>5th International Summer School on
6229 Advanced Functional Programming</citetitle>,
6230 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6232 This paper includes another introduction to the notation,
6233 with practical examples.
6239 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6240 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6241 A terse enumeration of the formal rules used
6242 (extracted from comments in the source code).
6248 The arrows web page at
6249 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6254 With the <option>-XArrows</option> flag, GHC supports the arrow
6255 notation described in the second of these papers,
6256 translating it using combinators from the
6257 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6259 What follows is a brief introduction to the notation;
6260 it won't make much sense unless you've read Hughes's paper.
6263 <para>The extension adds a new kind of expression for defining arrows:
6265 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6266 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6268 where <literal>proc</literal> is a new keyword.
6269 The variables of the pattern are bound in the body of the
6270 <literal>proc</literal>-expression,
6271 which is a new sort of thing called a <firstterm>command</firstterm>.
6272 The syntax of commands is as follows:
6274 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6275 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6276 | <replaceable>cmd</replaceable><superscript>0</superscript>
6278 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6279 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6280 infix operators as for expressions, and
6282 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6283 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6284 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6285 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6286 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6287 | <replaceable>fcmd</replaceable>
6289 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6290 | ( <replaceable>cmd</replaceable> )
6291 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6293 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6294 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6295 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6296 | <replaceable>cmd</replaceable>
6298 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6299 except that the bodies are commands instead of expressions.
6303 Commands produce values, but (like monadic computations)
6304 may yield more than one value,
6305 or none, and may do other things as well.
6306 For the most part, familiarity with monadic notation is a good guide to
6308 However the values of expressions, even monadic ones,
6309 are determined by the values of the variables they contain;
6310 this is not necessarily the case for commands.
6314 A simple example of the new notation is the expression
6316 proc x -> f -< x+1
6318 We call this a <firstterm>procedure</firstterm> or
6319 <firstterm>arrow abstraction</firstterm>.
6320 As with a lambda expression, the variable <literal>x</literal>
6321 is a new variable bound within the <literal>proc</literal>-expression.
6322 It refers to the input to the arrow.
6323 In the above example, <literal>-<</literal> is not an identifier but an
6324 new reserved symbol used for building commands from an expression of arrow
6325 type and an expression to be fed as input to that arrow.
6326 (The weird look will make more sense later.)
6327 It may be read as analogue of application for arrows.
6328 The above example is equivalent to the Haskell expression
6330 arr (\ x -> x+1) >>> f
6332 That would make no sense if the expression to the left of
6333 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6334 More generally, the expression to the left of <literal>-<</literal>
6335 may not involve any <firstterm>local variable</firstterm>,
6336 i.e. a variable bound in the current arrow abstraction.
6337 For such a situation there is a variant <literal>-<<</literal>, as in
6339 proc x -> f x -<< x+1
6341 which is equivalent to
6343 arr (\ x -> (f x, x+1)) >>> app
6345 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6347 Such an arrow is equivalent to a monad, so if you're using this form
6348 you may find a monadic formulation more convenient.
6352 <title>do-notation for commands</title>
6355 Another form of command is a form of <literal>do</literal>-notation.
6356 For example, you can write
6365 You can read this much like ordinary <literal>do</literal>-notation,
6366 but with commands in place of monadic expressions.
6367 The first line sends the value of <literal>x+1</literal> as an input to
6368 the arrow <literal>f</literal>, and matches its output against
6369 <literal>y</literal>.
6370 In the next line, the output is discarded.
6371 The arrow <function>returnA</function> is defined in the
6372 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6373 module as <literal>arr id</literal>.
6374 The above example is treated as an abbreviation for
6376 arr (\ x -> (x, x)) >>>
6377 first (arr (\ x -> x+1) >>> f) >>>
6378 arr (\ (y, x) -> (y, (x, y))) >>>
6379 first (arr (\ y -> 2*y) >>> g) >>>
6381 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6382 first (arr (\ (x, z) -> x*z) >>> h) >>>
6383 arr (\ (t, z) -> t+z) >>>
6386 Note that variables not used later in the composition are projected out.
6387 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6389 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6390 module, this reduces to
6392 arr (\ x -> (x+1, x)) >>>
6394 arr (\ (y, x) -> (2*y, (x, y))) >>>
6396 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6398 arr (\ (t, z) -> t+z)
6400 which is what you might have written by hand.
6401 With arrow notation, GHC keeps track of all those tuples of variables for you.
6405 Note that although the above translation suggests that
6406 <literal>let</literal>-bound variables like <literal>z</literal> must be
6407 monomorphic, the actual translation produces Core,
6408 so polymorphic variables are allowed.
6412 It's also possible to have mutually recursive bindings,
6413 using the new <literal>rec</literal> keyword, as in the following example:
6415 counter :: ArrowCircuit a => a Bool Int
6416 counter = proc reset -> do
6417 rec output <- returnA -< if reset then 0 else next
6418 next <- delay 0 -< output+1
6419 returnA -< output
6421 The translation of such forms uses the <function>loop</function> combinator,
6422 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6428 <title>Conditional commands</title>
6431 In the previous example, we used a conditional expression to construct the
6433 Sometimes we want to conditionally execute different commands, as in
6440 which is translated to
6442 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6443 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6445 Since the translation uses <function>|||</function>,
6446 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6450 There are also <literal>case</literal> commands, like
6456 y <- h -< (x1, x2)
6460 The syntax is the same as for <literal>case</literal> expressions,
6461 except that the bodies of the alternatives are commands rather than expressions.
6462 The translation is similar to that of <literal>if</literal> commands.
6468 <title>Defining your own control structures</title>
6471 As we're seen, arrow notation provides constructs,
6472 modelled on those for expressions,
6473 for sequencing, value recursion and conditionals.
6474 But suitable combinators,
6475 which you can define in ordinary Haskell,
6476 may also be used to build new commands out of existing ones.
6477 The basic idea is that a command defines an arrow from environments to values.
6478 These environments assign values to the free local variables of the command.
6479 Thus combinators that produce arrows from arrows
6480 may also be used to build commands from commands.
6481 For example, the <literal>ArrowChoice</literal> class includes a combinator
6483 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6485 so we can use it to build commands:
6487 expr' = proc x -> do
6490 symbol Plus -< ()
6491 y <- term -< ()
6494 symbol Minus -< ()
6495 y <- term -< ()
6498 (The <literal>do</literal> on the first line is needed to prevent the first
6499 <literal><+> ...</literal> from being interpreted as part of the
6500 expression on the previous line.)
6501 This is equivalent to
6503 expr' = (proc x -> returnA -< x)
6504 <+> (proc x -> do
6505 symbol Plus -< ()
6506 y <- term -< ()
6508 <+> (proc x -> do
6509 symbol Minus -< ()
6510 y <- term -< ()
6513 It is essential that this operator be polymorphic in <literal>e</literal>
6514 (representing the environment input to the command
6515 and thence to its subcommands)
6516 and satisfy the corresponding naturality property
6518 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6520 at least for strict <literal>k</literal>.
6521 (This should be automatic if you're not using <function>seq</function>.)
6522 This ensures that environments seen by the subcommands are environments
6523 of the whole command,
6524 and also allows the translation to safely trim these environments.
6525 The operator must also not use any variable defined within the current
6530 We could define our own operator
6532 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6533 untilA body cond = proc x ->
6534 b <- cond -< x
6535 if b then returnA -< ()
6538 untilA body cond -< x
6540 and use it in the same way.
6541 Of course this infix syntax only makes sense for binary operators;
6542 there is also a more general syntax involving special brackets:
6546 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6553 <title>Primitive constructs</title>
6556 Some operators will need to pass additional inputs to their subcommands.
6557 For example, in an arrow type supporting exceptions,
6558 the operator that attaches an exception handler will wish to pass the
6559 exception that occurred to the handler.
6560 Such an operator might have a type
6562 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6564 where <literal>Ex</literal> is the type of exceptions handled.
6565 You could then use this with arrow notation by writing a command
6567 body `handleA` \ ex -> handler
6569 so that if an exception is raised in the command <literal>body</literal>,
6570 the variable <literal>ex</literal> is bound to the value of the exception
6571 and the command <literal>handler</literal>,
6572 which typically refers to <literal>ex</literal>, is entered.
6573 Though the syntax here looks like a functional lambda,
6574 we are talking about commands, and something different is going on.
6575 The input to the arrow represented by a command consists of values for
6576 the free local variables in the command, plus a stack of anonymous values.
6577 In all the prior examples, this stack was empty.
6578 In the second argument to <function>handleA</function>,
6579 this stack consists of one value, the value of the exception.
6580 The command form of lambda merely gives this value a name.
6585 the values on the stack are paired to the right of the environment.
6586 So operators like <function>handleA</function> that pass
6587 extra inputs to their subcommands can be designed for use with the notation
6588 by pairing the values with the environment in this way.
6589 More precisely, the type of each argument of the operator (and its result)
6590 should have the form
6592 a (...(e,t1), ... tn) t
6594 where <replaceable>e</replaceable> is a polymorphic variable
6595 (representing the environment)
6596 and <replaceable>ti</replaceable> are the types of the values on the stack,
6597 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6598 The polymorphic variable <replaceable>e</replaceable> must not occur in
6599 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6600 <replaceable>t</replaceable>.
6601 However the arrows involved need not be the same.
6602 Here are some more examples of suitable operators:
6604 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6605 runReader :: ... => a e c -> a' (e,State) c
6606 runState :: ... => a e c -> a' (e,State) (c,State)
6608 We can supply the extra input required by commands built with the last two
6609 by applying them to ordinary expressions, as in
6613 (|runReader (do { ... })|) s
6615 which adds <literal>s</literal> to the stack of inputs to the command
6616 built using <function>runReader</function>.
6620 The command versions of lambda abstraction and application are analogous to
6621 the expression versions.
6622 In particular, the beta and eta rules describe equivalences of commands.
6623 These three features (operators, lambda abstraction and application)
6624 are the core of the notation; everything else can be built using them,
6625 though the results would be somewhat clumsy.
6626 For example, we could simulate <literal>do</literal>-notation by defining
6628 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6629 u `bind` f = returnA &&& u >>> f
6631 bind_ :: Arrow a => a e b -> a e c -> a e c
6632 u `bind_` f = u `bind` (arr fst >>> f)
6634 We could simulate <literal>if</literal> by defining
6636 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6637 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6644 <title>Differences with the paper</title>
6649 <para>Instead of a single form of arrow application (arrow tail) with two
6650 translations, the implementation provides two forms
6651 <quote><literal>-<</literal></quote> (first-order)
6652 and <quote><literal>-<<</literal></quote> (higher-order).
6657 <para>User-defined operators are flagged with banana brackets instead of
6658 a new <literal>form</literal> keyword.
6667 <title>Portability</title>
6670 Although only GHC implements arrow notation directly,
6671 there is also a preprocessor
6673 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6674 that translates arrow notation into Haskell 98
6675 for use with other Haskell systems.
6676 You would still want to check arrow programs with GHC;
6677 tracing type errors in the preprocessor output is not easy.
6678 Modules intended for both GHC and the preprocessor must observe some
6679 additional restrictions:
6684 The module must import
6685 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6691 The preprocessor cannot cope with other Haskell extensions.
6692 These would have to go in separate modules.
6698 Because the preprocessor targets Haskell (rather than Core),
6699 <literal>let</literal>-bound variables are monomorphic.
6710 <!-- ==================== BANG PATTERNS ================= -->
6712 <sect1 id="bang-patterns">
6713 <title>Bang patterns
6714 <indexterm><primary>Bang patterns</primary></indexterm>
6716 <para>GHC supports an extension of pattern matching called <emphasis>bang
6717 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6718 Bang patterns are under consideration for Haskell Prime.
6720 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6721 prime feature description</ulink> contains more discussion and examples
6722 than the material below.
6725 The key change is the addition of a new rule to the
6726 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6727 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6728 against a value <replaceable>v</replaceable> behaves as follows:
6730 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6731 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6735 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
6738 <sect2 id="bang-patterns-informal">
6739 <title>Informal description of bang patterns
6742 The main idea is to add a single new production to the syntax of patterns:
6746 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
6747 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
6752 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
6753 whereas without the bang it would be lazy.
6754 Bang patterns can be nested of course:
6758 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
6759 <literal>y</literal>.
6760 A bang only really has an effect if it precedes a variable or wild-card pattern:
6765 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
6766 putting a bang before a pattern that
6767 forces evaluation anyway does nothing.
6770 There is one (apparent) exception to this general rule that a bang only
6771 makes a difference when it precedes a variable or wild-card: a bang at the
6772 top level of a <literal>let</literal> or <literal>where</literal>
6773 binding makes the binding strict, regardless of the pattern. For example:
6777 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
6778 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
6779 (We say "apparent" exception because the Right Way to think of it is that the bang
6780 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
6781 is part of the syntax of the <emphasis>binding</emphasis>.)
6782 Nested bangs in a pattern binding behave uniformly with all other forms of
6783 pattern matching. For example
6785 let (!x,[y]) = e in b
6787 is equivalent to this:
6789 let { t = case e of (x,[y]) -> x `seq` (x,y)
6794 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
6795 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
6796 evaluation of <literal>x</literal>.
6799 Bang patterns work in <literal>case</literal> expressions too, of course:
6801 g5 x = let y = f x in body
6802 g6 x = case f x of { y -> body }
6803 g7 x = case f x of { !y -> body }
6805 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
6806 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
6807 result, and then evaluates <literal>body</literal>.
6812 <sect2 id="bang-patterns-sem">
6813 <title>Syntax and semantics
6817 We add a single new production to the syntax of patterns:
6821 There is one problem with syntactic ambiguity. Consider:
6825 Is this a definition of the infix function "<literal>(!)</literal>",
6826 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
6827 ambiguity in favour of the latter. If you want to define
6828 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
6833 The semantics of Haskell pattern matching is described in <ulink
6834 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
6835 Section 3.17.2</ulink> of the Haskell Report. To this description add
6836 one extra item 10, saying:
6837 <itemizedlist><listitem><para>Matching
6838 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
6839 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
6840 <listitem><para>otherwise, <literal>pat</literal> is matched against
6841 <literal>v</literal></para></listitem>
6843 </para></listitem></itemizedlist>
6844 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
6845 Section 3.17.3</ulink>, add a new case (t):
6847 case v of { !pat -> e; _ -> e' }
6848 = v `seq` case v of { pat -> e; _ -> e' }
6851 That leaves let expressions, whose translation is given in
6852 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
6854 of the Haskell Report.
6855 In the translation box, first apply
6856 the following transformation: for each pattern <literal>pi</literal> that is of
6857 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
6858 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
6859 have a bang at the top, apply the rules in the existing box.
6861 <para>The effect of the let rule is to force complete matching of the pattern
6862 <literal>qi</literal> before evaluation of the body is begun. The bang is
6863 retained in the translated form in case <literal>qi</literal> is a variable,
6871 The let-binding can be recursive. However, it is much more common for
6872 the let-binding to be non-recursive, in which case the following law holds:
6873 <literal>(let !p = rhs in body)</literal>
6875 <literal>(case rhs of !p -> body)</literal>
6878 A pattern with a bang at the outermost level is not allowed at the top level of
6884 <!-- ==================== ASSERTIONS ================= -->
6886 <sect1 id="assertions">
6888 <indexterm><primary>Assertions</primary></indexterm>
6892 If you want to make use of assertions in your standard Haskell code, you
6893 could define a function like the following:
6899 assert :: Bool -> a -> a
6900 assert False x = error "assertion failed!"
6907 which works, but gives you back a less than useful error message --
6908 an assertion failed, but which and where?
6912 One way out is to define an extended <function>assert</function> function which also
6913 takes a descriptive string to include in the error message and
6914 perhaps combine this with the use of a pre-processor which inserts
6915 the source location where <function>assert</function> was used.
6919 Ghc offers a helping hand here, doing all of this for you. For every
6920 use of <function>assert</function> in the user's source:
6926 kelvinToC :: Double -> Double
6927 kelvinToC k = assert (k >= 0.0) (k+273.15)
6933 Ghc will rewrite this to also include the source location where the
6940 assert pred val ==> assertError "Main.hs|15" pred val
6946 The rewrite is only performed by the compiler when it spots
6947 applications of <function>Control.Exception.assert</function>, so you
6948 can still define and use your own versions of
6949 <function>assert</function>, should you so wish. If not, import
6950 <literal>Control.Exception</literal> to make use
6951 <function>assert</function> in your code.
6955 GHC ignores assertions when optimisation is turned on with the
6956 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
6957 <literal>assert pred e</literal> will be rewritten to
6958 <literal>e</literal>. You can also disable assertions using the
6959 <option>-fignore-asserts</option>
6960 option<indexterm><primary><option>-fignore-asserts</option></primary>
6961 </indexterm>.</para>
6964 Assertion failures can be caught, see the documentation for the
6965 <literal>Control.Exception</literal> library for the details.
6971 <!-- =============================== PRAGMAS =========================== -->
6973 <sect1 id="pragmas">
6974 <title>Pragmas</title>
6976 <indexterm><primary>pragma</primary></indexterm>
6978 <para>GHC supports several pragmas, or instructions to the
6979 compiler placed in the source code. Pragmas don't normally affect
6980 the meaning of the program, but they might affect the efficiency
6981 of the generated code.</para>
6983 <para>Pragmas all take the form
6985 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
6987 where <replaceable>word</replaceable> indicates the type of
6988 pragma, and is followed optionally by information specific to that
6989 type of pragma. Case is ignored in
6990 <replaceable>word</replaceable>. The various values for
6991 <replaceable>word</replaceable> that GHC understands are described
6992 in the following sections; any pragma encountered with an
6993 unrecognised <replaceable>word</replaceable> is
6994 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
6995 should start in a column to the right of the opening <literal>{-#</literal>. </para>
6997 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7001 pragma must precede the <literal>module</literal> keyword in the file.
7004 There can be as many file-header pragmas as you please, and they can be
7005 preceded or followed by comments.
7008 File-header pragmas are read once only, before
7009 pre-processing the file (e.g. with cpp).
7012 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7013 <literal>{-# OPTIONS_GHC #-}</literal>, and
7014 <literal>{-# INCLUDE #-}</literal>.
7019 <sect2 id="language-pragma">
7020 <title>LANGUAGE pragma</title>
7022 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7023 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7025 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7027 It is the intention that all Haskell compilers support the
7028 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7029 all extensions are supported by all compilers, of
7030 course. The <literal>LANGUAGE</literal> pragma should be used instead
7031 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7033 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7035 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7037 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7039 <para>Every language extension can also be turned into a command-line flag
7040 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7041 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7044 <para>A list of all supported language extensions can be obtained by invoking
7045 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7047 <para>Any extension from the <literal>Extension</literal> type defined in
7049 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7050 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7054 <sect2 id="options-pragma">
7055 <title>OPTIONS_GHC pragma</title>
7056 <indexterm><primary>OPTIONS_GHC</primary>
7058 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7061 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7062 additional options that are given to the compiler when compiling
7063 this source file. See <xref linkend="source-file-options"/> for
7066 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7067 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7070 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7072 <sect2 id="include-pragma">
7073 <title>INCLUDE pragma</title>
7075 <para>The <literal>INCLUDE</literal> pragma is for specifying the names
7076 of C header files that should be <literal>#include</literal>'d into
7077 the C source code generated by the compiler for the current module (if
7078 compiling via C). For example:</para>
7081 {-# INCLUDE "foo.h" #-}
7082 {-# INCLUDE <stdio.h> #-}</programlisting>
7084 <para><literal>INCLUDE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7086 <para>An <literal>INCLUDE</literal> pragma is the preferred alternative
7087 to the <option>-#include</option> option (<xref
7088 linkend="options-C-compiler" />), because the
7089 <literal>INCLUDE</literal> pragma is understood by other
7090 compilers. Yet another alternative is to add the include file to each
7091 <literal>foreign import</literal> declaration in your code, but we
7092 don't recommend using this approach with GHC.</para>
7095 <sect2 id="warning-deprecated-pragma">
7096 <title>WARNING and DEPRECATED pragmas</title>
7097 <indexterm><primary>WARNING</primary></indexterm>
7098 <indexterm><primary>DEPRECATED</primary></indexterm>
7100 <para>The WARNING pragma allows you to attach an arbitrary warning
7101 to a particular function, class, or type.
7102 A DEPRECATED pragma lets you specify that
7103 a particular function, class, or type is deprecated.
7104 There are two ways of using these pragmas.
7108 <para>You can work on an entire module thus:</para>
7110 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7115 module Wibble {-# WARNING "This is an unstable interface." #-} where
7118 <para>When you compile any module that import
7119 <literal>Wibble</literal>, GHC will print the specified
7124 <para>You can attach a warning to a function, class, type, or data constructor, with the
7125 following top-level declarations:</para>
7127 {-# DEPRECATED f, C, T "Don't use these" #-}
7128 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7130 <para>When you compile any module that imports and uses any
7131 of the specified entities, GHC will print the specified
7133 <para> You can only attach to entities declared at top level in the module
7134 being compiled, and you can only use unqualified names in the list of
7135 entities. A capitalised name, such as <literal>T</literal>
7136 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7137 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7138 both are in scope. If both are in scope, there is currently no way to
7139 specify one without the other (c.f. fixities
7140 <xref linkend="infix-tycons"/>).</para>
7143 Warnings and deprecations are not reported for
7144 (a) uses within the defining module, and
7145 (b) uses in an export list.
7146 The latter reduces spurious complaints within a library
7147 in which one module gathers together and re-exports
7148 the exports of several others.
7150 <para>You can suppress the warnings with the flag
7151 <option>-fno-warn-warnings-deprecations</option>.</para>
7154 <sect2 id="inline-noinline-pragma">
7155 <title>INLINE and NOINLINE pragmas</title>
7157 <para>These pragmas control the inlining of function
7160 <sect3 id="inline-pragma">
7161 <title>INLINE pragma</title>
7162 <indexterm><primary>INLINE</primary></indexterm>
7164 <para>GHC (with <option>-O</option>, as always) tries to
7165 inline (or “unfold”) functions/values that are
7166 “small enough,” thus avoiding the call overhead
7167 and possibly exposing other more-wonderful optimisations.
7168 Normally, if GHC decides a function is “too
7169 expensive” to inline, it will not do so, nor will it
7170 export that unfolding for other modules to use.</para>
7172 <para>The sledgehammer you can bring to bear is the
7173 <literal>INLINE</literal><indexterm><primary>INLINE
7174 pragma</primary></indexterm> pragma, used thusly:</para>
7177 key_function :: Int -> String -> (Bool, Double)
7178 {-# INLINE key_function #-}
7181 <para>The major effect of an <literal>INLINE</literal> pragma
7182 is to declare a function's “cost” to be very low.
7183 The normal unfolding machinery will then be very keen to
7184 inline it. However, an <literal>INLINE</literal> pragma for a
7185 function "<literal>f</literal>" has a number of other effects:
7188 No functions are inlined into <literal>f</literal>. Otherwise
7189 GHC might inline a big function into <literal>f</literal>'s right hand side,
7190 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7193 The float-in, float-out, and common-sub-expression transformations are not
7194 applied to the body of <literal>f</literal>.
7197 An INLINE function is not worker/wrappered by strictness analysis.
7198 It's going to be inlined wholesale instead.
7201 All of these effects are aimed at ensuring that what gets inlined is
7202 exactly what you asked for, no more and no less.
7204 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7205 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7206 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7207 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7208 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7209 when there is no choice even an INLINE function can be selected, in which case
7210 the INLINE pragma is ignored.
7211 For example, for a self-recursive function, the loop breaker can only be the function
7212 itself, so an INLINE pragma is always ignored.</para>
7214 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7215 function can be put anywhere its type signature could be
7218 <para><literal>INLINE</literal> pragmas are a particularly
7220 <literal>then</literal>/<literal>return</literal> (or
7221 <literal>bind</literal>/<literal>unit</literal>) functions in
7222 a monad. For example, in GHC's own
7223 <literal>UniqueSupply</literal> monad code, we have:</para>
7226 {-# INLINE thenUs #-}
7227 {-# INLINE returnUs #-}
7230 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7231 linkend="noinline-pragma"/>).</para>
7233 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7234 so if you want your code to be HBC-compatible you'll have to surround
7235 the pragma with C pre-processor directives
7236 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7240 <sect3 id="noinline-pragma">
7241 <title>NOINLINE pragma</title>
7243 <indexterm><primary>NOINLINE</primary></indexterm>
7244 <indexterm><primary>NOTINLINE</primary></indexterm>
7246 <para>The <literal>NOINLINE</literal> pragma does exactly what
7247 you'd expect: it stops the named function from being inlined
7248 by the compiler. You shouldn't ever need to do this, unless
7249 you're very cautious about code size.</para>
7251 <para><literal>NOTINLINE</literal> is a synonym for
7252 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7253 specified by Haskell 98 as the standard way to disable
7254 inlining, so it should be used if you want your code to be
7258 <sect3 id="phase-control">
7259 <title>Phase control</title>
7261 <para> Sometimes you want to control exactly when in GHC's
7262 pipeline the INLINE pragma is switched on. Inlining happens
7263 only during runs of the <emphasis>simplifier</emphasis>. Each
7264 run of the simplifier has a different <emphasis>phase
7265 number</emphasis>; the phase number decreases towards zero.
7266 If you use <option>-dverbose-core2core</option> you'll see the
7267 sequence of phase numbers for successive runs of the
7268 simplifier. In an INLINE pragma you can optionally specify a
7272 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7273 <literal>f</literal>
7274 until phase <literal>k</literal>, but from phase
7275 <literal>k</literal> onwards be very keen to inline it.
7278 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7279 <literal>f</literal>
7280 until phase <literal>k</literal>, but from phase
7281 <literal>k</literal> onwards do not inline it.
7284 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7285 <literal>f</literal>
7286 until phase <literal>k</literal>, but from phase
7287 <literal>k</literal> onwards be willing to inline it (as if
7288 there was no pragma).
7291 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7292 <literal>f</literal>
7293 until phase <literal>k</literal>, but from phase
7294 <literal>k</literal> onwards do not inline it.
7297 The same information is summarised here:
7299 -- Before phase 2 Phase 2 and later
7300 {-# INLINE [2] f #-} -- No Yes
7301 {-# INLINE [~2] f #-} -- Yes No
7302 {-# NOINLINE [2] f #-} -- No Maybe
7303 {-# NOINLINE [~2] f #-} -- Maybe No
7305 {-# INLINE f #-} -- Yes Yes
7306 {-# NOINLINE f #-} -- No No
7308 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7309 function body is small, or it is applied to interesting-looking arguments etc).
7310 Another way to understand the semantics is this:
7312 <listitem><para>For both INLINE and NOINLINE, the phase number says
7313 when inlining is allowed at all.</para></listitem>
7314 <listitem><para>The INLINE pragma has the additional effect of making the
7315 function body look small, so that when inlining is allowed it is very likely to
7320 <para>The same phase-numbering control is available for RULES
7321 (<xref linkend="rewrite-rules"/>).</para>
7325 <sect2 id="annotation-pragmas">
7326 <title>ANN pragmas</title>
7328 <para>GHC offers the ability to annotate various code constructs with additional
7329 data by using three pragmas. This data can then be inspected at a later date by
7330 using GHC-as-a-library.</para>
7332 <sect3 id="ann-pragma">
7333 <title>Annotating values</title>
7335 <indexterm><primary>ANN</primary></indexterm>
7337 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7338 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7339 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7340 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7341 you would do this:</para>
7344 {-# ANN foo (Just "Hello") #-}
7349 A number of restrictions apply to use of annotations:
7351 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7352 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7353 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7354 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7355 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7357 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7358 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7361 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7362 please give the GHC team a shout</ulink>.
7365 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7366 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7369 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7374 <sect3 id="typeann-pragma">
7375 <title>Annotating types</title>
7377 <indexterm><primary>ANN type</primary></indexterm>
7378 <indexterm><primary>ANN</primary></indexterm>
7380 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7383 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7388 <sect3 id="modann-pragma">
7389 <title>Annotating modules</title>
7391 <indexterm><primary>ANN module</primary></indexterm>
7392 <indexterm><primary>ANN</primary></indexterm>
7394 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7397 {-# ANN module (Just "A `Maybe String' annotation") #-}
7402 <sect2 id="line-pragma">
7403 <title>LINE pragma</title>
7405 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7406 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7407 <para>This pragma is similar to C's <literal>#line</literal>
7408 pragma, and is mainly for use in automatically generated Haskell
7409 code. It lets you specify the line number and filename of the
7410 original code; for example</para>
7412 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7414 <para>if you'd generated the current file from something called
7415 <filename>Foo.vhs</filename> and this line corresponds to line
7416 42 in the original. GHC will adjust its error messages to refer
7417 to the line/file named in the <literal>LINE</literal>
7422 <title>RULES pragma</title>
7424 <para>The RULES pragma lets you specify rewrite rules. It is
7425 described in <xref linkend="rewrite-rules"/>.</para>
7428 <sect2 id="specialize-pragma">
7429 <title>SPECIALIZE pragma</title>
7431 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7432 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7433 <indexterm><primary>overloading, death to</primary></indexterm>
7435 <para>(UK spelling also accepted.) For key overloaded
7436 functions, you can create extra versions (NB: more code space)
7437 specialised to particular types. Thus, if you have an
7438 overloaded function:</para>
7441 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7444 <para>If it is heavily used on lists with
7445 <literal>Widget</literal> keys, you could specialise it as
7449 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7452 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7453 be put anywhere its type signature could be put.</para>
7455 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7456 (a) a specialised version of the function and (b) a rewrite rule
7457 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7458 un-specialised function into a call to the specialised one.</para>
7460 <para>The type in a SPECIALIZE pragma can be any type that is less
7461 polymorphic than the type of the original function. In concrete terms,
7462 if the original function is <literal>f</literal> then the pragma
7464 {-# SPECIALIZE f :: <type> #-}
7466 is valid if and only if the definition
7468 f_spec :: <type>
7471 is valid. Here are some examples (where we only give the type signature
7472 for the original function, not its code):
7474 f :: Eq a => a -> b -> b
7475 {-# SPECIALISE f :: Int -> b -> b #-}
7477 g :: (Eq a, Ix b) => a -> b -> b
7478 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7480 h :: Eq a => a -> a -> a
7481 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7483 The last of these examples will generate a
7484 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7485 well. If you use this kind of specialisation, let us know how well it works.
7488 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7489 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7490 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7491 The <literal>INLINE</literal> pragma affects the specialised version of the
7492 function (only), and applies even if the function is recursive. The motivating
7495 -- A GADT for arrays with type-indexed representation
7497 ArrInt :: !Int -> ByteArray# -> Arr Int
7498 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7500 (!:) :: Arr e -> Int -> e
7501 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7502 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7503 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7504 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7506 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7507 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7508 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7509 the specialised function will be inlined. It has two calls to
7510 <literal>(!:)</literal>,
7511 both at type <literal>Int</literal>. Both these calls fire the first
7512 specialisation, whose body is also inlined. The result is a type-based
7513 unrolling of the indexing function.</para>
7514 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7515 on an ordinarily-recursive function.</para>
7517 <para>Note: In earlier versions of GHC, it was possible to provide your own
7518 specialised function for a given type:
7521 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7524 This feature has been removed, as it is now subsumed by the
7525 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7529 <sect2 id="specialize-instance-pragma">
7530 <title>SPECIALIZE instance pragma
7534 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7535 <indexterm><primary>overloading, death to</primary></indexterm>
7536 Same idea, except for instance declarations. For example:
7539 instance (Eq a) => Eq (Foo a) where {
7540 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7544 The pragma must occur inside the <literal>where</literal> part
7545 of the instance declaration.
7548 Compatible with HBC, by the way, except perhaps in the placement
7554 <sect2 id="unpack-pragma">
7555 <title>UNPACK pragma</title>
7557 <indexterm><primary>UNPACK</primary></indexterm>
7559 <para>The <literal>UNPACK</literal> indicates to the compiler
7560 that it should unpack the contents of a constructor field into
7561 the constructor itself, removing a level of indirection. For
7565 data T = T {-# UNPACK #-} !Float
7566 {-# UNPACK #-} !Float
7569 <para>will create a constructor <literal>T</literal> containing
7570 two unboxed floats. This may not always be an optimisation: if
7571 the <function>T</function> constructor is scrutinised and the
7572 floats passed to a non-strict function for example, they will
7573 have to be reboxed (this is done automatically by the
7576 <para>Unpacking constructor fields should only be used in
7577 conjunction with <option>-O</option>, in order to expose
7578 unfoldings to the compiler so the reboxing can be removed as
7579 often as possible. For example:</para>
7583 f (T f1 f2) = f1 + f2
7586 <para>The compiler will avoid reboxing <function>f1</function>
7587 and <function>f2</function> by inlining <function>+</function>
7588 on floats, but only when <option>-O</option> is on.</para>
7590 <para>Any single-constructor data is eligible for unpacking; for
7594 data T = T {-# UNPACK #-} !(Int,Int)
7597 <para>will store the two <literal>Int</literal>s directly in the
7598 <function>T</function> constructor, by flattening the pair.
7599 Multi-level unpacking is also supported:
7602 data T = T {-# UNPACK #-} !S
7603 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7606 will store two unboxed <literal>Int#</literal>s
7607 directly in the <function>T</function> constructor. The
7608 unpacker can see through newtypes, too.</para>
7610 <para>If a field cannot be unpacked, you will not get a warning,
7611 so it might be an idea to check the generated code with
7612 <option>-ddump-simpl</option>.</para>
7614 <para>See also the <option>-funbox-strict-fields</option> flag,
7615 which essentially has the effect of adding
7616 <literal>{-# UNPACK #-}</literal> to every strict
7617 constructor field.</para>
7620 <sect2 id="source-pragma">
7621 <title>SOURCE pragma</title>
7623 <indexterm><primary>SOURCE</primary></indexterm>
7624 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7625 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7631 <!-- ======================= REWRITE RULES ======================== -->
7633 <sect1 id="rewrite-rules">
7634 <title>Rewrite rules
7636 <indexterm><primary>RULES pragma</primary></indexterm>
7637 <indexterm><primary>pragma, RULES</primary></indexterm>
7638 <indexterm><primary>rewrite rules</primary></indexterm></title>
7641 The programmer can specify rewrite rules as part of the source program
7647 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7652 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7653 If you need more information, then <option>-ddump-rule-firings</option> shows you
7654 each individual rule firing in detail.
7658 <title>Syntax</title>
7661 From a syntactic point of view:
7667 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7668 may be generated by the layout rule).
7674 The layout rule applies in a pragma.
7675 Currently no new indentation level
7676 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7677 you must lay out the starting in the same column as the enclosing definitions.
7680 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7681 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7684 Furthermore, the closing <literal>#-}</literal>
7685 should start in a column to the right of the opening <literal>{-#</literal>.
7691 Each rule has a name, enclosed in double quotes. The name itself has
7692 no significance at all. It is only used when reporting how many times the rule fired.
7698 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7699 immediately after the name of the rule. Thus:
7702 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7705 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7706 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7715 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7716 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7717 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7718 by spaces, just like in a type <literal>forall</literal>.
7724 A pattern variable may optionally have a type signature.
7725 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7726 For example, here is the <literal>foldr/build</literal> rule:
7729 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7730 foldr k z (build g) = g k z
7733 Since <function>g</function> has a polymorphic type, it must have a type signature.
7740 The left hand side of a rule must consist of a top-level variable applied
7741 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7744 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7745 "wrong2" forall f. f True = True
7748 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
7755 A rule does not need to be in the same module as (any of) the
7756 variables it mentions, though of course they need to be in scope.
7762 All rules are implicitly exported from the module, and are therefore
7763 in force in any module that imports the module that defined the rule, directly
7764 or indirectly. (That is, if A imports B, which imports C, then C's rules are
7765 in force when compiling A.) The situation is very similar to that for instance
7773 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
7774 any other flag settings. Furthermore, inside a RULE, the language extension
7775 <option>-XScopedTypeVariables</option> is automatically enabled; see
7776 <xref linkend="scoped-type-variables"/>.
7782 Like other pragmas, RULE pragmas are always checked for scope errors, and
7783 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
7784 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
7785 if the <option>-fenable-rewrite-rules</option> flag is
7786 on (see <xref linkend="rule-semantics"/>).
7795 <sect2 id="rule-semantics">
7796 <title>Semantics</title>
7799 From a semantic point of view:
7804 Rules are enabled (that is, used during optimisation)
7805 by the <option>-fenable-rewrite-rules</option> flag.
7806 This flag is implied by <option>-O</option>, and may be switched
7807 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
7808 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
7809 may not do what you expect, though, because without <option>-O</option> GHC
7810 ignores all optimisation information in interface files;
7811 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
7812 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
7813 has no effect on parsing or typechecking.
7819 Rules are regarded as left-to-right rewrite rules.
7820 When GHC finds an expression that is a substitution instance of the LHS
7821 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
7822 By "a substitution instance" we mean that the LHS can be made equal to the
7823 expression by substituting for the pattern variables.
7830 GHC makes absolutely no attempt to verify that the LHS and RHS
7831 of a rule have the same meaning. That is undecidable in general, and
7832 infeasible in most interesting cases. The responsibility is entirely the programmer's!
7839 GHC makes no attempt to make sure that the rules are confluent or
7840 terminating. For example:
7843 "loop" forall x y. f x y = f y x
7846 This rule will cause the compiler to go into an infinite loop.
7853 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
7859 GHC currently uses a very simple, syntactic, matching algorithm
7860 for matching a rule LHS with an expression. It seeks a substitution
7861 which makes the LHS and expression syntactically equal modulo alpha
7862 conversion. The pattern (rule), but not the expression, is eta-expanded if
7863 necessary. (Eta-expanding the expression can lead to laziness bugs.)
7864 But not beta conversion (that's called higher-order matching).
7868 Matching is carried out on GHC's intermediate language, which includes
7869 type abstractions and applications. So a rule only matches if the
7870 types match too. See <xref linkend="rule-spec"/> below.
7876 GHC keeps trying to apply the rules as it optimises the program.
7877 For example, consider:
7886 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
7887 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
7888 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
7889 not be substituted, and the rule would not fire.
7896 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
7897 results. Consider this (artificial) example
7900 {-# RULES "f" f True = False #-}
7906 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
7911 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
7913 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
7914 would have been a better chance that <literal>f</literal>'s RULE might fire.
7917 The way to get predictable behaviour is to use a NOINLINE
7918 pragma on <literal>f</literal>, to ensure
7919 that it is not inlined until its RULEs have had a chance to fire.
7929 <title>List fusion</title>
7932 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
7933 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
7934 intermediate list should be eliminated entirely.
7938 The following are good producers:
7950 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
7956 Explicit lists (e.g. <literal>[True, False]</literal>)
7962 The cons constructor (e.g <literal>3:4:[]</literal>)
7968 <function>++</function>
7974 <function>map</function>
7980 <function>take</function>, <function>filter</function>
7986 <function>iterate</function>, <function>repeat</function>
7992 <function>zip</function>, <function>zipWith</function>
8001 The following are good consumers:
8013 <function>array</function> (on its second argument)
8019 <function>++</function> (on its first argument)
8025 <function>foldr</function>
8031 <function>map</function>
8037 <function>take</function>, <function>filter</function>
8043 <function>concat</function>
8049 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8055 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8056 will fuse with one but not the other)
8062 <function>partition</function>
8068 <function>head</function>
8074 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8080 <function>sequence_</function>
8086 <function>msum</function>
8092 <function>sortBy</function>
8101 So, for example, the following should generate no intermediate lists:
8104 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8110 This list could readily be extended; if there are Prelude functions that you use
8111 a lot which are not included, please tell us.
8115 If you want to write your own good consumers or producers, look at the
8116 Prelude definitions of the above functions to see how to do so.
8121 <sect2 id="rule-spec">
8122 <title>Specialisation
8126 Rewrite rules can be used to get the same effect as a feature
8127 present in earlier versions of GHC.
8128 For example, suppose that:
8131 genericLookup :: Ord a => Table a b -> a -> b
8132 intLookup :: Table Int b -> Int -> b
8135 where <function>intLookup</function> is an implementation of
8136 <function>genericLookup</function> that works very fast for
8137 keys of type <literal>Int</literal>. You might wish
8138 to tell GHC to use <function>intLookup</function> instead of
8139 <function>genericLookup</function> whenever the latter was called with
8140 type <literal>Table Int b -> Int -> b</literal>.
8141 It used to be possible to write
8144 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8147 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8150 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8153 This slightly odd-looking rule instructs GHC to replace
8154 <function>genericLookup</function> by <function>intLookup</function>
8155 <emphasis>whenever the types match</emphasis>.
8156 What is more, this rule does not need to be in the same
8157 file as <function>genericLookup</function>, unlike the
8158 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8159 have an original definition available to specialise).
8162 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8163 <function>intLookup</function> really behaves as a specialised version
8164 of <function>genericLookup</function>!!!</para>
8166 <para>An example in which using <literal>RULES</literal> for
8167 specialisation will Win Big:
8170 toDouble :: Real a => a -> Double
8171 toDouble = fromRational . toRational
8173 {-# RULES "toDouble/Int" toDouble = i2d #-}
8174 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8177 The <function>i2d</function> function is virtually one machine
8178 instruction; the default conversion—via an intermediate
8179 <literal>Rational</literal>—is obscenely expensive by
8186 <title>Controlling what's going on</title>
8194 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8200 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8201 If you add <option>-dppr-debug</option> you get a more detailed listing.
8207 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8210 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8211 {-# INLINE build #-}
8215 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8216 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8217 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8218 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8225 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8226 see how to write rules that will do fusion and yet give an efficient
8227 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8237 <sect2 id="core-pragma">
8238 <title>CORE pragma</title>
8240 <indexterm><primary>CORE pragma</primary></indexterm>
8241 <indexterm><primary>pragma, CORE</primary></indexterm>
8242 <indexterm><primary>core, annotation</primary></indexterm>
8245 The external core format supports <quote>Note</quote> annotations;
8246 the <literal>CORE</literal> pragma gives a way to specify what these
8247 should be in your Haskell source code. Syntactically, core
8248 annotations are attached to expressions and take a Haskell string
8249 literal as an argument. The following function definition shows an
8253 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8256 Semantically, this is equivalent to:
8264 However, when external core is generated (via
8265 <option>-fext-core</option>), there will be Notes attached to the
8266 expressions <function>show</function> and <varname>x</varname>.
8267 The core function declaration for <function>f</function> is:
8271 f :: %forall a . GHCziShow.ZCTShow a ->
8272 a -> GHCziBase.ZMZN GHCziBase.Char =
8273 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8275 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8277 (tpl1::GHCziBase.Int ->
8279 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8281 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8282 (tpl3::GHCziBase.ZMZN a ->
8283 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8291 Here, we can see that the function <function>show</function> (which
8292 has been expanded out to a case expression over the Show dictionary)
8293 has a <literal>%note</literal> attached to it, as does the
8294 expression <varname>eta</varname> (which used to be called
8295 <varname>x</varname>).
8302 <sect1 id="special-ids">
8303 <title>Special built-in functions</title>
8304 <para>GHC has a few built-in functions with special behaviour. These
8305 are now described in the module <ulink
8306 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8307 in the library documentation.</para>
8311 <sect1 id="generic-classes">
8312 <title>Generic classes</title>
8315 The ideas behind this extension are described in detail in "Derivable type classes",
8316 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8317 An example will give the idea:
8325 fromBin :: [Int] -> (a, [Int])
8327 toBin {| Unit |} Unit = []
8328 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8329 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8330 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8332 fromBin {| Unit |} bs = (Unit, bs)
8333 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8334 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8335 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8336 (y,bs'') = fromBin bs'
8339 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8340 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8341 which are defined thus in the library module <literal>Generics</literal>:
8345 data a :+: b = Inl a | Inr b
8346 data a :*: b = a :*: b
8349 Now you can make a data type into an instance of Bin like this:
8351 instance (Bin a, Bin b) => Bin (a,b)
8352 instance Bin a => Bin [a]
8354 That is, just leave off the "where" clause. Of course, you can put in the
8355 where clause and over-ride whichever methods you please.
8359 <title> Using generics </title>
8360 <para>To use generics you need to</para>
8363 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8364 <option>-XGenerics</option> (to generate extra per-data-type code),
8365 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8369 <para>Import the module <literal>Generics</literal> from the
8370 <literal>lang</literal> package. This import brings into
8371 scope the data types <literal>Unit</literal>,
8372 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8373 don't need this import if you don't mention these types
8374 explicitly; for example, if you are simply giving instance
8375 declarations.)</para>
8380 <sect2> <title> Changes wrt the paper </title>
8382 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8383 can be written infix (indeed, you can now use
8384 any operator starting in a colon as an infix type constructor). Also note that
8385 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8386 Finally, note that the syntax of the type patterns in the class declaration
8387 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8388 alone would ambiguous when they appear on right hand sides (an extension we
8389 anticipate wanting).
8393 <sect2> <title>Terminology and restrictions</title>
8395 Terminology. A "generic default method" in a class declaration
8396 is one that is defined using type patterns as above.
8397 A "polymorphic default method" is a default method defined as in Haskell 98.
8398 A "generic class declaration" is a class declaration with at least one
8399 generic default method.
8407 Alas, we do not yet implement the stuff about constructor names and
8414 A generic class can have only one parameter; you can't have a generic
8415 multi-parameter class.
8421 A default method must be defined entirely using type patterns, or entirely
8422 without. So this is illegal:
8425 op :: a -> (a, Bool)
8426 op {| Unit |} Unit = (Unit, True)
8429 However it is perfectly OK for some methods of a generic class to have
8430 generic default methods and others to have polymorphic default methods.
8436 The type variable(s) in the type pattern for a generic method declaration
8437 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:
8441 op {| p :*: q |} (x :*: y) = op (x :: p)
8449 The type patterns in a generic default method must take one of the forms:
8455 where "a" and "b" are type variables. Furthermore, all the type patterns for
8456 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8457 must use the same type variables. So this is illegal:
8461 op {| a :+: b |} (Inl x) = True
8462 op {| p :+: q |} (Inr y) = False
8464 The type patterns must be identical, even in equations for different methods of the class.
8465 So this too is illegal:
8469 op1 {| a :*: b |} (x :*: y) = True
8472 op2 {| p :*: q |} (x :*: y) = False
8474 (The reason for this restriction is that we gather all the equations for a particular type constructor
8475 into a single generic instance declaration.)
8481 A generic method declaration must give a case for each of the three type constructors.
8487 The type for a generic method can be built only from:
8489 <listitem> <para> Function arrows </para> </listitem>
8490 <listitem> <para> Type variables </para> </listitem>
8491 <listitem> <para> Tuples </para> </listitem>
8492 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8494 Here are some example type signatures for generic methods:
8497 op2 :: Bool -> (a,Bool)
8498 op3 :: [Int] -> a -> a
8501 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8505 This restriction is an implementation restriction: we just haven't got around to
8506 implementing the necessary bidirectional maps over arbitrary type constructors.
8507 It would be relatively easy to add specific type constructors, such as Maybe and list,
8508 to the ones that are allowed.</para>
8513 In an instance declaration for a generic class, the idea is that the compiler
8514 will fill in the methods for you, based on the generic templates. However it can only
8519 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8524 No constructor of the instance type has unboxed fields.
8528 (Of course, these things can only arise if you are already using GHC extensions.)
8529 However, you can still give an instance declarations for types which break these rules,
8530 provided you give explicit code to override any generic default methods.
8538 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8539 what the compiler does with generic declarations.
8544 <sect2> <title> Another example </title>
8546 Just to finish with, here's another example I rather like:
8550 nCons {| Unit |} _ = 1
8551 nCons {| a :*: b |} _ = 1
8552 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8555 tag {| Unit |} _ = 1
8556 tag {| a :*: b |} _ = 1
8557 tag {| a :+: b |} (Inl x) = tag x
8558 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8564 <sect1 id="monomorphism">
8565 <title>Control over monomorphism</title>
8567 <para>GHC supports two flags that control the way in which generalisation is
8568 carried out at let and where bindings.
8572 <title>Switching off the dreaded Monomorphism Restriction</title>
8573 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8575 <para>Haskell's monomorphism restriction (see
8576 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8578 of the Haskell Report)
8579 can be completely switched off by
8580 <option>-XNoMonomorphismRestriction</option>.
8585 <title>Monomorphic pattern bindings</title>
8586 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8587 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8589 <para> As an experimental change, we are exploring the possibility of
8590 making pattern bindings monomorphic; that is, not generalised at all.
8591 A pattern binding is a binding whose LHS has no function arguments,
8592 and is not a simple variable. For example:
8594 f x = x -- Not a pattern binding
8595 f = \x -> x -- Not a pattern binding
8596 f :: Int -> Int = \x -> x -- Not a pattern binding
8598 (g,h) = e -- A pattern binding
8599 (f) = e -- A pattern binding
8600 [x] = e -- A pattern binding
8602 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8603 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
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