1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Language options can be controlled in two ways:
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
54 </itemizedlist></para>
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 <option>-XPrintExplicitForalls</option>,
60 <option>-XForeignFunctionInterface</option>,
61 <option>-XUnliftedFFITypes</option>,
62 <option>-XGADTs</option>,
63 <option>-XImplicitParams</option>,
64 <option>-XScopedTypeVariables</option>,
65 <option>-XUnboxedTuples</option>,
66 <option>-XTypeSynonymInstances</option>,
67 <option>-XStandaloneDeriving</option>,
68 <option>-XDeriveDataTypeable</option>,
69 <option>-XFlexibleContexts</option>,
70 <option>-XFlexibleInstances</option>,
71 <option>-XConstrainedClassMethods</option>,
72 <option>-XMultiParamTypeClasses</option>,
73 <option>-XFunctionalDependencies</option>,
74 <option>-XMagicHash</option>,
75 <option>-XPolymorphicComponents</option>,
76 <option>-XExistentialQuantification</option>,
77 <option>-XUnicodeSyntax</option>,
78 <option>-XPostfixOperators</option>,
79 <option>-XPatternGuards</option>,
80 <option>-XLiberalTypeSynonyms</option>,
81 <option>-XExplicitForAll</option>,
82 <option>-XRankNTypes</option>,
83 <option>-XImpredicativeTypes</option>,
84 <option>-XTypeOperators</option>,
85 <option>-XDoRec</option>,
86 <option>-XParallelListComp</option>,
87 <option>-XEmptyDataDecls</option>,
88 <option>-XKindSignatures</option>,
89 <option>-XGeneralizedNewtypeDeriving</option>,
90 <option>-XTypeFamilies</option>.
91 Enabling these options is the <emphasis>only</emphasis>
92 effect of <option>-fglasgow-exts</option>.
93 We are trying to move away from this portmanteau flag,
94 and towards enabling features individually.</para>
98 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
99 <sect1 id="primitives">
100 <title>Unboxed types and primitive operations</title>
102 <para>GHC is built on a raft of primitive data types and operations;
103 "primitive" in the sense that they cannot be defined in Haskell itself.
104 While you really can use this stuff to write fast code,
105 we generally find it a lot less painful, and more satisfying in the
106 long run, to use higher-level language features and libraries. With
107 any luck, the code you write will be optimised to the efficient
108 unboxed version in any case. And if it isn't, we'd like to know
111 <para>All these primitive data types and operations are exported by the
112 library <literal>GHC.Prim</literal>, for which there is
113 <ulink url="&libraryGhcPrimLocation;/GHC-Prim.html">detailed online documentation</ulink>.
114 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
117 If you want to mention any of the primitive data types or operations in your
118 program, you must first import <literal>GHC.Prim</literal> to bring them
119 into scope. Many of them have names ending in "#", and to mention such
120 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
123 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
124 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
125 we briefly summarise here. </para>
127 <sect2 id="glasgow-unboxed">
132 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
135 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
136 that values of that type are represented by a pointer to a heap
137 object. The representation of a Haskell <literal>Int</literal>, for
138 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
139 type, however, is represented by the value itself, no pointers or heap
140 allocation are involved.
144 Unboxed types correspond to the “raw machine” types you
145 would use in C: <literal>Int#</literal> (long int),
146 <literal>Double#</literal> (double), <literal>Addr#</literal>
147 (void *), etc. The <emphasis>primitive operations</emphasis>
148 (PrimOps) on these types are what you might expect; e.g.,
149 <literal>(+#)</literal> is addition on
150 <literal>Int#</literal>s, and is the machine-addition that we all
151 know and love—usually one instruction.
155 Primitive (unboxed) types cannot be defined in Haskell, and are
156 therefore built into the language and compiler. Primitive types are
157 always unlifted; that is, a value of a primitive type cannot be
158 bottom. We use the convention (but it is only a convention)
159 that primitive types, values, and
160 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
161 For some primitive types we have special syntax for literals, also
162 described in the <link linkend="magic-hash">same section</link>.
166 Primitive values are often represented by a simple bit-pattern, such
167 as <literal>Int#</literal>, <literal>Float#</literal>,
168 <literal>Double#</literal>. But this is not necessarily the case:
169 a primitive value might be represented by a pointer to a
170 heap-allocated object. Examples include
171 <literal>Array#</literal>, the type of primitive arrays. A
172 primitive array is heap-allocated because it is too big a value to fit
173 in a register, and would be too expensive to copy around; in a sense,
174 it is accidental that it is represented by a pointer. If a pointer
175 represents a primitive value, then it really does point to that value:
176 no unevaluated thunks, no indirections…nothing can be at the
177 other end of the pointer than the primitive value.
178 A numerically-intensive program using unboxed types can
179 go a <emphasis>lot</emphasis> faster than its “standard”
180 counterpart—we saw a threefold speedup on one example.
184 There are some restrictions on the use of primitive types:
186 <listitem><para>The main restriction
187 is that you can't pass a primitive value to a polymorphic
188 function or store one in a polymorphic data type. This rules out
189 things like <literal>[Int#]</literal> (i.e. lists of primitive
190 integers). The reason for this restriction is that polymorphic
191 arguments and constructor fields are assumed to be pointers: if an
192 unboxed integer is stored in one of these, the garbage collector would
193 attempt to follow it, leading to unpredictable space leaks. Or a
194 <function>seq</function> operation on the polymorphic component may
195 attempt to dereference the pointer, with disastrous results. Even
196 worse, the unboxed value might be larger than a pointer
197 (<literal>Double#</literal> for instance).
200 <listitem><para> You cannot define a newtype whose representation type
201 (the argument type of the data constructor) is an unboxed type. Thus,
207 <listitem><para> You cannot bind a variable with an unboxed type
208 in a <emphasis>top-level</emphasis> binding.
210 <listitem><para> You cannot bind a variable with an unboxed type
211 in a <emphasis>recursive</emphasis> binding.
213 <listitem><para> You may bind unboxed variables in a (non-recursive,
214 non-top-level) pattern binding, but you must make any such pattern-match
215 strict. For example, rather than:
217 data Foo = Foo Int Int#
219 f x = let (Foo a b, w) = ..rhs.. in ..body..
223 data Foo = Foo Int Int#
225 f x = let !(Foo a b, w) = ..rhs.. in ..body..
227 since <literal>b</literal> has type <literal>Int#</literal>.
235 <sect2 id="unboxed-tuples">
236 <title>Unboxed Tuples
240 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
241 they're available by default with <option>-fglasgow-exts</option>. An
242 unboxed tuple looks like this:
254 where <literal>e_1..e_n</literal> are expressions of any
255 type (primitive or non-primitive). The type of an unboxed tuple looks
260 Unboxed tuples are used for functions that need to return multiple
261 values, but they avoid the heap allocation normally associated with
262 using fully-fledged tuples. When an unboxed tuple is returned, the
263 components are put directly into registers or on the stack; the
264 unboxed tuple itself does not have a composite representation. Many
265 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
267 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
268 tuples to avoid unnecessary allocation during sequences of operations.
272 There are some pretty stringent restrictions on the use of unboxed tuples:
277 Values of unboxed tuple types are subject to the same restrictions as
278 other unboxed types; i.e. they may not be stored in polymorphic data
279 structures or passed to polymorphic functions.
286 No variable can have an unboxed tuple type, nor may a constructor or function
287 argument have an unboxed tuple type. The following are all illegal:
291 data Foo = Foo (# Int, Int #)
293 f :: (# Int, Int #) -> (# Int, Int #)
296 g :: (# Int, Int #) -> Int
299 h x = let y = (# x,x #) in ...
306 The typical use of unboxed tuples is simply to return multiple values,
307 binding those multiple results with a <literal>case</literal> expression, thus:
309 f x y = (# x+1, y-1 #)
310 g x = case f x x of { (# a, b #) -> a + b }
312 You can have an unboxed tuple in a pattern binding, thus
314 f x = let (# p,q #) = h x in ..body..
316 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
317 the resulting binding is lazy like any other Haskell pattern binding. The
318 above example desugars like this:
320 f x = let t = case h x o f{ (# p,q #) -> (p,q)
325 Indeed, the bindings can even be recursive.
332 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
334 <sect1 id="syntax-extns">
335 <title>Syntactic extensions</title>
337 <sect2 id="unicode-syntax">
338 <title>Unicode syntax</title>
340 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
341 enables Unicode characters to be used to stand for certain ASCII
342 character sequences. The following alternatives are provided:</para>
345 <tgroup cols="2" align="left" colsep="1" rowsep="1">
349 <entry>Unicode alternative</entry>
350 <entry>Code point</entry>
356 to find the DocBook entities for these characters, find
357 the Unicode code point (e.g. 0x2237), and grep for it in
358 /usr/share/sgml/docbook/xml-dtd-*/ent/* (or equivalent on
359 your system. Some of these Unicode code points don't have
360 equivalent DocBook entities.
365 <entry><literal>::</literal></entry>
366 <entry>::</entry> <!-- no special char, apparently -->
367 <entry>0x2237</entry>
368 <entry>PROPORTION</entry>
373 <entry><literal>=></literal></entry>
374 <entry>⇒</entry>
375 <entry>0x21D2</entry>
376 <entry>RIGHTWARDS DOUBLE ARROW</entry>
381 <entry><literal>forall</literal></entry>
382 <entry>∀</entry>
383 <entry>0x2200</entry>
384 <entry>FOR ALL</entry>
389 <entry><literal>-></literal></entry>
390 <entry>→</entry>
391 <entry>0x2192</entry>
392 <entry>RIGHTWARDS ARROW</entry>
397 <entry><literal><-</literal></entry>
398 <entry>←</entry>
399 <entry>0x2190</entry>
400 <entry>LEFTWARDS ARROW</entry>
407 <entry>↢</entry>
408 <entry>0x2919</entry>
409 <entry>LEFTWARDS ARROW-TAIL</entry>
416 <entry>↣</entry>
417 <entry>0x291A</entry>
418 <entry>RIGHTWARDS ARROW-TAIL</entry>
424 <entry>-<<</entry>
426 <entry>0x291B</entry>
427 <entry>LEFTWARDS DOUBLE ARROW-TAIL</entry>
433 <entry>>>-</entry>
435 <entry>0x291C</entry>
436 <entry>RIGHTWARDS DOUBLE ARROW-TAIL</entry>
443 <entry>★</entry>
444 <entry>0x2605</entry>
445 <entry>BLACK STAR</entry>
453 <sect2 id="magic-hash">
454 <title>The magic hash</title>
455 <para>The language extension <option>-XMagicHash</option> allows "#" as a
456 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
457 a valid type constructor or data constructor.</para>
459 <para>The hash sign does not change sematics at all. We tend to use variable
460 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
461 but there is no requirement to do so; they are just plain ordinary variables.
462 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
463 For example, to bring <literal>Int#</literal> into scope you must
464 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
465 the <option>-XMagicHash</option> extension
466 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
467 that is now in scope.</para>
468 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
470 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
471 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
472 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
473 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
474 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
475 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
476 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
477 is a <literal>Word#</literal>. </para> </listitem>
478 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
479 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
484 <sect2 id="new-qualified-operators">
485 <title>New qualified operator syntax</title>
487 <para>A new syntax for referencing qualified operators is
488 planned to be introduced by Haskell', and is enabled in GHC
490 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
491 option. In the new syntax, the prefix form of a qualified
493 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
494 (in Haskell 98 this would
495 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
496 and the infix form is
497 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
498 (in Haskell 98 this would
499 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
502 add x y = Prelude.(+) x y
503 subtract y = (`Prelude.(-)` y)
505 The new form of qualified operators is intended to regularise
506 the syntax by eliminating odd cases
507 like <literal>Prelude..</literal>. For example,
508 when <literal>NewQualifiedOperators</literal> is on, it is possible to
509 write the enumerated sequence <literal>[Monday..]</literal>
510 without spaces, whereas in Haskell 98 this would be a
511 reference to the operator ‘<literal>.</literal>‘
512 from module <literal>Monday</literal>.</para>
514 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
515 98 syntax for qualified operators is not accepted, so this
516 option may cause existing Haskell 98 code to break.</para>
521 <!-- ====================== HIERARCHICAL MODULES ======================= -->
524 <sect2 id="hierarchical-modules">
525 <title>Hierarchical Modules</title>
527 <para>GHC supports a small extension to the syntax of module
528 names: a module name is allowed to contain a dot
529 <literal>‘.’</literal>. This is also known as the
530 “hierarchical module namespace” extension, because
531 it extends the normally flat Haskell module namespace into a
532 more flexible hierarchy of modules.</para>
534 <para>This extension has very little impact on the language
535 itself; modules names are <emphasis>always</emphasis> fully
536 qualified, so you can just think of the fully qualified module
537 name as <quote>the module name</quote>. In particular, this
538 means that the full module name must be given after the
539 <literal>module</literal> keyword at the beginning of the
540 module; for example, the module <literal>A.B.C</literal> must
543 <programlisting>module A.B.C</programlisting>
546 <para>It is a common strategy to use the <literal>as</literal>
547 keyword to save some typing when using qualified names with
548 hierarchical modules. For example:</para>
551 import qualified Control.Monad.ST.Strict as ST
554 <para>For details on how GHC searches for source and interface
555 files in the presence of hierarchical modules, see <xref
556 linkend="search-path"/>.</para>
558 <para>GHC comes with a large collection of libraries arranged
559 hierarchically; see the accompanying <ulink
560 url="../libraries/index.html">library
561 documentation</ulink>. More libraries to install are available
563 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
566 <!-- ====================== PATTERN GUARDS ======================= -->
568 <sect2 id="pattern-guards">
569 <title>Pattern guards</title>
572 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
573 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.)
577 Suppose we have an abstract data type of finite maps, with a
581 lookup :: FiniteMap -> Int -> Maybe Int
584 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
585 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
589 clunky env var1 var2 | ok1 && ok2 = val1 + val2
590 | otherwise = var1 + var2
601 The auxiliary functions are
605 maybeToBool :: Maybe a -> Bool
606 maybeToBool (Just x) = True
607 maybeToBool Nothing = False
609 expectJust :: Maybe a -> a
610 expectJust (Just x) = x
611 expectJust Nothing = error "Unexpected Nothing"
615 What is <function>clunky</function> doing? The guard <literal>ok1 &&
616 ok2</literal> checks that both lookups succeed, using
617 <function>maybeToBool</function> to convert the <function>Maybe</function>
618 types to booleans. The (lazily evaluated) <function>expectJust</function>
619 calls extract the values from the results of the lookups, and binds the
620 returned values to <varname>val1</varname> and <varname>val2</varname>
621 respectively. If either lookup fails, then clunky takes the
622 <literal>otherwise</literal> case and returns the sum of its arguments.
626 This is certainly legal Haskell, but it is a tremendously verbose and
627 un-obvious way to achieve the desired effect. Arguably, a more direct way
628 to write clunky would be to use case expressions:
632 clunky env var1 var2 = case lookup env var1 of
634 Just val1 -> case lookup env var2 of
636 Just val2 -> val1 + val2
642 This is a bit shorter, but hardly better. Of course, we can rewrite any set
643 of pattern-matching, guarded equations as case expressions; that is
644 precisely what the compiler does when compiling equations! The reason that
645 Haskell provides guarded equations is because they allow us to write down
646 the cases we want to consider, one at a time, independently of each other.
647 This structure is hidden in the case version. Two of the right-hand sides
648 are really the same (<function>fail</function>), and the whole expression
649 tends to become more and more indented.
653 Here is how I would write clunky:
658 | Just val1 <- lookup env var1
659 , Just val2 <- lookup env var2
661 ...other equations for clunky...
665 The semantics should be clear enough. The qualifiers are matched in order.
666 For a <literal><-</literal> qualifier, which I call a pattern guard, the
667 right hand side is evaluated and matched against the pattern on the left.
668 If the match fails then the whole guard fails and the next equation is
669 tried. If it succeeds, then the appropriate binding takes place, and the
670 next qualifier is matched, in the augmented environment. Unlike list
671 comprehensions, however, the type of the expression to the right of the
672 <literal><-</literal> is the same as the type of the pattern to its
673 left. The bindings introduced by pattern guards scope over all the
674 remaining guard qualifiers, and over the right hand side of the equation.
678 Just as with list comprehensions, boolean expressions can be freely mixed
679 with among the pattern guards. For example:
690 Haskell's current guards therefore emerge as a special case, in which the
691 qualifier list has just one element, a boolean expression.
695 <!-- ===================== View patterns =================== -->
697 <sect2 id="view-patterns">
702 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
703 More information and examples of view patterns can be found on the
704 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
709 View patterns are somewhat like pattern guards that can be nested inside
710 of other patterns. They are a convenient way of pattern-matching
711 against values of abstract types. For example, in a programming language
712 implementation, we might represent the syntax of the types of the
721 view :: Type -> TypeView
723 -- additional operations for constructing Typ's ...
726 The representation of Typ is held abstract, permitting implementations
727 to use a fancy representation (e.g., hash-consing to manage sharing).
729 Without view patterns, using this signature a little inconvenient:
731 size :: Typ -> Integer
732 size t = case view t of
734 Arrow t1 t2 -> size t1 + size t2
737 It is necessary to iterate the case, rather than using an equational
738 function definition. And the situation is even worse when the matching
739 against <literal>t</literal> is buried deep inside another pattern.
743 View patterns permit calling the view function inside the pattern and
744 matching against the result:
746 size (view -> Unit) = 1
747 size (view -> Arrow t1 t2) = size t1 + size t2
750 That is, we add a new form of pattern, written
751 <replaceable>expression</replaceable> <literal>-></literal>
752 <replaceable>pattern</replaceable> that means "apply the expression to
753 whatever we're trying to match against, and then match the result of
754 that application against the pattern". The expression can be any Haskell
755 expression of function type, and view patterns can be used wherever
760 The semantics of a pattern <literal>(</literal>
761 <replaceable>exp</replaceable> <literal>-></literal>
762 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
768 <para>The variables bound by the view pattern are the variables bound by
769 <replaceable>pat</replaceable>.
773 Any variables in <replaceable>exp</replaceable> are bound occurrences,
774 but variables bound "to the left" in a pattern are in scope. This
775 feature permits, for example, one argument to a function to be used in
776 the view of another argument. For example, the function
777 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
778 written using view patterns as follows:
781 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
782 ...other equations for clunky...
787 More precisely, the scoping rules are:
791 In a single pattern, variables bound by patterns to the left of a view
792 pattern expression are in scope. For example:
794 example :: Maybe ((String -> Integer,Integer), String) -> Bool
795 example Just ((f,_), f -> 4) = True
798 Additionally, in function definitions, variables bound by matching earlier curried
799 arguments may be used in view pattern expressions in later arguments:
801 example :: (String -> Integer) -> String -> Bool
802 example f (f -> 4) = True
804 That is, the scoping is the same as it would be if the curried arguments
805 were collected into a tuple.
811 In mutually recursive bindings, such as <literal>let</literal>,
812 <literal>where</literal>, or the top level, view patterns in one
813 declaration may not mention variables bound by other declarations. That
814 is, each declaration must be self-contained. For example, the following
815 program is not allowed:
821 (For some amplification on this design choice see
822 <ulink url="http://hackage.haskell.org/trac/ghc/ticket/4061">Trac #4061</ulink>.)
831 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
832 <replaceable>T1</replaceable> <literal>-></literal>
833 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
834 a <replaceable>T2</replaceable>, then the whole view pattern matches a
835 <replaceable>T1</replaceable>.
838 <listitem><para> Matching: To the equations in Section 3.17.3 of the
839 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
840 Report</ulink>, add the following:
842 case v of { (e -> p) -> e1 ; _ -> e2 }
844 case (e v) of { p -> e1 ; _ -> e2 }
846 That is, to match a variable <replaceable>v</replaceable> against a pattern
847 <literal>(</literal> <replaceable>exp</replaceable>
848 <literal>-></literal> <replaceable>pat</replaceable>
849 <literal>)</literal>, evaluate <literal>(</literal>
850 <replaceable>exp</replaceable> <replaceable> v</replaceable>
851 <literal>)</literal> and match the result against
852 <replaceable>pat</replaceable>.
855 <listitem><para> Efficiency: When the same view function is applied in
856 multiple branches of a function definition or a case expression (e.g.,
857 in <literal>size</literal> above), GHC makes an attempt to collect these
858 applications into a single nested case expression, so that the view
859 function is only applied once. Pattern compilation in GHC follows the
860 matrix algorithm described in Chapter 4 of <ulink
861 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
862 Implementation of Functional Programming Languages</ulink>. When the
863 top rows of the first column of a matrix are all view patterns with the
864 "same" expression, these patterns are transformed into a single nested
865 case. This includes, for example, adjacent view patterns that line up
868 f ((view -> A, p1), p2) = e1
869 f ((view -> B, p3), p4) = e2
873 <para> The current notion of when two view pattern expressions are "the
874 same" is very restricted: it is not even full syntactic equality.
875 However, it does include variables, literals, applications, and tuples;
876 e.g., two instances of <literal>view ("hi", "there")</literal> will be
877 collected. However, the current implementation does not compare up to
878 alpha-equivalence, so two instances of <literal>(x, view x ->
879 y)</literal> will not be coalesced.
889 <!-- ===================== n+k patterns =================== -->
891 <sect2 id="n-k-patterns">
892 <title>n+k patterns</title>
893 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
896 <literal>n+k</literal> pattern support is enabled by default. To disable
897 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
902 <!-- ===================== Recursive do-notation =================== -->
904 <sect2 id="recursive-do-notation">
905 <title>The recursive do-notation
909 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
910 that is, the variables bound in a do-expression are visible only in the textually following
911 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
912 group. It turns out that several applications can benefit from recursive bindings in
913 the do-notation. The <option>-XDoRec</option> flag provides the necessary syntactic support.
916 Here is a simple (albeit contrived) example:
918 {-# LANGUAGE DoRec #-}
919 justOnes = do { rec { xs <- Just (1:xs) }
920 ; return (map negate xs) }
922 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
925 The background and motivation for recursive do-notation is described in
926 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
927 by Levent Erkok, John Launchbury,
928 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
929 The theory behind monadic value recursion is explained further in Erkok's thesis
930 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.
931 However, note that GHC uses a different syntax than the one described in these documents.
935 <title>Details of recursive do-notation</title>
937 The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
938 the LANGUAGE pragma <option>DoRec</option>. It introduces the single new keyword "<literal>rec</literal>",
939 which wraps a mutually-recursive group of monadic statements,
940 producing a single statement.
942 <para>Similar to a <literal>let</literal>
943 statement, the variables bound in the <literal>rec</literal> are
944 visible throughout the <literal>rec</literal> group, and below it.
947 do { a <- getChar do { a <- getChar
948 ; let { r1 = f a r2 ; rec { r1 <- f a r2
949 ; r2 = g r1 } ; r2 <- g r1 }
950 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
952 In both cases, <literal>r1</literal> and <literal>r2</literal> are
953 available both throughout the <literal>let</literal> or <literal>rec</literal> block, and
954 in the statements that follow it. The difference is that <literal>let</literal> is non-monadic,
955 while <literal>rec</literal> is monadic. (In Haskell <literal>let</literal> is
956 really <literal>letrec</literal>, of course.)
959 The static and dynamic semantics of <literal>rec</literal> can be described as follows:
963 similar to let-bindings, the <literal>rec</literal> is broken into
964 minimal recursive groups, a process known as <emphasis>segmentation</emphasis>.
967 rec { a <- getChar ===> a <- getChar
968 ; b <- f a c rec { b <- f a c
969 ; c <- f b a ; c <- f b a }
970 ; putChar c } putChar c
972 The details of segmentation are described in Section 3.2 of
973 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>.
974 Segmentation improves polymorphism, reduces the size of the recursive "knot", and, as the paper
975 describes, also has a semantic effect (unless the monad satisfies the right-shrinking law).
978 Then each resulting <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal>.
979 For example, the <literal>rec</literal> group in the preceding example is desugared like this:
981 rec { b <- f a c ===> (b,c) <- mfix (\~(b,c) -> do { b <- f a c
982 ; c <- f b a } ; c <- f b a
985 In general, the statment <literal>rec <replaceable>ss</replaceable></literal>
986 is desugared to the statement
988 <replaceable>vs</replaceable> <- mfix (\~<replaceable>vs</replaceable> -> do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
990 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
992 The original <literal>rec</literal> typechecks exactly
993 when the above desugared version would do so. For example, this means that
994 the variables <replaceable>vs</replaceable> are all monomorphic in the statements
995 following the <literal>rec</literal>, because they are bound by a lambda.
998 The <literal>mfix</literal> function is defined in the <literal>MonadFix</literal>
999 class, in <literal>Control.Monad.Fix</literal>, thus:
1001 class Monad m => MonadFix m where
1002 mfix :: (a -> m a) -> m a
1009 Here are some other important points in using the recursive-do notation:
1012 It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
1013 <literal>-fglasgow-exts</literal>.
1017 If recursive bindings are required for a monad,
1018 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
1022 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
1023 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
1024 for Haskell's internal state monad (strict and lazy, respectively).
1028 Like <literal>let</literal> and <literal>where</literal> bindings,
1029 name shadowing is not allowed within a <literal>rec</literal>;
1030 that is, all the names bound in a single <literal>rec</literal> must
1031 be distinct (Section 3.3 of the paper).
1034 It supports rebindable syntax (see <xref linkend="rebindable-syntax"/>).
1040 <sect3 id="mdo-notation"> <title> Mdo-notation (deprecated) </title>
1042 <para> GHC used to support the flag <option>-XRecursiveDo</option>,
1043 which enabled the keyword <literal>mdo</literal>, precisely as described in
1044 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
1045 but this is now deprecated. Instead of <literal>mdo { Q; e }</literal>, write
1046 <literal>do { rec Q; e }</literal>.
1049 Historical note: The old implementation of the mdo-notation (and most
1050 of the existing documents) used the name
1051 <literal>MonadRec</literal> for the class and the corresponding library.
1052 This name is not supported by GHC.
1059 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1061 <sect2 id="parallel-list-comprehensions">
1062 <title>Parallel List Comprehensions</title>
1063 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1065 <indexterm><primary>parallel list comprehensions</primary>
1068 <para>Parallel list comprehensions are a natural extension to list
1069 comprehensions. List comprehensions can be thought of as a nice
1070 syntax for writing maps and filters. Parallel comprehensions
1071 extend this to include the zipWith family.</para>
1073 <para>A parallel list comprehension has multiple independent
1074 branches of qualifier lists, each separated by a `|' symbol. For
1075 example, the following zips together two lists:</para>
1078 [ (x, y) | x <- xs | y <- ys ]
1081 <para>The behavior of parallel list comprehensions follows that of
1082 zip, in that the resulting list will have the same length as the
1083 shortest branch.</para>
1085 <para>We can define parallel list comprehensions by translation to
1086 regular comprehensions. Here's the basic idea:</para>
1088 <para>Given a parallel comprehension of the form: </para>
1091 [ e | p1 <- e11, p2 <- e12, ...
1092 | q1 <- e21, q2 <- e22, ...
1097 <para>This will be translated to: </para>
1100 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1101 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1106 <para>where `zipN' is the appropriate zip for the given number of
1111 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1113 <sect2 id="generalised-list-comprehensions">
1114 <title>Generalised (SQL-Like) List Comprehensions</title>
1115 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1117 <indexterm><primary>extended list comprehensions</primary>
1119 <indexterm><primary>group</primary></indexterm>
1120 <indexterm><primary>sql</primary></indexterm>
1123 <para>Generalised list comprehensions are a further enhancement to the
1124 list comprehension syntactic sugar to allow operations such as sorting
1125 and grouping which are familiar from SQL. They are fully described in the
1126 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1127 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1128 except that the syntax we use differs slightly from the paper.</para>
1129 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1130 <para>Here is an example:
1132 employees = [ ("Simon", "MS", 80)
1133 , ("Erik", "MS", 100)
1134 , ("Phil", "Ed", 40)
1135 , ("Gordon", "Ed", 45)
1136 , ("Paul", "Yale", 60)]
1138 output = [ (the dept, sum salary)
1139 | (name, dept, salary) <- employees
1140 , then group by dept
1141 , then sortWith by (sum salary)
1144 In this example, the list <literal>output</literal> would take on
1148 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1151 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1152 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1153 function that is exported by <literal>GHC.Exts</literal>.)</para>
1155 <para>There are five new forms of comprehension qualifier,
1156 all introduced by the (existing) keyword <literal>then</literal>:
1164 This statement requires that <literal>f</literal> have the type <literal>
1165 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1166 motivating example, as this form is used to apply <literal>take 5</literal>.
1177 This form is similar to the previous one, but allows you to create a function
1178 which will be passed as the first argument to f. As a consequence f must have
1179 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1180 from the type, this function lets f "project out" some information
1181 from the elements of the list it is transforming.</para>
1183 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1184 is supplied with a function that lets it find out the <literal>sum salary</literal>
1185 for any item in the list comprehension it transforms.</para>
1193 then group by e using f
1196 <para>This is the most general of the grouping-type statements. In this form,
1197 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1198 As with the <literal>then f by e</literal> case above, the first argument
1199 is a function supplied to f by the compiler which lets it compute e on every
1200 element of the list being transformed. However, unlike the non-grouping case,
1201 f additionally partitions the list into a number of sublists: this means that
1202 at every point after this statement, binders occurring before it in the comprehension
1203 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1204 this, let's look at an example:</para>
1207 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1208 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1209 groupRuns f = groupBy (\x y -> f x == f y)
1211 output = [ (the x, y)
1212 | x <- ([1..3] ++ [1..2])
1214 , then group by x using groupRuns ]
1217 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1220 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1223 <para>Note that we have used the <literal>the</literal> function to change the type
1224 of x from a list to its original numeric type. The variable y, in contrast, is left
1225 unchanged from the list form introduced by the grouping.</para>
1235 <para>This form of grouping is essentially the same as the one described above. However,
1236 since no function to use for the grouping has been supplied it will fall back on the
1237 <literal>groupWith</literal> function defined in
1238 <ulink url="&libraryBaseLocation;/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1239 is the form of the group statement that we made use of in the opening example.</para>
1250 <para>With this form of the group statement, f is required to simply have the type
1251 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1252 comprehension so far directly. An example of this form is as follows:</para>
1258 , then group using inits]
1261 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1264 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1272 <!-- ===================== REBINDABLE SYNTAX =================== -->
1274 <sect2 id="rebindable-syntax">
1275 <title>Rebindable syntax and the implicit Prelude import</title>
1277 <para><indexterm><primary>-XNoImplicitPrelude
1278 option</primary></indexterm> GHC normally imports
1279 <filename>Prelude.hi</filename> files for you. If you'd
1280 rather it didn't, then give it a
1281 <option>-XNoImplicitPrelude</option> option. The idea is
1282 that you can then import a Prelude of your own. (But don't
1283 call it <literal>Prelude</literal>; the Haskell module
1284 namespace is flat, and you must not conflict with any
1285 Prelude module.)</para>
1287 <para>Suppose you are importing a Prelude of your own
1288 in order to define your own numeric class
1289 hierarchy. It completely defeats that purpose if the
1290 literal "1" means "<literal>Prelude.fromInteger
1291 1</literal>", which is what the Haskell Report specifies.
1292 So the <option>-XNoImplicitPrelude</option>
1293 flag <emphasis>also</emphasis> causes
1294 the following pieces of built-in syntax to refer to
1295 <emphasis>whatever is in scope</emphasis>, not the Prelude
1299 <para>An integer literal <literal>368</literal> means
1300 "<literal>fromInteger (368::Integer)</literal>", rather than
1301 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1304 <listitem><para>Fractional literals are handed in just the same way,
1305 except that the translation is
1306 <literal>fromRational (3.68::Rational)</literal>.
1309 <listitem><para>The equality test in an overloaded numeric pattern
1310 uses whatever <literal>(==)</literal> is in scope.
1313 <listitem><para>The subtraction operation, and the
1314 greater-than-or-equal test, in <literal>n+k</literal> patterns
1315 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1319 <para>Negation (e.g. "<literal>- (f x)</literal>")
1320 means "<literal>negate (f x)</literal>", both in numeric
1321 patterns, and expressions.
1325 <para>"Do" notation is translated using whatever
1326 functions <literal>(>>=)</literal>,
1327 <literal>(>>)</literal>, and <literal>fail</literal>,
1328 are in scope (not the Prelude
1329 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1330 comprehensions, are unaffected. </para></listitem>
1334 notation (see <xref linkend="arrow-notation"/>)
1335 uses whatever <literal>arr</literal>,
1336 <literal>(>>>)</literal>, <literal>first</literal>,
1337 <literal>app</literal>, <literal>(|||)</literal> and
1338 <literal>loop</literal> functions are in scope. But unlike the
1339 other constructs, the types of these functions must match the
1340 Prelude types very closely. Details are in flux; if you want
1344 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1345 even if that is a little unexpected. For example, the
1346 static semantics of the literal <literal>368</literal>
1347 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1348 <literal>fromInteger</literal> to have any of the types:
1350 fromInteger :: Integer -> Integer
1351 fromInteger :: forall a. Foo a => Integer -> a
1352 fromInteger :: Num a => a -> Integer
1353 fromInteger :: Integer -> Bool -> Bool
1357 <para>Be warned: this is an experimental facility, with
1358 fewer checks than usual. Use <literal>-dcore-lint</literal>
1359 to typecheck the desugared program. If Core Lint is happy
1360 you should be all right.</para>
1364 <sect2 id="postfix-operators">
1365 <title>Postfix operators</title>
1368 The <option>-XPostfixOperators</option> flag enables a small
1369 extension to the syntax of left operator sections, which allows you to
1370 define postfix operators. The extension is this: the left section
1374 is equivalent (from the point of view of both type checking and execution) to the expression
1378 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1379 The strict Haskell 98 interpretation is that the section is equivalent to
1383 That is, the operator must be a function of two arguments. GHC allows it to
1384 take only one argument, and that in turn allows you to write the function
1387 <para>The extension does not extend to the left-hand side of function
1388 definitions; you must define such a function in prefix form.</para>
1392 <sect2 id="tuple-sections">
1393 <title>Tuple sections</title>
1396 The <option>-XTupleSections</option> flag enables Python-style partially applied
1397 tuple constructors. For example, the following program
1401 is considered to be an alternative notation for the more unwieldy alternative
1405 You can omit any combination of arguments to the tuple, as in the following
1407 (, "I", , , "Love", , 1337)
1411 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1416 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1417 will also be available for them, like so
1421 Because there is no unboxed unit tuple, the following expression
1425 continues to stand for the unboxed singleton tuple data constructor.
1430 <sect2 id="disambiguate-fields">
1431 <title>Record field disambiguation</title>
1433 In record construction and record pattern matching
1434 it is entirely unambiguous which field is referred to, even if there are two different
1435 data types in scope with a common field name. For example:
1438 data S = MkS { x :: Int, y :: Bool }
1443 data T = MkT { x :: Int }
1445 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1446 ok2 n = MkT { x = n+1 } -- Unambiguous
1448 bad1 k = k { x = 3 } -- Ambiguous
1449 bad2 k = x k -- Ambiguous
1451 Even though there are two <literal>x</literal>'s in scope,
1452 it is clear that the <literal>x</literal> in the pattern in the
1453 definition of <literal>ok1</literal> can only mean the field
1454 <literal>x</literal> from type <literal>S</literal>. Similarly for
1455 the function <literal>ok2</literal>. However, in the record update
1456 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1457 it is not clear which of the two types is intended.
1460 Haskell 98 regards all four as ambiguous, but with the
1461 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1462 the former two. The rules are precisely the same as those for instance
1463 declarations in Haskell 98, where the method names on the left-hand side
1464 of the method bindings in an instance declaration refer unambiguously
1465 to the method of that class (provided they are in scope at all), even
1466 if there are other variables in scope with the same name.
1467 This reduces the clutter of qualified names when you import two
1468 records from different modules that use the same field name.
1474 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1479 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1484 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1485 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1486 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1489 import qualified M -- Note qualified
1491 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1493 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1494 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1495 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1496 is not. (In effect, it is qualified by the constructor.)
1503 <!-- ===================== Record puns =================== -->
1505 <sect2 id="record-puns">
1510 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1514 When using records, it is common to write a pattern that binds a
1515 variable with the same name as a record field, such as:
1518 data C = C {a :: Int}
1524 Record punning permits the variable name to be elided, so one can simply
1531 to mean the same pattern as above. That is, in a record pattern, the
1532 pattern <literal>a</literal> expands into the pattern <literal>a =
1533 a</literal> for the same name <literal>a</literal>.
1540 Record punning can also be used in an expression, writing, for example,
1546 let a = 1 in C {a = a}
1548 The expansion is purely syntactic, so the expanded right-hand side
1549 expression refers to the nearest enclosing variable that is spelled the
1550 same as the field name.
1554 Puns and other patterns can be mixed in the same record:
1556 data C = C {a :: Int, b :: Int}
1557 f (C {a, b = 4}) = a
1562 Puns can be used wherever record patterns occur (e.g. in
1563 <literal>let</literal> bindings or at the top-level).
1567 A pun on a qualified field name is expanded by stripping off the module qualifier.
1574 f (M.C {M.a = a}) = a
1576 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1577 is only in scope in qualified form.)
1585 <!-- ===================== Record wildcards =================== -->
1587 <sect2 id="record-wildcards">
1588 <title>Record wildcards
1592 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1593 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1597 For records with many fields, it can be tiresome to write out each field
1598 individually in a record pattern, as in
1600 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1601 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1606 Record wildcard syntax permits a "<literal>..</literal>" in a record
1607 pattern, where each elided field <literal>f</literal> is replaced by the
1608 pattern <literal>f = f</literal>. For example, the above pattern can be
1611 f (C {a = 1, ..}) = b + c + d
1619 Wildcards can be mixed with other patterns, including puns
1620 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1621 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1622 wherever record patterns occur, including in <literal>let</literal>
1623 bindings and at the top-level. For example, the top-level binding
1627 defines <literal>b</literal>, <literal>c</literal>, and
1628 <literal>d</literal>.
1632 Record wildcards can also be used in expressions, writing, for example,
1634 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1638 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1640 The expansion is purely syntactic, so the record wildcard
1641 expression refers to the nearest enclosing variables that are spelled
1642 the same as the omitted field names.
1646 The "<literal>..</literal>" expands to the missing
1647 <emphasis>in-scope</emphasis> record fields, where "in scope"
1648 includes both unqualified and qualified-only.
1649 Any fields that are not in scope are not filled in. For example
1652 data R = R { a,b,c :: Int }
1654 import qualified M( R(a,b) )
1657 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1658 omitting <literal>c</literal> since it is not in scope at all.
1665 <!-- ===================== Local fixity declarations =================== -->
1667 <sect2 id="local-fixity-declarations">
1668 <title>Local Fixity Declarations
1671 <para>A careful reading of the Haskell 98 Report reveals that fixity
1672 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1673 <literal>infixr</literal>) are permitted to appear inside local bindings
1674 such those introduced by <literal>let</literal> and
1675 <literal>where</literal>. However, the Haskell Report does not specify
1676 the semantics of such bindings very precisely.
1679 <para>In GHC, a fixity declaration may accompany a local binding:
1686 and the fixity declaration applies wherever the binding is in scope.
1687 For example, in a <literal>let</literal>, it applies in the right-hand
1688 sides of other <literal>let</literal>-bindings and the body of the
1689 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1690 expressions (<xref linkend="recursive-do-notation"/>), the local fixity
1691 declarations of a <literal>let</literal> statement scope over other
1692 statements in the group, just as the bound name does.
1696 Moreover, a local fixity declaration *must* accompany a local binding of
1697 that name: it is not possible to revise the fixity of name bound
1700 let infixr 9 $ in ...
1703 Because local fixity declarations are technically Haskell 98, no flag is
1704 necessary to enable them.
1708 <sect2 id="package-imports">
1709 <title>Package-qualified imports</title>
1711 <para>With the <option>-XPackageImports</option> flag, GHC allows
1712 import declarations to be qualified by the package name that the
1713 module is intended to be imported from. For example:</para>
1716 import "network" Network.Socket
1719 <para>would import the module <literal>Network.Socket</literal> from
1720 the package <literal>network</literal> (any version). This may
1721 be used to disambiguate an import when the same module is
1722 available from multiple packages, or is present in both the
1723 current package being built and an external package.</para>
1725 <para>Note: you probably don't need to use this feature, it was
1726 added mainly so that we can build backwards-compatible versions of
1727 packages when APIs change. It can lead to fragile dependencies in
1728 the common case: modules occasionally move from one package to
1729 another, rendering any package-qualified imports broken.</para>
1732 <sect2 id="syntax-stolen">
1733 <title>Summary of stolen syntax</title>
1735 <para>Turning on an option that enables special syntax
1736 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1737 to compile, perhaps because it uses a variable name which has
1738 become a reserved word. This section lists the syntax that is
1739 "stolen" by language extensions.
1741 notation and nonterminal names from the Haskell 98 lexical syntax
1742 (see the Haskell 98 Report).
1743 We only list syntax changes here that might affect
1744 existing working programs (i.e. "stolen" syntax). Many of these
1745 extensions will also enable new context-free syntax, but in all
1746 cases programs written to use the new syntax would not be
1747 compilable without the option enabled.</para>
1749 <para>There are two classes of special
1754 <para>New reserved words and symbols: character sequences
1755 which are no longer available for use as identifiers in the
1759 <para>Other special syntax: sequences of characters that have
1760 a different meaning when this particular option is turned
1765 The following syntax is stolen:
1770 <literal>forall</literal>
1771 <indexterm><primary><literal>forall</literal></primary></indexterm>
1774 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1775 <option>-XScopedTypeVariables</option>,
1776 <option>-XLiberalTypeSynonyms</option>,
1777 <option>-XRank2Types</option>,
1778 <option>-XRankNTypes</option>,
1779 <option>-XPolymorphicComponents</option>,
1780 <option>-XExistentialQuantification</option>
1786 <literal>mdo</literal>
1787 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1790 Stolen by: <option>-XRecursiveDo</option>,
1796 <literal>foreign</literal>
1797 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1800 Stolen by: <option>-XForeignFunctionInterface</option>,
1806 <literal>rec</literal>,
1807 <literal>proc</literal>, <literal>-<</literal>,
1808 <literal>>-</literal>, <literal>-<<</literal>,
1809 <literal>>>-</literal>, and <literal>(|</literal>,
1810 <literal>|)</literal> brackets
1811 <indexterm><primary><literal>proc</literal></primary></indexterm>
1814 Stolen by: <option>-XArrows</option>,
1820 <literal>?<replaceable>varid</replaceable></literal>,
1821 <literal>%<replaceable>varid</replaceable></literal>
1822 <indexterm><primary>implicit parameters</primary></indexterm>
1825 Stolen by: <option>-XImplicitParams</option>,
1831 <literal>[|</literal>,
1832 <literal>[e|</literal>, <literal>[p|</literal>,
1833 <literal>[d|</literal>, <literal>[t|</literal>,
1834 <literal>$(</literal>,
1835 <literal>$<replaceable>varid</replaceable></literal>
1836 <indexterm><primary>Template Haskell</primary></indexterm>
1839 Stolen by: <option>-XTemplateHaskell</option>,
1845 <literal>[:<replaceable>varid</replaceable>|</literal>
1846 <indexterm><primary>quasi-quotation</primary></indexterm>
1849 Stolen by: <option>-XQuasiQuotes</option>,
1855 <replaceable>varid</replaceable>{<literal>#</literal>},
1856 <replaceable>char</replaceable><literal>#</literal>,
1857 <replaceable>string</replaceable><literal>#</literal>,
1858 <replaceable>integer</replaceable><literal>#</literal>,
1859 <replaceable>float</replaceable><literal>#</literal>,
1860 <replaceable>float</replaceable><literal>##</literal>,
1861 <literal>(#</literal>, <literal>#)</literal>,
1864 Stolen by: <option>-XMagicHash</option>,
1873 <!-- TYPE SYSTEM EXTENSIONS -->
1874 <sect1 id="data-type-extensions">
1875 <title>Extensions to data types and type synonyms</title>
1877 <sect2 id="nullary-types">
1878 <title>Data types with no constructors</title>
1880 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1881 a data type with no constructors. For example:</para>
1885 data T a -- T :: * -> *
1888 <para>Syntactically, the declaration lacks the "= constrs" part. The
1889 type can be parameterised over types of any kind, but if the kind is
1890 not <literal>*</literal> then an explicit kind annotation must be used
1891 (see <xref linkend="kinding"/>).</para>
1893 <para>Such data types have only one value, namely bottom.
1894 Nevertheless, they can be useful when defining "phantom types".</para>
1897 <sect2 id="infix-tycons">
1898 <title>Infix type constructors, classes, and type variables</title>
1901 GHC allows type constructors, classes, and type variables to be operators, and
1902 to be written infix, very much like expressions. More specifically:
1905 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1906 The lexical syntax is the same as that for data constructors.
1909 Data type and type-synonym declarations can be written infix, parenthesised
1910 if you want further arguments. E.g.
1912 data a :*: b = Foo a b
1913 type a :+: b = Either a b
1914 class a :=: b where ...
1916 data (a :**: b) x = Baz a b x
1917 type (a :++: b) y = Either (a,b) y
1921 Types, and class constraints, can be written infix. For example
1924 f :: (a :=: b) => a -> b
1928 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1929 The lexical syntax is the same as that for variable operators, excluding "(.)",
1930 "(!)", and "(*)". In a binding position, the operator must be
1931 parenthesised. For example:
1933 type T (+) = Int + Int
1937 liftA2 :: Arrow (~>)
1938 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1944 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1945 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1948 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1949 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1950 sets the fixity for a data constructor and the corresponding type constructor. For example:
1954 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1955 and similarly for <literal>:*:</literal>.
1956 <literal>Int `a` Bool</literal>.
1959 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1966 <sect2 id="type-synonyms">
1967 <title>Liberalised type synonyms</title>
1970 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1971 on individual synonym declarations.
1972 With the <option>-XLiberalTypeSynonyms</option> extension,
1973 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1974 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1977 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1978 in a type synonym, thus:
1980 type Discard a = forall b. Show b => a -> b -> (a, String)
1985 g :: Discard Int -> (Int,String) -- A rank-2 type
1992 If you also use <option>-XUnboxedTuples</option>,
1993 you can write an unboxed tuple in a type synonym:
1995 type Pr = (# Int, Int #)
2003 You can apply a type synonym to a forall type:
2005 type Foo a = a -> a -> Bool
2007 f :: Foo (forall b. b->b)
2009 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2011 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2016 You can apply a type synonym to a partially applied type synonym:
2018 type Generic i o = forall x. i x -> o x
2021 foo :: Generic Id []
2023 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2025 foo :: forall x. x -> [x]
2033 GHC currently does kind checking before expanding synonyms (though even that
2037 After expanding type synonyms, GHC does validity checking on types, looking for
2038 the following mal-formedness which isn't detected simply by kind checking:
2041 Type constructor applied to a type involving for-alls.
2044 Unboxed tuple on left of an arrow.
2047 Partially-applied type synonym.
2051 this will be rejected:
2053 type Pr = (# Int, Int #)
2058 because GHC does not allow unboxed tuples on the left of a function arrow.
2063 <sect2 id="existential-quantification">
2064 <title>Existentially quantified data constructors
2068 The idea of using existential quantification in data type declarations
2069 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2070 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2071 London, 1991). It was later formalised by Laufer and Odersky
2072 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2073 TOPLAS, 16(5), pp1411-1430, 1994).
2074 It's been in Lennart
2075 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2076 proved very useful. Here's the idea. Consider the declaration:
2082 data Foo = forall a. MkFoo a (a -> Bool)
2089 The data type <literal>Foo</literal> has two constructors with types:
2095 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2102 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2103 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2104 For example, the following expression is fine:
2110 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2116 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2117 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2118 isUpper</function> packages a character with a compatible function. These
2119 two things are each of type <literal>Foo</literal> and can be put in a list.
2123 What can we do with a value of type <literal>Foo</literal>?. In particular,
2124 what happens when we pattern-match on <function>MkFoo</function>?
2130 f (MkFoo val fn) = ???
2136 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2137 are compatible, the only (useful) thing we can do with them is to
2138 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2145 f (MkFoo val fn) = fn val
2151 What this allows us to do is to package heterogeneous values
2152 together with a bunch of functions that manipulate them, and then treat
2153 that collection of packages in a uniform manner. You can express
2154 quite a bit of object-oriented-like programming this way.
2157 <sect3 id="existential">
2158 <title>Why existential?
2162 What has this to do with <emphasis>existential</emphasis> quantification?
2163 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2169 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2175 But Haskell programmers can safely think of the ordinary
2176 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2177 adding a new existential quantification construct.
2182 <sect3 id="existential-with-context">
2183 <title>Existentials and type classes</title>
2186 An easy extension is to allow
2187 arbitrary contexts before the constructor. For example:
2193 data Baz = forall a. Eq a => Baz1 a a
2194 | forall b. Show b => Baz2 b (b -> b)
2200 The two constructors have the types you'd expect:
2206 Baz1 :: forall a. Eq a => a -> a -> Baz
2207 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2213 But when pattern matching on <function>Baz1</function> the matched values can be compared
2214 for equality, and when pattern matching on <function>Baz2</function> the first matched
2215 value can be converted to a string (as well as applying the function to it).
2216 So this program is legal:
2223 f (Baz1 p q) | p == q = "Yes"
2225 f (Baz2 v fn) = show (fn v)
2231 Operationally, in a dictionary-passing implementation, the
2232 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2233 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2234 extract it on pattern matching.
2239 <sect3 id="existential-records">
2240 <title>Record Constructors</title>
2243 GHC allows existentials to be used with records syntax as well. For example:
2246 data Counter a = forall self. NewCounter
2248 , _inc :: self -> self
2249 , _display :: self -> IO ()
2253 Here <literal>tag</literal> is a public field, with a well-typed selector
2254 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2255 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2256 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2257 compile-time error. In other words, <emphasis>GHC defines a record selector function
2258 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2259 (This example used an underscore in the fields for which record selectors
2260 will not be defined, but that is only programming style; GHC ignores them.)
2264 To make use of these hidden fields, we need to create some helper functions:
2267 inc :: Counter a -> Counter a
2268 inc (NewCounter x i d t) = NewCounter
2269 { _this = i x, _inc = i, _display = d, tag = t }
2271 display :: Counter a -> IO ()
2272 display NewCounter{ _this = x, _display = d } = d x
2275 Now we can define counters with different underlying implementations:
2278 counterA :: Counter String
2279 counterA = NewCounter
2280 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2282 counterB :: Counter String
2283 counterB = NewCounter
2284 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2287 display (inc counterA) -- prints "1"
2288 display (inc (inc counterB)) -- prints "##"
2291 Record update syntax is supported for existentials (and GADTs):
2293 setTag :: Counter a -> a -> Counter a
2294 setTag obj t = obj{ tag = t }
2296 The rule for record update is this: <emphasis>
2297 the types of the updated fields may
2298 mention only the universally-quantified type variables
2299 of the data constructor. For GADTs, the field may mention only types
2300 that appear as a simple type-variable argument in the constructor's result
2301 type</emphasis>. For example:
2303 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2304 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2305 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2306 -- existentially quantified)
2308 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2309 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2310 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2311 -- type-variable argument in G1's result type)
2319 <title>Restrictions</title>
2322 There are several restrictions on the ways in which existentially-quantified
2323 constructors can be use.
2332 When pattern matching, each pattern match introduces a new,
2333 distinct, type for each existential type variable. These types cannot
2334 be unified with any other type, nor can they escape from the scope of
2335 the pattern match. For example, these fragments are incorrect:
2343 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2344 is the result of <function>f1</function>. One way to see why this is wrong is to
2345 ask what type <function>f1</function> has:
2349 f1 :: Foo -> a -- Weird!
2353 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2358 f1 :: forall a. Foo -> a -- Wrong!
2362 The original program is just plain wrong. Here's another sort of error
2366 f2 (Baz1 a b) (Baz1 p q) = a==q
2370 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2371 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2372 from the two <function>Baz1</function> constructors.
2380 You can't pattern-match on an existentially quantified
2381 constructor in a <literal>let</literal> or <literal>where</literal> group of
2382 bindings. So this is illegal:
2386 f3 x = a==b where { Baz1 a b = x }
2389 Instead, use a <literal>case</literal> expression:
2392 f3 x = case x of Baz1 a b -> a==b
2395 In general, you can only pattern-match
2396 on an existentially-quantified constructor in a <literal>case</literal> expression or
2397 in the patterns of a function definition.
2399 The reason for this restriction is really an implementation one.
2400 Type-checking binding groups is already a nightmare without
2401 existentials complicating the picture. Also an existential pattern
2402 binding at the top level of a module doesn't make sense, because it's
2403 not clear how to prevent the existentially-quantified type "escaping".
2404 So for now, there's a simple-to-state restriction. We'll see how
2412 You can't use existential quantification for <literal>newtype</literal>
2413 declarations. So this is illegal:
2417 newtype T = forall a. Ord a => MkT a
2421 Reason: a value of type <literal>T</literal> must be represented as a
2422 pair of a dictionary for <literal>Ord t</literal> and a value of type
2423 <literal>t</literal>. That contradicts the idea that
2424 <literal>newtype</literal> should have no concrete representation.
2425 You can get just the same efficiency and effect by using
2426 <literal>data</literal> instead of <literal>newtype</literal>. If
2427 there is no overloading involved, then there is more of a case for
2428 allowing an existentially-quantified <literal>newtype</literal>,
2429 because the <literal>data</literal> version does carry an
2430 implementation cost, but single-field existentially quantified
2431 constructors aren't much use. So the simple restriction (no
2432 existential stuff on <literal>newtype</literal>) stands, unless there
2433 are convincing reasons to change it.
2441 You can't use <literal>deriving</literal> to define instances of a
2442 data type with existentially quantified data constructors.
2444 Reason: in most cases it would not make sense. For example:;
2447 data T = forall a. MkT [a] deriving( Eq )
2450 To derive <literal>Eq</literal> in the standard way we would need to have equality
2451 between the single component of two <function>MkT</function> constructors:
2455 (MkT a) == (MkT b) = ???
2458 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2459 It's just about possible to imagine examples in which the derived instance
2460 would make sense, but it seems altogether simpler simply to prohibit such
2461 declarations. Define your own instances!
2472 <!-- ====================== Generalised algebraic data types ======================= -->
2474 <sect2 id="gadt-style">
2475 <title>Declaring data types with explicit constructor signatures</title>
2477 <para>GHC allows you to declare an algebraic data type by
2478 giving the type signatures of constructors explicitly. For example:
2482 Just :: a -> Maybe a
2484 The form is called a "GADT-style declaration"
2485 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2486 can only be declared using this form.</para>
2487 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2488 For example, these two declarations are equivalent:
2490 data Foo = forall a. MkFoo a (a -> Bool)
2491 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2494 <para>Any data type that can be declared in standard Haskell-98 syntax
2495 can also be declared using GADT-style syntax.
2496 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2497 they treat class constraints on the data constructors differently.
2498 Specifically, if the constructor is given a type-class context, that
2499 context is made available by pattern matching. For example:
2502 MkSet :: Eq a => [a] -> Set a
2504 makeSet :: Eq a => [a] -> Set a
2505 makeSet xs = MkSet (nub xs)
2507 insert :: a -> Set a -> Set a
2508 insert a (MkSet as) | a `elem` as = MkSet as
2509 | otherwise = MkSet (a:as)
2511 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2512 gives rise to a <literal>(Eq a)</literal>
2513 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2514 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2515 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2516 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2517 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2518 In the example, the equality dictionary is used to satisfy the equality constraint
2519 generated by the call to <literal>elem</literal>, so that the type of
2520 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2523 For example, one possible application is to reify dictionaries:
2525 data NumInst a where
2526 MkNumInst :: Num a => NumInst a
2528 intInst :: NumInst Int
2531 plus :: NumInst a -> a -> a -> a
2532 plus MkNumInst p q = p + q
2534 Here, a value of type <literal>NumInst a</literal> is equivalent
2535 to an explicit <literal>(Num a)</literal> dictionary.
2538 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2539 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2543 = Num a => MkNumInst (NumInst a)
2545 Notice that, unlike the situation when declaring an existential, there is
2546 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2547 data type's universally quantified type variable <literal>a</literal>.
2548 A constructor may have both universal and existential type variables: for example,
2549 the following two declarations are equivalent:
2552 = forall b. (Num a, Eq b) => MkT1 a b
2554 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2557 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2558 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2559 In Haskell 98 the definition
2561 data Eq a => Set' a = MkSet' [a]
2563 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2564 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2565 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2566 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2567 GHC's behaviour is much more useful, as well as much more intuitive.
2571 The rest of this section gives further details about GADT-style data
2576 The result type of each data constructor must begin with the type constructor being defined.
2577 If the result type of all constructors
2578 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2579 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2580 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2584 As with other type signatures, you can give a single signature for several data constructors.
2585 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2594 The type signature of
2595 each constructor is independent, and is implicitly universally quantified as usual.
2596 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2597 have no scope, and different constructors may have different universally-quantified type variables:
2599 data T a where -- The 'a' has no scope
2600 T1,T2 :: b -> T b -- Means forall b. b -> T b
2601 T3 :: T a -- Means forall a. T a
2606 A constructor signature may mention type class constraints, which can differ for
2607 different constructors. For example, this is fine:
2610 T1 :: Eq b => b -> b -> T b
2611 T2 :: (Show c, Ix c) => c -> [c] -> T c
2613 When patten matching, these constraints are made available to discharge constraints
2614 in the body of the match. For example:
2617 f (T1 x y) | x==y = "yes"
2621 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2622 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2623 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2627 Unlike a Haskell-98-style
2628 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2629 have no scope. Indeed, one can write a kind signature instead:
2631 data Set :: * -> * where ...
2633 or even a mixture of the two:
2635 data Bar a :: (* -> *) -> * where ...
2637 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2640 data Bar a (b :: * -> *) where ...
2646 You can use strictness annotations, in the obvious places
2647 in the constructor type:
2650 Lit :: !Int -> Term Int
2651 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2652 Pair :: Term a -> Term b -> Term (a,b)
2657 You can use a <literal>deriving</literal> clause on a GADT-style data type
2658 declaration. For example, these two declarations are equivalent
2660 data Maybe1 a where {
2661 Nothing1 :: Maybe1 a ;
2662 Just1 :: a -> Maybe1 a
2663 } deriving( Eq, Ord )
2665 data Maybe2 a = Nothing2 | Just2 a
2671 The type signature may have quantified type variables that do not appear
2675 MkFoo :: a -> (a->Bool) -> Foo
2678 Here the type variable <literal>a</literal> does not appear in the result type
2679 of either constructor.
2680 Although it is universally quantified in the type of the constructor, such
2681 a type variable is often called "existential".
2682 Indeed, the above declaration declares precisely the same type as
2683 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2685 The type may contain a class context too, of course:
2688 MkShowable :: Show a => a -> Showable
2693 You can use record syntax on a GADT-style data type declaration:
2697 Adult :: { name :: String, children :: [Person] } -> Person
2698 Child :: Show a => { name :: !String, funny :: a } -> Person
2700 As usual, for every constructor that has a field <literal>f</literal>, the type of
2701 field <literal>f</literal> must be the same (modulo alpha conversion).
2702 The <literal>Child</literal> constructor above shows that the signature
2703 may have a context, existentially-quantified variables, and strictness annotations,
2704 just as in the non-record case. (NB: the "type" that follows the double-colon
2705 is not really a type, because of the record syntax and strictness annotations.
2706 A "type" of this form can appear only in a constructor signature.)
2710 Record updates are allowed with GADT-style declarations,
2711 only fields that have the following property: the type of the field
2712 mentions no existential type variables.
2716 As in the case of existentials declared using the Haskell-98-like record syntax
2717 (<xref linkend="existential-records"/>),
2718 record-selector functions are generated only for those fields that have well-typed
2720 Here is the example of that section, in GADT-style syntax:
2722 data Counter a where
2723 NewCounter { _this :: self
2724 , _inc :: self -> self
2725 , _display :: self -> IO ()
2730 As before, only one selector function is generated here, that for <literal>tag</literal>.
2731 Nevertheless, you can still use all the field names in pattern matching and record construction.
2733 </itemizedlist></para>
2737 <title>Generalised Algebraic Data Types (GADTs)</title>
2739 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2740 by allowing constructors to have richer return types. Here is an example:
2743 Lit :: Int -> Term Int
2744 Succ :: Term Int -> Term Int
2745 IsZero :: Term Int -> Term Bool
2746 If :: Term Bool -> Term a -> Term a -> Term a
2747 Pair :: Term a -> Term b -> Term (a,b)
2749 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2750 case with ordinary data types. This generality allows us to
2751 write a well-typed <literal>eval</literal> function
2752 for these <literal>Terms</literal>:
2756 eval (Succ t) = 1 + eval t
2757 eval (IsZero t) = eval t == 0
2758 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2759 eval (Pair e1 e2) = (eval e1, eval e2)
2761 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2762 For example, in the right hand side of the equation
2767 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2768 A precise specification of the type rules is beyond what this user manual aspires to,
2769 but the design closely follows that described in
2771 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2772 unification-based type inference for GADTs</ulink>,
2774 The general principle is this: <emphasis>type refinement is only carried out
2775 based on user-supplied type annotations</emphasis>.
2776 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2777 and lots of obscure error messages will
2778 occur. However, the refinement is quite general. For example, if we had:
2780 eval :: Term a -> a -> a
2781 eval (Lit i) j = i+j
2783 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2784 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2785 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2788 These and many other examples are given in papers by Hongwei Xi, and
2789 Tim Sheard. There is a longer introduction
2790 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2792 <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
2793 may use different notation to that implemented in GHC.
2796 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2797 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2800 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2801 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2802 The result type of each constructor must begin with the type constructor being defined,
2803 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2804 For example, in the <literal>Term</literal> data
2805 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2806 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2811 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2812 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2813 whose result type is not just <literal>T a b</literal>.
2817 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2818 an ordinary data type.
2822 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2826 Lit { val :: Int } :: Term Int
2827 Succ { num :: Term Int } :: Term Int
2828 Pred { num :: Term Int } :: Term Int
2829 IsZero { arg :: Term Int } :: Term Bool
2830 Pair { arg1 :: Term a
2833 If { cnd :: Term Bool
2838 However, for GADTs there is the following additional constraint:
2839 every constructor that has a field <literal>f</literal> must have
2840 the same result type (modulo alpha conversion)
2841 Hence, in the above example, we cannot merge the <literal>num</literal>
2842 and <literal>arg</literal> fields above into a
2843 single name. Although their field types are both <literal>Term Int</literal>,
2844 their selector functions actually have different types:
2847 num :: Term Int -> Term Int
2848 arg :: Term Bool -> Term Int
2853 When pattern-matching against data constructors drawn from a GADT,
2854 for example in a <literal>case</literal> expression, the following rules apply:
2856 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2857 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2858 <listitem><para>The type of any free variable mentioned in any of
2859 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2861 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2862 way to ensure that a variable a rigid type is to give it a type signature.
2863 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2864 Simple unification-based type inference for GADTs
2865 </ulink>. The criteria implemented by GHC are given in the Appendix.
2875 <!-- ====================== End of Generalised algebraic data types ======================= -->
2877 <sect1 id="deriving">
2878 <title>Extensions to the "deriving" mechanism</title>
2880 <sect2 id="deriving-inferred">
2881 <title>Inferred context for deriving clauses</title>
2884 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2887 data T0 f a = MkT0 a deriving( Eq )
2888 data T1 f a = MkT1 (f a) deriving( Eq )
2889 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2891 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2893 instance Eq a => Eq (T0 f a) where ...
2894 instance Eq (f a) => Eq (T1 f a) where ...
2895 instance Eq (f (f a)) => Eq (T2 f a) where ...
2897 The first of these is obviously fine. The second is still fine, although less obviously.
2898 The third is not Haskell 98, and risks losing termination of instances.
2901 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2902 each constraint in the inferred instance context must consist only of type variables,
2903 with no repetitions.
2906 This rule is applied regardless of flags. If you want a more exotic context, you can write
2907 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2911 <sect2 id="stand-alone-deriving">
2912 <title>Stand-alone deriving declarations</title>
2915 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2917 data Foo a = Bar a | Baz String
2919 deriving instance Eq a => Eq (Foo a)
2921 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2922 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2923 Note the following points:
2926 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2927 exactly as you would in an ordinary instance declaration.
2928 (In contrast, in a <literal>deriving</literal> clause
2929 attached to a data type declaration, the context is inferred.)
2933 A <literal>deriving instance</literal> declaration
2934 must obey the same rules concerning form and termination as ordinary instance declarations,
2935 controlled by the same flags; see <xref linkend="instance-decls"/>.
2939 Unlike a <literal>deriving</literal>
2940 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2941 than the data type (assuming you also use
2942 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2945 data Foo a = Bar a | Baz String
2947 deriving instance Eq a => Eq (Foo [a])
2948 deriving instance Eq a => Eq (Foo (Maybe a))
2950 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2951 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2955 Unlike a <literal>deriving</literal>
2956 declaration attached to a <literal>data</literal> declaration,
2957 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2958 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2959 your problem. (GHC will show you the offending code if it has a type error.)
2960 The merit of this is that you can derive instances for GADTs and other exotic
2961 data types, providing only that the boilerplate code does indeed typecheck. For example:
2967 deriving instance Show (T a)
2969 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2970 data type declaration for <literal>T</literal>,
2971 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2972 the instance declaration using stand-alone deriving.
2977 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2978 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2981 newtype Foo a = MkFoo (State Int a)
2983 deriving instance MonadState Int Foo
2985 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2986 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2988 </itemizedlist></para>
2993 <sect2 id="deriving-typeable">
2994 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2997 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2998 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2999 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3000 classes <literal>Eq</literal>, <literal>Ord</literal>,
3001 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3004 GHC extends this list with several more classes that may be automatically derived:
3006 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
3007 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
3008 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
3010 <para>An instance of <literal>Typeable</literal> can only be derived if the
3011 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3012 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3014 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3015 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3017 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3018 are used, and only <literal>Typeable1</literal> up to
3019 <literal>Typeable7</literal> are provided in the library.)
3020 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3021 class, whose kind suits that of the data type constructor, and
3022 then writing the data type instance by hand.
3026 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3027 the class <literal>Functor</literal>,
3028 defined in <literal>GHC.Base</literal>.
3031 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3032 the class <literal>Foldable</literal>,
3033 defined in <literal>Data.Foldable</literal>.
3036 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3037 the class <literal>Traversable</literal>,
3038 defined in <literal>Data.Traversable</literal>.
3041 In each case the appropriate class must be in scope before it
3042 can be mentioned in the <literal>deriving</literal> clause.
3046 <sect2 id="newtype-deriving">
3047 <title>Generalised derived instances for newtypes</title>
3050 When you define an abstract type using <literal>newtype</literal>, you may want
3051 the new type to inherit some instances from its representation. In
3052 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3053 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3054 other classes you have to write an explicit instance declaration. For
3055 example, if you define
3058 newtype Dollars = Dollars Int
3061 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3062 explicitly define an instance of <literal>Num</literal>:
3065 instance Num Dollars where
3066 Dollars a + Dollars b = Dollars (a+b)
3069 All the instance does is apply and remove the <literal>newtype</literal>
3070 constructor. It is particularly galling that, since the constructor
3071 doesn't appear at run-time, this instance declaration defines a
3072 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3073 dictionary, only slower!
3077 <sect3> <title> Generalising the deriving clause </title>
3079 GHC now permits such instances to be derived instead,
3080 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3083 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3086 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3087 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3088 derives an instance declaration of the form
3091 instance Num Int => Num Dollars
3094 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3098 We can also derive instances of constructor classes in a similar
3099 way. For example, suppose we have implemented state and failure monad
3100 transformers, such that
3103 instance Monad m => Monad (State s m)
3104 instance Monad m => Monad (Failure m)
3106 In Haskell 98, we can define a parsing monad by
3108 type Parser tok m a = State [tok] (Failure m) a
3111 which is automatically a monad thanks to the instance declarations
3112 above. With the extension, we can make the parser type abstract,
3113 without needing to write an instance of class <literal>Monad</literal>, via
3116 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3119 In this case the derived instance declaration is of the form
3121 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3124 Notice that, since <literal>Monad</literal> is a constructor class, the
3125 instance is a <emphasis>partial application</emphasis> of the new type, not the
3126 entire left hand side. We can imagine that the type declaration is
3127 "eta-converted" to generate the context of the instance
3132 We can even derive instances of multi-parameter classes, provided the
3133 newtype is the last class parameter. In this case, a ``partial
3134 application'' of the class appears in the <literal>deriving</literal>
3135 clause. For example, given the class
3138 class StateMonad s m | m -> s where ...
3139 instance Monad m => StateMonad s (State s m) where ...
3141 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3143 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3144 deriving (Monad, StateMonad [tok])
3147 The derived instance is obtained by completing the application of the
3148 class to the new type:
3151 instance StateMonad [tok] (State [tok] (Failure m)) =>
3152 StateMonad [tok] (Parser tok m)
3157 As a result of this extension, all derived instances in newtype
3158 declarations are treated uniformly (and implemented just by reusing
3159 the dictionary for the representation type), <emphasis>except</emphasis>
3160 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3161 the newtype and its representation.
3165 <sect3> <title> A more precise specification </title>
3167 Derived instance declarations are constructed as follows. Consider the
3168 declaration (after expansion of any type synonyms)
3171 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3177 The <literal>ci</literal> are partial applications of
3178 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3179 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3182 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3185 The type <literal>t</literal> is an arbitrary type.
3188 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3189 nor in the <literal>ci</literal>, and
3192 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3193 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3194 should not "look through" the type or its constructor. You can still
3195 derive these classes for a newtype, but it happens in the usual way, not
3196 via this new mechanism.
3199 Then, for each <literal>ci</literal>, the derived instance
3202 instance ci t => ci (T v1...vk)
3204 As an example which does <emphasis>not</emphasis> work, consider
3206 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3208 Here we cannot derive the instance
3210 instance Monad (State s m) => Monad (NonMonad m)
3213 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3214 and so cannot be "eta-converted" away. It is a good thing that this
3215 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3216 not, in fact, a monad --- for the same reason. Try defining
3217 <literal>>>=</literal> with the correct type: you won't be able to.
3221 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3222 important, since we can only derive instances for the last one. If the
3223 <literal>StateMonad</literal> class above were instead defined as
3226 class StateMonad m s | m -> s where ...
3229 then we would not have been able to derive an instance for the
3230 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3231 classes usually have one "main" parameter for which deriving new
3232 instances is most interesting.
3234 <para>Lastly, all of this applies only for classes other than
3235 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3236 and <literal>Data</literal>, for which the built-in derivation applies (section
3237 4.3.3. of the Haskell Report).
3238 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3239 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3240 the standard method is used or the one described here.)
3247 <!-- TYPE SYSTEM EXTENSIONS -->
3248 <sect1 id="type-class-extensions">
3249 <title>Class and instances declarations</title>
3251 <sect2 id="multi-param-type-classes">
3252 <title>Class declarations</title>
3255 This section, and the next one, documents GHC's type-class extensions.
3256 There's lots of background in the paper <ulink
3257 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3258 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3259 Jones, Erik Meijer).
3262 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3266 <title>Multi-parameter type classes</title>
3268 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3273 class Collection c a where
3274 union :: c a -> c a -> c a
3281 <sect3 id="superclass-rules">
3282 <title>The superclasses of a class declaration</title>
3285 In Haskell 98 the context of a class declaration (which introduces superclasses)
3286 must be simple; that is, each predicate must consist of a class applied to
3287 type variables. The flag <option>-XFlexibleContexts</option>
3288 (<xref linkend="flexible-contexts"/>)
3289 lifts this restriction,
3290 so that the only restriction on the context in a class declaration is
3291 that the class hierarchy must be acyclic. So these class declarations are OK:
3295 class Functor (m k) => FiniteMap m k where
3298 class (Monad m, Monad (t m)) => Transform t m where
3299 lift :: m a -> (t m) a
3305 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3306 of "acyclic" involves only the superclass relationships. For example,
3312 op :: D b => a -> b -> b
3315 class C a => D a where { ... }
3319 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3320 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3321 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3328 <sect3 id="class-method-types">
3329 <title>Class method types</title>
3332 Haskell 98 prohibits class method types to mention constraints on the
3333 class type variable, thus:
3336 fromList :: [a] -> s a
3337 elem :: Eq a => a -> s a -> Bool
3339 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3340 contains the constraint <literal>Eq a</literal>, constrains only the
3341 class type variable (in this case <literal>a</literal>).
3342 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3349 <sect2 id="functional-dependencies">
3350 <title>Functional dependencies
3353 <para> Functional dependencies are implemented as described by Mark Jones
3354 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3355 In Proceedings of the 9th European Symposium on Programming,
3356 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3360 Functional dependencies are introduced by a vertical bar in the syntax of a
3361 class declaration; e.g.
3363 class (Monad m) => MonadState s m | m -> s where ...
3365 class Foo a b c | a b -> c where ...
3367 There should be more documentation, but there isn't (yet). Yell if you need it.
3370 <sect3><title>Rules for functional dependencies </title>
3372 In a class declaration, all of the class type variables must be reachable (in the sense
3373 mentioned in <xref linkend="flexible-contexts"/>)
3374 from the free variables of each method type.
3378 class Coll s a where
3380 insert :: s -> a -> s
3383 is not OK, because the type of <literal>empty</literal> doesn't mention
3384 <literal>a</literal>. Functional dependencies can make the type variable
3387 class Coll s a | s -> a where
3389 insert :: s -> a -> s
3392 Alternatively <literal>Coll</literal> might be rewritten
3395 class Coll s a where
3397 insert :: s a -> a -> s a
3401 which makes the connection between the type of a collection of
3402 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3403 Occasionally this really doesn't work, in which case you can split the
3411 class CollE s => Coll s a where
3412 insert :: s -> a -> s
3419 <title>Background on functional dependencies</title>
3421 <para>The following description of the motivation and use of functional dependencies is taken
3422 from the Hugs user manual, reproduced here (with minor changes) by kind
3423 permission of Mark Jones.
3426 Consider the following class, intended as part of a
3427 library for collection types:
3429 class Collects e ce where
3431 insert :: e -> ce -> ce
3432 member :: e -> ce -> Bool
3434 The type variable e used here represents the element type, while ce is the type
3435 of the container itself. Within this framework, we might want to define
3436 instances of this class for lists or characteristic functions (both of which
3437 can be used to represent collections of any equality type), bit sets (which can
3438 be used to represent collections of characters), or hash tables (which can be
3439 used to represent any collection whose elements have a hash function). Omitting
3440 standard implementation details, this would lead to the following declarations:
3442 instance Eq e => Collects e [e] where ...
3443 instance Eq e => Collects e (e -> Bool) where ...
3444 instance Collects Char BitSet where ...
3445 instance (Hashable e, Collects a ce)
3446 => Collects e (Array Int ce) where ...
3448 All this looks quite promising; we have a class and a range of interesting
3449 implementations. Unfortunately, there are some serious problems with the class
3450 declaration. First, the empty function has an ambiguous type:
3452 empty :: Collects e ce => ce
3454 By "ambiguous" we mean that there is a type variable e that appears on the left
3455 of the <literal>=></literal> symbol, but not on the right. The problem with
3456 this is that, according to the theoretical foundations of Haskell overloading,
3457 we cannot guarantee a well-defined semantics for any term with an ambiguous
3461 We can sidestep this specific problem by removing the empty member from the
3462 class declaration. However, although the remaining members, insert and member,
3463 do not have ambiguous types, we still run into problems when we try to use
3464 them. For example, consider the following two functions:
3466 f x y = insert x . insert y
3469 for which GHC infers the following types:
3471 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3472 g :: (Collects Bool c, Collects Char c) => c -> c
3474 Notice that the type for f allows the two parameters x and y to be assigned
3475 different types, even though it attempts to insert each of the two values, one
3476 after the other, into the same collection. If we're trying to model collections
3477 that contain only one type of value, then this is clearly an inaccurate
3478 type. Worse still, the definition for g is accepted, without causing a type
3479 error. As a result, the error in this code will not be flagged at the point
3480 where it appears. Instead, it will show up only when we try to use g, which
3481 might even be in a different module.
3484 <sect4><title>An attempt to use constructor classes</title>
3487 Faced with the problems described above, some Haskell programmers might be
3488 tempted to use something like the following version of the class declaration:
3490 class Collects e c where
3492 insert :: e -> c e -> c e
3493 member :: e -> c e -> Bool
3495 The key difference here is that we abstract over the type constructor c that is
3496 used to form the collection type c e, and not over that collection type itself,
3497 represented by ce in the original class declaration. This avoids the immediate
3498 problems that we mentioned above: empty has type <literal>Collects e c => c
3499 e</literal>, which is not ambiguous.
3502 The function f from the previous section has a more accurate type:
3504 f :: (Collects e c) => e -> e -> c e -> c e
3506 The function g from the previous section is now rejected with a type error as
3507 we would hope because the type of f does not allow the two arguments to have
3509 This, then, is an example of a multiple parameter class that does actually work
3510 quite well in practice, without ambiguity problems.
3511 There is, however, a catch. This version of the Collects class is nowhere near
3512 as general as the original class seemed to be: only one of the four instances
3513 for <literal>Collects</literal>
3514 given above can be used with this version of Collects because only one of
3515 them---the instance for lists---has a collection type that can be written in
3516 the form c e, for some type constructor c, and element type e.
3520 <sect4><title>Adding functional dependencies</title>
3523 To get a more useful version of the Collects class, Hugs provides a mechanism
3524 that allows programmers to specify dependencies between the parameters of a
3525 multiple parameter class (For readers with an interest in theoretical
3526 foundations and previous work: The use of dependency information can be seen
3527 both as a generalization of the proposal for `parametric type classes' that was
3528 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3529 later framework for "improvement" of qualified types. The
3530 underlying ideas are also discussed in a more theoretical and abstract setting
3531 in a manuscript [implparam], where they are identified as one point in a
3532 general design space for systems of implicit parameterization.).
3534 To start with an abstract example, consider a declaration such as:
3536 class C a b where ...
3538 which tells us simply that C can be thought of as a binary relation on types
3539 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3540 included in the definition of classes to add information about dependencies
3541 between parameters, as in the following examples:
3543 class D a b | a -> b where ...
3544 class E a b | a -> b, b -> a where ...
3546 The notation <literal>a -> b</literal> used here between the | and where
3547 symbols --- not to be
3548 confused with a function type --- indicates that the a parameter uniquely
3549 determines the b parameter, and might be read as "a determines b." Thus D is
3550 not just a relation, but actually a (partial) function. Similarly, from the two
3551 dependencies that are included in the definition of E, we can see that E
3552 represents a (partial) one-one mapping between types.
3555 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3556 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3557 m>=0, meaning that the y parameters are uniquely determined by the x
3558 parameters. Spaces can be used as separators if more than one variable appears
3559 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3560 annotated with multiple dependencies using commas as separators, as in the
3561 definition of E above. Some dependencies that we can write in this notation are
3562 redundant, and will be rejected because they don't serve any useful
3563 purpose, and may instead indicate an error in the program. Examples of
3564 dependencies like this include <literal>a -> a </literal>,
3565 <literal>a -> a a </literal>,
3566 <literal>a -> </literal>, etc. There can also be
3567 some redundancy if multiple dependencies are given, as in
3568 <literal>a->b</literal>,
3569 <literal>b->c </literal>, <literal>a->c </literal>, and
3570 in which some subset implies the remaining dependencies. Examples like this are
3571 not treated as errors. Note that dependencies appear only in class
3572 declarations, and not in any other part of the language. In particular, the
3573 syntax for instance declarations, class constraints, and types is completely
3577 By including dependencies in a class declaration, we provide a mechanism for
3578 the programmer to specify each multiple parameter class more precisely. The
3579 compiler, on the other hand, is responsible for ensuring that the set of
3580 instances that are in scope at any given point in the program is consistent
3581 with any declared dependencies. For example, the following pair of instance
3582 declarations cannot appear together in the same scope because they violate the
3583 dependency for D, even though either one on its own would be acceptable:
3585 instance D Bool Int where ...
3586 instance D Bool Char where ...
3588 Note also that the following declaration is not allowed, even by itself:
3590 instance D [a] b where ...
3592 The problem here is that this instance would allow one particular choice of [a]
3593 to be associated with more than one choice for b, which contradicts the
3594 dependency specified in the definition of D. More generally, this means that,
3595 in any instance of the form:
3597 instance D t s where ...
3599 for some particular types t and s, the only variables that can appear in s are
3600 the ones that appear in t, and hence, if the type t is known, then s will be
3601 uniquely determined.
3604 The benefit of including dependency information is that it allows us to define
3605 more general multiple parameter classes, without ambiguity problems, and with
3606 the benefit of more accurate types. To illustrate this, we return to the
3607 collection class example, and annotate the original definition of <literal>Collects</literal>
3608 with a simple dependency:
3610 class Collects e ce | ce -> e where
3612 insert :: e -> ce -> ce
3613 member :: e -> ce -> Bool
3615 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3616 determined by the type of the collection ce. Note that both parameters of
3617 Collects are of kind *; there are no constructor classes here. Note too that
3618 all of the instances of Collects that we gave earlier can be used
3619 together with this new definition.
3622 What about the ambiguity problems that we encountered with the original
3623 definition? The empty function still has type Collects e ce => ce, but it is no
3624 longer necessary to regard that as an ambiguous type: Although the variable e
3625 does not appear on the right of the => symbol, the dependency for class
3626 Collects tells us that it is uniquely determined by ce, which does appear on
3627 the right of the => symbol. Hence the context in which empty is used can still
3628 give enough information to determine types for both ce and e, without
3629 ambiguity. More generally, we need only regard a type as ambiguous if it
3630 contains a variable on the left of the => that is not uniquely determined
3631 (either directly or indirectly) by the variables on the right.
3634 Dependencies also help to produce more accurate types for user defined
3635 functions, and hence to provide earlier detection of errors, and less cluttered
3636 types for programmers to work with. Recall the previous definition for a
3639 f x y = insert x y = insert x . insert y
3641 for which we originally obtained a type:
3643 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3645 Given the dependency information that we have for Collects, however, we can
3646 deduce that a and b must be equal because they both appear as the second
3647 parameter in a Collects constraint with the same first parameter c. Hence we
3648 can infer a shorter and more accurate type for f:
3650 f :: (Collects a c) => a -> a -> c -> c
3652 In a similar way, the earlier definition of g will now be flagged as a type error.
3655 Although we have given only a few examples here, it should be clear that the
3656 addition of dependency information can help to make multiple parameter classes
3657 more useful in practice, avoiding ambiguity problems, and allowing more general
3658 sets of instance declarations.
3664 <sect2 id="instance-decls">
3665 <title>Instance declarations</title>
3667 <para>An instance declaration has the form
3669 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 ...
3671 The part before the "<literal>=></literal>" is the
3672 <emphasis>context</emphasis>, while the part after the
3673 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3676 <sect3 id="flexible-instance-head">
3677 <title>Relaxed rules for the instance head</title>
3680 In Haskell 98 the head of an instance declaration
3681 must be of the form <literal>C (T a1 ... an)</literal>, where
3682 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3683 and the <literal>a1 ... an</literal> are distinct type variables.
3684 GHC relaxes these rules in two ways.
3688 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3689 declaration to mention arbitrary nested types.
3690 For example, this becomes a legal instance declaration
3692 instance C (Maybe Int) where ...
3694 See also the <link linkend="instance-overlap">rules on overlap</link>.
3697 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3698 synonyms. As always, using a type synonym is just shorthand for
3699 writing the RHS of the type synonym definition. For example:
3703 type Point = (Int,Int)
3704 instance C Point where ...
3705 instance C [Point] where ...
3709 is legal. However, if you added
3713 instance C (Int,Int) where ...
3717 as well, then the compiler will complain about the overlapping
3718 (actually, identical) instance declarations. As always, type synonyms
3719 must be fully applied. You cannot, for example, write:
3723 instance Monad P where ...
3731 <sect3 id="instance-rules">
3732 <title>Relaxed rules for instance contexts</title>
3734 <para>In Haskell 98, the assertions in the context of the instance declaration
3735 must be of the form <literal>C a</literal> where <literal>a</literal>
3736 is a type variable that occurs in the head.
3740 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3741 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3742 With this flag the context of the instance declaration can each consist of arbitrary
3743 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3747 The Paterson Conditions: for each assertion in the context
3749 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3750 <listitem><para>The assertion has fewer constructors and variables (taken together
3751 and counting repetitions) than the head</para></listitem>
3755 <listitem><para>The Coverage Condition. For each functional dependency,
3756 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3757 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3758 every type variable in
3759 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3760 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3761 substitution mapping each type variable in the class declaration to the
3762 corresponding type in the instance declaration.
3765 These restrictions ensure that context reduction terminates: each reduction
3766 step makes the problem smaller by at least one
3767 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3768 if you give the <option>-XUndecidableInstances</option>
3769 flag (<xref linkend="undecidable-instances"/>).
3770 You can find lots of background material about the reason for these
3771 restrictions in the paper <ulink
3772 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3773 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3776 For example, these are OK:
3778 instance C Int [a] -- Multiple parameters
3779 instance Eq (S [a]) -- Structured type in head
3781 -- Repeated type variable in head
3782 instance C4 a a => C4 [a] [a]
3783 instance Stateful (ST s) (MutVar s)
3785 -- Head can consist of type variables only
3787 instance (Eq a, Show b) => C2 a b
3789 -- Non-type variables in context
3790 instance Show (s a) => Show (Sized s a)
3791 instance C2 Int a => C3 Bool [a]
3792 instance C2 Int a => C3 [a] b
3796 -- Context assertion no smaller than head
3797 instance C a => C a where ...
3798 -- (C b b) has more more occurrences of b than the head
3799 instance C b b => Foo [b] where ...
3804 The same restrictions apply to instances generated by
3805 <literal>deriving</literal> clauses. Thus the following is accepted:
3807 data MinHeap h a = H a (h a)
3810 because the derived instance
3812 instance (Show a, Show (h a)) => Show (MinHeap h a)
3814 conforms to the above rules.
3818 A useful idiom permitted by the above rules is as follows.
3819 If one allows overlapping instance declarations then it's quite
3820 convenient to have a "default instance" declaration that applies if
3821 something more specific does not:
3829 <sect3 id="undecidable-instances">
3830 <title>Undecidable instances</title>
3833 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3834 For example, sometimes you might want to use the following to get the
3835 effect of a "class synonym":
3837 class (C1 a, C2 a, C3 a) => C a where { }
3839 instance (C1 a, C2 a, C3 a) => C a where { }
3841 This allows you to write shorter signatures:
3847 f :: (C1 a, C2 a, C3 a) => ...
3849 The restrictions on functional dependencies (<xref
3850 linkend="functional-dependencies"/>) are particularly troublesome.
3851 It is tempting to introduce type variables in the context that do not appear in
3852 the head, something that is excluded by the normal rules. For example:
3854 class HasConverter a b | a -> b where
3857 data Foo a = MkFoo a
3859 instance (HasConverter a b,Show b) => Show (Foo a) where
3860 show (MkFoo value) = show (convert value)
3862 This is dangerous territory, however. Here, for example, is a program that would make the
3867 instance F [a] [[a]]
3868 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3870 Similarly, it can be tempting to lift the coverage condition:
3872 class Mul a b c | a b -> c where
3873 (.*.) :: a -> b -> c
3875 instance Mul Int Int Int where (.*.) = (*)
3876 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3877 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3879 The third instance declaration does not obey the coverage condition;
3880 and indeed the (somewhat strange) definition:
3882 f = \ b x y -> if b then x .*. [y] else y
3884 makes instance inference go into a loop, because it requires the constraint
3885 <literal>(Mul a [b] b)</literal>.
3888 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3889 the experimental flag <option>-XUndecidableInstances</option>
3890 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3891 both the Paterson Conditions and the Coverage Condition
3892 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3893 fixed-depth recursion stack. If you exceed the stack depth you get a
3894 sort of backtrace, and the opportunity to increase the stack depth
3895 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3901 <sect3 id="instance-overlap">
3902 <title>Overlapping instances</title>
3904 In general, <emphasis>GHC requires that that it be unambiguous which instance
3906 should be used to resolve a type-class constraint</emphasis>. This behaviour
3907 can be modified by two flags: <option>-XOverlappingInstances</option>
3908 <indexterm><primary>-XOverlappingInstances
3909 </primary></indexterm>
3910 and <option>-XIncoherentInstances</option>
3911 <indexterm><primary>-XIncoherentInstances
3912 </primary></indexterm>, as this section discusses. Both these
3913 flags are dynamic flags, and can be set on a per-module basis, using
3914 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3916 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3917 it tries to match every instance declaration against the
3919 by instantiating the head of the instance declaration. For example, consider
3922 instance context1 => C Int a where ... -- (A)
3923 instance context2 => C a Bool where ... -- (B)
3924 instance context3 => C Int [a] where ... -- (C)
3925 instance context4 => C Int [Int] where ... -- (D)
3927 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3928 but (C) and (D) do not. When matching, GHC takes
3929 no account of the context of the instance declaration
3930 (<literal>context1</literal> etc).
3931 GHC's default behaviour is that <emphasis>exactly one instance must match the
3932 constraint it is trying to resolve</emphasis>.
3933 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3934 including both declarations (A) and (B), say); an error is only reported if a
3935 particular constraint matches more than one.
3939 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3940 more than one instance to match, provided there is a most specific one. For
3941 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3942 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3943 most-specific match, the program is rejected.
3946 However, GHC is conservative about committing to an overlapping instance. For example:
3951 Suppose that from the RHS of <literal>f</literal> we get the constraint
3952 <literal>C Int [b]</literal>. But
3953 GHC does not commit to instance (C), because in a particular
3954 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3955 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3956 So GHC rejects the program.
3957 (If you add the flag <option>-XIncoherentInstances</option>,
3958 GHC will instead pick (C), without complaining about
3959 the problem of subsequent instantiations.)
3962 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3963 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3964 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3965 it instead. In this case, GHC will refrain from
3966 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3967 as before) but, rather than rejecting the program, it will infer the type
3969 f :: C Int [b] => [b] -> [b]
3971 That postpones the question of which instance to pick to the
3972 call site for <literal>f</literal>
3973 by which time more is known about the type <literal>b</literal>.
3974 You can write this type signature yourself if you use the
3975 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3979 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3983 instance Foo [b] where
3986 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3987 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3988 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3989 declaration. The solution is to postpone the choice by adding the constraint to the context
3990 of the instance declaration, thus:
3992 instance C Int [b] => Foo [b] where
3995 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3998 Warning: overlapping instances must be used with care. They
3999 can give rise to incoherence (ie different instance choices are made
4000 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
4002 {-# LANGUAGE OverlappingInstances #-}
4005 class MyShow a where
4006 myshow :: a -> String
4008 instance MyShow a => MyShow [a] where
4009 myshow xs = concatMap myshow xs
4011 showHelp :: MyShow a => [a] -> String
4012 showHelp xs = myshow xs
4014 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
4020 instance MyShow T where
4021 myshow x = "Used generic instance"
4023 instance MyShow [T] where
4024 myshow xs = "Used more specific instance"
4026 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
4028 In function <literal>showHelp</literal> GHC sees no overlapping
4029 instances, and so uses the <literal>MyShow [a]</literal> instance
4030 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
4031 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
4032 instance declaration in module <literal>Main</literal>. As a result,
4035 "Used more specific instance"
4036 "Used generic instance"
4038 (An alternative possible behaviour, not currently implemented,
4039 would be to reject module <literal>Help</literal>
4040 on the grounds that a later instance declaration might overlap the local one.)
4043 The willingness to be overlapped or incoherent is a property of
4044 the <emphasis>instance declaration</emphasis> itself, controlled by the
4045 presence or otherwise of the <option>-XOverlappingInstances</option>
4046 and <option>-XIncoherentInstances</option> flags when that module is
4047 being defined. Neither flag is required in a module that imports and uses the
4048 instance declaration. Specifically, during the lookup process:
4051 An instance declaration is ignored during the lookup process if (a) a more specific
4052 match is found, and (b) the instance declaration was compiled with
4053 <option>-XOverlappingInstances</option>. The flag setting for the
4054 more-specific instance does not matter.
4057 Suppose an instance declaration does not match the constraint being looked up, but
4058 does unify with it, so that it might match when the constraint is further
4059 instantiated. Usually GHC will regard this as a reason for not committing to
4060 some other constraint. But if the instance declaration was compiled with
4061 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4062 check for that declaration.
4065 These rules make it possible for a library author to design a library that relies on
4066 overlapping instances without the library client having to know.
4069 If an instance declaration is compiled without
4070 <option>-XOverlappingInstances</option>,
4071 then that instance can never be overlapped. This could perhaps be
4072 inconvenient. Perhaps the rule should instead say that the
4073 <emphasis>overlapping</emphasis> instance declaration should be compiled in
4074 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
4075 at a usage site should be permitted regardless of how the instance declarations
4076 are compiled, if the <option>-XOverlappingInstances</option> flag is
4077 used at the usage site. (Mind you, the exact usage site can occasionally be
4078 hard to pin down.) We are interested to receive feedback on these points.
4080 <para>The <option>-XIncoherentInstances</option> flag implies the
4081 <option>-XOverlappingInstances</option> flag, but not vice versa.
4089 <sect2 id="overloaded-strings">
4090 <title>Overloaded string literals
4094 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4095 string literal has type <literal>String</literal>, but with overloaded string
4096 literals enabled (with <literal>-XOverloadedStrings</literal>)
4097 a string literal has type <literal>(IsString a) => a</literal>.
4100 This means that the usual string syntax can be used, e.g., for packed strings
4101 and other variations of string like types. String literals behave very much
4102 like integer literals, i.e., they can be used in both expressions and patterns.
4103 If used in a pattern the literal with be replaced by an equality test, in the same
4104 way as an integer literal is.
4107 The class <literal>IsString</literal> is defined as:
4109 class IsString a where
4110 fromString :: String -> a
4112 The only predefined instance is the obvious one to make strings work as usual:
4114 instance IsString [Char] where
4117 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4118 it explicitly (for example, to give an instance declaration for it), you can import it
4119 from module <literal>GHC.Exts</literal>.
4122 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4126 Each type in a default declaration must be an
4127 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4131 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4132 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4133 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4134 <emphasis>or</emphasis> <literal>IsString</literal>.
4143 import GHC.Exts( IsString(..) )
4145 newtype MyString = MyString String deriving (Eq, Show)
4146 instance IsString MyString where
4147 fromString = MyString
4149 greet :: MyString -> MyString
4150 greet "hello" = "world"
4154 print $ greet "hello"
4155 print $ greet "fool"
4159 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4160 to work since it gets translated into an equality comparison.
4166 <sect1 id="type-families">
4167 <title>Type families</title>
4170 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4171 facilitate type-level
4172 programming. Type families are a generalisation of <firstterm>associated
4173 data types</firstterm>
4174 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4175 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4176 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4177 Symposium on Principles of Programming Languages (POPL'05)”, pages
4178 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4179 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4180 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4182 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4183 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4184 themselves are described in the paper “<ulink
4185 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4186 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4188 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4189 13th ACM SIGPLAN International Conference on Functional
4190 Programming”, ACM Press, pages 51-62, 2008. Type families
4191 essentially provide type-indexed data types and named functions on types,
4192 which are useful for generic programming and highly parameterised library
4193 interfaces as well as interfaces with enhanced static information, much like
4194 dependent types. They might also be regarded as an alternative to functional
4195 dependencies, but provide a more functional style of type-level programming
4196 than the relational style of functional dependencies.
4199 Indexed type families, or type families for short, are type constructors that
4200 represent sets of types. Set members are denoted by supplying the type family
4201 constructor with type parameters, which are called <firstterm>type
4202 indices</firstterm>. The
4203 difference between vanilla parametrised type constructors and family
4204 constructors is much like between parametrically polymorphic functions and
4205 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4206 behave the same at all type instances, whereas class methods can change their
4207 behaviour in dependence on the class type parameters. Similarly, vanilla type
4208 constructors imply the same data representation for all type instances, but
4209 family constructors can have varying representation types for varying type
4213 Indexed type families come in two flavours: <firstterm>data
4214 families</firstterm> and <firstterm>type synonym
4215 families</firstterm>. They are the indexed family variants of algebraic
4216 data types and type synonyms, respectively. The instances of data families
4217 can be data types and newtypes.
4220 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4221 Additional information on the use of type families in GHC is available on
4222 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4223 Haskell wiki page on type families</ulink>.
4226 <sect2 id="data-families">
4227 <title>Data families</title>
4230 Data families appear in two flavours: (1) they can be defined on the
4232 or (2) they can appear inside type classes (in which case they are known as
4233 associated types). The former is the more general variant, as it lacks the
4234 requirement for the type-indexes to coincide with the class
4235 parameters. However, the latter can lead to more clearly structured code and
4236 compiler warnings if some type instances were - possibly accidentally -
4237 omitted. In the following, we always discuss the general toplevel form first
4238 and then cover the additional constraints placed on associated types.
4241 <sect3 id="data-family-declarations">
4242 <title>Data family declarations</title>
4245 Indexed data families are introduced by a signature, such as
4247 data family GMap k :: * -> *
4249 The special <literal>family</literal> distinguishes family from standard
4250 data declarations. The result kind annotation is optional and, as
4251 usual, defaults to <literal>*</literal> if omitted. An example is
4255 Named arguments can also be given explicit kind signatures if needed.
4257 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4258 declarations] named arguments are entirely optional, so that we can
4259 declare <literal>Array</literal> alternatively with
4261 data family Array :: * -> *
4265 <sect4 id="assoc-data-family-decl">
4266 <title>Associated data family declarations</title>
4268 When a data family is declared as part of a type class, we drop
4269 the <literal>family</literal> special. The <literal>GMap</literal>
4270 declaration takes the following form
4272 class GMapKey k where
4273 data GMap k :: * -> *
4276 In contrast to toplevel declarations, named arguments must be used for
4277 all type parameters that are to be used as type-indexes. Moreover,
4278 the argument names must be class parameters. Each class parameter may
4279 only be used at most once per associated type, but some may be omitted
4280 and they may be in an order other than in the class head. Hence, the
4281 following contrived example is admissible:
4290 <sect3 id="data-instance-declarations">
4291 <title>Data instance declarations</title>
4294 Instance declarations of data and newtype families are very similar to
4295 standard data and newtype declarations. The only two differences are
4296 that the keyword <literal>data</literal> or <literal>newtype</literal>
4297 is followed by <literal>instance</literal> and that some or all of the
4298 type arguments can be non-variable types, but may not contain forall
4299 types or type synonym families. However, data families are generally
4300 allowed in type parameters, and type synonyms are allowed as long as
4301 they are fully applied and expand to a type that is itself admissible -
4302 exactly as this is required for occurrences of type synonyms in class
4303 instance parameters. For example, the <literal>Either</literal>
4304 instance for <literal>GMap</literal> is
4306 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4308 In this example, the declaration has only one variant. In general, it
4312 Data and newtype instance declarations are only permitted when an
4313 appropriate family declaration is in scope - just as a class instance declaratoin
4314 requires the class declaration to be visible. Moreover, each instance
4315 declaration has to conform to the kind determined by its family
4316 declaration. This implies that the number of parameters of an instance
4317 declaration matches the arity determined by the kind of the family.
4320 A data family instance declaration can use the full exprssiveness of
4321 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4323 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4324 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4325 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4328 data instance T Int = T1 Int | T2 Bool
4329 newtype instance T Char = TC Bool
4332 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4333 and indeed can define a GADT. For example:
4336 data instance G [a] b where
4337 G1 :: c -> G [Int] b
4341 <listitem><para> You can use a <literal>deriving</literal> clause on a
4342 <literal>data instance</literal> or <literal>newtype instance</literal>
4349 Even if type families are defined as toplevel declarations, functions
4350 that perform different computations for different family instances may still
4351 need to be defined as methods of type classes. In particular, the
4352 following is not possible:
4355 data instance T Int = A
4356 data instance T Char = B
4358 foo A = 1 -- WRONG: These two equations together...
4359 foo B = 2 -- ...will produce a type error.
4361 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4365 instance Foo Int where
4367 instance Foo Char where
4370 (Given the functionality provided by GADTs (Generalised Algebraic Data
4371 Types), it might seem as if a definition, such as the above, should be
4372 feasible. However, type families are - in contrast to GADTs - are
4373 <emphasis>open;</emphasis> i.e., new instances can always be added,
4375 modules. Supporting pattern matching across different data instances
4376 would require a form of extensible case construct.)
4379 <sect4 id="assoc-data-inst">
4380 <title>Associated data instances</title>
4382 When an associated data family instance is declared within a type
4383 class instance, we drop the <literal>instance</literal> keyword in the
4384 family instance. So, the <literal>Either</literal> instance
4385 for <literal>GMap</literal> becomes:
4387 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4388 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4391 The most important point about associated family instances is that the
4392 type indexes corresponding to class parameters must be identical to
4393 the type given in the instance head; here this is the first argument
4394 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4395 which coincides with the only class parameter. Any parameters to the
4396 family constructor that do not correspond to class parameters, need to
4397 be variables in every instance; here this is the
4398 variable <literal>v</literal>.
4401 Instances for an associated family can only appear as part of
4402 instances declarations of the class in which the family was declared -
4403 just as with the equations of the methods of a class. Also in
4404 correspondence to how methods are handled, declarations of associated
4405 types can be omitted in class instances. If an associated family
4406 instance is omitted, the corresponding instance type is not inhabited;
4407 i.e., only diverging expressions, such
4408 as <literal>undefined</literal>, can assume the type.
4412 <sect4 id="scoping-class-params">
4413 <title>Scoping of class parameters</title>
4415 In the case of multi-parameter type classes, the visibility of class
4416 parameters in the right-hand side of associated family instances
4417 depends <emphasis>solely</emphasis> on the parameters of the data
4418 family. As an example, consider the simple class declaration
4423 Only one of the two class parameters is a parameter to the data
4424 family. Hence, the following instance declaration is invalid:
4426 instance C [c] d where
4427 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4429 Here, the right-hand side of the data instance mentions the type
4430 variable <literal>d</literal> that does not occur in its left-hand
4431 side. We cannot admit such data instances as they would compromise
4436 <sect4 id="family-class-inst">
4437 <title>Type class instances of family instances</title>
4439 Type class instances of instances of data families can be defined as
4440 usual, and in particular data instance declarations can
4441 have <literal>deriving</literal> clauses. For example, we can write
4443 data GMap () v = GMapUnit (Maybe v)
4446 which implicitly defines an instance of the form
4448 instance Show v => Show (GMap () v) where ...
4452 Note that class instances are always for
4453 particular <emphasis>instances</emphasis> of a data family and never
4454 for an entire family as a whole. This is for essentially the same
4455 reasons that we cannot define a toplevel function that performs
4456 pattern matching on the data constructors
4457 of <emphasis>different</emphasis> instances of a single type family.
4458 It would require a form of extensible case construct.
4462 <sect4 id="data-family-overlap">
4463 <title>Overlap of data instances</title>
4465 The instance declarations of a data family used in a single program
4466 may not overlap at all, independent of whether they are associated or
4467 not. In contrast to type class instances, this is not only a matter
4468 of consistency, but one of type safety.
4474 <sect3 id="data-family-import-export">
4475 <title>Import and export</title>
4478 The association of data constructors with type families is more dynamic
4479 than that is the case with standard data and newtype declarations. In
4480 the standard case, the notation <literal>T(..)</literal> in an import or
4481 export list denotes the type constructor and all the data constructors
4482 introduced in its declaration. However, a family declaration never
4483 introduces any data constructors; instead, data constructors are
4484 introduced by family instances. As a result, which data constructors
4485 are associated with a type family depends on the currently visible
4486 instance declarations for that family. Consequently, an import or
4487 export item of the form <literal>T(..)</literal> denotes the family
4488 constructor and all currently visible data constructors - in the case of
4489 an export item, these may be either imported or defined in the current
4490 module. The treatment of import and export items that explicitly list
4491 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4495 <sect4 id="data-family-impexp-assoc">
4496 <title>Associated families</title>
4498 As expected, an import or export item of the
4499 form <literal>C(..)</literal> denotes all of the class' methods and
4500 associated types. However, when associated types are explicitly
4501 listed as subitems of a class, we need some new syntax, as uppercase
4502 identifiers as subitems are usually data constructors, not type
4503 constructors. To clarify that we denote types here, each associated
4504 type name needs to be prefixed by the keyword <literal>type</literal>.
4505 So for example, when explicitly listing the components of
4506 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4507 GMap, empty, lookup, insert)</literal>.
4511 <sect4 id="data-family-impexp-examples">
4512 <title>Examples</title>
4514 Assuming our running <literal>GMapKey</literal> class example, let us
4515 look at some export lists and their meaning:
4518 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4519 just the class name.</para>
4522 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4523 Exports the class, the associated type <literal>GMap</literal>
4525 functions <literal>empty</literal>, <literal>lookup</literal>,
4526 and <literal>insert</literal>. None of the data constructors is
4530 <para><literal>module GMap (GMapKey(..), GMap(..))
4531 where...</literal>: As before, but also exports all the data
4532 constructors <literal>GMapInt</literal>,
4533 <literal>GMapChar</literal>,
4534 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4535 and <literal>GMapUnit</literal>.</para>
4538 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4539 GMap(..)) where...</literal>: As before.</para>
4542 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4543 where...</literal>: As before.</para>
4548 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4549 both the class <literal>GMapKey</literal> as well as its associated
4550 type <literal>GMap</literal>. However, you cannot
4551 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4552 sub-component specifications cannot be nested. To
4553 specify <literal>GMap</literal>'s data constructors, you have to list
4558 <sect4 id="data-family-impexp-instances">
4559 <title>Instances</title>
4561 Family instances are implicitly exported, just like class instances.
4562 However, this applies only to the heads of instances, not to the data
4563 constructors an instance defines.
4571 <sect2 id="synonym-families">
4572 <title>Synonym families</title>
4575 Type families appear in two flavours: (1) they can be defined on the
4576 toplevel or (2) they can appear inside type classes (in which case they
4577 are known as associated type synonyms). The former is the more general
4578 variant, as it lacks the requirement for the type-indexes to coincide with
4579 the class parameters. However, the latter can lead to more clearly
4580 structured code and compiler warnings if some type instances were -
4581 possibly accidentally - omitted. In the following, we always discuss the
4582 general toplevel form first and then cover the additional constraints
4583 placed on associated types.
4586 <sect3 id="type-family-declarations">
4587 <title>Type family declarations</title>
4590 Indexed type families are introduced by a signature, such as
4592 type family Elem c :: *
4594 The special <literal>family</literal> distinguishes family from standard
4595 type declarations. The result kind annotation is optional and, as
4596 usual, defaults to <literal>*</literal> if omitted. An example is
4600 Parameters can also be given explicit kind signatures if needed. We
4601 call the number of parameters in a type family declaration, the family's
4602 arity, and all applications of a type family must be fully saturated
4603 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4604 and it implies that the kind of a type family is not sufficient to
4605 determine a family's arity, and hence in general, also insufficient to
4606 determine whether a type family application is well formed. As an
4607 example, consider the following declaration:
4609 type family F a b :: * -> * -- F's arity is 2,
4610 -- although its overall kind is * -> * -> * -> *
4612 Given this declaration the following are examples of well-formed and
4615 F Char [Int] -- OK! Kind: * -> *
4616 F Char [Int] Bool -- OK! Kind: *
4617 F IO Bool -- WRONG: kind mismatch in the first argument
4618 F Bool -- WRONG: unsaturated application
4622 <sect4 id="assoc-type-family-decl">
4623 <title>Associated type family declarations</title>
4625 When a type family is declared as part of a type class, we drop
4626 the <literal>family</literal> special. The <literal>Elem</literal>
4627 declaration takes the following form
4629 class Collects ce where
4633 The argument names of the type family must be class parameters. Each
4634 class parameter may only be used at most once per associated type, but
4635 some may be omitted and they may be in an order other than in the
4636 class head. Hence, the following contrived example is admissible:
4641 These rules are exactly as for associated data families.
4646 <sect3 id="type-instance-declarations">
4647 <title>Type instance declarations</title>
4649 Instance declarations of type families are very similar to standard type
4650 synonym declarations. The only two differences are that the
4651 keyword <literal>type</literal> is followed
4652 by <literal>instance</literal> and that some or all of the type
4653 arguments can be non-variable types, but may not contain forall types or
4654 type synonym families. However, data families are generally allowed, and
4655 type synonyms are allowed as long as they are fully applied and expand
4656 to a type that is admissible - these are the exact same requirements as
4657 for data instances. For example, the <literal>[e]</literal> instance
4658 for <literal>Elem</literal> is
4660 type instance Elem [e] = e
4664 Type family instance declarations are only legitimate when an
4665 appropriate family declaration is in scope - just like class instances
4666 require the class declaration to be visible. Moreover, each instance
4667 declaration has to conform to the kind determined by its family
4668 declaration, and the number of type parameters in an instance
4669 declaration must match the number of type parameters in the family
4670 declaration. Finally, the right-hand side of a type instance must be a
4671 monotype (i.e., it may not include foralls) and after the expansion of
4672 all saturated vanilla type synonyms, no synonyms, except family synonyms
4673 may remain. Here are some examples of admissible and illegal type
4676 type family F a :: *
4677 type instance F [Int] = Int -- OK!
4678 type instance F String = Char -- OK!
4679 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4680 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4681 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4683 type family G a b :: * -> *
4684 type instance G Int = (,) -- WRONG: must be two type parameters
4685 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4689 <sect4 id="assoc-type-instance">
4690 <title>Associated type instance declarations</title>
4692 When an associated family instance is declared within a type class
4693 instance, we drop the <literal>instance</literal> keyword in the family
4694 instance. So, the <literal>[e]</literal> instance
4695 for <literal>Elem</literal> becomes:
4697 instance (Eq (Elem [e])) => Collects ([e]) where
4701 The most important point about associated family instances is that the
4702 type indexes corresponding to class parameters must be identical to the
4703 type given in the instance head; here this is <literal>[e]</literal>,
4704 which coincides with the only class parameter.
4707 Instances for an associated family can only appear as part of instances
4708 declarations of the class in which the family was declared - just as
4709 with the equations of the methods of a class. Also in correspondence to
4710 how methods are handled, declarations of associated types can be omitted
4711 in class instances. If an associated family instance is omitted, the
4712 corresponding instance type is not inhabited; i.e., only diverging
4713 expressions, such as <literal>undefined</literal>, can assume the type.
4717 <sect4 id="type-family-overlap">
4718 <title>Overlap of type synonym instances</title>
4720 The instance declarations of a type family used in a single program
4721 may only overlap if the right-hand sides of the overlapping instances
4722 coincide for the overlapping types. More formally, two instance
4723 declarations overlap if there is a substitution that makes the
4724 left-hand sides of the instances syntactically the same. Whenever
4725 that is the case, the right-hand sides of the instances must also be
4726 syntactically equal under the same substitution. This condition is
4727 independent of whether the type family is associated or not, and it is
4728 not only a matter of consistency, but one of type safety.
4731 Here are two example to illustrate the condition under which overlap
4734 type instance F (a, Int) = [a]
4735 type instance F (Int, b) = [b] -- overlap permitted
4737 type instance G (a, Int) = [a]
4738 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4743 <sect4 id="type-family-decidability">
4744 <title>Decidability of type synonym instances</title>
4746 In order to guarantee that type inference in the presence of type
4747 families decidable, we need to place a number of additional
4748 restrictions on the formation of type instance declarations (c.f.,
4749 Definition 5 (Relaxed Conditions) of “<ulink
4750 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4751 Checking with Open Type Functions</ulink>”). Instance
4752 declarations have the general form
4754 type instance F t1 .. tn = t
4756 where we require that for every type family application <literal>(G s1
4757 .. sm)</literal> in <literal>t</literal>,
4760 <para><literal>s1 .. sm</literal> do not contain any type family
4761 constructors,</para>
4764 <para>the total number of symbols (data type constructors and type
4765 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4766 in <literal>t1 .. tn</literal>, and</para>
4769 <para>for every type
4770 variable <literal>a</literal>, <literal>a</literal> occurs
4771 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4772 .. tn</literal>.</para>
4775 These restrictions are easily verified and ensure termination of type
4776 inference. However, they are not sufficient to guarantee completeness
4777 of type inference in the presence of, so called, ''loopy equalities'',
4778 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4779 a type variable is underneath a family application and data
4780 constructor application - see the above mentioned paper for details.
4783 If the option <option>-XUndecidableInstances</option> is passed to the
4784 compiler, the above restrictions are not enforced and it is on the
4785 programmer to ensure termination of the normalisation of type families
4786 during type inference.
4791 <sect3 id-="equality-constraints">
4792 <title>Equality constraints</title>
4794 Type context can include equality constraints of the form <literal>t1 ~
4795 t2</literal>, which denote that the types <literal>t1</literal>
4796 and <literal>t2</literal> need to be the same. In the presence of type
4797 families, whether two types are equal cannot generally be decided
4798 locally. Hence, the contexts of function signatures may include
4799 equality constraints, as in the following example:
4801 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4803 where we require that the element type of <literal>c1</literal>
4804 and <literal>c2</literal> are the same. In general, the
4805 types <literal>t1</literal> and <literal>t2</literal> of an equality
4806 constraint may be arbitrary monotypes; i.e., they may not contain any
4807 quantifiers, independent of whether higher-rank types are otherwise
4811 Equality constraints can also appear in class and instance contexts.
4812 The former enable a simple translation of programs using functional
4813 dependencies into programs using family synonyms instead. The general
4814 idea is to rewrite a class declaration of the form
4816 class C a b | a -> b
4820 class (F a ~ b) => C a b where
4823 That is, we represent every functional dependency (FD) <literal>a1 .. an
4824 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4825 superclass context equality <literal>F a1 .. an ~ b</literal>,
4826 essentially giving a name to the functional dependency. In class
4827 instances, we define the type instances of FD families in accordance
4828 with the class head. Method signatures are not affected by that
4832 NB: Equalities in superclass contexts are not fully implemented in
4837 <sect3 id-="ty-fams-in-instances">
4838 <title>Type families and instance declarations</title>
4839 <para>Type families require us to extend the rules for
4840 the form of instance heads, which are given
4841 in <xref linkend="flexible-instance-head"/>.
4844 <listitem><para>Data type families may appear in an instance head</para></listitem>
4845 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4847 The reason for the latter restriction is that there is no way to check for. Consider
4850 type instance F Bool = Int
4857 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4858 The situation is especially bad because the type instance for <literal>F Bool</literal>
4859 might be in another module, or even in a module that is not yet written.
4866 <sect1 id="other-type-extensions">
4867 <title>Other type system extensions</title>
4869 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4871 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4872 is used, the keyword <literal>forall</literal>
4873 allows us to say exactly what this means. For example:
4881 g :: forall b. (b -> b)
4883 The two are treated identically.
4886 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4887 a type variable any more!
4892 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4894 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4895 that the type-class constraints in a type signature must have the
4896 form <emphasis>(class type-variable)</emphasis> or
4897 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4898 With <option>-XFlexibleContexts</option>
4899 these type signatures are perfectly OK
4902 g :: Ord (T a ()) => ...
4904 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4905 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4906 (<xref linkend="instance-rules"/>).
4910 GHC imposes the following restrictions on the constraints in a type signature.
4914 forall tv1..tvn (c1, ...,cn) => type
4917 (Here, we write the "foralls" explicitly, although the Haskell source
4918 language omits them; in Haskell 98, all the free type variables of an
4919 explicit source-language type signature are universally quantified,
4920 except for the class type variables in a class declaration. However,
4921 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4930 <emphasis>Each universally quantified type variable
4931 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4933 A type variable <literal>a</literal> is "reachable" if it appears
4934 in the same constraint as either a type variable free in
4935 <literal>type</literal>, or another reachable type variable.
4936 A value with a type that does not obey
4937 this reachability restriction cannot be used without introducing
4938 ambiguity; that is why the type is rejected.
4939 Here, for example, is an illegal type:
4943 forall a. Eq a => Int
4947 When a value with this type was used, the constraint <literal>Eq tv</literal>
4948 would be introduced where <literal>tv</literal> is a fresh type variable, and
4949 (in the dictionary-translation implementation) the value would be
4950 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4951 can never know which instance of <literal>Eq</literal> to use because we never
4952 get any more information about <literal>tv</literal>.
4956 that the reachability condition is weaker than saying that <literal>a</literal> is
4957 functionally dependent on a type variable free in
4958 <literal>type</literal> (see <xref
4959 linkend="functional-dependencies"/>). The reason for this is there
4960 might be a "hidden" dependency, in a superclass perhaps. So
4961 "reachable" is a conservative approximation to "functionally dependent".
4962 For example, consider:
4964 class C a b | a -> b where ...
4965 class C a b => D a b where ...
4966 f :: forall a b. D a b => a -> a
4968 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4969 but that is not immediately apparent from <literal>f</literal>'s type.
4975 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4976 universally quantified type variables <literal>tvi</literal></emphasis>.
4978 For example, this type is OK because <literal>C a b</literal> mentions the
4979 universally quantified type variable <literal>b</literal>:
4983 forall a. C a b => burble
4987 The next type is illegal because the constraint <literal>Eq b</literal> does not
4988 mention <literal>a</literal>:
4992 forall a. Eq b => burble
4996 The reason for this restriction is milder than the other one. The
4997 excluded types are never useful or necessary (because the offending
4998 context doesn't need to be witnessed at this point; it can be floated
4999 out). Furthermore, floating them out increases sharing. Lastly,
5000 excluding them is a conservative choice; it leaves a patch of
5001 territory free in case we need it later.
5012 <sect2 id="implicit-parameters">
5013 <title>Implicit parameters</title>
5015 <para> Implicit parameters are implemented as described in
5016 "Implicit parameters: dynamic scoping with static types",
5017 J Lewis, MB Shields, E Meijer, J Launchbury,
5018 27th ACM Symposium on Principles of Programming Languages (POPL'00),
5022 <para>(Most of the following, still rather incomplete, documentation is
5023 due to Jeff Lewis.)</para>
5025 <para>Implicit parameter support is enabled with the option
5026 <option>-XImplicitParams</option>.</para>
5029 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
5030 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
5031 context. In Haskell, all variables are statically bound. Dynamic
5032 binding of variables is a notion that goes back to Lisp, but was later
5033 discarded in more modern incarnations, such as Scheme. Dynamic binding
5034 can be very confusing in an untyped language, and unfortunately, typed
5035 languages, in particular Hindley-Milner typed languages like Haskell,
5036 only support static scoping of variables.
5039 However, by a simple extension to the type class system of Haskell, we
5040 can support dynamic binding. Basically, we express the use of a
5041 dynamically bound variable as a constraint on the type. These
5042 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
5043 function uses a dynamically-bound variable <literal>?x</literal>
5044 of type <literal>t'</literal>". For
5045 example, the following expresses the type of a sort function,
5046 implicitly parameterized by a comparison function named <literal>cmp</literal>.
5048 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5050 The dynamic binding constraints are just a new form of predicate in the type class system.
5053 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5054 where <literal>x</literal> is
5055 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5056 Use of this construct also introduces a new
5057 dynamic-binding constraint in the type of the expression.
5058 For example, the following definition
5059 shows how we can define an implicitly parameterized sort function in
5060 terms of an explicitly parameterized <literal>sortBy</literal> function:
5062 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5064 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5070 <title>Implicit-parameter type constraints</title>
5072 Dynamic binding constraints behave just like other type class
5073 constraints in that they are automatically propagated. Thus, when a
5074 function is used, its implicit parameters are inherited by the
5075 function that called it. For example, our <literal>sort</literal> function might be used
5076 to pick out the least value in a list:
5078 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5079 least xs = head (sort xs)
5081 Without lifting a finger, the <literal>?cmp</literal> parameter is
5082 propagated to become a parameter of <literal>least</literal> as well. With explicit
5083 parameters, the default is that parameters must always be explicit
5084 propagated. With implicit parameters, the default is to always
5088 An implicit-parameter type constraint differs from other type class constraints in the
5089 following way: All uses of a particular implicit parameter must have
5090 the same type. This means that the type of <literal>(?x, ?x)</literal>
5091 is <literal>(?x::a) => (a,a)</literal>, and not
5092 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5096 <para> You can't have an implicit parameter in the context of a class or instance
5097 declaration. For example, both these declarations are illegal:
5099 class (?x::Int) => C a where ...
5100 instance (?x::a) => Foo [a] where ...
5102 Reason: exactly which implicit parameter you pick up depends on exactly where
5103 you invoke a function. But the ``invocation'' of instance declarations is done
5104 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5105 Easiest thing is to outlaw the offending types.</para>
5107 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5109 f :: (?x :: [a]) => Int -> Int
5112 g :: (Read a, Show a) => String -> String
5115 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5116 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5117 quite unambiguous, and fixes the type <literal>a</literal>.
5122 <title>Implicit-parameter bindings</title>
5125 An implicit parameter is <emphasis>bound</emphasis> using the standard
5126 <literal>let</literal> or <literal>where</literal> binding forms.
5127 For example, we define the <literal>min</literal> function by binding
5128 <literal>cmp</literal>.
5131 min = let ?cmp = (<=) in least
5135 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5136 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5137 (including in a list comprehension, or do-notation, or pattern guards),
5138 or a <literal>where</literal> clause.
5139 Note the following points:
5142 An implicit-parameter binding group must be a
5143 collection of simple bindings to implicit-style variables (no
5144 function-style bindings, and no type signatures); these bindings are
5145 neither polymorphic or recursive.
5148 You may not mix implicit-parameter bindings with ordinary bindings in a
5149 single <literal>let</literal>
5150 expression; use two nested <literal>let</literal>s instead.
5151 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5155 You may put multiple implicit-parameter bindings in a
5156 single binding group; but they are <emphasis>not</emphasis> treated
5157 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5158 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5159 parameter. The bindings are not nested, and may be re-ordered without changing
5160 the meaning of the program.
5161 For example, consider:
5163 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5165 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5166 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5168 f :: (?x::Int) => Int -> Int
5176 <sect3><title>Implicit parameters and polymorphic recursion</title>
5179 Consider these two definitions:
5182 len1 xs = let ?acc = 0 in len_acc1 xs
5185 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5190 len2 xs = let ?acc = 0 in len_acc2 xs
5192 len_acc2 :: (?acc :: Int) => [a] -> Int
5194 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5196 The only difference between the two groups is that in the second group
5197 <literal>len_acc</literal> is given a type signature.
5198 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5199 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5200 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5201 has a type signature, the recursive call is made to the
5202 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5203 as an implicit parameter. So we get the following results in GHCi:
5210 Adding a type signature dramatically changes the result! This is a rather
5211 counter-intuitive phenomenon, worth watching out for.
5215 <sect3><title>Implicit parameters and monomorphism</title>
5217 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5218 Haskell Report) to implicit parameters. For example, consider:
5226 Since the binding for <literal>y</literal> falls under the Monomorphism
5227 Restriction it is not generalised, so the type of <literal>y</literal> is
5228 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5229 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5230 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5231 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5232 <literal>y</literal> in the body of the <literal>let</literal> will see the
5233 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5234 <literal>14</literal>.
5239 <!-- ======================= COMMENTED OUT ========================
5241 We intend to remove linear implicit parameters, so I'm at least removing
5242 them from the 6.6 user manual
5244 <sect2 id="linear-implicit-parameters">
5245 <title>Linear implicit parameters</title>
5247 Linear implicit parameters are an idea developed by Koen Claessen,
5248 Mark Shields, and Simon PJ. They address the long-standing
5249 problem that monads seem over-kill for certain sorts of problem, notably:
5252 <listitem> <para> distributing a supply of unique names </para> </listitem>
5253 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5254 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5258 Linear implicit parameters are just like ordinary implicit parameters,
5259 except that they are "linear"; that is, they cannot be copied, and
5260 must be explicitly "split" instead. Linear implicit parameters are
5261 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5262 (The '/' in the '%' suggests the split!)
5267 import GHC.Exts( Splittable )
5269 data NameSupply = ...
5271 splitNS :: NameSupply -> (NameSupply, NameSupply)
5272 newName :: NameSupply -> Name
5274 instance Splittable NameSupply where
5278 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5279 f env (Lam x e) = Lam x' (f env e)
5282 env' = extend env x x'
5283 ...more equations for f...
5285 Notice that the implicit parameter %ns is consumed
5287 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5288 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5292 So the translation done by the type checker makes
5293 the parameter explicit:
5295 f :: NameSupply -> Env -> Expr -> Expr
5296 f ns env (Lam x e) = Lam x' (f ns1 env e)
5298 (ns1,ns2) = splitNS ns
5300 env = extend env x x'
5302 Notice the call to 'split' introduced by the type checker.
5303 How did it know to use 'splitNS'? Because what it really did
5304 was to introduce a call to the overloaded function 'split',
5305 defined by the class <literal>Splittable</literal>:
5307 class Splittable a where
5310 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5311 split for name supplies. But we can simply write
5317 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5319 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5320 <literal>GHC.Exts</literal>.
5325 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5326 are entirely distinct implicit parameters: you
5327 can use them together and they won't interfere with each other. </para>
5330 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5332 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5333 in the context of a class or instance declaration. </para></listitem>
5337 <sect3><title>Warnings</title>
5340 The monomorphism restriction is even more important than usual.
5341 Consider the example above:
5343 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5344 f env (Lam x e) = Lam x' (f env e)
5347 env' = extend env x x'
5349 If we replaced the two occurrences of x' by (newName %ns), which is
5350 usually a harmless thing to do, we get:
5352 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5353 f env (Lam x e) = Lam (newName %ns) (f env e)
5355 env' = extend env x (newName %ns)
5357 But now the name supply is consumed in <emphasis>three</emphasis> places
5358 (the two calls to newName,and the recursive call to f), so
5359 the result is utterly different. Urk! We don't even have
5363 Well, this is an experimental change. With implicit
5364 parameters we have already lost beta reduction anyway, and
5365 (as John Launchbury puts it) we can't sensibly reason about
5366 Haskell programs without knowing their typing.
5371 <sect3><title>Recursive functions</title>
5372 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5375 foo :: %x::T => Int -> [Int]
5377 foo n = %x : foo (n-1)
5379 where T is some type in class Splittable.</para>
5381 Do you get a list of all the same T's or all different T's
5382 (assuming that split gives two distinct T's back)?
5384 If you supply the type signature, taking advantage of polymorphic
5385 recursion, you get what you'd probably expect. Here's the
5386 translated term, where the implicit param is made explicit:
5389 foo x n = let (x1,x2) = split x
5390 in x1 : foo x2 (n-1)
5392 But if you don't supply a type signature, GHC uses the Hindley
5393 Milner trick of using a single monomorphic instance of the function
5394 for the recursive calls. That is what makes Hindley Milner type inference
5395 work. So the translation becomes
5399 foom n = x : foom (n-1)
5403 Result: 'x' is not split, and you get a list of identical T's. So the
5404 semantics of the program depends on whether or not foo has a type signature.
5407 You may say that this is a good reason to dislike linear implicit parameters
5408 and you'd be right. That is why they are an experimental feature.
5414 ================ END OF Linear Implicit Parameters commented out -->
5416 <sect2 id="kinding">
5417 <title>Explicitly-kinded quantification</title>
5420 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5421 to give the kind explicitly as (machine-checked) documentation,
5422 just as it is nice to give a type signature for a function. On some occasions,
5423 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5424 John Hughes had to define the data type:
5426 data Set cxt a = Set [a]
5427 | Unused (cxt a -> ())
5429 The only use for the <literal>Unused</literal> constructor was to force the correct
5430 kind for the type variable <literal>cxt</literal>.
5433 GHC now instead allows you to specify the kind of a type variable directly, wherever
5434 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5437 This flag enables kind signatures in the following places:
5439 <listitem><para><literal>data</literal> declarations:
5441 data Set (cxt :: * -> *) a = Set [a]
5442 </screen></para></listitem>
5443 <listitem><para><literal>type</literal> declarations:
5445 type T (f :: * -> *) = f Int
5446 </screen></para></listitem>
5447 <listitem><para><literal>class</literal> declarations:
5449 class (Eq a) => C (f :: * -> *) a where ...
5450 </screen></para></listitem>
5451 <listitem><para><literal>forall</literal>'s in type signatures:
5453 f :: forall (cxt :: * -> *). Set cxt Int
5454 </screen></para></listitem>
5459 The parentheses are required. Some of the spaces are required too, to
5460 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5461 will get a parse error, because "<literal>::*->*</literal>" is a
5462 single lexeme in Haskell.
5466 As part of the same extension, you can put kind annotations in types
5469 f :: (Int :: *) -> Int
5470 g :: forall a. a -> (a :: *)
5474 atype ::= '(' ctype '::' kind ')
5476 The parentheses are required.
5481 <sect2 id="universal-quantification">
5482 <title>Arbitrary-rank polymorphism
5486 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5487 explicit universal quantification in
5489 For example, all the following types are legal:
5491 f1 :: forall a b. a -> b -> a
5492 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5494 f2 :: (forall a. a->a) -> Int -> Int
5495 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5497 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5499 f4 :: Int -> (forall a. a -> a)
5501 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5502 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5503 The <literal>forall</literal> makes explicit the universal quantification that
5504 is implicitly added by Haskell.
5507 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5508 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5509 shows, the polymorphic type on the left of the function arrow can be overloaded.
5512 The function <literal>f3</literal> has a rank-3 type;
5513 it has rank-2 types on the left of a function arrow.
5516 GHC has three flags to control higher-rank types:
5519 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5522 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5525 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5526 That is, you can nest <literal>forall</literal>s
5527 arbitrarily deep in function arrows.
5528 In particular, a forall-type (also called a "type scheme"),
5529 including an operational type class context, is legal:
5531 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5532 of a function arrow </para> </listitem>
5533 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5534 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5535 field type signatures.</para> </listitem>
5536 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5537 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5549 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5550 the types of the constructor arguments. Here are several examples:
5556 data T a = T1 (forall b. b -> b -> b) a
5558 data MonadT m = MkMonad { return :: forall a. a -> m a,
5559 bind :: forall a b. m a -> (a -> m b) -> m b
5562 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5568 The constructors have rank-2 types:
5574 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5575 MkMonad :: forall m. (forall a. a -> m a)
5576 -> (forall a b. m a -> (a -> m b) -> m b)
5578 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5584 Notice that you don't need to use a <literal>forall</literal> if there's an
5585 explicit context. For example in the first argument of the
5586 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5587 prefixed to the argument type. The implicit <literal>forall</literal>
5588 quantifies all type variables that are not already in scope, and are
5589 mentioned in the type quantified over.
5593 As for type signatures, implicit quantification happens for non-overloaded
5594 types too. So if you write this:
5597 data T a = MkT (Either a b) (b -> b)
5600 it's just as if you had written this:
5603 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5606 That is, since the type variable <literal>b</literal> isn't in scope, it's
5607 implicitly universally quantified. (Arguably, it would be better
5608 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5609 where that is what is wanted. Feedback welcomed.)
5613 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5614 the constructor to suitable values, just as usual. For example,
5625 a3 = MkSwizzle reverse
5628 a4 = let r x = Just x
5635 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5636 mkTs f x y = [T1 f x, T1 f y]
5642 The type of the argument can, as usual, be more general than the type
5643 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5644 does not need the <literal>Ord</literal> constraint.)
5648 When you use pattern matching, the bound variables may now have
5649 polymorphic types. For example:
5655 f :: T a -> a -> (a, Char)
5656 f (T1 w k) x = (w k x, w 'c' 'd')
5658 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5659 g (MkSwizzle s) xs f = s (map f (s xs))
5661 h :: MonadT m -> [m a] -> m [a]
5662 h m [] = return m []
5663 h m (x:xs) = bind m x $ \y ->
5664 bind m (h m xs) $ \ys ->
5671 In the function <function>h</function> we use the record selectors <literal>return</literal>
5672 and <literal>bind</literal> to extract the polymorphic bind and return functions
5673 from the <literal>MonadT</literal> data structure, rather than using pattern
5679 <title>Type inference</title>
5682 In general, type inference for arbitrary-rank types is undecidable.
5683 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5684 to get a decidable algorithm by requiring some help from the programmer.
5685 We do not yet have a formal specification of "some help" but the rule is this:
5688 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5689 provides an explicit polymorphic type for x, or GHC's type inference will assume
5690 that x's type has no foralls in it</emphasis>.
5693 What does it mean to "provide" an explicit type for x? You can do that by
5694 giving a type signature for x directly, using a pattern type signature
5695 (<xref linkend="scoped-type-variables"/>), thus:
5697 \ f :: (forall a. a->a) -> (f True, f 'c')
5699 Alternatively, you can give a type signature to the enclosing
5700 context, which GHC can "push down" to find the type for the variable:
5702 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5704 Here the type signature on the expression can be pushed inwards
5705 to give a type signature for f. Similarly, and more commonly,
5706 one can give a type signature for the function itself:
5708 h :: (forall a. a->a) -> (Bool,Char)
5709 h f = (f True, f 'c')
5711 You don't need to give a type signature if the lambda bound variable
5712 is a constructor argument. Here is an example we saw earlier:
5714 f :: T a -> a -> (a, Char)
5715 f (T1 w k) x = (w k x, w 'c' 'd')
5717 Here we do not need to give a type signature to <literal>w</literal>, because
5718 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5725 <sect3 id="implicit-quant">
5726 <title>Implicit quantification</title>
5729 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5730 user-written types, if and only if there is no explicit <literal>forall</literal>,
5731 GHC finds all the type variables mentioned in the type that are not already
5732 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5736 f :: forall a. a -> a
5743 h :: forall b. a -> b -> b
5749 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5752 f :: (a -> a) -> Int
5754 f :: forall a. (a -> a) -> Int
5756 f :: (forall a. a -> a) -> Int
5759 g :: (Ord a => a -> a) -> Int
5760 -- MEANS the illegal type
5761 g :: forall a. (Ord a => a -> a) -> Int
5763 g :: (forall a. Ord a => a -> a) -> Int
5765 The latter produces an illegal type, which you might think is silly,
5766 but at least the rule is simple. If you want the latter type, you
5767 can write your for-alls explicitly. Indeed, doing so is strongly advised
5774 <sect2 id="impredicative-polymorphism">
5775 <title>Impredicative polymorphism
5777 <para><emphasis>NOTE: the impredicative-polymorphism feature is deprecated in GHC 6.12, and
5778 will be removed or replaced in GHC 6.14.</emphasis></para>
5780 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5781 enabled with <option>-XImpredicativeTypes</option>.
5783 that you can call a polymorphic function at a polymorphic type, and
5784 parameterise data structures over polymorphic types. For example:
5786 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5787 f (Just g) = Just (g [3], g "hello")
5790 Notice here that the <literal>Maybe</literal> type is parameterised by the
5791 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5794 <para>The technical details of this extension are described in the paper
5795 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5796 type inference for higher-rank types and impredicativity</ulink>,
5797 which appeared at ICFP 2006.
5801 <sect2 id="scoped-type-variables">
5802 <title>Lexically scoped type variables
5806 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5807 which some type signatures are simply impossible to write. For example:
5809 f :: forall a. [a] -> [a]
5815 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5816 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5817 The type variables bound by a <literal>forall</literal> scope over
5818 the entire definition of the accompanying value declaration.
5819 In this example, the type variable <literal>a</literal> scopes over the whole
5820 definition of <literal>f</literal>, including over
5821 the type signature for <varname>ys</varname>.
5822 In Haskell 98 it is not possible to declare
5823 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5824 it becomes possible to do so.
5826 <para>Lexically-scoped type variables are enabled by
5827 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5829 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5830 variables work, compared to earlier releases. Read this section
5834 <title>Overview</title>
5836 <para>The design follows the following principles
5838 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5839 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5840 design.)</para></listitem>
5841 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5842 type variables. This means that every programmer-written type signature
5843 (including one that contains free scoped type variables) denotes a
5844 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5845 checker, and no inference is involved.</para></listitem>
5846 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5847 changing the program.</para></listitem>
5851 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5853 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5854 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5855 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5856 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5860 In Haskell, a programmer-written type signature is implicitly quantified over
5861 its free type variables (<ulink
5862 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5864 of the Haskell Report).
5865 Lexically scoped type variables affect this implicit quantification rules
5866 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5867 quantified. For example, if type variable <literal>a</literal> is in scope,
5870 (e :: a -> a) means (e :: a -> a)
5871 (e :: b -> b) means (e :: forall b. b->b)
5872 (e :: a -> b) means (e :: forall b. a->b)
5880 <sect3 id="decl-type-sigs">
5881 <title>Declaration type signatures</title>
5882 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5883 quantification (using <literal>forall</literal>) brings into scope the
5884 explicitly-quantified
5885 type variables, in the definition of the named function. For example:
5887 f :: forall a. [a] -> [a]
5888 f (x:xs) = xs ++ [ x :: a ]
5890 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5891 the definition of "<literal>f</literal>".
5893 <para>This only happens if:
5895 <listitem><para> The quantification in <literal>f</literal>'s type
5896 signature is explicit. For example:
5899 g (x:xs) = xs ++ [ x :: a ]
5901 This program will be rejected, because "<literal>a</literal>" does not scope
5902 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5903 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5904 quantification rules.
5906 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5907 not a pattern binding.
5910 f1 :: forall a. [a] -> [a]
5911 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5913 f2 :: forall a. [a] -> [a]
5914 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5916 f3 :: forall a. [a] -> [a]
5917 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5919 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5920 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5921 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5922 the type signature brings <literal>a</literal> into scope.
5928 <sect3 id="exp-type-sigs">
5929 <title>Expression type signatures</title>
5931 <para>An expression type signature that has <emphasis>explicit</emphasis>
5932 quantification (using <literal>forall</literal>) brings into scope the
5933 explicitly-quantified
5934 type variables, in the annotated expression. For example:
5936 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5938 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5939 type variable <literal>s</literal> into scope, in the annotated expression
5940 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5945 <sect3 id="pattern-type-sigs">
5946 <title>Pattern type signatures</title>
5948 A type signature may occur in any pattern; this is a <emphasis>pattern type
5949 signature</emphasis>.
5952 -- f and g assume that 'a' is already in scope
5953 f = \(x::Int, y::a) -> x
5955 h ((x,y) :: (Int,Bool)) = (y,x)
5957 In the case where all the type variables in the pattern type signature are
5958 already in scope (i.e. bound by the enclosing context), matters are simple: the
5959 signature simply constrains the type of the pattern in the obvious way.
5962 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5963 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5964 that are already in scope. For example:
5966 f :: forall a. [a] -> (Int, [a])
5969 (ys::[a], n) = (reverse xs, length xs) -- OK
5970 zs::[a] = xs ++ ys -- OK
5972 Just (v::b) = ... -- Not OK; b is not in scope
5974 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5975 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5979 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5980 type signature may mention a type variable that is not in scope; in this case,
5981 <emphasis>the signature brings that type variable into scope</emphasis>.
5982 This is particularly important for existential data constructors. For example:
5984 data T = forall a. MkT [a]
5987 k (MkT [t::a]) = MkT t3
5991 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5992 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5993 because it is bound by the pattern match. GHC's rule is that in this situation
5994 (and only then), a pattern type signature can mention a type variable that is
5995 not already in scope; the effect is to bring it into scope, standing for the
5996 existentially-bound type variable.
5999 When a pattern type signature binds a type variable in this way, GHC insists that the
6000 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
6001 This means that any user-written type signature always stands for a completely known type.
6004 If all this seems a little odd, we think so too. But we must have
6005 <emphasis>some</emphasis> way to bring such type variables into scope, else we
6006 could not name existentially-bound type variables in subsequent type signatures.
6009 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
6010 signature is allowed to mention a lexical variable that is not already in
6012 For example, both <literal>f</literal> and <literal>g</literal> would be
6013 illegal if <literal>a</literal> was not already in scope.
6019 <!-- ==================== Commented out part about result type signatures
6021 <sect3 id="result-type-sigs">
6022 <title>Result type signatures</title>
6025 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
6028 {- f assumes that 'a' is already in scope -}
6029 f x y :: [a] = [x,y,x]
6031 g = \ x :: [Int] -> [3,4]
6033 h :: forall a. [a] -> a
6037 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
6038 the result of the function. Similarly, the body of the lambda in the RHS of
6039 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
6040 alternative in <literal>h</literal> is <literal>a</literal>.
6042 <para> A result type signature never brings new type variables into scope.</para>
6044 There are a couple of syntactic wrinkles. First, notice that all three
6045 examples would parse quite differently with parentheses:
6047 {- f assumes that 'a' is already in scope -}
6048 f x (y :: [a]) = [x,y,x]
6050 g = \ (x :: [Int]) -> [3,4]
6052 h :: forall a. [a] -> a
6056 Now the signature is on the <emphasis>pattern</emphasis>; and
6057 <literal>h</literal> would certainly be ill-typed (since the pattern
6058 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6060 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6061 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6062 token or a parenthesised type of some sort). To see why,
6063 consider how one would parse this:
6072 <sect3 id="cls-inst-scoped-tyvars">
6073 <title>Class and instance declarations</title>
6076 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6077 scope over the methods defined in the <literal>where</literal> part. For example:
6095 <sect2 id="typing-binds">
6096 <title>Generalised typing of mutually recursive bindings</title>
6099 The Haskell Report specifies that a group of bindings (at top level, or in a
6100 <literal>let</literal> or <literal>where</literal>) should be sorted into
6101 strongly-connected components, and then type-checked in dependency order
6102 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6103 Report, Section 4.5.1</ulink>).
6104 As each group is type-checked, any binders of the group that
6106 an explicit type signature are put in the type environment with the specified
6108 and all others are monomorphic until the group is generalised
6109 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6112 <para>Following a suggestion of Mark Jones, in his paper
6113 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6115 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6117 <emphasis>the dependency analysis ignores references to variables that have an explicit
6118 type signature</emphasis>.
6119 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6120 typecheck. For example, consider:
6122 f :: Eq a => a -> Bool
6123 f x = (x == x) || g True || g "Yes"
6125 g y = (y <= y) || f True
6127 This is rejected by Haskell 98, but under Jones's scheme the definition for
6128 <literal>g</literal> is typechecked first, separately from that for
6129 <literal>f</literal>,
6130 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6131 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6132 type is generalised, to get
6134 g :: Ord a => a -> Bool
6136 Now, the definition for <literal>f</literal> is typechecked, with this type for
6137 <literal>g</literal> in the type environment.
6141 The same refined dependency analysis also allows the type signatures of
6142 mutually-recursive functions to have different contexts, something that is illegal in
6143 Haskell 98 (Section 4.5.2, last sentence). With
6144 <option>-XRelaxedPolyRec</option>
6145 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6146 type signatures; in practice this means that only variables bound by the same
6147 pattern binding must have the same context. For example, this is fine:
6149 f :: Eq a => a -> Bool
6150 f x = (x == x) || g True
6152 g :: Ord a => a -> Bool
6153 g y = (y <= y) || f True
6158 <sect2 id="mono-local-binds">
6159 <title>Monomorphic local bindings</title>
6161 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6162 The rationale is described in the paper
6163 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6166 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6167 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6168 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6169 If you supply a type signature, then the flag has no effect.
6174 <!-- ==================== End of type system extensions ================= -->
6176 <!-- ====================== TEMPLATE HASKELL ======================= -->
6178 <sect1 id="template-haskell">
6179 <title>Template Haskell</title>
6181 <para>Template Haskell allows you to do compile-time meta-programming in
6184 the main technical innovations is discussed in "<ulink
6185 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6186 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6189 There is a Wiki page about
6190 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6191 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6195 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6196 Haskell library reference material</ulink>
6197 (look for module <literal>Language.Haskell.TH</literal>).
6198 Many changes to the original design are described in
6199 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6200 Notes on Template Haskell version 2</ulink>.
6201 Not all of these changes are in GHC, however.
6204 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6205 as a worked example to help get you started.
6209 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6210 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6215 <title>Syntax</title>
6217 <para> Template Haskell has the following new syntactic
6218 constructions. You need to use the flag
6219 <option>-XTemplateHaskell</option>
6220 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6221 </indexterm>to switch these syntactic extensions on
6222 (<option>-XTemplateHaskell</option> is no longer implied by
6223 <option>-fglasgow-exts</option>).</para>
6227 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6228 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6229 There must be no space between the "$" and the identifier or parenthesis. This use
6230 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6231 of "." as an infix operator. If you want the infix operator, put spaces around it.
6233 <para> A splice can occur in place of
6235 <listitem><para> an expression; the spliced expression must
6236 have type <literal>Q Exp</literal></para></listitem>
6237 <listitem><para> an type; the spliced expression must
6238 have type <literal>Q Typ</literal></para></listitem>
6239 <listitem><para> a list of top-level declarations; the spliced expression
6240 must have type <literal>Q [Dec]</literal></para></listitem>
6242 Note that pattern splices are not supported.
6243 Inside a splice you can can only call functions defined in imported modules,
6244 not functions defined elsewhere in the same module.</para></listitem>
6247 A expression quotation is written in Oxford brackets, thus:
6249 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6250 where the "..." is an expression;
6251 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6252 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6253 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6254 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6255 the quotation has type <literal>Q Type</literal>.</para></listitem>
6256 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6257 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6258 </itemizedlist></para></listitem>
6261 A quasi-quotation can appear in either a pattern context or an
6262 expression context and is also written in Oxford brackets:
6264 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6265 where the "..." is an arbitrary string; a full description of the
6266 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6267 </itemizedlist></para></listitem>
6270 A name can be quoted with either one or two prefix single quotes:
6272 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6273 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6274 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6276 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6277 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6280 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6281 may also be given as an argument to the <literal>reify</literal> function.
6285 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6286 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6293 $(deriveStuff 'f) -- Uses the $(...) notation
6297 deriveStuff 'g -- Omits the $(...)
6301 This abbreviation makes top-level declaration slices quieter and less intimidating.
6306 (Compared to the original paper, there are many differences of detail.
6307 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6308 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6309 Pattern splices and quotations are not implemented.)
6313 <sect2> <title> Using Template Haskell </title>
6317 The data types and monadic constructor functions for Template Haskell are in the library
6318 <literal>Language.Haskell.THSyntax</literal>.
6322 You can only run a function at compile time if it is imported from another module. That is,
6323 you can't define a function in a module, and call it from within a splice in the same module.
6324 (It would make sense to do so, but it's hard to implement.)
6328 You can only run a function at compile time if it is imported
6329 from another module <emphasis>that is not part of a mutually-recursive group of modules
6330 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6331 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6332 splice is to be run.</para>
6334 For example, when compiling module A,
6335 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6336 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6340 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6343 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6344 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6345 compiles and runs a program, and then looks at the result. So it's important that
6346 the program it compiles produces results whose representations are identical to
6347 those of the compiler itself.
6351 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6352 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6357 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6358 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6359 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6366 -- Import our template "pr"
6367 import Printf ( pr )
6369 -- The splice operator $ takes the Haskell source code
6370 -- generated at compile time by "pr" and splices it into
6371 -- the argument of "putStrLn".
6372 main = putStrLn ( $(pr "Hello") )
6378 -- Skeletal printf from the paper.
6379 -- It needs to be in a separate module to the one where
6380 -- you intend to use it.
6382 -- Import some Template Haskell syntax
6383 import Language.Haskell.TH
6385 -- Describe a format string
6386 data Format = D | S | L String
6388 -- Parse a format string. This is left largely to you
6389 -- as we are here interested in building our first ever
6390 -- Template Haskell program and not in building printf.
6391 parse :: String -> [Format]
6394 -- Generate Haskell source code from a parsed representation
6395 -- of the format string. This code will be spliced into
6396 -- the module which calls "pr", at compile time.
6397 gen :: [Format] -> Q Exp
6398 gen [D] = [| \n -> show n |]
6399 gen [S] = [| \s -> s |]
6400 gen [L s] = stringE s
6402 -- Here we generate the Haskell code for the splice
6403 -- from an input format string.
6404 pr :: String -> Q Exp
6405 pr s = gen (parse s)
6408 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6411 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6414 <para>Run "main.exe" and here is your output:</para>
6424 <title>Using Template Haskell with Profiling</title>
6425 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6427 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6428 interpreter to run the splice expressions. The bytecode interpreter
6429 runs the compiled expression on top of the same runtime on which GHC
6430 itself is running; this means that the compiled code referred to by
6431 the interpreted expression must be compatible with this runtime, and
6432 in particular this means that object code that is compiled for
6433 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6434 expression, because profiled object code is only compatible with the
6435 profiling version of the runtime.</para>
6437 <para>This causes difficulties if you have a multi-module program
6438 containing Template Haskell code and you need to compile it for
6439 profiling, because GHC cannot load the profiled object code and use it
6440 when executing the splices. Fortunately GHC provides a workaround.
6441 The basic idea is to compile the program twice:</para>
6445 <para>Compile the program or library first the normal way, without
6446 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6449 <para>Then compile it again with <option>-prof</option>, and
6450 additionally use <option>-osuf
6451 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6452 to name the object files differently (you can choose any suffix
6453 that isn't the normal object suffix here). GHC will automatically
6454 load the object files built in the first step when executing splice
6455 expressions. If you omit the <option>-osuf</option> flag when
6456 building with <option>-prof</option> and Template Haskell is used,
6457 GHC will emit an error message. </para>
6462 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6463 <para>Quasi-quotation allows patterns and expressions to be written using
6464 programmer-defined concrete syntax; the motivation behind the extension and
6465 several examples are documented in
6466 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6467 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6468 2007). The example below shows how to write a quasiquoter for a simple
6469 expression language.</para>
6471 Here are the salient features
6474 A quasi-quote has the form
6475 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6478 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6479 quoter; it cannot be an arbitrary expression.
6482 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6483 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6484 those overlap with Template Haskell quotations.
6487 There must be no spaces in the token
6488 <literal>[<replaceable>quoter</replaceable>|</literal>.
6491 The quoted <replaceable>string</replaceable>
6492 can be arbitrary, and may contain newlines.
6498 A quasiquote may appear in place of
6500 <listitem><para>An expression</para></listitem>
6501 <listitem><para>A pattern</para></listitem>
6502 <listitem><para>A type</para></listitem>
6503 <listitem><para>A top-level declaration</para></listitem>
6505 (Only the first two are described in the paper.)
6509 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6510 which is defined thus:
6512 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6513 quotePat :: String -> Q Pat,
6514 quoteType :: String -> Q Type,
6515 quoteDec :: String -> Q [Dec] }
6517 That is, a quoter is a tuple of four parsers, one for each of the contexts
6518 in which a quasi-quote can occur.
6521 A quasi-quote is expanded by applying the appropriate parser to the string
6522 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6523 type, declaration) determines which of the parsers is called.
6528 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6529 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6530 The example makes use of an antiquoted
6531 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6532 (this syntax for anti-quotation was defined by the parser's
6533 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6534 integer value argument of the constructor <literal>IntExpr</literal> when
6535 pattern matching. Please see the referenced paper for further details regarding
6536 anti-quotation as well as the description of a technique that uses SYB to
6537 leverage a single parser of type <literal>String -> a</literal> to generate both
6538 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6539 pattern parser that returns a value of type <literal>Q Pat</literal>.
6543 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6544 the example, <literal>expr</literal> cannot be defined
6545 in <literal>Main.hs</literal> where it is used, but must be imported.
6549 {- ------------- file Main.hs --------------- -}
6555 main = do { print $ eval [expr|1 + 2|]
6557 { [expr|'int:n|] -> print n
6563 {- ------------- file Expr.hs --------------- -}
6566 import qualified Language.Haskell.TH as TH
6567 import Language.Haskell.TH.Quote
6569 data Expr = IntExpr Integer
6570 | AntiIntExpr String
6571 | BinopExpr BinOp Expr Expr
6573 deriving(Show, Typeable, Data)
6579 deriving(Show, Typeable, Data)
6581 eval :: Expr -> Integer
6582 eval (IntExpr n) = n
6583 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6590 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6592 -- Parse an Expr, returning its representation as
6593 -- either a Q Exp or a Q Pat. See the referenced paper
6594 -- for how to use SYB to do this by writing a single
6595 -- parser of type String -> Expr instead of two
6596 -- separate parsers.
6598 parseExprExp :: String -> Q Exp
6601 parseExprPat :: String -> Q Pat
6605 <para>Now run the compiler:
6607 $ ghc --make -XQuasiQuotes Main.hs -o main
6611 <para>Run "main" and here is your output:
6622 <!-- ===================== Arrow notation =================== -->
6624 <sect1 id="arrow-notation">
6625 <title>Arrow notation
6628 <para>Arrows are a generalization of monads introduced by John Hughes.
6629 For more details, see
6634 “Generalising Monads to Arrows”,
6635 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6636 pp67–111, May 2000.
6637 The paper that introduced arrows: a friendly introduction, motivated with
6638 programming examples.
6644 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6645 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6646 Introduced the notation described here.
6652 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6653 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6660 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6661 John Hughes, in <citetitle>5th International Summer School on
6662 Advanced Functional Programming</citetitle>,
6663 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6665 This paper includes another introduction to the notation,
6666 with practical examples.
6672 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6673 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6674 A terse enumeration of the formal rules used
6675 (extracted from comments in the source code).
6681 The arrows web page at
6682 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6687 With the <option>-XArrows</option> flag, GHC supports the arrow
6688 notation described in the second of these papers,
6689 translating it using combinators from the
6690 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6692 What follows is a brief introduction to the notation;
6693 it won't make much sense unless you've read Hughes's paper.
6696 <para>The extension adds a new kind of expression for defining arrows:
6698 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6699 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6701 where <literal>proc</literal> is a new keyword.
6702 The variables of the pattern are bound in the body of the
6703 <literal>proc</literal>-expression,
6704 which is a new sort of thing called a <firstterm>command</firstterm>.
6705 The syntax of commands is as follows:
6707 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6708 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6709 | <replaceable>cmd</replaceable><superscript>0</superscript>
6711 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6712 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6713 infix operators as for expressions, and
6715 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6716 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6717 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6718 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6719 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6720 | <replaceable>fcmd</replaceable>
6722 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6723 | ( <replaceable>cmd</replaceable> )
6724 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6726 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6727 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6728 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6729 | <replaceable>cmd</replaceable>
6731 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6732 except that the bodies are commands instead of expressions.
6736 Commands produce values, but (like monadic computations)
6737 may yield more than one value,
6738 or none, and may do other things as well.
6739 For the most part, familiarity with monadic notation is a good guide to
6741 However the values of expressions, even monadic ones,
6742 are determined by the values of the variables they contain;
6743 this is not necessarily the case for commands.
6747 A simple example of the new notation is the expression
6749 proc x -> f -< x+1
6751 We call this a <firstterm>procedure</firstterm> or
6752 <firstterm>arrow abstraction</firstterm>.
6753 As with a lambda expression, the variable <literal>x</literal>
6754 is a new variable bound within the <literal>proc</literal>-expression.
6755 It refers to the input to the arrow.
6756 In the above example, <literal>-<</literal> is not an identifier but an
6757 new reserved symbol used for building commands from an expression of arrow
6758 type and an expression to be fed as input to that arrow.
6759 (The weird look will make more sense later.)
6760 It may be read as analogue of application for arrows.
6761 The above example is equivalent to the Haskell expression
6763 arr (\ x -> x+1) >>> f
6765 That would make no sense if the expression to the left of
6766 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6767 More generally, the expression to the left of <literal>-<</literal>
6768 may not involve any <firstterm>local variable</firstterm>,
6769 i.e. a variable bound in the current arrow abstraction.
6770 For such a situation there is a variant <literal>-<<</literal>, as in
6772 proc x -> f x -<< x+1
6774 which is equivalent to
6776 arr (\ x -> (f x, x+1)) >>> app
6778 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6780 Such an arrow is equivalent to a monad, so if you're using this form
6781 you may find a monadic formulation more convenient.
6785 <title>do-notation for commands</title>
6788 Another form of command is a form of <literal>do</literal>-notation.
6789 For example, you can write
6798 You can read this much like ordinary <literal>do</literal>-notation,
6799 but with commands in place of monadic expressions.
6800 The first line sends the value of <literal>x+1</literal> as an input to
6801 the arrow <literal>f</literal>, and matches its output against
6802 <literal>y</literal>.
6803 In the next line, the output is discarded.
6804 The arrow <function>returnA</function> is defined in the
6805 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6806 module as <literal>arr id</literal>.
6807 The above example is treated as an abbreviation for
6809 arr (\ x -> (x, x)) >>>
6810 first (arr (\ x -> x+1) >>> f) >>>
6811 arr (\ (y, x) -> (y, (x, y))) >>>
6812 first (arr (\ y -> 2*y) >>> g) >>>
6814 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6815 first (arr (\ (x, z) -> x*z) >>> h) >>>
6816 arr (\ (t, z) -> t+z) >>>
6819 Note that variables not used later in the composition are projected out.
6820 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6822 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6823 module, this reduces to
6825 arr (\ x -> (x+1, x)) >>>
6827 arr (\ (y, x) -> (2*y, (x, y))) >>>
6829 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6831 arr (\ (t, z) -> t+z)
6833 which is what you might have written by hand.
6834 With arrow notation, GHC keeps track of all those tuples of variables for you.
6838 Note that although the above translation suggests that
6839 <literal>let</literal>-bound variables like <literal>z</literal> must be
6840 monomorphic, the actual translation produces Core,
6841 so polymorphic variables are allowed.
6845 It's also possible to have mutually recursive bindings,
6846 using the new <literal>rec</literal> keyword, as in the following example:
6848 counter :: ArrowCircuit a => a Bool Int
6849 counter = proc reset -> do
6850 rec output <- returnA -< if reset then 0 else next
6851 next <- delay 0 -< output+1
6852 returnA -< output
6854 The translation of such forms uses the <function>loop</function> combinator,
6855 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6861 <title>Conditional commands</title>
6864 In the previous example, we used a conditional expression to construct the
6866 Sometimes we want to conditionally execute different commands, as in
6873 which is translated to
6875 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6876 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6878 Since the translation uses <function>|||</function>,
6879 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6883 There are also <literal>case</literal> commands, like
6889 y <- h -< (x1, x2)
6893 The syntax is the same as for <literal>case</literal> expressions,
6894 except that the bodies of the alternatives are commands rather than expressions.
6895 The translation is similar to that of <literal>if</literal> commands.
6901 <title>Defining your own control structures</title>
6904 As we're seen, arrow notation provides constructs,
6905 modelled on those for expressions,
6906 for sequencing, value recursion and conditionals.
6907 But suitable combinators,
6908 which you can define in ordinary Haskell,
6909 may also be used to build new commands out of existing ones.
6910 The basic idea is that a command defines an arrow from environments to values.
6911 These environments assign values to the free local variables of the command.
6912 Thus combinators that produce arrows from arrows
6913 may also be used to build commands from commands.
6914 For example, the <literal>ArrowChoice</literal> class includes a combinator
6916 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6918 so we can use it to build commands:
6920 expr' = proc x -> do
6923 symbol Plus -< ()
6924 y <- term -< ()
6927 symbol Minus -< ()
6928 y <- term -< ()
6931 (The <literal>do</literal> on the first line is needed to prevent the first
6932 <literal><+> ...</literal> from being interpreted as part of the
6933 expression on the previous line.)
6934 This is equivalent to
6936 expr' = (proc x -> returnA -< x)
6937 <+> (proc x -> do
6938 symbol Plus -< ()
6939 y <- term -< ()
6941 <+> (proc x -> do
6942 symbol Minus -< ()
6943 y <- term -< ()
6946 It is essential that this operator be polymorphic in <literal>e</literal>
6947 (representing the environment input to the command
6948 and thence to its subcommands)
6949 and satisfy the corresponding naturality property
6951 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6953 at least for strict <literal>k</literal>.
6954 (This should be automatic if you're not using <function>seq</function>.)
6955 This ensures that environments seen by the subcommands are environments
6956 of the whole command,
6957 and also allows the translation to safely trim these environments.
6958 The operator must also not use any variable defined within the current
6963 We could define our own operator
6965 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6966 untilA body cond = proc x ->
6967 b <- cond -< x
6968 if b then returnA -< ()
6971 untilA body cond -< x
6973 and use it in the same way.
6974 Of course this infix syntax only makes sense for binary operators;
6975 there is also a more general syntax involving special brackets:
6979 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6986 <title>Primitive constructs</title>
6989 Some operators will need to pass additional inputs to their subcommands.
6990 For example, in an arrow type supporting exceptions,
6991 the operator that attaches an exception handler will wish to pass the
6992 exception that occurred to the handler.
6993 Such an operator might have a type
6995 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6997 where <literal>Ex</literal> is the type of exceptions handled.
6998 You could then use this with arrow notation by writing a command
7000 body `handleA` \ ex -> handler
7002 so that if an exception is raised in the command <literal>body</literal>,
7003 the variable <literal>ex</literal> is bound to the value of the exception
7004 and the command <literal>handler</literal>,
7005 which typically refers to <literal>ex</literal>, is entered.
7006 Though the syntax here looks like a functional lambda,
7007 we are talking about commands, and something different is going on.
7008 The input to the arrow represented by a command consists of values for
7009 the free local variables in the command, plus a stack of anonymous values.
7010 In all the prior examples, this stack was empty.
7011 In the second argument to <function>handleA</function>,
7012 this stack consists of one value, the value of the exception.
7013 The command form of lambda merely gives this value a name.
7018 the values on the stack are paired to the right of the environment.
7019 So operators like <function>handleA</function> that pass
7020 extra inputs to their subcommands can be designed for use with the notation
7021 by pairing the values with the environment in this way.
7022 More precisely, the type of each argument of the operator (and its result)
7023 should have the form
7025 a (...(e,t1), ... tn) t
7027 where <replaceable>e</replaceable> is a polymorphic variable
7028 (representing the environment)
7029 and <replaceable>ti</replaceable> are the types of the values on the stack,
7030 with <replaceable>t1</replaceable> being the <quote>top</quote>.
7031 The polymorphic variable <replaceable>e</replaceable> must not occur in
7032 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
7033 <replaceable>t</replaceable>.
7034 However the arrows involved need not be the same.
7035 Here are some more examples of suitable operators:
7037 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
7038 runReader :: ... => a e c -> a' (e,State) c
7039 runState :: ... => a e c -> a' (e,State) (c,State)
7041 We can supply the extra input required by commands built with the last two
7042 by applying them to ordinary expressions, as in
7046 (|runReader (do { ... })|) s
7048 which adds <literal>s</literal> to the stack of inputs to the command
7049 built using <function>runReader</function>.
7053 The command versions of lambda abstraction and application are analogous to
7054 the expression versions.
7055 In particular, the beta and eta rules describe equivalences of commands.
7056 These three features (operators, lambda abstraction and application)
7057 are the core of the notation; everything else can be built using them,
7058 though the results would be somewhat clumsy.
7059 For example, we could simulate <literal>do</literal>-notation by defining
7061 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7062 u `bind` f = returnA &&& u >>> f
7064 bind_ :: Arrow a => a e b -> a e c -> a e c
7065 u `bind_` f = u `bind` (arr fst >>> f)
7067 We could simulate <literal>if</literal> by defining
7069 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7070 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7077 <title>Differences with the paper</title>
7082 <para>Instead of a single form of arrow application (arrow tail) with two
7083 translations, the implementation provides two forms
7084 <quote><literal>-<</literal></quote> (first-order)
7085 and <quote><literal>-<<</literal></quote> (higher-order).
7090 <para>User-defined operators are flagged with banana brackets instead of
7091 a new <literal>form</literal> keyword.
7100 <title>Portability</title>
7103 Although only GHC implements arrow notation directly,
7104 there is also a preprocessor
7106 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7107 that translates arrow notation into Haskell 98
7108 for use with other Haskell systems.
7109 You would still want to check arrow programs with GHC;
7110 tracing type errors in the preprocessor output is not easy.
7111 Modules intended for both GHC and the preprocessor must observe some
7112 additional restrictions:
7117 The module must import
7118 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7124 The preprocessor cannot cope with other Haskell extensions.
7125 These would have to go in separate modules.
7131 Because the preprocessor targets Haskell (rather than Core),
7132 <literal>let</literal>-bound variables are monomorphic.
7143 <!-- ==================== BANG PATTERNS ================= -->
7145 <sect1 id="bang-patterns">
7146 <title>Bang patterns
7147 <indexterm><primary>Bang patterns</primary></indexterm>
7149 <para>GHC supports an extension of pattern matching called <emphasis>bang
7150 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7151 Bang patterns are under consideration for Haskell Prime.
7153 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7154 prime feature description</ulink> contains more discussion and examples
7155 than the material below.
7158 The key change is the addition of a new rule to the
7159 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7160 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7161 against a value <replaceable>v</replaceable> behaves as follows:
7163 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7164 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7168 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7171 <sect2 id="bang-patterns-informal">
7172 <title>Informal description of bang patterns
7175 The main idea is to add a single new production to the syntax of patterns:
7179 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7180 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7185 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7186 whereas without the bang it would be lazy.
7187 Bang patterns can be nested of course:
7191 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7192 <literal>y</literal>.
7193 A bang only really has an effect if it precedes a variable or wild-card pattern:
7198 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7199 putting a bang before a pattern that
7200 forces evaluation anyway does nothing.
7203 There is one (apparent) exception to this general rule that a bang only
7204 makes a difference when it precedes a variable or wild-card: a bang at the
7205 top level of a <literal>let</literal> or <literal>where</literal>
7206 binding makes the binding strict, regardless of the pattern. For example:
7210 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7211 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7212 (We say "apparent" exception because the Right Way to think of it is that the bang
7213 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7214 is part of the syntax of the <emphasis>binding</emphasis>.)
7215 Nested bangs in a pattern binding behave uniformly with all other forms of
7216 pattern matching. For example
7218 let (!x,[y]) = e in b
7220 is equivalent to this:
7222 let { t = case e of (x,[y]) -> x `seq` (x,y)
7227 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7228 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7229 evaluation of <literal>x</literal>.
7232 Bang patterns work in <literal>case</literal> expressions too, of course:
7234 g5 x = let y = f x in body
7235 g6 x = case f x of { y -> body }
7236 g7 x = case f x of { !y -> body }
7238 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7239 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7240 result, and then evaluates <literal>body</literal>.
7245 <sect2 id="bang-patterns-sem">
7246 <title>Syntax and semantics
7250 We add a single new production to the syntax of patterns:
7254 There is one problem with syntactic ambiguity. Consider:
7258 Is this a definition of the infix function "<literal>(!)</literal>",
7259 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7260 ambiguity in favour of the latter. If you want to define
7261 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7266 The semantics of Haskell pattern matching is described in <ulink
7267 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7268 Section 3.17.2</ulink> of the Haskell Report. To this description add
7269 one extra item 10, saying:
7270 <itemizedlist><listitem><para>Matching
7271 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7272 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7273 <listitem><para>otherwise, <literal>pat</literal> is matched against
7274 <literal>v</literal></para></listitem>
7276 </para></listitem></itemizedlist>
7277 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7278 Section 3.17.3</ulink>, add a new case (t):
7280 case v of { !pat -> e; _ -> e' }
7281 = v `seq` case v of { pat -> e; _ -> e' }
7284 That leaves let expressions, whose translation is given in
7285 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7287 of the Haskell Report.
7288 In the translation box, first apply
7289 the following transformation: for each pattern <literal>pi</literal> that is of
7290 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7291 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7292 have a bang at the top, apply the rules in the existing box.
7294 <para>The effect of the let rule is to force complete matching of the pattern
7295 <literal>qi</literal> before evaluation of the body is begun. The bang is
7296 retained in the translated form in case <literal>qi</literal> is a variable,
7304 The let-binding can be recursive. However, it is much more common for
7305 the let-binding to be non-recursive, in which case the following law holds:
7306 <literal>(let !p = rhs in body)</literal>
7308 <literal>(case rhs of !p -> body)</literal>
7311 A pattern with a bang at the outermost level is not allowed at the top level of
7317 <!-- ==================== ASSERTIONS ================= -->
7319 <sect1 id="assertions">
7321 <indexterm><primary>Assertions</primary></indexterm>
7325 If you want to make use of assertions in your standard Haskell code, you
7326 could define a function like the following:
7332 assert :: Bool -> a -> a
7333 assert False x = error "assertion failed!"
7340 which works, but gives you back a less than useful error message --
7341 an assertion failed, but which and where?
7345 One way out is to define an extended <function>assert</function> function which also
7346 takes a descriptive string to include in the error message and
7347 perhaps combine this with the use of a pre-processor which inserts
7348 the source location where <function>assert</function> was used.
7352 Ghc offers a helping hand here, doing all of this for you. For every
7353 use of <function>assert</function> in the user's source:
7359 kelvinToC :: Double -> Double
7360 kelvinToC k = assert (k >= 0.0) (k+273.15)
7366 Ghc will rewrite this to also include the source location where the
7373 assert pred val ==> assertError "Main.hs|15" pred val
7379 The rewrite is only performed by the compiler when it spots
7380 applications of <function>Control.Exception.assert</function>, so you
7381 can still define and use your own versions of
7382 <function>assert</function>, should you so wish. If not, import
7383 <literal>Control.Exception</literal> to make use
7384 <function>assert</function> in your code.
7388 GHC ignores assertions when optimisation is turned on with the
7389 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7390 <literal>assert pred e</literal> will be rewritten to
7391 <literal>e</literal>. You can also disable assertions using the
7392 <option>-fignore-asserts</option>
7393 option<indexterm><primary><option>-fignore-asserts</option></primary>
7394 </indexterm>.</para>
7397 Assertion failures can be caught, see the documentation for the
7398 <literal>Control.Exception</literal> library for the details.
7404 <!-- =============================== PRAGMAS =========================== -->
7406 <sect1 id="pragmas">
7407 <title>Pragmas</title>
7409 <indexterm><primary>pragma</primary></indexterm>
7411 <para>GHC supports several pragmas, or instructions to the
7412 compiler placed in the source code. Pragmas don't normally affect
7413 the meaning of the program, but they might affect the efficiency
7414 of the generated code.</para>
7416 <para>Pragmas all take the form
7418 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7420 where <replaceable>word</replaceable> indicates the type of
7421 pragma, and is followed optionally by information specific to that
7422 type of pragma. Case is ignored in
7423 <replaceable>word</replaceable>. The various values for
7424 <replaceable>word</replaceable> that GHC understands are described
7425 in the following sections; any pragma encountered with an
7426 unrecognised <replaceable>word</replaceable> is
7427 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7428 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7430 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7434 pragma must precede the <literal>module</literal> keyword in the file.
7437 There can be as many file-header pragmas as you please, and they can be
7438 preceded or followed by comments.
7441 File-header pragmas are read once only, before
7442 pre-processing the file (e.g. with cpp).
7445 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7446 <literal>{-# OPTIONS_GHC #-}</literal>, and
7447 <literal>{-# INCLUDE #-}</literal>.
7452 <sect2 id="language-pragma">
7453 <title>LANGUAGE pragma</title>
7455 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7456 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7458 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7460 It is the intention that all Haskell compilers support the
7461 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7462 all extensions are supported by all compilers, of
7463 course. The <literal>LANGUAGE</literal> pragma should be used instead
7464 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7466 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7468 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7470 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7472 <para>Every language extension can also be turned into a command-line flag
7473 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7474 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7477 <para>A list of all supported language extensions can be obtained by invoking
7478 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7480 <para>Any extension from the <literal>Extension</literal> type defined in
7482 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7483 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7487 <sect2 id="options-pragma">
7488 <title>OPTIONS_GHC pragma</title>
7489 <indexterm><primary>OPTIONS_GHC</primary>
7491 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7494 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7495 additional options that are given to the compiler when compiling
7496 this source file. See <xref linkend="source-file-options"/> for
7499 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7500 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7503 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7505 <sect2 id="include-pragma">
7506 <title>INCLUDE pragma</title>
7508 <para>The <literal>INCLUDE</literal> used to be necessary for
7509 specifying header files to be included when using the FFI and
7510 compiling via C. It is no longer required for GHC, but is
7511 accepted (and ignored) for compatibility with other
7515 <sect2 id="warning-deprecated-pragma">
7516 <title>WARNING and DEPRECATED pragmas</title>
7517 <indexterm><primary>WARNING</primary></indexterm>
7518 <indexterm><primary>DEPRECATED</primary></indexterm>
7520 <para>The WARNING pragma allows you to attach an arbitrary warning
7521 to a particular function, class, or type.
7522 A DEPRECATED pragma lets you specify that
7523 a particular function, class, or type is deprecated.
7524 There are two ways of using these pragmas.
7528 <para>You can work on an entire module thus:</para>
7530 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7535 module Wibble {-# WARNING "This is an unstable interface." #-} where
7538 <para>When you compile any module that import
7539 <literal>Wibble</literal>, GHC will print the specified
7544 <para>You can attach a warning to a function, class, type, or data constructor, with the
7545 following top-level declarations:</para>
7547 {-# DEPRECATED f, C, T "Don't use these" #-}
7548 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7550 <para>When you compile any module that imports and uses any
7551 of the specified entities, GHC will print the specified
7553 <para> You can only attach to entities declared at top level in the module
7554 being compiled, and you can only use unqualified names in the list of
7555 entities. A capitalised name, such as <literal>T</literal>
7556 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7557 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7558 both are in scope. If both are in scope, there is currently no way to
7559 specify one without the other (c.f. fixities
7560 <xref linkend="infix-tycons"/>).</para>
7563 Warnings and deprecations are not reported for
7564 (a) uses within the defining module, and
7565 (b) uses in an export list.
7566 The latter reduces spurious complaints within a library
7567 in which one module gathers together and re-exports
7568 the exports of several others.
7570 <para>You can suppress the warnings with the flag
7571 <option>-fno-warn-warnings-deprecations</option>.</para>
7574 <sect2 id="inline-noinline-pragma">
7575 <title>INLINE and NOINLINE pragmas</title>
7577 <para>These pragmas control the inlining of function
7580 <sect3 id="inline-pragma">
7581 <title>INLINE pragma</title>
7582 <indexterm><primary>INLINE</primary></indexterm>
7584 <para>GHC (with <option>-O</option>, as always) tries to
7585 inline (or “unfold”) functions/values that are
7586 “small enough,” thus avoiding the call overhead
7587 and possibly exposing other more-wonderful optimisations.
7588 Normally, if GHC decides a function is “too
7589 expensive” to inline, it will not do so, nor will it
7590 export that unfolding for other modules to use.</para>
7592 <para>The sledgehammer you can bring to bear is the
7593 <literal>INLINE</literal><indexterm><primary>INLINE
7594 pragma</primary></indexterm> pragma, used thusly:</para>
7597 key_function :: Int -> String -> (Bool, Double)
7598 {-# INLINE key_function #-}
7601 <para>The major effect of an <literal>INLINE</literal> pragma
7602 is to declare a function's “cost” to be very low.
7603 The normal unfolding machinery will then be very keen to
7604 inline it. However, an <literal>INLINE</literal> pragma for a
7605 function "<literal>f</literal>" has a number of other effects:
7608 No functions are inlined into <literal>f</literal>. Otherwise
7609 GHC might inline a big function into <literal>f</literal>'s right hand side,
7610 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7613 The float-in, float-out, and common-sub-expression transformations are not
7614 applied to the body of <literal>f</literal>.
7617 An INLINE function is not worker/wrappered by strictness analysis.
7618 It's going to be inlined wholesale instead.
7621 All of these effects are aimed at ensuring that what gets inlined is
7622 exactly what you asked for, no more and no less.
7624 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7625 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7626 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7627 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7628 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7629 when there is no choice even an INLINE function can be selected, in which case
7630 the INLINE pragma is ignored.
7631 For example, for a self-recursive function, the loop breaker can only be the function
7632 itself, so an INLINE pragma is always ignored.</para>
7634 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7635 function can be put anywhere its type signature could be
7638 <para><literal>INLINE</literal> pragmas are a particularly
7640 <literal>then</literal>/<literal>return</literal> (or
7641 <literal>bind</literal>/<literal>unit</literal>) functions in
7642 a monad. For example, in GHC's own
7643 <literal>UniqueSupply</literal> monad code, we have:</para>
7646 {-# INLINE thenUs #-}
7647 {-# INLINE returnUs #-}
7650 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7651 linkend="noinline-pragma"/>).</para>
7653 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7654 so if you want your code to be HBC-compatible you'll have to surround
7655 the pragma with C pre-processor directives
7656 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7660 <sect3 id="noinline-pragma">
7661 <title>NOINLINE pragma</title>
7663 <indexterm><primary>NOINLINE</primary></indexterm>
7664 <indexterm><primary>NOTINLINE</primary></indexterm>
7666 <para>The <literal>NOINLINE</literal> pragma does exactly what
7667 you'd expect: it stops the named function from being inlined
7668 by the compiler. You shouldn't ever need to do this, unless
7669 you're very cautious about code size.</para>
7671 <para><literal>NOTINLINE</literal> is a synonym for
7672 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7673 specified by Haskell 98 as the standard way to disable
7674 inlining, so it should be used if you want your code to be
7678 <sect3 id="conlike-pragma">
7679 <title>CONLIKE modifier</title>
7680 <indexterm><primary>CONLIKE</primary></indexterm>
7681 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7682 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7686 <sect3 id="phase-control">
7687 <title>Phase control</title>
7689 <para> Sometimes you want to control exactly when in GHC's
7690 pipeline the INLINE pragma is switched on. Inlining happens
7691 only during runs of the <emphasis>simplifier</emphasis>. Each
7692 run of the simplifier has a different <emphasis>phase
7693 number</emphasis>; the phase number decreases towards zero.
7694 If you use <option>-dverbose-core2core</option> you'll see the
7695 sequence of phase numbers for successive runs of the
7696 simplifier. In an INLINE pragma you can optionally specify a
7700 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7701 <literal>f</literal>
7702 until phase <literal>k</literal>, but from phase
7703 <literal>k</literal> onwards be very keen to inline it.
7706 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7707 <literal>f</literal>
7708 until phase <literal>k</literal>, but from phase
7709 <literal>k</literal> onwards do not inline it.
7712 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7713 <literal>f</literal>
7714 until phase <literal>k</literal>, but from phase
7715 <literal>k</literal> onwards be willing to inline it (as if
7716 there was no pragma).
7719 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7720 <literal>f</literal>
7721 until phase <literal>k</literal>, but from phase
7722 <literal>k</literal> onwards do not inline it.
7725 The same information is summarised here:
7727 -- Before phase 2 Phase 2 and later
7728 {-# INLINE [2] f #-} -- No Yes
7729 {-# INLINE [~2] f #-} -- Yes No
7730 {-# NOINLINE [2] f #-} -- No Maybe
7731 {-# NOINLINE [~2] f #-} -- Maybe No
7733 {-# INLINE f #-} -- Yes Yes
7734 {-# NOINLINE f #-} -- No No
7736 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7737 function body is small, or it is applied to interesting-looking arguments etc).
7738 Another way to understand the semantics is this:
7740 <listitem><para>For both INLINE and NOINLINE, the phase number says
7741 when inlining is allowed at all.</para></listitem>
7742 <listitem><para>The INLINE pragma has the additional effect of making the
7743 function body look small, so that when inlining is allowed it is very likely to
7748 <para>The same phase-numbering control is available for RULES
7749 (<xref linkend="rewrite-rules"/>).</para>
7753 <sect2 id="annotation-pragmas">
7754 <title>ANN pragmas</title>
7756 <para>GHC offers the ability to annotate various code constructs with additional
7757 data by using three pragmas. This data can then be inspected at a later date by
7758 using GHC-as-a-library.</para>
7760 <sect3 id="ann-pragma">
7761 <title>Annotating values</title>
7763 <indexterm><primary>ANN</primary></indexterm>
7765 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7766 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7767 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7768 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7769 you would do this:</para>
7772 {-# ANN foo (Just "Hello") #-}
7777 A number of restrictions apply to use of annotations:
7779 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7780 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7781 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7782 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7783 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7785 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7786 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7789 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7790 please give the GHC team a shout</ulink>.
7793 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7794 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7797 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7802 <sect3 id="typeann-pragma">
7803 <title>Annotating types</title>
7805 <indexterm><primary>ANN type</primary></indexterm>
7806 <indexterm><primary>ANN</primary></indexterm>
7808 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7811 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7816 <sect3 id="modann-pragma">
7817 <title>Annotating modules</title>
7819 <indexterm><primary>ANN module</primary></indexterm>
7820 <indexterm><primary>ANN</primary></indexterm>
7822 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7825 {-# ANN module (Just "A `Maybe String' annotation") #-}
7830 <sect2 id="line-pragma">
7831 <title>LINE pragma</title>
7833 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7834 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7835 <para>This pragma is similar to C's <literal>#line</literal>
7836 pragma, and is mainly for use in automatically generated Haskell
7837 code. It lets you specify the line number and filename of the
7838 original code; for example</para>
7840 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7842 <para>if you'd generated the current file from something called
7843 <filename>Foo.vhs</filename> and this line corresponds to line
7844 42 in the original. GHC will adjust its error messages to refer
7845 to the line/file named in the <literal>LINE</literal>
7850 <title>RULES pragma</title>
7852 <para>The RULES pragma lets you specify rewrite rules. It is
7853 described in <xref linkend="rewrite-rules"/>.</para>
7856 <sect2 id="specialize-pragma">
7857 <title>SPECIALIZE pragma</title>
7859 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7860 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7861 <indexterm><primary>overloading, death to</primary></indexterm>
7863 <para>(UK spelling also accepted.) For key overloaded
7864 functions, you can create extra versions (NB: more code space)
7865 specialised to particular types. Thus, if you have an
7866 overloaded function:</para>
7869 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7872 <para>If it is heavily used on lists with
7873 <literal>Widget</literal> keys, you could specialise it as
7877 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7880 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7881 be put anywhere its type signature could be put.</para>
7883 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7884 (a) a specialised version of the function and (b) a rewrite rule
7885 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7886 un-specialised function into a call to the specialised one.</para>
7888 <para>The type in a SPECIALIZE pragma can be any type that is less
7889 polymorphic than the type of the original function. In concrete terms,
7890 if the original function is <literal>f</literal> then the pragma
7892 {-# SPECIALIZE f :: <type> #-}
7894 is valid if and only if the definition
7896 f_spec :: <type>
7899 is valid. Here are some examples (where we only give the type signature
7900 for the original function, not its code):
7902 f :: Eq a => a -> b -> b
7903 {-# SPECIALISE f :: Int -> b -> b #-}
7905 g :: (Eq a, Ix b) => a -> b -> b
7906 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7908 h :: Eq a => a -> a -> a
7909 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7911 The last of these examples will generate a
7912 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7913 well. If you use this kind of specialisation, let us know how well it works.
7916 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7917 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7918 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7919 The <literal>INLINE</literal> pragma affects the specialised version of the
7920 function (only), and applies even if the function is recursive. The motivating
7923 -- A GADT for arrays with type-indexed representation
7925 ArrInt :: !Int -> ByteArray# -> Arr Int
7926 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7928 (!:) :: Arr e -> Int -> e
7929 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7930 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7931 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7932 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7934 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7935 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7936 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7937 the specialised function will be inlined. It has two calls to
7938 <literal>(!:)</literal>,
7939 both at type <literal>Int</literal>. Both these calls fire the first
7940 specialisation, whose body is also inlined. The result is a type-based
7941 unrolling of the indexing function.</para>
7942 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7943 on an ordinarily-recursive function.</para>
7945 <para>Note: In earlier versions of GHC, it was possible to provide your own
7946 specialised function for a given type:
7949 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7952 This feature has been removed, as it is now subsumed by the
7953 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7957 <sect2 id="specialize-instance-pragma">
7958 <title>SPECIALIZE instance pragma
7962 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7963 <indexterm><primary>overloading, death to</primary></indexterm>
7964 Same idea, except for instance declarations. For example:
7967 instance (Eq a) => Eq (Foo a) where {
7968 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7972 The pragma must occur inside the <literal>where</literal> part
7973 of the instance declaration.
7976 Compatible with HBC, by the way, except perhaps in the placement
7982 <sect2 id="unpack-pragma">
7983 <title>UNPACK pragma</title>
7985 <indexterm><primary>UNPACK</primary></indexterm>
7987 <para>The <literal>UNPACK</literal> indicates to the compiler
7988 that it should unpack the contents of a constructor field into
7989 the constructor itself, removing a level of indirection. For
7993 data T = T {-# UNPACK #-} !Float
7994 {-# UNPACK #-} !Float
7997 <para>will create a constructor <literal>T</literal> containing
7998 two unboxed floats. This may not always be an optimisation: if
7999 the <function>T</function> constructor is scrutinised and the
8000 floats passed to a non-strict function for example, they will
8001 have to be reboxed (this is done automatically by the
8004 <para>Unpacking constructor fields should only be used in
8005 conjunction with <option>-O</option>, in order to expose
8006 unfoldings to the compiler so the reboxing can be removed as
8007 often as possible. For example:</para>
8011 f (T f1 f2) = f1 + f2
8014 <para>The compiler will avoid reboxing <function>f1</function>
8015 and <function>f2</function> by inlining <function>+</function>
8016 on floats, but only when <option>-O</option> is on.</para>
8018 <para>Any single-constructor data is eligible for unpacking; for
8022 data T = T {-# UNPACK #-} !(Int,Int)
8025 <para>will store the two <literal>Int</literal>s directly in the
8026 <function>T</function> constructor, by flattening the pair.
8027 Multi-level unpacking is also supported:
8030 data T = T {-# UNPACK #-} !S
8031 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8034 will store two unboxed <literal>Int#</literal>s
8035 directly in the <function>T</function> constructor. The
8036 unpacker can see through newtypes, too.</para>
8038 <para>If a field cannot be unpacked, you will not get a warning,
8039 so it might be an idea to check the generated code with
8040 <option>-ddump-simpl</option>.</para>
8042 <para>See also the <option>-funbox-strict-fields</option> flag,
8043 which essentially has the effect of adding
8044 <literal>{-# UNPACK #-}</literal> to every strict
8045 constructor field.</para>
8048 <sect2 id="source-pragma">
8049 <title>SOURCE pragma</title>
8051 <indexterm><primary>SOURCE</primary></indexterm>
8052 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8053 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8059 <!-- ======================= REWRITE RULES ======================== -->
8061 <sect1 id="rewrite-rules">
8062 <title>Rewrite rules
8064 <indexterm><primary>RULES pragma</primary></indexterm>
8065 <indexterm><primary>pragma, RULES</primary></indexterm>
8066 <indexterm><primary>rewrite rules</primary></indexterm></title>
8069 The programmer can specify rewrite rules as part of the source program
8075 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8080 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8081 If you need more information, then <option>-ddump-rule-firings</option> shows you
8082 each individual rule firing in detail.
8086 <title>Syntax</title>
8089 From a syntactic point of view:
8095 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8096 may be generated by the layout rule).
8102 The layout rule applies in a pragma.
8103 Currently no new indentation level
8104 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8105 you must lay out the starting in the same column as the enclosing definitions.
8108 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8109 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8112 Furthermore, the closing <literal>#-}</literal>
8113 should start in a column to the right of the opening <literal>{-#</literal>.
8119 Each rule has a name, enclosed in double quotes. The name itself has
8120 no significance at all. It is only used when reporting how many times the rule fired.
8126 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8127 immediately after the name of the rule. Thus:
8130 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8133 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8134 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8143 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8144 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8145 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8146 by spaces, just like in a type <literal>forall</literal>.
8152 A pattern variable may optionally have a type signature.
8153 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8154 For example, here is the <literal>foldr/build</literal> rule:
8157 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8158 foldr k z (build g) = g k z
8161 Since <function>g</function> has a polymorphic type, it must have a type signature.
8168 The left hand side of a rule must consist of a top-level variable applied
8169 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8172 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8173 "wrong2" forall f. f True = True
8176 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8183 A rule does not need to be in the same module as (any of) the
8184 variables it mentions, though of course they need to be in scope.
8190 All rules are implicitly exported from the module, and are therefore
8191 in force in any module that imports the module that defined the rule, directly
8192 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8193 in force when compiling A.) The situation is very similar to that for instance
8201 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8202 any other flag settings. Furthermore, inside a RULE, the language extension
8203 <option>-XScopedTypeVariables</option> is automatically enabled; see
8204 <xref linkend="scoped-type-variables"/>.
8210 Like other pragmas, RULE pragmas are always checked for scope errors, and
8211 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8212 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8213 if the <option>-fenable-rewrite-rules</option> flag is
8214 on (see <xref linkend="rule-semantics"/>).
8223 <sect2 id="rule-semantics">
8224 <title>Semantics</title>
8227 From a semantic point of view:
8232 Rules are enabled (that is, used during optimisation)
8233 by the <option>-fenable-rewrite-rules</option> flag.
8234 This flag is implied by <option>-O</option>, and may be switched
8235 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8236 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8237 may not do what you expect, though, because without <option>-O</option> GHC
8238 ignores all optimisation information in interface files;
8239 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8240 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8241 has no effect on parsing or typechecking.
8247 Rules are regarded as left-to-right rewrite rules.
8248 When GHC finds an expression that is a substitution instance of the LHS
8249 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8250 By "a substitution instance" we mean that the LHS can be made equal to the
8251 expression by substituting for the pattern variables.
8258 GHC makes absolutely no attempt to verify that the LHS and RHS
8259 of a rule have the same meaning. That is undecidable in general, and
8260 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8267 GHC makes no attempt to make sure that the rules are confluent or
8268 terminating. For example:
8271 "loop" forall x y. f x y = f y x
8274 This rule will cause the compiler to go into an infinite loop.
8281 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8287 GHC currently uses a very simple, syntactic, matching algorithm
8288 for matching a rule LHS with an expression. It seeks a substitution
8289 which makes the LHS and expression syntactically equal modulo alpha
8290 conversion. The pattern (rule), but not the expression, is eta-expanded if
8291 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8292 But not beta conversion (that's called higher-order matching).
8296 Matching is carried out on GHC's intermediate language, which includes
8297 type abstractions and applications. So a rule only matches if the
8298 types match too. See <xref linkend="rule-spec"/> below.
8304 GHC keeps trying to apply the rules as it optimises the program.
8305 For example, consider:
8314 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8315 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8316 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8317 not be substituted, and the rule would not fire.
8327 <sect2 id="conlike">
8328 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8331 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8332 results. Consider this (artificial) example
8338 {-# RULES "f" f True = False #-}
8340 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8345 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8347 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8348 would have been a better chance that <literal>f</literal>'s RULE might fire.
8351 The way to get predictable behaviour is to use a NOINLINE
8352 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8353 that it is not inlined until its RULEs have had a chance to fire.
8356 GHC is very cautious about duplicating work. For example, consider
8358 f k z xs = let xs = build g
8359 in ...(foldr k z xs)...sum xs...
8360 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8362 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8363 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8364 duplicated if the rule fired.
8367 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8368 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8369 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8371 {-# INLINE[1] CONLIKE f #-}
8372 f x = <replaceable>blah</replaceable>
8374 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8375 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8376 should be considered cheap enough to duplicate, if such a duplication would make rule
8377 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8378 have such a property.)
8379 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8380 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8381 not going to be inlined before the rule has a chance to fire.
8386 <title>List fusion</title>
8389 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8390 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8391 intermediate list should be eliminated entirely.
8395 The following are good producers:
8407 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8413 Explicit lists (e.g. <literal>[True, False]</literal>)
8419 The cons constructor (e.g <literal>3:4:[]</literal>)
8425 <function>++</function>
8431 <function>map</function>
8437 <function>take</function>, <function>filter</function>
8443 <function>iterate</function>, <function>repeat</function>
8449 <function>zip</function>, <function>zipWith</function>
8458 The following are good consumers:
8470 <function>array</function> (on its second argument)
8476 <function>++</function> (on its first argument)
8482 <function>foldr</function>
8488 <function>map</function>
8494 <function>take</function>, <function>filter</function>
8500 <function>concat</function>
8506 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8512 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8513 will fuse with one but not the other)
8519 <function>partition</function>
8525 <function>head</function>
8531 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8537 <function>sequence_</function>
8543 <function>msum</function>
8549 <function>sortBy</function>
8558 So, for example, the following should generate no intermediate lists:
8561 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8567 This list could readily be extended; if there are Prelude functions that you use
8568 a lot which are not included, please tell us.
8572 If you want to write your own good consumers or producers, look at the
8573 Prelude definitions of the above functions to see how to do so.
8578 <sect2 id="rule-spec">
8579 <title>Specialisation
8583 Rewrite rules can be used to get the same effect as a feature
8584 present in earlier versions of GHC.
8585 For example, suppose that:
8588 genericLookup :: Ord a => Table a b -> a -> b
8589 intLookup :: Table Int b -> Int -> b
8592 where <function>intLookup</function> is an implementation of
8593 <function>genericLookup</function> that works very fast for
8594 keys of type <literal>Int</literal>. You might wish
8595 to tell GHC to use <function>intLookup</function> instead of
8596 <function>genericLookup</function> whenever the latter was called with
8597 type <literal>Table Int b -> Int -> b</literal>.
8598 It used to be possible to write
8601 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8604 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8607 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8610 This slightly odd-looking rule instructs GHC to replace
8611 <function>genericLookup</function> by <function>intLookup</function>
8612 <emphasis>whenever the types match</emphasis>.
8613 What is more, this rule does not need to be in the same
8614 file as <function>genericLookup</function>, unlike the
8615 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8616 have an original definition available to specialise).
8619 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8620 <function>intLookup</function> really behaves as a specialised version
8621 of <function>genericLookup</function>!!!</para>
8623 <para>An example in which using <literal>RULES</literal> for
8624 specialisation will Win Big:
8627 toDouble :: Real a => a -> Double
8628 toDouble = fromRational . toRational
8630 {-# RULES "toDouble/Int" toDouble = i2d #-}
8631 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8634 The <function>i2d</function> function is virtually one machine
8635 instruction; the default conversion—via an intermediate
8636 <literal>Rational</literal>—is obscenely expensive by
8642 <sect2 id="controlling-rules">
8643 <title>Controlling what's going on in rewrite rules</title>
8651 Use <option>-ddump-rules</option> to see the rules that are defined
8652 <emphasis>in this module</emphasis>.
8653 This includes rules generated by the specialisation pass, but excludes
8654 rules imported from other modules.
8660 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8661 If you add <option>-dppr-debug</option> you get a more detailed listing.
8667 Use <option>-ddump-rule-firings</option> to see in great detail what rules are being fired.
8668 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8674 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8677 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8678 {-# INLINE build #-}
8682 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8683 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8684 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8685 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8692 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8693 see how to write rules that will do fusion and yet give an efficient
8694 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8704 <sect2 id="core-pragma">
8705 <title>CORE pragma</title>
8707 <indexterm><primary>CORE pragma</primary></indexterm>
8708 <indexterm><primary>pragma, CORE</primary></indexterm>
8709 <indexterm><primary>core, annotation</primary></indexterm>
8712 The external core format supports <quote>Note</quote> annotations;
8713 the <literal>CORE</literal> pragma gives a way to specify what these
8714 should be in your Haskell source code. Syntactically, core
8715 annotations are attached to expressions and take a Haskell string
8716 literal as an argument. The following function definition shows an
8720 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8723 Semantically, this is equivalent to:
8731 However, when external core is generated (via
8732 <option>-fext-core</option>), there will be Notes attached to the
8733 expressions <function>show</function> and <varname>x</varname>.
8734 The core function declaration for <function>f</function> is:
8738 f :: %forall a . GHCziShow.ZCTShow a ->
8739 a -> GHCziBase.ZMZN GHCziBase.Char =
8740 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8742 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8744 (tpl1::GHCziBase.Int ->
8746 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8748 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8749 (tpl3::GHCziBase.ZMZN a ->
8750 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8758 Here, we can see that the function <function>show</function> (which
8759 has been expanded out to a case expression over the Show dictionary)
8760 has a <literal>%note</literal> attached to it, as does the
8761 expression <varname>eta</varname> (which used to be called
8762 <varname>x</varname>).
8769 <sect1 id="special-ids">
8770 <title>Special built-in functions</title>
8771 <para>GHC has a few built-in functions with special behaviour. These
8772 are now described in the module <ulink
8773 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8774 in the library documentation.</para>
8778 <sect1 id="generic-classes">
8779 <title>Generic classes</title>
8782 The ideas behind this extension are described in detail in "Derivable type classes",
8783 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8784 An example will give the idea:
8792 fromBin :: [Int] -> (a, [Int])
8794 toBin {| Unit |} Unit = []
8795 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8796 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8797 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8799 fromBin {| Unit |} bs = (Unit, bs)
8800 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8801 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8802 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8803 (y,bs'') = fromBin bs'
8806 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8807 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8808 which are defined thus in the library module <literal>Generics</literal>:
8812 data a :+: b = Inl a | Inr b
8813 data a :*: b = a :*: b
8816 Now you can make a data type into an instance of Bin like this:
8818 instance (Bin a, Bin b) => Bin (a,b)
8819 instance Bin a => Bin [a]
8821 That is, just leave off the "where" clause. Of course, you can put in the
8822 where clause and over-ride whichever methods you please.
8826 <title> Using generics </title>
8827 <para>To use generics you need to</para>
8830 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8831 <option>-XGenerics</option> (to generate extra per-data-type code),
8832 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8836 <para>Import the module <literal>Generics</literal> from the
8837 <literal>lang</literal> package. This import brings into
8838 scope the data types <literal>Unit</literal>,
8839 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8840 don't need this import if you don't mention these types
8841 explicitly; for example, if you are simply giving instance
8842 declarations.)</para>
8847 <sect2> <title> Changes wrt the paper </title>
8849 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8850 can be written infix (indeed, you can now use
8851 any operator starting in a colon as an infix type constructor). Also note that
8852 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8853 Finally, note that the syntax of the type patterns in the class declaration
8854 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8855 alone would ambiguous when they appear on right hand sides (an extension we
8856 anticipate wanting).
8860 <sect2> <title>Terminology and restrictions</title>
8862 Terminology. A "generic default method" in a class declaration
8863 is one that is defined using type patterns as above.
8864 A "polymorphic default method" is a default method defined as in Haskell 98.
8865 A "generic class declaration" is a class declaration with at least one
8866 generic default method.
8874 Alas, we do not yet implement the stuff about constructor names and
8881 A generic class can have only one parameter; you can't have a generic
8882 multi-parameter class.
8888 A default method must be defined entirely using type patterns, or entirely
8889 without. So this is illegal:
8892 op :: a -> (a, Bool)
8893 op {| Unit |} Unit = (Unit, True)
8896 However it is perfectly OK for some methods of a generic class to have
8897 generic default methods and others to have polymorphic default methods.
8903 The type variable(s) in the type pattern for a generic method declaration
8904 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:
8908 op {| p :*: q |} (x :*: y) = op (x :: p)
8916 The type patterns in a generic default method must take one of the forms:
8922 where "a" and "b" are type variables. Furthermore, all the type patterns for
8923 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8924 must use the same type variables. So this is illegal:
8928 op {| a :+: b |} (Inl x) = True
8929 op {| p :+: q |} (Inr y) = False
8931 The type patterns must be identical, even in equations for different methods of the class.
8932 So this too is illegal:
8936 op1 {| a :*: b |} (x :*: y) = True
8939 op2 {| p :*: q |} (x :*: y) = False
8941 (The reason for this restriction is that we gather all the equations for a particular type constructor
8942 into a single generic instance declaration.)
8948 A generic method declaration must give a case for each of the three type constructors.
8954 The type for a generic method can be built only from:
8956 <listitem> <para> Function arrows </para> </listitem>
8957 <listitem> <para> Type variables </para> </listitem>
8958 <listitem> <para> Tuples </para> </listitem>
8959 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8961 Here are some example type signatures for generic methods:
8964 op2 :: Bool -> (a,Bool)
8965 op3 :: [Int] -> a -> a
8968 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8972 This restriction is an implementation restriction: we just haven't got around to
8973 implementing the necessary bidirectional maps over arbitrary type constructors.
8974 It would be relatively easy to add specific type constructors, such as Maybe and list,
8975 to the ones that are allowed.</para>
8980 In an instance declaration for a generic class, the idea is that the compiler
8981 will fill in the methods for you, based on the generic templates. However it can only
8986 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8991 No constructor of the instance type has unboxed fields.
8995 (Of course, these things can only arise if you are already using GHC extensions.)
8996 However, you can still give an instance declarations for types which break these rules,
8997 provided you give explicit code to override any generic default methods.
9005 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9006 what the compiler does with generic declarations.
9011 <sect2> <title> Another example </title>
9013 Just to finish with, here's another example I rather like:
9017 nCons {| Unit |} _ = 1
9018 nCons {| a :*: b |} _ = 1
9019 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9022 tag {| Unit |} _ = 1
9023 tag {| a :*: b |} _ = 1
9024 tag {| a :+: b |} (Inl x) = tag x
9025 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9031 <sect1 id="monomorphism">
9032 <title>Control over monomorphism</title>
9034 <para>GHC supports two flags that control the way in which generalisation is
9035 carried out at let and where bindings.
9039 <title>Switching off the dreaded Monomorphism Restriction</title>
9040 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9042 <para>Haskell's monomorphism restriction (see
9043 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9045 of the Haskell Report)
9046 can be completely switched off by
9047 <option>-XNoMonomorphismRestriction</option>.
9052 <title>Monomorphic pattern bindings</title>
9053 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9054 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9056 <para> As an experimental change, we are exploring the possibility of
9057 making pattern bindings monomorphic; that is, not generalised at all.
9058 A pattern binding is a binding whose LHS has no function arguments,
9059 and is not a simple variable. For example:
9061 f x = x -- Not a pattern binding
9062 f = \x -> x -- Not a pattern binding
9063 f :: Int -> Int = \x -> x -- Not a pattern binding
9065 (g,h) = e -- A pattern binding
9066 (f) = e -- A pattern binding
9067 [x] = e -- A pattern binding
9069 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9070 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
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