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="datatype-contexts">
1898 <title>Data type contexts</title>
1900 <para>Haskell allows datatypes to be given contexts, e.g.</para>
1903 data Eq a => Set a = NilSet | ConsSet a (Set a)
1906 <para>give constructors with types:</para>
1910 ConsSet :: Eq a => a -> Set a -> Set a
1913 <para>In GHC this feature is an extension called
1914 <literal>DatatypeContexts</literal>, and on by default.</para>
1917 <sect2 id="infix-tycons">
1918 <title>Infix type constructors, classes, and type variables</title>
1921 GHC allows type constructors, classes, and type variables to be operators, and
1922 to be written infix, very much like expressions. More specifically:
1925 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1926 The lexical syntax is the same as that for data constructors.
1929 Data type and type-synonym declarations can be written infix, parenthesised
1930 if you want further arguments. E.g.
1932 data a :*: b = Foo a b
1933 type a :+: b = Either a b
1934 class a :=: b where ...
1936 data (a :**: b) x = Baz a b x
1937 type (a :++: b) y = Either (a,b) y
1941 Types, and class constraints, can be written infix. For example
1944 f :: (a :=: b) => a -> b
1948 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1949 The lexical syntax is the same as that for variable operators, excluding "(.)",
1950 "(!)", and "(*)". In a binding position, the operator must be
1951 parenthesised. For example:
1953 type T (+) = Int + Int
1957 liftA2 :: Arrow (~>)
1958 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1964 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1965 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1968 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1969 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1970 sets the fixity for a data constructor and the corresponding type constructor. For example:
1974 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1975 and similarly for <literal>:*:</literal>.
1976 <literal>Int `a` Bool</literal>.
1979 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1986 <sect2 id="type-synonyms">
1987 <title>Liberalised type synonyms</title>
1990 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1991 on individual synonym declarations.
1992 With the <option>-XLiberalTypeSynonyms</option> extension,
1993 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1994 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1997 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1998 in a type synonym, thus:
2000 type Discard a = forall b. Show b => a -> b -> (a, String)
2005 g :: Discard Int -> (Int,String) -- A rank-2 type
2012 If you also use <option>-XUnboxedTuples</option>,
2013 you can write an unboxed tuple in a type synonym:
2015 type Pr = (# Int, Int #)
2023 You can apply a type synonym to a forall type:
2025 type Foo a = a -> a -> Bool
2027 f :: Foo (forall b. b->b)
2029 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2031 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2036 You can apply a type synonym to a partially applied type synonym:
2038 type Generic i o = forall x. i x -> o x
2041 foo :: Generic Id []
2043 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2045 foo :: forall x. x -> [x]
2053 GHC currently does kind checking before expanding synonyms (though even that
2057 After expanding type synonyms, GHC does validity checking on types, looking for
2058 the following mal-formedness which isn't detected simply by kind checking:
2061 Type constructor applied to a type involving for-alls.
2064 Unboxed tuple on left of an arrow.
2067 Partially-applied type synonym.
2071 this will be rejected:
2073 type Pr = (# Int, Int #)
2078 because GHC does not allow unboxed tuples on the left of a function arrow.
2083 <sect2 id="existential-quantification">
2084 <title>Existentially quantified data constructors
2088 The idea of using existential quantification in data type declarations
2089 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2090 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2091 London, 1991). It was later formalised by Laufer and Odersky
2092 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2093 TOPLAS, 16(5), pp1411-1430, 1994).
2094 It's been in Lennart
2095 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2096 proved very useful. Here's the idea. Consider the declaration:
2102 data Foo = forall a. MkFoo a (a -> Bool)
2109 The data type <literal>Foo</literal> has two constructors with types:
2115 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2122 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2123 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2124 For example, the following expression is fine:
2130 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2136 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2137 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2138 isUpper</function> packages a character with a compatible function. These
2139 two things are each of type <literal>Foo</literal> and can be put in a list.
2143 What can we do with a value of type <literal>Foo</literal>?. In particular,
2144 what happens when we pattern-match on <function>MkFoo</function>?
2150 f (MkFoo val fn) = ???
2156 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2157 are compatible, the only (useful) thing we can do with them is to
2158 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2165 f (MkFoo val fn) = fn val
2171 What this allows us to do is to package heterogeneous values
2172 together with a bunch of functions that manipulate them, and then treat
2173 that collection of packages in a uniform manner. You can express
2174 quite a bit of object-oriented-like programming this way.
2177 <sect3 id="existential">
2178 <title>Why existential?
2182 What has this to do with <emphasis>existential</emphasis> quantification?
2183 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2189 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2195 But Haskell programmers can safely think of the ordinary
2196 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2197 adding a new existential quantification construct.
2202 <sect3 id="existential-with-context">
2203 <title>Existentials and type classes</title>
2206 An easy extension is to allow
2207 arbitrary contexts before the constructor. For example:
2213 data Baz = forall a. Eq a => Baz1 a a
2214 | forall b. Show b => Baz2 b (b -> b)
2220 The two constructors have the types you'd expect:
2226 Baz1 :: forall a. Eq a => a -> a -> Baz
2227 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2233 But when pattern matching on <function>Baz1</function> the matched values can be compared
2234 for equality, and when pattern matching on <function>Baz2</function> the first matched
2235 value can be converted to a string (as well as applying the function to it).
2236 So this program is legal:
2243 f (Baz1 p q) | p == q = "Yes"
2245 f (Baz2 v fn) = show (fn v)
2251 Operationally, in a dictionary-passing implementation, the
2252 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2253 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2254 extract it on pattern matching.
2259 <sect3 id="existential-records">
2260 <title>Record Constructors</title>
2263 GHC allows existentials to be used with records syntax as well. For example:
2266 data Counter a = forall self. NewCounter
2268 , _inc :: self -> self
2269 , _display :: self -> IO ()
2273 Here <literal>tag</literal> is a public field, with a well-typed selector
2274 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2275 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2276 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2277 compile-time error. In other words, <emphasis>GHC defines a record selector function
2278 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2279 (This example used an underscore in the fields for which record selectors
2280 will not be defined, but that is only programming style; GHC ignores them.)
2284 To make use of these hidden fields, we need to create some helper functions:
2287 inc :: Counter a -> Counter a
2288 inc (NewCounter x i d t) = NewCounter
2289 { _this = i x, _inc = i, _display = d, tag = t }
2291 display :: Counter a -> IO ()
2292 display NewCounter{ _this = x, _display = d } = d x
2295 Now we can define counters with different underlying implementations:
2298 counterA :: Counter String
2299 counterA = NewCounter
2300 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2302 counterB :: Counter String
2303 counterB = NewCounter
2304 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2307 display (inc counterA) -- prints "1"
2308 display (inc (inc counterB)) -- prints "##"
2311 Record update syntax is supported for existentials (and GADTs):
2313 setTag :: Counter a -> a -> Counter a
2314 setTag obj t = obj{ tag = t }
2316 The rule for record update is this: <emphasis>
2317 the types of the updated fields may
2318 mention only the universally-quantified type variables
2319 of the data constructor. For GADTs, the field may mention only types
2320 that appear as a simple type-variable argument in the constructor's result
2321 type</emphasis>. For example:
2323 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2324 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2325 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2326 -- existentially quantified)
2328 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2329 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2330 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2331 -- type-variable argument in G1's result type)
2339 <title>Restrictions</title>
2342 There are several restrictions on the ways in which existentially-quantified
2343 constructors can be use.
2352 When pattern matching, each pattern match introduces a new,
2353 distinct, type for each existential type variable. These types cannot
2354 be unified with any other type, nor can they escape from the scope of
2355 the pattern match. For example, these fragments are incorrect:
2363 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2364 is the result of <function>f1</function>. One way to see why this is wrong is to
2365 ask what type <function>f1</function> has:
2369 f1 :: Foo -> a -- Weird!
2373 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2378 f1 :: forall a. Foo -> a -- Wrong!
2382 The original program is just plain wrong. Here's another sort of error
2386 f2 (Baz1 a b) (Baz1 p q) = a==q
2390 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2391 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2392 from the two <function>Baz1</function> constructors.
2400 You can't pattern-match on an existentially quantified
2401 constructor in a <literal>let</literal> or <literal>where</literal> group of
2402 bindings. So this is illegal:
2406 f3 x = a==b where { Baz1 a b = x }
2409 Instead, use a <literal>case</literal> expression:
2412 f3 x = case x of Baz1 a b -> a==b
2415 In general, you can only pattern-match
2416 on an existentially-quantified constructor in a <literal>case</literal> expression or
2417 in the patterns of a function definition.
2419 The reason for this restriction is really an implementation one.
2420 Type-checking binding groups is already a nightmare without
2421 existentials complicating the picture. Also an existential pattern
2422 binding at the top level of a module doesn't make sense, because it's
2423 not clear how to prevent the existentially-quantified type "escaping".
2424 So for now, there's a simple-to-state restriction. We'll see how
2432 You can't use existential quantification for <literal>newtype</literal>
2433 declarations. So this is illegal:
2437 newtype T = forall a. Ord a => MkT a
2441 Reason: a value of type <literal>T</literal> must be represented as a
2442 pair of a dictionary for <literal>Ord t</literal> and a value of type
2443 <literal>t</literal>. That contradicts the idea that
2444 <literal>newtype</literal> should have no concrete representation.
2445 You can get just the same efficiency and effect by using
2446 <literal>data</literal> instead of <literal>newtype</literal>. If
2447 there is no overloading involved, then there is more of a case for
2448 allowing an existentially-quantified <literal>newtype</literal>,
2449 because the <literal>data</literal> version does carry an
2450 implementation cost, but single-field existentially quantified
2451 constructors aren't much use. So the simple restriction (no
2452 existential stuff on <literal>newtype</literal>) stands, unless there
2453 are convincing reasons to change it.
2461 You can't use <literal>deriving</literal> to define instances of a
2462 data type with existentially quantified data constructors.
2464 Reason: in most cases it would not make sense. For example:;
2467 data T = forall a. MkT [a] deriving( Eq )
2470 To derive <literal>Eq</literal> in the standard way we would need to have equality
2471 between the single component of two <function>MkT</function> constructors:
2475 (MkT a) == (MkT b) = ???
2478 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2479 It's just about possible to imagine examples in which the derived instance
2480 would make sense, but it seems altogether simpler simply to prohibit such
2481 declarations. Define your own instances!
2492 <!-- ====================== Generalised algebraic data types ======================= -->
2494 <sect2 id="gadt-style">
2495 <title>Declaring data types with explicit constructor signatures</title>
2497 <para>GHC allows you to declare an algebraic data type by
2498 giving the type signatures of constructors explicitly. For example:
2502 Just :: a -> Maybe a
2504 The form is called a "GADT-style declaration"
2505 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2506 can only be declared using this form.</para>
2507 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2508 For example, these two declarations are equivalent:
2510 data Foo = forall a. MkFoo a (a -> Bool)
2511 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2514 <para>Any data type that can be declared in standard Haskell-98 syntax
2515 can also be declared using GADT-style syntax.
2516 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2517 they treat class constraints on the data constructors differently.
2518 Specifically, if the constructor is given a type-class context, that
2519 context is made available by pattern matching. For example:
2522 MkSet :: Eq a => [a] -> Set a
2524 makeSet :: Eq a => [a] -> Set a
2525 makeSet xs = MkSet (nub xs)
2527 insert :: a -> Set a -> Set a
2528 insert a (MkSet as) | a `elem` as = MkSet as
2529 | otherwise = MkSet (a:as)
2531 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2532 gives rise to a <literal>(Eq a)</literal>
2533 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2534 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2535 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2536 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2537 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2538 In the example, the equality dictionary is used to satisfy the equality constraint
2539 generated by the call to <literal>elem</literal>, so that the type of
2540 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2543 For example, one possible application is to reify dictionaries:
2545 data NumInst a where
2546 MkNumInst :: Num a => NumInst a
2548 intInst :: NumInst Int
2551 plus :: NumInst a -> a -> a -> a
2552 plus MkNumInst p q = p + q
2554 Here, a value of type <literal>NumInst a</literal> is equivalent
2555 to an explicit <literal>(Num a)</literal> dictionary.
2558 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2559 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2563 = Num a => MkNumInst (NumInst a)
2565 Notice that, unlike the situation when declaring an existential, there is
2566 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2567 data type's universally quantified type variable <literal>a</literal>.
2568 A constructor may have both universal and existential type variables: for example,
2569 the following two declarations are equivalent:
2572 = forall b. (Num a, Eq b) => MkT1 a b
2574 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2577 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2578 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2579 In Haskell 98 the definition
2581 data Eq a => Set' a = MkSet' [a]
2583 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2584 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2585 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2586 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2587 GHC's behaviour is much more useful, as well as much more intuitive.
2591 The rest of this section gives further details about GADT-style data
2596 The result type of each data constructor must begin with the type constructor being defined.
2597 If the result type of all constructors
2598 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2599 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2600 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2604 As with other type signatures, you can give a single signature for several data constructors.
2605 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2614 The type signature of
2615 each constructor is independent, and is implicitly universally quantified as usual.
2616 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2617 have no scope, and different constructors may have different universally-quantified type variables:
2619 data T a where -- The 'a' has no scope
2620 T1,T2 :: b -> T b -- Means forall b. b -> T b
2621 T3 :: T a -- Means forall a. T a
2626 A constructor signature may mention type class constraints, which can differ for
2627 different constructors. For example, this is fine:
2630 T1 :: Eq b => b -> b -> T b
2631 T2 :: (Show c, Ix c) => c -> [c] -> T c
2633 When patten matching, these constraints are made available to discharge constraints
2634 in the body of the match. For example:
2637 f (T1 x y) | x==y = "yes"
2641 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2642 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2643 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2647 Unlike a Haskell-98-style
2648 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2649 have no scope. Indeed, one can write a kind signature instead:
2651 data Set :: * -> * where ...
2653 or even a mixture of the two:
2655 data Bar a :: (* -> *) -> * where ...
2657 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2660 data Bar a (b :: * -> *) where ...
2666 You can use strictness annotations, in the obvious places
2667 in the constructor type:
2670 Lit :: !Int -> Term Int
2671 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2672 Pair :: Term a -> Term b -> Term (a,b)
2677 You can use a <literal>deriving</literal> clause on a GADT-style data type
2678 declaration. For example, these two declarations are equivalent
2680 data Maybe1 a where {
2681 Nothing1 :: Maybe1 a ;
2682 Just1 :: a -> Maybe1 a
2683 } deriving( Eq, Ord )
2685 data Maybe2 a = Nothing2 | Just2 a
2691 The type signature may have quantified type variables that do not appear
2695 MkFoo :: a -> (a->Bool) -> Foo
2698 Here the type variable <literal>a</literal> does not appear in the result type
2699 of either constructor.
2700 Although it is universally quantified in the type of the constructor, such
2701 a type variable is often called "existential".
2702 Indeed, the above declaration declares precisely the same type as
2703 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2705 The type may contain a class context too, of course:
2708 MkShowable :: Show a => a -> Showable
2713 You can use record syntax on a GADT-style data type declaration:
2717 Adult :: { name :: String, children :: [Person] } -> Person
2718 Child :: Show a => { name :: !String, funny :: a } -> Person
2720 As usual, for every constructor that has a field <literal>f</literal>, the type of
2721 field <literal>f</literal> must be the same (modulo alpha conversion).
2722 The <literal>Child</literal> constructor above shows that the signature
2723 may have a context, existentially-quantified variables, and strictness annotations,
2724 just as in the non-record case. (NB: the "type" that follows the double-colon
2725 is not really a type, because of the record syntax and strictness annotations.
2726 A "type" of this form can appear only in a constructor signature.)
2730 Record updates are allowed with GADT-style declarations,
2731 only fields that have the following property: the type of the field
2732 mentions no existential type variables.
2736 As in the case of existentials declared using the Haskell-98-like record syntax
2737 (<xref linkend="existential-records"/>),
2738 record-selector functions are generated only for those fields that have well-typed
2740 Here is the example of that section, in GADT-style syntax:
2742 data Counter a where
2743 NewCounter { _this :: self
2744 , _inc :: self -> self
2745 , _display :: self -> IO ()
2750 As before, only one selector function is generated here, that for <literal>tag</literal>.
2751 Nevertheless, you can still use all the field names in pattern matching and record construction.
2753 </itemizedlist></para>
2757 <title>Generalised Algebraic Data Types (GADTs)</title>
2759 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2760 by allowing constructors to have richer return types. Here is an example:
2763 Lit :: Int -> Term Int
2764 Succ :: Term Int -> Term Int
2765 IsZero :: Term Int -> Term Bool
2766 If :: Term Bool -> Term a -> Term a -> Term a
2767 Pair :: Term a -> Term b -> Term (a,b)
2769 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2770 case with ordinary data types. This generality allows us to
2771 write a well-typed <literal>eval</literal> function
2772 for these <literal>Terms</literal>:
2776 eval (Succ t) = 1 + eval t
2777 eval (IsZero t) = eval t == 0
2778 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2779 eval (Pair e1 e2) = (eval e1, eval e2)
2781 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2782 For example, in the right hand side of the equation
2787 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2788 A precise specification of the type rules is beyond what this user manual aspires to,
2789 but the design closely follows that described in
2791 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2792 unification-based type inference for GADTs</ulink>,
2794 The general principle is this: <emphasis>type refinement is only carried out
2795 based on user-supplied type annotations</emphasis>.
2796 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2797 and lots of obscure error messages will
2798 occur. However, the refinement is quite general. For example, if we had:
2800 eval :: Term a -> a -> a
2801 eval (Lit i) j = i+j
2803 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2804 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2805 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2808 These and many other examples are given in papers by Hongwei Xi, and
2809 Tim Sheard. There is a longer introduction
2810 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2812 <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
2813 may use different notation to that implemented in GHC.
2816 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2817 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2820 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2821 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2822 The result type of each constructor must begin with the type constructor being defined,
2823 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2824 For example, in the <literal>Term</literal> data
2825 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2826 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2831 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2832 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2833 whose result type is not just <literal>T a b</literal>.
2837 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2838 an ordinary data type.
2842 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2846 Lit { val :: Int } :: Term Int
2847 Succ { num :: Term Int } :: Term Int
2848 Pred { num :: Term Int } :: Term Int
2849 IsZero { arg :: Term Int } :: Term Bool
2850 Pair { arg1 :: Term a
2853 If { cnd :: Term Bool
2858 However, for GADTs there is the following additional constraint:
2859 every constructor that has a field <literal>f</literal> must have
2860 the same result type (modulo alpha conversion)
2861 Hence, in the above example, we cannot merge the <literal>num</literal>
2862 and <literal>arg</literal> fields above into a
2863 single name. Although their field types are both <literal>Term Int</literal>,
2864 their selector functions actually have different types:
2867 num :: Term Int -> Term Int
2868 arg :: Term Bool -> Term Int
2873 When pattern-matching against data constructors drawn from a GADT,
2874 for example in a <literal>case</literal> expression, the following rules apply:
2876 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2877 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2878 <listitem><para>The type of any free variable mentioned in any of
2879 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2881 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2882 way to ensure that a variable a rigid type is to give it a type signature.
2883 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2884 Simple unification-based type inference for GADTs
2885 </ulink>. The criteria implemented by GHC are given in the Appendix.
2895 <!-- ====================== End of Generalised algebraic data types ======================= -->
2897 <sect1 id="deriving">
2898 <title>Extensions to the "deriving" mechanism</title>
2900 <sect2 id="deriving-inferred">
2901 <title>Inferred context for deriving clauses</title>
2904 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2907 data T0 f a = MkT0 a deriving( Eq )
2908 data T1 f a = MkT1 (f a) deriving( Eq )
2909 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2911 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2913 instance Eq a => Eq (T0 f a) where ...
2914 instance Eq (f a) => Eq (T1 f a) where ...
2915 instance Eq (f (f a)) => Eq (T2 f a) where ...
2917 The first of these is obviously fine. The second is still fine, although less obviously.
2918 The third is not Haskell 98, and risks losing termination of instances.
2921 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2922 each constraint in the inferred instance context must consist only of type variables,
2923 with no repetitions.
2926 This rule is applied regardless of flags. If you want a more exotic context, you can write
2927 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2931 <sect2 id="stand-alone-deriving">
2932 <title>Stand-alone deriving declarations</title>
2935 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2937 data Foo a = Bar a | Baz String
2939 deriving instance Eq a => Eq (Foo a)
2941 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2942 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2943 Note the following points:
2946 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2947 exactly as you would in an ordinary instance declaration.
2948 (In contrast, in a <literal>deriving</literal> clause
2949 attached to a data type declaration, the context is inferred.)
2953 A <literal>deriving instance</literal> declaration
2954 must obey the same rules concerning form and termination as ordinary instance declarations,
2955 controlled by the same flags; see <xref linkend="instance-decls"/>.
2959 Unlike a <literal>deriving</literal>
2960 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2961 than the data type (assuming you also use
2962 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2965 data Foo a = Bar a | Baz String
2967 deriving instance Eq a => Eq (Foo [a])
2968 deriving instance Eq a => Eq (Foo (Maybe a))
2970 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2971 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2975 Unlike a <literal>deriving</literal>
2976 declaration attached to a <literal>data</literal> declaration,
2977 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2978 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2979 your problem. (GHC will show you the offending code if it has a type error.)
2980 The merit of this is that you can derive instances for GADTs and other exotic
2981 data types, providing only that the boilerplate code does indeed typecheck. For example:
2987 deriving instance Show (T a)
2989 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2990 data type declaration for <literal>T</literal>,
2991 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2992 the instance declaration using stand-alone deriving.
2997 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2998 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
3001 newtype Foo a = MkFoo (State Int a)
3003 deriving instance MonadState Int Foo
3005 GHC always treats the <emphasis>last</emphasis> parameter of the instance
3006 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
3008 </itemizedlist></para>
3013 <sect2 id="deriving-typeable">
3014 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
3017 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
3018 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
3019 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
3020 classes <literal>Eq</literal>, <literal>Ord</literal>,
3021 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
3024 GHC extends this list with several more classes that may be automatically derived:
3026 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
3027 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
3028 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
3030 <para>An instance of <literal>Typeable</literal> can only be derived if the
3031 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
3032 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
3034 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
3035 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
3037 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
3038 are used, and only <literal>Typeable1</literal> up to
3039 <literal>Typeable7</literal> are provided in the library.)
3040 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
3041 class, whose kind suits that of the data type constructor, and
3042 then writing the data type instance by hand.
3046 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
3047 the class <literal>Functor</literal>,
3048 defined in <literal>GHC.Base</literal>.
3051 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
3052 the class <literal>Foldable</literal>,
3053 defined in <literal>Data.Foldable</literal>.
3056 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
3057 the class <literal>Traversable</literal>,
3058 defined in <literal>Data.Traversable</literal>.
3061 In each case the appropriate class must be in scope before it
3062 can be mentioned in the <literal>deriving</literal> clause.
3066 <sect2 id="newtype-deriving">
3067 <title>Generalised derived instances for newtypes</title>
3070 When you define an abstract type using <literal>newtype</literal>, you may want
3071 the new type to inherit some instances from its representation. In
3072 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3073 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3074 other classes you have to write an explicit instance declaration. For
3075 example, if you define
3078 newtype Dollars = Dollars Int
3081 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3082 explicitly define an instance of <literal>Num</literal>:
3085 instance Num Dollars where
3086 Dollars a + Dollars b = Dollars (a+b)
3089 All the instance does is apply and remove the <literal>newtype</literal>
3090 constructor. It is particularly galling that, since the constructor
3091 doesn't appear at run-time, this instance declaration defines a
3092 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3093 dictionary, only slower!
3097 <sect3> <title> Generalising the deriving clause </title>
3099 GHC now permits such instances to be derived instead,
3100 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3103 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3106 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3107 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3108 derives an instance declaration of the form
3111 instance Num Int => Num Dollars
3114 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3118 We can also derive instances of constructor classes in a similar
3119 way. For example, suppose we have implemented state and failure monad
3120 transformers, such that
3123 instance Monad m => Monad (State s m)
3124 instance Monad m => Monad (Failure m)
3126 In Haskell 98, we can define a parsing monad by
3128 type Parser tok m a = State [tok] (Failure m) a
3131 which is automatically a monad thanks to the instance declarations
3132 above. With the extension, we can make the parser type abstract,
3133 without needing to write an instance of class <literal>Monad</literal>, via
3136 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3139 In this case the derived instance declaration is of the form
3141 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3144 Notice that, since <literal>Monad</literal> is a constructor class, the
3145 instance is a <emphasis>partial application</emphasis> of the new type, not the
3146 entire left hand side. We can imagine that the type declaration is
3147 "eta-converted" to generate the context of the instance
3152 We can even derive instances of multi-parameter classes, provided the
3153 newtype is the last class parameter. In this case, a ``partial
3154 application'' of the class appears in the <literal>deriving</literal>
3155 clause. For example, given the class
3158 class StateMonad s m | m -> s where ...
3159 instance Monad m => StateMonad s (State s m) where ...
3161 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3163 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3164 deriving (Monad, StateMonad [tok])
3167 The derived instance is obtained by completing the application of the
3168 class to the new type:
3171 instance StateMonad [tok] (State [tok] (Failure m)) =>
3172 StateMonad [tok] (Parser tok m)
3177 As a result of this extension, all derived instances in newtype
3178 declarations are treated uniformly (and implemented just by reusing
3179 the dictionary for the representation type), <emphasis>except</emphasis>
3180 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3181 the newtype and its representation.
3185 <sect3> <title> A more precise specification </title>
3187 Derived instance declarations are constructed as follows. Consider the
3188 declaration (after expansion of any type synonyms)
3191 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3197 The <literal>ci</literal> are partial applications of
3198 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3199 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3202 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3205 The type <literal>t</literal> is an arbitrary type.
3208 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3209 nor in the <literal>ci</literal>, and
3212 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3213 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3214 should not "look through" the type or its constructor. You can still
3215 derive these classes for a newtype, but it happens in the usual way, not
3216 via this new mechanism.
3219 Then, for each <literal>ci</literal>, the derived instance
3222 instance ci t => ci (T v1...vk)
3224 As an example which does <emphasis>not</emphasis> work, consider
3226 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3228 Here we cannot derive the instance
3230 instance Monad (State s m) => Monad (NonMonad m)
3233 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3234 and so cannot be "eta-converted" away. It is a good thing that this
3235 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3236 not, in fact, a monad --- for the same reason. Try defining
3237 <literal>>>=</literal> with the correct type: you won't be able to.
3241 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3242 important, since we can only derive instances for the last one. If the
3243 <literal>StateMonad</literal> class above were instead defined as
3246 class StateMonad m s | m -> s where ...
3249 then we would not have been able to derive an instance for the
3250 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3251 classes usually have one "main" parameter for which deriving new
3252 instances is most interesting.
3254 <para>Lastly, all of this applies only for classes other than
3255 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3256 and <literal>Data</literal>, for which the built-in derivation applies (section
3257 4.3.3. of the Haskell Report).
3258 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3259 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3260 the standard method is used or the one described here.)
3267 <!-- TYPE SYSTEM EXTENSIONS -->
3268 <sect1 id="type-class-extensions">
3269 <title>Class and instances declarations</title>
3271 <sect2 id="multi-param-type-classes">
3272 <title>Class declarations</title>
3275 This section, and the next one, documents GHC's type-class extensions.
3276 There's lots of background in the paper <ulink
3277 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3278 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3279 Jones, Erik Meijer).
3282 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3286 <title>Multi-parameter type classes</title>
3288 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3293 class Collection c a where
3294 union :: c a -> c a -> c a
3301 <sect3 id="superclass-rules">
3302 <title>The superclasses of a class declaration</title>
3305 In Haskell 98 the context of a class declaration (which introduces superclasses)
3306 must be simple; that is, each predicate must consist of a class applied to
3307 type variables. The flag <option>-XFlexibleContexts</option>
3308 (<xref linkend="flexible-contexts"/>)
3309 lifts this restriction,
3310 so that the only restriction on the context in a class declaration is
3311 that the class hierarchy must be acyclic. So these class declarations are OK:
3315 class Functor (m k) => FiniteMap m k where
3318 class (Monad m, Monad (t m)) => Transform t m where
3319 lift :: m a -> (t m) a
3325 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3326 of "acyclic" involves only the superclass relationships. For example,
3332 op :: D b => a -> b -> b
3335 class C a => D a where { ... }
3339 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3340 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3341 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3348 <sect3 id="class-method-types">
3349 <title>Class method types</title>
3352 Haskell 98 prohibits class method types to mention constraints on the
3353 class type variable, thus:
3356 fromList :: [a] -> s a
3357 elem :: Eq a => a -> s a -> Bool
3359 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3360 contains the constraint <literal>Eq a</literal>, constrains only the
3361 class type variable (in this case <literal>a</literal>).
3362 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3369 <sect2 id="functional-dependencies">
3370 <title>Functional dependencies
3373 <para> Functional dependencies are implemented as described by Mark Jones
3374 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3375 In Proceedings of the 9th European Symposium on Programming,
3376 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3380 Functional dependencies are introduced by a vertical bar in the syntax of a
3381 class declaration; e.g.
3383 class (Monad m) => MonadState s m | m -> s where ...
3385 class Foo a b c | a b -> c where ...
3387 There should be more documentation, but there isn't (yet). Yell if you need it.
3390 <sect3><title>Rules for functional dependencies </title>
3392 In a class declaration, all of the class type variables must be reachable (in the sense
3393 mentioned in <xref linkend="flexible-contexts"/>)
3394 from the free variables of each method type.
3398 class Coll s a where
3400 insert :: s -> a -> s
3403 is not OK, because the type of <literal>empty</literal> doesn't mention
3404 <literal>a</literal>. Functional dependencies can make the type variable
3407 class Coll s a | s -> a where
3409 insert :: s -> a -> s
3412 Alternatively <literal>Coll</literal> might be rewritten
3415 class Coll s a where
3417 insert :: s a -> a -> s a
3421 which makes the connection between the type of a collection of
3422 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3423 Occasionally this really doesn't work, in which case you can split the
3431 class CollE s => Coll s a where
3432 insert :: s -> a -> s
3439 <title>Background on functional dependencies</title>
3441 <para>The following description of the motivation and use of functional dependencies is taken
3442 from the Hugs user manual, reproduced here (with minor changes) by kind
3443 permission of Mark Jones.
3446 Consider the following class, intended as part of a
3447 library for collection types:
3449 class Collects e ce where
3451 insert :: e -> ce -> ce
3452 member :: e -> ce -> Bool
3454 The type variable e used here represents the element type, while ce is the type
3455 of the container itself. Within this framework, we might want to define
3456 instances of this class for lists or characteristic functions (both of which
3457 can be used to represent collections of any equality type), bit sets (which can
3458 be used to represent collections of characters), or hash tables (which can be
3459 used to represent any collection whose elements have a hash function). Omitting
3460 standard implementation details, this would lead to the following declarations:
3462 instance Eq e => Collects e [e] where ...
3463 instance Eq e => Collects e (e -> Bool) where ...
3464 instance Collects Char BitSet where ...
3465 instance (Hashable e, Collects a ce)
3466 => Collects e (Array Int ce) where ...
3468 All this looks quite promising; we have a class and a range of interesting
3469 implementations. Unfortunately, there are some serious problems with the class
3470 declaration. First, the empty function has an ambiguous type:
3472 empty :: Collects e ce => ce
3474 By "ambiguous" we mean that there is a type variable e that appears on the left
3475 of the <literal>=></literal> symbol, but not on the right. The problem with
3476 this is that, according to the theoretical foundations of Haskell overloading,
3477 we cannot guarantee a well-defined semantics for any term with an ambiguous
3481 We can sidestep this specific problem by removing the empty member from the
3482 class declaration. However, although the remaining members, insert and member,
3483 do not have ambiguous types, we still run into problems when we try to use
3484 them. For example, consider the following two functions:
3486 f x y = insert x . insert y
3489 for which GHC infers the following types:
3491 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3492 g :: (Collects Bool c, Collects Char c) => c -> c
3494 Notice that the type for f allows the two parameters x and y to be assigned
3495 different types, even though it attempts to insert each of the two values, one
3496 after the other, into the same collection. If we're trying to model collections
3497 that contain only one type of value, then this is clearly an inaccurate
3498 type. Worse still, the definition for g is accepted, without causing a type
3499 error. As a result, the error in this code will not be flagged at the point
3500 where it appears. Instead, it will show up only when we try to use g, which
3501 might even be in a different module.
3504 <sect4><title>An attempt to use constructor classes</title>
3507 Faced with the problems described above, some Haskell programmers might be
3508 tempted to use something like the following version of the class declaration:
3510 class Collects e c where
3512 insert :: e -> c e -> c e
3513 member :: e -> c e -> Bool
3515 The key difference here is that we abstract over the type constructor c that is
3516 used to form the collection type c e, and not over that collection type itself,
3517 represented by ce in the original class declaration. This avoids the immediate
3518 problems that we mentioned above: empty has type <literal>Collects e c => c
3519 e</literal>, which is not ambiguous.
3522 The function f from the previous section has a more accurate type:
3524 f :: (Collects e c) => e -> e -> c e -> c e
3526 The function g from the previous section is now rejected with a type error as
3527 we would hope because the type of f does not allow the two arguments to have
3529 This, then, is an example of a multiple parameter class that does actually work
3530 quite well in practice, without ambiguity problems.
3531 There is, however, a catch. This version of the Collects class is nowhere near
3532 as general as the original class seemed to be: only one of the four instances
3533 for <literal>Collects</literal>
3534 given above can be used with this version of Collects because only one of
3535 them---the instance for lists---has a collection type that can be written in
3536 the form c e, for some type constructor c, and element type e.
3540 <sect4><title>Adding functional dependencies</title>
3543 To get a more useful version of the Collects class, Hugs provides a mechanism
3544 that allows programmers to specify dependencies between the parameters of a
3545 multiple parameter class (For readers with an interest in theoretical
3546 foundations and previous work: The use of dependency information can be seen
3547 both as a generalization of the proposal for `parametric type classes' that was
3548 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3549 later framework for "improvement" of qualified types. The
3550 underlying ideas are also discussed in a more theoretical and abstract setting
3551 in a manuscript [implparam], where they are identified as one point in a
3552 general design space for systems of implicit parameterization.).
3554 To start with an abstract example, consider a declaration such as:
3556 class C a b where ...
3558 which tells us simply that C can be thought of as a binary relation on types
3559 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3560 included in the definition of classes to add information about dependencies
3561 between parameters, as in the following examples:
3563 class D a b | a -> b where ...
3564 class E a b | a -> b, b -> a where ...
3566 The notation <literal>a -> b</literal> used here between the | and where
3567 symbols --- not to be
3568 confused with a function type --- indicates that the a parameter uniquely
3569 determines the b parameter, and might be read as "a determines b." Thus D is
3570 not just a relation, but actually a (partial) function. Similarly, from the two
3571 dependencies that are included in the definition of E, we can see that E
3572 represents a (partial) one-one mapping between types.
3575 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3576 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3577 m>=0, meaning that the y parameters are uniquely determined by the x
3578 parameters. Spaces can be used as separators if more than one variable appears
3579 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3580 annotated with multiple dependencies using commas as separators, as in the
3581 definition of E above. Some dependencies that we can write in this notation are
3582 redundant, and will be rejected because they don't serve any useful
3583 purpose, and may instead indicate an error in the program. Examples of
3584 dependencies like this include <literal>a -> a </literal>,
3585 <literal>a -> a a </literal>,
3586 <literal>a -> </literal>, etc. There can also be
3587 some redundancy if multiple dependencies are given, as in
3588 <literal>a->b</literal>,
3589 <literal>b->c </literal>, <literal>a->c </literal>, and
3590 in which some subset implies the remaining dependencies. Examples like this are
3591 not treated as errors. Note that dependencies appear only in class
3592 declarations, and not in any other part of the language. In particular, the
3593 syntax for instance declarations, class constraints, and types is completely
3597 By including dependencies in a class declaration, we provide a mechanism for
3598 the programmer to specify each multiple parameter class more precisely. The
3599 compiler, on the other hand, is responsible for ensuring that the set of
3600 instances that are in scope at any given point in the program is consistent
3601 with any declared dependencies. For example, the following pair of instance
3602 declarations cannot appear together in the same scope because they violate the
3603 dependency for D, even though either one on its own would be acceptable:
3605 instance D Bool Int where ...
3606 instance D Bool Char where ...
3608 Note also that the following declaration is not allowed, even by itself:
3610 instance D [a] b where ...
3612 The problem here is that this instance would allow one particular choice of [a]
3613 to be associated with more than one choice for b, which contradicts the
3614 dependency specified in the definition of D. More generally, this means that,
3615 in any instance of the form:
3617 instance D t s where ...
3619 for some particular types t and s, the only variables that can appear in s are
3620 the ones that appear in t, and hence, if the type t is known, then s will be
3621 uniquely determined.
3624 The benefit of including dependency information is that it allows us to define
3625 more general multiple parameter classes, without ambiguity problems, and with
3626 the benefit of more accurate types. To illustrate this, we return to the
3627 collection class example, and annotate the original definition of <literal>Collects</literal>
3628 with a simple dependency:
3630 class Collects e ce | ce -> e where
3632 insert :: e -> ce -> ce
3633 member :: e -> ce -> Bool
3635 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3636 determined by the type of the collection ce. Note that both parameters of
3637 Collects are of kind *; there are no constructor classes here. Note too that
3638 all of the instances of Collects that we gave earlier can be used
3639 together with this new definition.
3642 What about the ambiguity problems that we encountered with the original
3643 definition? The empty function still has type Collects e ce => ce, but it is no
3644 longer necessary to regard that as an ambiguous type: Although the variable e
3645 does not appear on the right of the => symbol, the dependency for class
3646 Collects tells us that it is uniquely determined by ce, which does appear on
3647 the right of the => symbol. Hence the context in which empty is used can still
3648 give enough information to determine types for both ce and e, without
3649 ambiguity. More generally, we need only regard a type as ambiguous if it
3650 contains a variable on the left of the => that is not uniquely determined
3651 (either directly or indirectly) by the variables on the right.
3654 Dependencies also help to produce more accurate types for user defined
3655 functions, and hence to provide earlier detection of errors, and less cluttered
3656 types for programmers to work with. Recall the previous definition for a
3659 f x y = insert x y = insert x . insert y
3661 for which we originally obtained a type:
3663 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3665 Given the dependency information that we have for Collects, however, we can
3666 deduce that a and b must be equal because they both appear as the second
3667 parameter in a Collects constraint with the same first parameter c. Hence we
3668 can infer a shorter and more accurate type for f:
3670 f :: (Collects a c) => a -> a -> c -> c
3672 In a similar way, the earlier definition of g will now be flagged as a type error.
3675 Although we have given only a few examples here, it should be clear that the
3676 addition of dependency information can help to make multiple parameter classes
3677 more useful in practice, avoiding ambiguity problems, and allowing more general
3678 sets of instance declarations.
3684 <sect2 id="instance-decls">
3685 <title>Instance declarations</title>
3687 <para>An instance declaration has the form
3689 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 ...
3691 The part before the "<literal>=></literal>" is the
3692 <emphasis>context</emphasis>, while the part after the
3693 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3696 <sect3 id="flexible-instance-head">
3697 <title>Relaxed rules for the instance head</title>
3700 In Haskell 98 the head of an instance declaration
3701 must be of the form <literal>C (T a1 ... an)</literal>, where
3702 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3703 and the <literal>a1 ... an</literal> are distinct type variables.
3704 GHC relaxes these rules in two ways.
3708 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3709 declaration to mention arbitrary nested types.
3710 For example, this becomes a legal instance declaration
3712 instance C (Maybe Int) where ...
3714 See also the <link linkend="instance-overlap">rules on overlap</link>.
3717 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3718 synonyms. As always, using a type synonym is just shorthand for
3719 writing the RHS of the type synonym definition. For example:
3723 type Point = (Int,Int)
3724 instance C Point where ...
3725 instance C [Point] where ...
3729 is legal. However, if you added
3733 instance C (Int,Int) where ...
3737 as well, then the compiler will complain about the overlapping
3738 (actually, identical) instance declarations. As always, type synonyms
3739 must be fully applied. You cannot, for example, write:
3743 instance Monad P where ...
3751 <sect3 id="instance-rules">
3752 <title>Relaxed rules for instance contexts</title>
3754 <para>In Haskell 98, the assertions in the context of the instance declaration
3755 must be of the form <literal>C a</literal> where <literal>a</literal>
3756 is a type variable that occurs in the head.
3760 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3761 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3762 With this flag the context of the instance declaration can each consist of arbitrary
3763 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3767 The Paterson Conditions: for each assertion in the context
3769 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3770 <listitem><para>The assertion has fewer constructors and variables (taken together
3771 and counting repetitions) than the head</para></listitem>
3775 <listitem><para>The Coverage Condition. For each functional dependency,
3776 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3777 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3778 every type variable in
3779 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3780 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3781 substitution mapping each type variable in the class declaration to the
3782 corresponding type in the instance declaration.
3785 These restrictions ensure that context reduction terminates: each reduction
3786 step makes the problem smaller by at least one
3787 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3788 if you give the <option>-XUndecidableInstances</option>
3789 flag (<xref linkend="undecidable-instances"/>).
3790 You can find lots of background material about the reason for these
3791 restrictions in the paper <ulink
3792 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3793 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3796 For example, these are OK:
3798 instance C Int [a] -- Multiple parameters
3799 instance Eq (S [a]) -- Structured type in head
3801 -- Repeated type variable in head
3802 instance C4 a a => C4 [a] [a]
3803 instance Stateful (ST s) (MutVar s)
3805 -- Head can consist of type variables only
3807 instance (Eq a, Show b) => C2 a b
3809 -- Non-type variables in context
3810 instance Show (s a) => Show (Sized s a)
3811 instance C2 Int a => C3 Bool [a]
3812 instance C2 Int a => C3 [a] b
3816 -- Context assertion no smaller than head
3817 instance C a => C a where ...
3818 -- (C b b) has more more occurrences of b than the head
3819 instance C b b => Foo [b] where ...
3824 The same restrictions apply to instances generated by
3825 <literal>deriving</literal> clauses. Thus the following is accepted:
3827 data MinHeap h a = H a (h a)
3830 because the derived instance
3832 instance (Show a, Show (h a)) => Show (MinHeap h a)
3834 conforms to the above rules.
3838 A useful idiom permitted by the above rules is as follows.
3839 If one allows overlapping instance declarations then it's quite
3840 convenient to have a "default instance" declaration that applies if
3841 something more specific does not:
3849 <sect3 id="undecidable-instances">
3850 <title>Undecidable instances</title>
3853 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3854 For example, sometimes you might want to use the following to get the
3855 effect of a "class synonym":
3857 class (C1 a, C2 a, C3 a) => C a where { }
3859 instance (C1 a, C2 a, C3 a) => C a where { }
3861 This allows you to write shorter signatures:
3867 f :: (C1 a, C2 a, C3 a) => ...
3869 The restrictions on functional dependencies (<xref
3870 linkend="functional-dependencies"/>) are particularly troublesome.
3871 It is tempting to introduce type variables in the context that do not appear in
3872 the head, something that is excluded by the normal rules. For example:
3874 class HasConverter a b | a -> b where
3877 data Foo a = MkFoo a
3879 instance (HasConverter a b,Show b) => Show (Foo a) where
3880 show (MkFoo value) = show (convert value)
3882 This is dangerous territory, however. Here, for example, is a program that would make the
3887 instance F [a] [[a]]
3888 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3890 Similarly, it can be tempting to lift the coverage condition:
3892 class Mul a b c | a b -> c where
3893 (.*.) :: a -> b -> c
3895 instance Mul Int Int Int where (.*.) = (*)
3896 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3897 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3899 The third instance declaration does not obey the coverage condition;
3900 and indeed the (somewhat strange) definition:
3902 f = \ b x y -> if b then x .*. [y] else y
3904 makes instance inference go into a loop, because it requires the constraint
3905 <literal>(Mul a [b] b)</literal>.
3908 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3909 the experimental flag <option>-XUndecidableInstances</option>
3910 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3911 both the Paterson Conditions and the Coverage Condition
3912 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3913 fixed-depth recursion stack. If you exceed the stack depth you get a
3914 sort of backtrace, and the opportunity to increase the stack depth
3915 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3921 <sect3 id="instance-overlap">
3922 <title>Overlapping instances</title>
3924 In general, <emphasis>GHC requires that that it be unambiguous which instance
3926 should be used to resolve a type-class constraint</emphasis>. This behaviour
3927 can be modified by two flags: <option>-XOverlappingInstances</option>
3928 <indexterm><primary>-XOverlappingInstances
3929 </primary></indexterm>
3930 and <option>-XIncoherentInstances</option>
3931 <indexterm><primary>-XIncoherentInstances
3932 </primary></indexterm>, as this section discusses. Both these
3933 flags are dynamic flags, and can be set on a per-module basis, using
3934 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3936 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3937 it tries to match every instance declaration against the
3939 by instantiating the head of the instance declaration. For example, consider
3942 instance context1 => C Int a where ... -- (A)
3943 instance context2 => C a Bool where ... -- (B)
3944 instance context3 => C Int [a] where ... -- (C)
3945 instance context4 => C Int [Int] where ... -- (D)
3947 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3948 but (C) and (D) do not. When matching, GHC takes
3949 no account of the context of the instance declaration
3950 (<literal>context1</literal> etc).
3951 GHC's default behaviour is that <emphasis>exactly one instance must match the
3952 constraint it is trying to resolve</emphasis>.
3953 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3954 including both declarations (A) and (B), say); an error is only reported if a
3955 particular constraint matches more than one.
3959 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3960 more than one instance to match, provided there is a most specific one. For
3961 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3962 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3963 most-specific match, the program is rejected.
3966 However, GHC is conservative about committing to an overlapping instance. For example:
3971 Suppose that from the RHS of <literal>f</literal> we get the constraint
3972 <literal>C Int [b]</literal>. But
3973 GHC does not commit to instance (C), because in a particular
3974 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3975 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3976 So GHC rejects the program.
3977 (If you add the flag <option>-XIncoherentInstances</option>,
3978 GHC will instead pick (C), without complaining about
3979 the problem of subsequent instantiations.)
3982 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3983 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3984 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3985 it instead. In this case, GHC will refrain from
3986 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3987 as before) but, rather than rejecting the program, it will infer the type
3989 f :: C Int [b] => [b] -> [b]
3991 That postpones the question of which instance to pick to the
3992 call site for <literal>f</literal>
3993 by which time more is known about the type <literal>b</literal>.
3994 You can write this type signature yourself if you use the
3995 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3999 Exactly the same situation can arise in instance declarations themselves. Suppose we have
4003 instance Foo [b] where
4006 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
4007 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
4008 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
4009 declaration. The solution is to postpone the choice by adding the constraint to the context
4010 of the instance declaration, thus:
4012 instance C Int [b] => Foo [b] where
4015 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
4018 Warning: overlapping instances must be used with care. They
4019 can give rise to incoherence (ie different instance choices are made
4020 in different parts of the program) even without <option>-XIncoherentInstances</option>. Consider:
4022 {-# LANGUAGE OverlappingInstances #-}
4025 class MyShow a where
4026 myshow :: a -> String
4028 instance MyShow a => MyShow [a] where
4029 myshow xs = concatMap myshow xs
4031 showHelp :: MyShow a => [a] -> String
4032 showHelp xs = myshow xs
4034 {-# LANGUAGE FlexibleInstances, OverlappingInstances #-}
4040 instance MyShow T where
4041 myshow x = "Used generic instance"
4043 instance MyShow [T] where
4044 myshow xs = "Used more specific instance"
4046 main = do { print (myshow [MkT]); print (showHelp [MkT]) }
4048 In function <literal>showHelp</literal> GHC sees no overlapping
4049 instances, and so uses the <literal>MyShow [a]</literal> instance
4050 without complaint. In the call to <literal>myshow</literal> in <literal>main</literal>,
4051 GHC resolves the <literal>MyShow [T]</literal> constraint using the overlapping
4052 instance declaration in module <literal>Main</literal>. As a result,
4055 "Used more specific instance"
4056 "Used generic instance"
4058 (An alternative possible behaviour, not currently implemented,
4059 would be to reject module <literal>Help</literal>
4060 on the grounds that a later instance declaration might overlap the local one.)
4063 The willingness to be overlapped or incoherent is a property of
4064 the <emphasis>instance declaration</emphasis> itself, controlled by the
4065 presence or otherwise of the <option>-XOverlappingInstances</option>
4066 and <option>-XIncoherentInstances</option> flags when that module is
4067 being defined. Neither flag is required in a module that imports and uses the
4068 instance declaration. Specifically, during the lookup process:
4071 An instance declaration is ignored during the lookup process if (a) a more specific
4072 match is found, and (b) the instance declaration was compiled with
4073 <option>-XOverlappingInstances</option>. The flag setting for the
4074 more-specific instance does not matter.
4077 Suppose an instance declaration does not match the constraint being looked up, but
4078 does unify with it, so that it might match when the constraint is further
4079 instantiated. Usually GHC will regard this as a reason for not committing to
4080 some other constraint. But if the instance declaration was compiled with
4081 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
4082 check for that declaration.
4085 These rules make it possible for a library author to design a library that relies on
4086 overlapping instances without the library client having to know.
4089 If an instance declaration is compiled without
4090 <option>-XOverlappingInstances</option>,
4091 then that instance can never be overlapped. This could perhaps be
4092 inconvenient. Perhaps the rule should instead say that the
4093 <emphasis>overlapping</emphasis> instance declaration should be compiled in
4094 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
4095 at a usage site should be permitted regardless of how the instance declarations
4096 are compiled, if the <option>-XOverlappingInstances</option> flag is
4097 used at the usage site. (Mind you, the exact usage site can occasionally be
4098 hard to pin down.) We are interested to receive feedback on these points.
4100 <para>The <option>-XIncoherentInstances</option> flag implies the
4101 <option>-XOverlappingInstances</option> flag, but not vice versa.
4109 <sect2 id="overloaded-strings">
4110 <title>Overloaded string literals
4114 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4115 string literal has type <literal>String</literal>, but with overloaded string
4116 literals enabled (with <literal>-XOverloadedStrings</literal>)
4117 a string literal has type <literal>(IsString a) => a</literal>.
4120 This means that the usual string syntax can be used, e.g., for packed strings
4121 and other variations of string like types. String literals behave very much
4122 like integer literals, i.e., they can be used in both expressions and patterns.
4123 If used in a pattern the literal with be replaced by an equality test, in the same
4124 way as an integer literal is.
4127 The class <literal>IsString</literal> is defined as:
4129 class IsString a where
4130 fromString :: String -> a
4132 The only predefined instance is the obvious one to make strings work as usual:
4134 instance IsString [Char] where
4137 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4138 it explicitly (for example, to give an instance declaration for it), you can import it
4139 from module <literal>GHC.Exts</literal>.
4142 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4146 Each type in a default declaration must be an
4147 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4151 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4152 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4153 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4154 <emphasis>or</emphasis> <literal>IsString</literal>.
4163 import GHC.Exts( IsString(..) )
4165 newtype MyString = MyString String deriving (Eq, Show)
4166 instance IsString MyString where
4167 fromString = MyString
4169 greet :: MyString -> MyString
4170 greet "hello" = "world"
4174 print $ greet "hello"
4175 print $ greet "fool"
4179 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4180 to work since it gets translated into an equality comparison.
4186 <sect1 id="type-families">
4187 <title>Type families</title>
4190 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4191 facilitate type-level
4192 programming. Type families are a generalisation of <firstterm>associated
4193 data types</firstterm>
4194 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4195 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4196 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4197 Symposium on Principles of Programming Languages (POPL'05)”, pages
4198 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4199 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4200 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4202 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4203 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4204 themselves are described in the paper “<ulink
4205 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4206 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4208 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4209 13th ACM SIGPLAN International Conference on Functional
4210 Programming”, ACM Press, pages 51-62, 2008. Type families
4211 essentially provide type-indexed data types and named functions on types,
4212 which are useful for generic programming and highly parameterised library
4213 interfaces as well as interfaces with enhanced static information, much like
4214 dependent types. They might also be regarded as an alternative to functional
4215 dependencies, but provide a more functional style of type-level programming
4216 than the relational style of functional dependencies.
4219 Indexed type families, or type families for short, are type constructors that
4220 represent sets of types. Set members are denoted by supplying the type family
4221 constructor with type parameters, which are called <firstterm>type
4222 indices</firstterm>. The
4223 difference between vanilla parametrised type constructors and family
4224 constructors is much like between parametrically polymorphic functions and
4225 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4226 behave the same at all type instances, whereas class methods can change their
4227 behaviour in dependence on the class type parameters. Similarly, vanilla type
4228 constructors imply the same data representation for all type instances, but
4229 family constructors can have varying representation types for varying type
4233 Indexed type families come in two flavours: <firstterm>data
4234 families</firstterm> and <firstterm>type synonym
4235 families</firstterm>. They are the indexed family variants of algebraic
4236 data types and type synonyms, respectively. The instances of data families
4237 can be data types and newtypes.
4240 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4241 Additional information on the use of type families in GHC is available on
4242 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4243 Haskell wiki page on type families</ulink>.
4246 <sect2 id="data-families">
4247 <title>Data families</title>
4250 Data families appear in two flavours: (1) they can be defined on the
4252 or (2) they can appear inside type classes (in which case they are known as
4253 associated types). The former is the more general variant, as it lacks the
4254 requirement for the type-indexes to coincide with the class
4255 parameters. However, the latter can lead to more clearly structured code and
4256 compiler warnings if some type instances were - possibly accidentally -
4257 omitted. In the following, we always discuss the general toplevel form first
4258 and then cover the additional constraints placed on associated types.
4261 <sect3 id="data-family-declarations">
4262 <title>Data family declarations</title>
4265 Indexed data families are introduced by a signature, such as
4267 data family GMap k :: * -> *
4269 The special <literal>family</literal> distinguishes family from standard
4270 data declarations. The result kind annotation is optional and, as
4271 usual, defaults to <literal>*</literal> if omitted. An example is
4275 Named arguments can also be given explicit kind signatures if needed.
4277 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4278 declarations] named arguments are entirely optional, so that we can
4279 declare <literal>Array</literal> alternatively with
4281 data family Array :: * -> *
4285 <sect4 id="assoc-data-family-decl">
4286 <title>Associated data family declarations</title>
4288 When a data family is declared as part of a type class, we drop
4289 the <literal>family</literal> special. The <literal>GMap</literal>
4290 declaration takes the following form
4292 class GMapKey k where
4293 data GMap k :: * -> *
4296 In contrast to toplevel declarations, named arguments must be used for
4297 all type parameters that are to be used as type-indexes. Moreover,
4298 the argument names must be class parameters. Each class parameter may
4299 only be used at most once per associated type, but some may be omitted
4300 and they may be in an order other than in the class head. Hence, the
4301 following contrived example is admissible:
4310 <sect3 id="data-instance-declarations">
4311 <title>Data instance declarations</title>
4314 Instance declarations of data and newtype families are very similar to
4315 standard data and newtype declarations. The only two differences are
4316 that the keyword <literal>data</literal> or <literal>newtype</literal>
4317 is followed by <literal>instance</literal> and that some or all of the
4318 type arguments can be non-variable types, but may not contain forall
4319 types or type synonym families. However, data families are generally
4320 allowed in type parameters, and type synonyms are allowed as long as
4321 they are fully applied and expand to a type that is itself admissible -
4322 exactly as this is required for occurrences of type synonyms in class
4323 instance parameters. For example, the <literal>Either</literal>
4324 instance for <literal>GMap</literal> is
4326 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4328 In this example, the declaration has only one variant. In general, it
4332 Data and newtype instance declarations are only permitted when an
4333 appropriate family declaration is in scope - just as a class instance declaratoin
4334 requires the class declaration to be visible. Moreover, each instance
4335 declaration has to conform to the kind determined by its family
4336 declaration. This implies that the number of parameters of an instance
4337 declaration matches the arity determined by the kind of the family.
4340 A data family instance declaration can use the full exprssiveness of
4341 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4343 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4344 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4345 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4348 data instance T Int = T1 Int | T2 Bool
4349 newtype instance T Char = TC Bool
4352 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4353 and indeed can define a GADT. For example:
4356 data instance G [a] b where
4357 G1 :: c -> G [Int] b
4361 <listitem><para> You can use a <literal>deriving</literal> clause on a
4362 <literal>data instance</literal> or <literal>newtype instance</literal>
4369 Even if type families are defined as toplevel declarations, functions
4370 that perform different computations for different family instances may still
4371 need to be defined as methods of type classes. In particular, the
4372 following is not possible:
4375 data instance T Int = A
4376 data instance T Char = B
4378 foo A = 1 -- WRONG: These two equations together...
4379 foo B = 2 -- ...will produce a type error.
4381 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4385 instance Foo Int where
4387 instance Foo Char where
4390 (Given the functionality provided by GADTs (Generalised Algebraic Data
4391 Types), it might seem as if a definition, such as the above, should be
4392 feasible. However, type families are - in contrast to GADTs - are
4393 <emphasis>open;</emphasis> i.e., new instances can always be added,
4395 modules. Supporting pattern matching across different data instances
4396 would require a form of extensible case construct.)
4399 <sect4 id="assoc-data-inst">
4400 <title>Associated data instances</title>
4402 When an associated data family instance is declared within a type
4403 class instance, we drop the <literal>instance</literal> keyword in the
4404 family instance. So, the <literal>Either</literal> instance
4405 for <literal>GMap</literal> becomes:
4407 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4408 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4411 The most important point about associated family instances is that the
4412 type indexes corresponding to class parameters must be identical to
4413 the type given in the instance head; here this is the first argument
4414 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4415 which coincides with the only class parameter. Any parameters to the
4416 family constructor that do not correspond to class parameters, need to
4417 be variables in every instance; here this is the
4418 variable <literal>v</literal>.
4421 Instances for an associated family can only appear as part of
4422 instances declarations of the class in which the family was declared -
4423 just as with the equations of the methods of a class. Also in
4424 correspondence to how methods are handled, declarations of associated
4425 types can be omitted in class instances. If an associated family
4426 instance is omitted, the corresponding instance type is not inhabited;
4427 i.e., only diverging expressions, such
4428 as <literal>undefined</literal>, can assume the type.
4432 <sect4 id="scoping-class-params">
4433 <title>Scoping of class parameters</title>
4435 In the case of multi-parameter type classes, the visibility of class
4436 parameters in the right-hand side of associated family instances
4437 depends <emphasis>solely</emphasis> on the parameters of the data
4438 family. As an example, consider the simple class declaration
4443 Only one of the two class parameters is a parameter to the data
4444 family. Hence, the following instance declaration is invalid:
4446 instance C [c] d where
4447 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4449 Here, the right-hand side of the data instance mentions the type
4450 variable <literal>d</literal> that does not occur in its left-hand
4451 side. We cannot admit such data instances as they would compromise
4456 <sect4 id="family-class-inst">
4457 <title>Type class instances of family instances</title>
4459 Type class instances of instances of data families can be defined as
4460 usual, and in particular data instance declarations can
4461 have <literal>deriving</literal> clauses. For example, we can write
4463 data GMap () v = GMapUnit (Maybe v)
4466 which implicitly defines an instance of the form
4468 instance Show v => Show (GMap () v) where ...
4472 Note that class instances are always for
4473 particular <emphasis>instances</emphasis> of a data family and never
4474 for an entire family as a whole. This is for essentially the same
4475 reasons that we cannot define a toplevel function that performs
4476 pattern matching on the data constructors
4477 of <emphasis>different</emphasis> instances of a single type family.
4478 It would require a form of extensible case construct.
4482 <sect4 id="data-family-overlap">
4483 <title>Overlap of data instances</title>
4485 The instance declarations of a data family used in a single program
4486 may not overlap at all, independent of whether they are associated or
4487 not. In contrast to type class instances, this is not only a matter
4488 of consistency, but one of type safety.
4494 <sect3 id="data-family-import-export">
4495 <title>Import and export</title>
4498 The association of data constructors with type families is more dynamic
4499 than that is the case with standard data and newtype declarations. In
4500 the standard case, the notation <literal>T(..)</literal> in an import or
4501 export list denotes the type constructor and all the data constructors
4502 introduced in its declaration. However, a family declaration never
4503 introduces any data constructors; instead, data constructors are
4504 introduced by family instances. As a result, which data constructors
4505 are associated with a type family depends on the currently visible
4506 instance declarations for that family. Consequently, an import or
4507 export item of the form <literal>T(..)</literal> denotes the family
4508 constructor and all currently visible data constructors - in the case of
4509 an export item, these may be either imported or defined in the current
4510 module. The treatment of import and export items that explicitly list
4511 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4515 <sect4 id="data-family-impexp-assoc">
4516 <title>Associated families</title>
4518 As expected, an import or export item of the
4519 form <literal>C(..)</literal> denotes all of the class' methods and
4520 associated types. However, when associated types are explicitly
4521 listed as subitems of a class, we need some new syntax, as uppercase
4522 identifiers as subitems are usually data constructors, not type
4523 constructors. To clarify that we denote types here, each associated
4524 type name needs to be prefixed by the keyword <literal>type</literal>.
4525 So for example, when explicitly listing the components of
4526 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4527 GMap, empty, lookup, insert)</literal>.
4531 <sect4 id="data-family-impexp-examples">
4532 <title>Examples</title>
4534 Assuming our running <literal>GMapKey</literal> class example, let us
4535 look at some export lists and their meaning:
4538 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4539 just the class name.</para>
4542 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4543 Exports the class, the associated type <literal>GMap</literal>
4545 functions <literal>empty</literal>, <literal>lookup</literal>,
4546 and <literal>insert</literal>. None of the data constructors is
4550 <para><literal>module GMap (GMapKey(..), GMap(..))
4551 where...</literal>: As before, but also exports all the data
4552 constructors <literal>GMapInt</literal>,
4553 <literal>GMapChar</literal>,
4554 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4555 and <literal>GMapUnit</literal>.</para>
4558 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4559 GMap(..)) where...</literal>: As before.</para>
4562 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4563 where...</literal>: As before.</para>
4568 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4569 both the class <literal>GMapKey</literal> as well as its associated
4570 type <literal>GMap</literal>. However, you cannot
4571 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4572 sub-component specifications cannot be nested. To
4573 specify <literal>GMap</literal>'s data constructors, you have to list
4578 <sect4 id="data-family-impexp-instances">
4579 <title>Instances</title>
4581 Family instances are implicitly exported, just like class instances.
4582 However, this applies only to the heads of instances, not to the data
4583 constructors an instance defines.
4591 <sect2 id="synonym-families">
4592 <title>Synonym families</title>
4595 Type families appear in two flavours: (1) they can be defined on the
4596 toplevel or (2) they can appear inside type classes (in which case they
4597 are known as associated type synonyms). The former is the more general
4598 variant, as it lacks the requirement for the type-indexes to coincide with
4599 the class parameters. However, the latter can lead to more clearly
4600 structured code and compiler warnings if some type instances were -
4601 possibly accidentally - omitted. In the following, we always discuss the
4602 general toplevel form first and then cover the additional constraints
4603 placed on associated types.
4606 <sect3 id="type-family-declarations">
4607 <title>Type family declarations</title>
4610 Indexed type families are introduced by a signature, such as
4612 type family Elem c :: *
4614 The special <literal>family</literal> distinguishes family from standard
4615 type declarations. The result kind annotation is optional and, as
4616 usual, defaults to <literal>*</literal> if omitted. An example is
4620 Parameters can also be given explicit kind signatures if needed. We
4621 call the number of parameters in a type family declaration, the family's
4622 arity, and all applications of a type family must be fully saturated
4623 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4624 and it implies that the kind of a type family is not sufficient to
4625 determine a family's arity, and hence in general, also insufficient to
4626 determine whether a type family application is well formed. As an
4627 example, consider the following declaration:
4629 type family F a b :: * -> * -- F's arity is 2,
4630 -- although its overall kind is * -> * -> * -> *
4632 Given this declaration the following are examples of well-formed and
4635 F Char [Int] -- OK! Kind: * -> *
4636 F Char [Int] Bool -- OK! Kind: *
4637 F IO Bool -- WRONG: kind mismatch in the first argument
4638 F Bool -- WRONG: unsaturated application
4642 <sect4 id="assoc-type-family-decl">
4643 <title>Associated type family declarations</title>
4645 When a type family is declared as part of a type class, we drop
4646 the <literal>family</literal> special. The <literal>Elem</literal>
4647 declaration takes the following form
4649 class Collects ce where
4653 The argument names of the type family must be class parameters. Each
4654 class parameter may only be used at most once per associated type, but
4655 some may be omitted and they may be in an order other than in the
4656 class head. Hence, the following contrived example is admissible:
4661 These rules are exactly as for associated data families.
4666 <sect3 id="type-instance-declarations">
4667 <title>Type instance declarations</title>
4669 Instance declarations of type families are very similar to standard type
4670 synonym declarations. The only two differences are that the
4671 keyword <literal>type</literal> is followed
4672 by <literal>instance</literal> and that some or all of the type
4673 arguments can be non-variable types, but may not contain forall types or
4674 type synonym families. However, data families are generally allowed, and
4675 type synonyms are allowed as long as they are fully applied and expand
4676 to a type that is admissible - these are the exact same requirements as
4677 for data instances. For example, the <literal>[e]</literal> instance
4678 for <literal>Elem</literal> is
4680 type instance Elem [e] = e
4684 Type family instance declarations are only legitimate when an
4685 appropriate family declaration is in scope - just like class instances
4686 require the class declaration to be visible. Moreover, each instance
4687 declaration has to conform to the kind determined by its family
4688 declaration, and the number of type parameters in an instance
4689 declaration must match the number of type parameters in the family
4690 declaration. Finally, the right-hand side of a type instance must be a
4691 monotype (i.e., it may not include foralls) and after the expansion of
4692 all saturated vanilla type synonyms, no synonyms, except family synonyms
4693 may remain. Here are some examples of admissible and illegal type
4696 type family F a :: *
4697 type instance F [Int] = Int -- OK!
4698 type instance F String = Char -- OK!
4699 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4700 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4701 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4703 type family G a b :: * -> *
4704 type instance G Int = (,) -- WRONG: must be two type parameters
4705 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4709 <sect4 id="assoc-type-instance">
4710 <title>Associated type instance declarations</title>
4712 When an associated family instance is declared within a type class
4713 instance, we drop the <literal>instance</literal> keyword in the family
4714 instance. So, the <literal>[e]</literal> instance
4715 for <literal>Elem</literal> becomes:
4717 instance (Eq (Elem [e])) => Collects ([e]) where
4721 The most important point about associated family instances is that the
4722 type indexes corresponding to class parameters must be identical to the
4723 type given in the instance head; here this is <literal>[e]</literal>,
4724 which coincides with the only class parameter.
4727 Instances for an associated family can only appear as part of instances
4728 declarations of the class in which the family was declared - just as
4729 with the equations of the methods of a class. Also in correspondence to
4730 how methods are handled, declarations of associated types can be omitted
4731 in class instances. If an associated family instance is omitted, the
4732 corresponding instance type is not inhabited; i.e., only diverging
4733 expressions, such as <literal>undefined</literal>, can assume the type.
4737 <sect4 id="type-family-overlap">
4738 <title>Overlap of type synonym instances</title>
4740 The instance declarations of a type family used in a single program
4741 may only overlap if the right-hand sides of the overlapping instances
4742 coincide for the overlapping types. More formally, two instance
4743 declarations overlap if there is a substitution that makes the
4744 left-hand sides of the instances syntactically the same. Whenever
4745 that is the case, the right-hand sides of the instances must also be
4746 syntactically equal under the same substitution. This condition is
4747 independent of whether the type family is associated or not, and it is
4748 not only a matter of consistency, but one of type safety.
4751 Here are two example to illustrate the condition under which overlap
4754 type instance F (a, Int) = [a]
4755 type instance F (Int, b) = [b] -- overlap permitted
4757 type instance G (a, Int) = [a]
4758 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4763 <sect4 id="type-family-decidability">
4764 <title>Decidability of type synonym instances</title>
4766 In order to guarantee that type inference in the presence of type
4767 families decidable, we need to place a number of additional
4768 restrictions on the formation of type instance declarations (c.f.,
4769 Definition 5 (Relaxed Conditions) of “<ulink
4770 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4771 Checking with Open Type Functions</ulink>”). Instance
4772 declarations have the general form
4774 type instance F t1 .. tn = t
4776 where we require that for every type family application <literal>(G s1
4777 .. sm)</literal> in <literal>t</literal>,
4780 <para><literal>s1 .. sm</literal> do not contain any type family
4781 constructors,</para>
4784 <para>the total number of symbols (data type constructors and type
4785 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4786 in <literal>t1 .. tn</literal>, and</para>
4789 <para>for every type
4790 variable <literal>a</literal>, <literal>a</literal> occurs
4791 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4792 .. tn</literal>.</para>
4795 These restrictions are easily verified and ensure termination of type
4796 inference. However, they are not sufficient to guarantee completeness
4797 of type inference in the presence of, so called, ''loopy equalities'',
4798 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4799 a type variable is underneath a family application and data
4800 constructor application - see the above mentioned paper for details.
4803 If the option <option>-XUndecidableInstances</option> is passed to the
4804 compiler, the above restrictions are not enforced and it is on the
4805 programmer to ensure termination of the normalisation of type families
4806 during type inference.
4811 <sect3 id-="equality-constraints">
4812 <title>Equality constraints</title>
4814 Type context can include equality constraints of the form <literal>t1 ~
4815 t2</literal>, which denote that the types <literal>t1</literal>
4816 and <literal>t2</literal> need to be the same. In the presence of type
4817 families, whether two types are equal cannot generally be decided
4818 locally. Hence, the contexts of function signatures may include
4819 equality constraints, as in the following example:
4821 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4823 where we require that the element type of <literal>c1</literal>
4824 and <literal>c2</literal> are the same. In general, the
4825 types <literal>t1</literal> and <literal>t2</literal> of an equality
4826 constraint may be arbitrary monotypes; i.e., they may not contain any
4827 quantifiers, independent of whether higher-rank types are otherwise
4831 Equality constraints can also appear in class and instance contexts.
4832 The former enable a simple translation of programs using functional
4833 dependencies into programs using family synonyms instead. The general
4834 idea is to rewrite a class declaration of the form
4836 class C a b | a -> b
4840 class (F a ~ b) => C a b where
4843 That is, we represent every functional dependency (FD) <literal>a1 .. an
4844 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4845 superclass context equality <literal>F a1 .. an ~ b</literal>,
4846 essentially giving a name to the functional dependency. In class
4847 instances, we define the type instances of FD families in accordance
4848 with the class head. Method signatures are not affected by that
4852 NB: Equalities in superclass contexts are not fully implemented in
4857 <sect3 id-="ty-fams-in-instances">
4858 <title>Type families and instance declarations</title>
4859 <para>Type families require us to extend the rules for
4860 the form of instance heads, which are given
4861 in <xref linkend="flexible-instance-head"/>.
4864 <listitem><para>Data type families may appear in an instance head</para></listitem>
4865 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4867 The reason for the latter restriction is that there is no way to check for. Consider
4870 type instance F Bool = Int
4877 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4878 The situation is especially bad because the type instance for <literal>F Bool</literal>
4879 might be in another module, or even in a module that is not yet written.
4886 <sect1 id="other-type-extensions">
4887 <title>Other type system extensions</title>
4889 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4891 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4892 is used, the keyword <literal>forall</literal>
4893 allows us to say exactly what this means. For example:
4901 g :: forall b. (b -> b)
4903 The two are treated identically.
4906 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4907 a type variable any more!
4912 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4914 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4915 that the type-class constraints in a type signature must have the
4916 form <emphasis>(class type-variable)</emphasis> or
4917 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4918 With <option>-XFlexibleContexts</option>
4919 these type signatures are perfectly OK
4922 g :: Ord (T a ()) => ...
4924 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4925 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4926 (<xref linkend="instance-rules"/>).
4930 GHC imposes the following restrictions on the constraints in a type signature.
4934 forall tv1..tvn (c1, ...,cn) => type
4937 (Here, we write the "foralls" explicitly, although the Haskell source
4938 language omits them; in Haskell 98, all the free type variables of an
4939 explicit source-language type signature are universally quantified,
4940 except for the class type variables in a class declaration. However,
4941 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4950 <emphasis>Each universally quantified type variable
4951 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4953 A type variable <literal>a</literal> is "reachable" if it appears
4954 in the same constraint as either a type variable free in
4955 <literal>type</literal>, or another reachable type variable.
4956 A value with a type that does not obey
4957 this reachability restriction cannot be used without introducing
4958 ambiguity; that is why the type is rejected.
4959 Here, for example, is an illegal type:
4963 forall a. Eq a => Int
4967 When a value with this type was used, the constraint <literal>Eq tv</literal>
4968 would be introduced where <literal>tv</literal> is a fresh type variable, and
4969 (in the dictionary-translation implementation) the value would be
4970 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4971 can never know which instance of <literal>Eq</literal> to use because we never
4972 get any more information about <literal>tv</literal>.
4976 that the reachability condition is weaker than saying that <literal>a</literal> is
4977 functionally dependent on a type variable free in
4978 <literal>type</literal> (see <xref
4979 linkend="functional-dependencies"/>). The reason for this is there
4980 might be a "hidden" dependency, in a superclass perhaps. So
4981 "reachable" is a conservative approximation to "functionally dependent".
4982 For example, consider:
4984 class C a b | a -> b where ...
4985 class C a b => D a b where ...
4986 f :: forall a b. D a b => a -> a
4988 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4989 but that is not immediately apparent from <literal>f</literal>'s type.
4995 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4996 universally quantified type variables <literal>tvi</literal></emphasis>.
4998 For example, this type is OK because <literal>C a b</literal> mentions the
4999 universally quantified type variable <literal>b</literal>:
5003 forall a. C a b => burble
5007 The next type is illegal because the constraint <literal>Eq b</literal> does not
5008 mention <literal>a</literal>:
5012 forall a. Eq b => burble
5016 The reason for this restriction is milder than the other one. The
5017 excluded types are never useful or necessary (because the offending
5018 context doesn't need to be witnessed at this point; it can be floated
5019 out). Furthermore, floating them out increases sharing. Lastly,
5020 excluding them is a conservative choice; it leaves a patch of
5021 territory free in case we need it later.
5032 <sect2 id="implicit-parameters">
5033 <title>Implicit parameters</title>
5035 <para> Implicit parameters are implemented as described in
5036 "Implicit parameters: dynamic scoping with static types",
5037 J Lewis, MB Shields, E Meijer, J Launchbury,
5038 27th ACM Symposium on Principles of Programming Languages (POPL'00),
5042 <para>(Most of the following, still rather incomplete, documentation is
5043 due to Jeff Lewis.)</para>
5045 <para>Implicit parameter support is enabled with the option
5046 <option>-XImplicitParams</option>.</para>
5049 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
5050 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
5051 context. In Haskell, all variables are statically bound. Dynamic
5052 binding of variables is a notion that goes back to Lisp, but was later
5053 discarded in more modern incarnations, such as Scheme. Dynamic binding
5054 can be very confusing in an untyped language, and unfortunately, typed
5055 languages, in particular Hindley-Milner typed languages like Haskell,
5056 only support static scoping of variables.
5059 However, by a simple extension to the type class system of Haskell, we
5060 can support dynamic binding. Basically, we express the use of a
5061 dynamically bound variable as a constraint on the type. These
5062 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
5063 function uses a dynamically-bound variable <literal>?x</literal>
5064 of type <literal>t'</literal>". For
5065 example, the following expresses the type of a sort function,
5066 implicitly parameterized by a comparison function named <literal>cmp</literal>.
5068 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5070 The dynamic binding constraints are just a new form of predicate in the type class system.
5073 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
5074 where <literal>x</literal> is
5075 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
5076 Use of this construct also introduces a new
5077 dynamic-binding constraint in the type of the expression.
5078 For example, the following definition
5079 shows how we can define an implicitly parameterized sort function in
5080 terms of an explicitly parameterized <literal>sortBy</literal> function:
5082 sortBy :: (a -> a -> Bool) -> [a] -> [a]
5084 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
5090 <title>Implicit-parameter type constraints</title>
5092 Dynamic binding constraints behave just like other type class
5093 constraints in that they are automatically propagated. Thus, when a
5094 function is used, its implicit parameters are inherited by the
5095 function that called it. For example, our <literal>sort</literal> function might be used
5096 to pick out the least value in a list:
5098 least :: (?cmp :: a -> a -> Bool) => [a] -> a
5099 least xs = head (sort xs)
5101 Without lifting a finger, the <literal>?cmp</literal> parameter is
5102 propagated to become a parameter of <literal>least</literal> as well. With explicit
5103 parameters, the default is that parameters must always be explicit
5104 propagated. With implicit parameters, the default is to always
5108 An implicit-parameter type constraint differs from other type class constraints in the
5109 following way: All uses of a particular implicit parameter must have
5110 the same type. This means that the type of <literal>(?x, ?x)</literal>
5111 is <literal>(?x::a) => (a,a)</literal>, and not
5112 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5116 <para> You can't have an implicit parameter in the context of a class or instance
5117 declaration. For example, both these declarations are illegal:
5119 class (?x::Int) => C a where ...
5120 instance (?x::a) => Foo [a] where ...
5122 Reason: exactly which implicit parameter you pick up depends on exactly where
5123 you invoke a function. But the ``invocation'' of instance declarations is done
5124 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5125 Easiest thing is to outlaw the offending types.</para>
5127 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5129 f :: (?x :: [a]) => Int -> Int
5132 g :: (Read a, Show a) => String -> String
5135 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5136 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5137 quite unambiguous, and fixes the type <literal>a</literal>.
5142 <title>Implicit-parameter bindings</title>
5145 An implicit parameter is <emphasis>bound</emphasis> using the standard
5146 <literal>let</literal> or <literal>where</literal> binding forms.
5147 For example, we define the <literal>min</literal> function by binding
5148 <literal>cmp</literal>.
5151 min = let ?cmp = (<=) in least
5155 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5156 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5157 (including in a list comprehension, or do-notation, or pattern guards),
5158 or a <literal>where</literal> clause.
5159 Note the following points:
5162 An implicit-parameter binding group must be a
5163 collection of simple bindings to implicit-style variables (no
5164 function-style bindings, and no type signatures); these bindings are
5165 neither polymorphic or recursive.
5168 You may not mix implicit-parameter bindings with ordinary bindings in a
5169 single <literal>let</literal>
5170 expression; use two nested <literal>let</literal>s instead.
5171 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5175 You may put multiple implicit-parameter bindings in a
5176 single binding group; but they are <emphasis>not</emphasis> treated
5177 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5178 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5179 parameter. The bindings are not nested, and may be re-ordered without changing
5180 the meaning of the program.
5181 For example, consider:
5183 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5185 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5186 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5188 f :: (?x::Int) => Int -> Int
5196 <sect3><title>Implicit parameters and polymorphic recursion</title>
5199 Consider these two definitions:
5202 len1 xs = let ?acc = 0 in len_acc1 xs
5205 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5210 len2 xs = let ?acc = 0 in len_acc2 xs
5212 len_acc2 :: (?acc :: Int) => [a] -> Int
5214 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5216 The only difference between the two groups is that in the second group
5217 <literal>len_acc</literal> is given a type signature.
5218 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5219 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5220 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5221 has a type signature, the recursive call is made to the
5222 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5223 as an implicit parameter. So we get the following results in GHCi:
5230 Adding a type signature dramatically changes the result! This is a rather
5231 counter-intuitive phenomenon, worth watching out for.
5235 <sect3><title>Implicit parameters and monomorphism</title>
5237 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5238 Haskell Report) to implicit parameters. For example, consider:
5246 Since the binding for <literal>y</literal> falls under the Monomorphism
5247 Restriction it is not generalised, so the type of <literal>y</literal> is
5248 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5249 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5250 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5251 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5252 <literal>y</literal> in the body of the <literal>let</literal> will see the
5253 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5254 <literal>14</literal>.
5259 <!-- ======================= COMMENTED OUT ========================
5261 We intend to remove linear implicit parameters, so I'm at least removing
5262 them from the 6.6 user manual
5264 <sect2 id="linear-implicit-parameters">
5265 <title>Linear implicit parameters</title>
5267 Linear implicit parameters are an idea developed by Koen Claessen,
5268 Mark Shields, and Simon PJ. They address the long-standing
5269 problem that monads seem over-kill for certain sorts of problem, notably:
5272 <listitem> <para> distributing a supply of unique names </para> </listitem>
5273 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5274 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5278 Linear implicit parameters are just like ordinary implicit parameters,
5279 except that they are "linear"; that is, they cannot be copied, and
5280 must be explicitly "split" instead. Linear implicit parameters are
5281 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5282 (The '/' in the '%' suggests the split!)
5287 import GHC.Exts( Splittable )
5289 data NameSupply = ...
5291 splitNS :: NameSupply -> (NameSupply, NameSupply)
5292 newName :: NameSupply -> Name
5294 instance Splittable NameSupply where
5298 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5299 f env (Lam x e) = Lam x' (f env e)
5302 env' = extend env x x'
5303 ...more equations for f...
5305 Notice that the implicit parameter %ns is consumed
5307 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5308 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5312 So the translation done by the type checker makes
5313 the parameter explicit:
5315 f :: NameSupply -> Env -> Expr -> Expr
5316 f ns env (Lam x e) = Lam x' (f ns1 env e)
5318 (ns1,ns2) = splitNS ns
5320 env = extend env x x'
5322 Notice the call to 'split' introduced by the type checker.
5323 How did it know to use 'splitNS'? Because what it really did
5324 was to introduce a call to the overloaded function 'split',
5325 defined by the class <literal>Splittable</literal>:
5327 class Splittable a where
5330 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5331 split for name supplies. But we can simply write
5337 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5339 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5340 <literal>GHC.Exts</literal>.
5345 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5346 are entirely distinct implicit parameters: you
5347 can use them together and they won't interfere with each other. </para>
5350 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5352 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5353 in the context of a class or instance declaration. </para></listitem>
5357 <sect3><title>Warnings</title>
5360 The monomorphism restriction is even more important than usual.
5361 Consider the example above:
5363 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5364 f env (Lam x e) = Lam x' (f env e)
5367 env' = extend env x x'
5369 If we replaced the two occurrences of x' by (newName %ns), which is
5370 usually a harmless thing to do, we get:
5372 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5373 f env (Lam x e) = Lam (newName %ns) (f env e)
5375 env' = extend env x (newName %ns)
5377 But now the name supply is consumed in <emphasis>three</emphasis> places
5378 (the two calls to newName,and the recursive call to f), so
5379 the result is utterly different. Urk! We don't even have
5383 Well, this is an experimental change. With implicit
5384 parameters we have already lost beta reduction anyway, and
5385 (as John Launchbury puts it) we can't sensibly reason about
5386 Haskell programs without knowing their typing.
5391 <sect3><title>Recursive functions</title>
5392 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5395 foo :: %x::T => Int -> [Int]
5397 foo n = %x : foo (n-1)
5399 where T is some type in class Splittable.</para>
5401 Do you get a list of all the same T's or all different T's
5402 (assuming that split gives two distinct T's back)?
5404 If you supply the type signature, taking advantage of polymorphic
5405 recursion, you get what you'd probably expect. Here's the
5406 translated term, where the implicit param is made explicit:
5409 foo x n = let (x1,x2) = split x
5410 in x1 : foo x2 (n-1)
5412 But if you don't supply a type signature, GHC uses the Hindley
5413 Milner trick of using a single monomorphic instance of the function
5414 for the recursive calls. That is what makes Hindley Milner type inference
5415 work. So the translation becomes
5419 foom n = x : foom (n-1)
5423 Result: 'x' is not split, and you get a list of identical T's. So the
5424 semantics of the program depends on whether or not foo has a type signature.
5427 You may say that this is a good reason to dislike linear implicit parameters
5428 and you'd be right. That is why they are an experimental feature.
5434 ================ END OF Linear Implicit Parameters commented out -->
5436 <sect2 id="kinding">
5437 <title>Explicitly-kinded quantification</title>
5440 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5441 to give the kind explicitly as (machine-checked) documentation,
5442 just as it is nice to give a type signature for a function. On some occasions,
5443 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5444 John Hughes had to define the data type:
5446 data Set cxt a = Set [a]
5447 | Unused (cxt a -> ())
5449 The only use for the <literal>Unused</literal> constructor was to force the correct
5450 kind for the type variable <literal>cxt</literal>.
5453 GHC now instead allows you to specify the kind of a type variable directly, wherever
5454 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5457 This flag enables kind signatures in the following places:
5459 <listitem><para><literal>data</literal> declarations:
5461 data Set (cxt :: * -> *) a = Set [a]
5462 </screen></para></listitem>
5463 <listitem><para><literal>type</literal> declarations:
5465 type T (f :: * -> *) = f Int
5466 </screen></para></listitem>
5467 <listitem><para><literal>class</literal> declarations:
5469 class (Eq a) => C (f :: * -> *) a where ...
5470 </screen></para></listitem>
5471 <listitem><para><literal>forall</literal>'s in type signatures:
5473 f :: forall (cxt :: * -> *). Set cxt Int
5474 </screen></para></listitem>
5479 The parentheses are required. Some of the spaces are required too, to
5480 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5481 will get a parse error, because "<literal>::*->*</literal>" is a
5482 single lexeme in Haskell.
5486 As part of the same extension, you can put kind annotations in types
5489 f :: (Int :: *) -> Int
5490 g :: forall a. a -> (a :: *)
5494 atype ::= '(' ctype '::' kind ')
5496 The parentheses are required.
5501 <sect2 id="universal-quantification">
5502 <title>Arbitrary-rank polymorphism
5506 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5507 explicit universal quantification in
5509 For example, all the following types are legal:
5511 f1 :: forall a b. a -> b -> a
5512 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5514 f2 :: (forall a. a->a) -> Int -> Int
5515 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5517 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5519 f4 :: Int -> (forall a. a -> a)
5521 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5522 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5523 The <literal>forall</literal> makes explicit the universal quantification that
5524 is implicitly added by Haskell.
5527 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5528 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5529 shows, the polymorphic type on the left of the function arrow can be overloaded.
5532 The function <literal>f3</literal> has a rank-3 type;
5533 it has rank-2 types on the left of a function arrow.
5536 GHC has three flags to control higher-rank types:
5539 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5542 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5545 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5546 That is, you can nest <literal>forall</literal>s
5547 arbitrarily deep in function arrows.
5548 In particular, a forall-type (also called a "type scheme"),
5549 including an operational type class context, is legal:
5551 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5552 of a function arrow </para> </listitem>
5553 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5554 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5555 field type signatures.</para> </listitem>
5556 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5557 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5569 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5570 the types of the constructor arguments. Here are several examples:
5576 data T a = T1 (forall b. b -> b -> b) a
5578 data MonadT m = MkMonad { return :: forall a. a -> m a,
5579 bind :: forall a b. m a -> (a -> m b) -> m b
5582 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5588 The constructors have rank-2 types:
5594 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5595 MkMonad :: forall m. (forall a. a -> m a)
5596 -> (forall a b. m a -> (a -> m b) -> m b)
5598 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5604 Notice that you don't need to use a <literal>forall</literal> if there's an
5605 explicit context. For example in the first argument of the
5606 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5607 prefixed to the argument type. The implicit <literal>forall</literal>
5608 quantifies all type variables that are not already in scope, and are
5609 mentioned in the type quantified over.
5613 As for type signatures, implicit quantification happens for non-overloaded
5614 types too. So if you write this:
5617 data T a = MkT (Either a b) (b -> b)
5620 it's just as if you had written this:
5623 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5626 That is, since the type variable <literal>b</literal> isn't in scope, it's
5627 implicitly universally quantified. (Arguably, it would be better
5628 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5629 where that is what is wanted. Feedback welcomed.)
5633 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5634 the constructor to suitable values, just as usual. For example,
5645 a3 = MkSwizzle reverse
5648 a4 = let r x = Just x
5655 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5656 mkTs f x y = [T1 f x, T1 f y]
5662 The type of the argument can, as usual, be more general than the type
5663 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5664 does not need the <literal>Ord</literal> constraint.)
5668 When you use pattern matching, the bound variables may now have
5669 polymorphic types. For example:
5675 f :: T a -> a -> (a, Char)
5676 f (T1 w k) x = (w k x, w 'c' 'd')
5678 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5679 g (MkSwizzle s) xs f = s (map f (s xs))
5681 h :: MonadT m -> [m a] -> m [a]
5682 h m [] = return m []
5683 h m (x:xs) = bind m x $ \y ->
5684 bind m (h m xs) $ \ys ->
5691 In the function <function>h</function> we use the record selectors <literal>return</literal>
5692 and <literal>bind</literal> to extract the polymorphic bind and return functions
5693 from the <literal>MonadT</literal> data structure, rather than using pattern
5699 <title>Type inference</title>
5702 In general, type inference for arbitrary-rank types is undecidable.
5703 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5704 to get a decidable algorithm by requiring some help from the programmer.
5705 We do not yet have a formal specification of "some help" but the rule is this:
5708 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5709 provides an explicit polymorphic type for x, or GHC's type inference will assume
5710 that x's type has no foralls in it</emphasis>.
5713 What does it mean to "provide" an explicit type for x? You can do that by
5714 giving a type signature for x directly, using a pattern type signature
5715 (<xref linkend="scoped-type-variables"/>), thus:
5717 \ f :: (forall a. a->a) -> (f True, f 'c')
5719 Alternatively, you can give a type signature to the enclosing
5720 context, which GHC can "push down" to find the type for the variable:
5722 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5724 Here the type signature on the expression can be pushed inwards
5725 to give a type signature for f. Similarly, and more commonly,
5726 one can give a type signature for the function itself:
5728 h :: (forall a. a->a) -> (Bool,Char)
5729 h f = (f True, f 'c')
5731 You don't need to give a type signature if the lambda bound variable
5732 is a constructor argument. Here is an example we saw earlier:
5734 f :: T a -> a -> (a, Char)
5735 f (T1 w k) x = (w k x, w 'c' 'd')
5737 Here we do not need to give a type signature to <literal>w</literal>, because
5738 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5745 <sect3 id="implicit-quant">
5746 <title>Implicit quantification</title>
5749 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5750 user-written types, if and only if there is no explicit <literal>forall</literal>,
5751 GHC finds all the type variables mentioned in the type that are not already
5752 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5756 f :: forall a. a -> a
5763 h :: forall b. a -> b -> b
5769 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5772 f :: (a -> a) -> Int
5774 f :: forall a. (a -> a) -> Int
5776 f :: (forall a. a -> a) -> Int
5779 g :: (Ord a => a -> a) -> Int
5780 -- MEANS the illegal type
5781 g :: forall a. (Ord a => a -> a) -> Int
5783 g :: (forall a. Ord a => a -> a) -> Int
5785 The latter produces an illegal type, which you might think is silly,
5786 but at least the rule is simple. If you want the latter type, you
5787 can write your for-alls explicitly. Indeed, doing so is strongly advised
5794 <sect2 id="impredicative-polymorphism">
5795 <title>Impredicative polymorphism
5797 <para><emphasis>NOTE: the impredicative-polymorphism feature is deprecated in GHC 6.12, and
5798 will be removed or replaced in GHC 6.14.</emphasis></para>
5800 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5801 enabled with <option>-XImpredicativeTypes</option>.
5803 that you can call a polymorphic function at a polymorphic type, and
5804 parameterise data structures over polymorphic types. For example:
5806 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5807 f (Just g) = Just (g [3], g "hello")
5810 Notice here that the <literal>Maybe</literal> type is parameterised by the
5811 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5814 <para>The technical details of this extension are described in the paper
5815 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5816 type inference for higher-rank types and impredicativity</ulink>,
5817 which appeared at ICFP 2006.
5821 <sect2 id="scoped-type-variables">
5822 <title>Lexically scoped type variables
5826 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5827 which some type signatures are simply impossible to write. For example:
5829 f :: forall a. [a] -> [a]
5835 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5836 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5837 The type variables bound by a <literal>forall</literal> scope over
5838 the entire definition of the accompanying value declaration.
5839 In this example, the type variable <literal>a</literal> scopes over the whole
5840 definition of <literal>f</literal>, including over
5841 the type signature for <varname>ys</varname>.
5842 In Haskell 98 it is not possible to declare
5843 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5844 it becomes possible to do so.
5846 <para>Lexically-scoped type variables are enabled by
5847 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5849 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5850 variables work, compared to earlier releases. Read this section
5854 <title>Overview</title>
5856 <para>The design follows the following principles
5858 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5859 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5860 design.)</para></listitem>
5861 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5862 type variables. This means that every programmer-written type signature
5863 (including one that contains free scoped type variables) denotes a
5864 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5865 checker, and no inference is involved.</para></listitem>
5866 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5867 changing the program.</para></listitem>
5871 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5873 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5874 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5875 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5876 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5880 In Haskell, a programmer-written type signature is implicitly quantified over
5881 its free type variables (<ulink
5882 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5884 of the Haskell Report).
5885 Lexically scoped type variables affect this implicit quantification rules
5886 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5887 quantified. For example, if type variable <literal>a</literal> is in scope,
5890 (e :: a -> a) means (e :: a -> a)
5891 (e :: b -> b) means (e :: forall b. b->b)
5892 (e :: a -> b) means (e :: forall b. a->b)
5900 <sect3 id="decl-type-sigs">
5901 <title>Declaration type signatures</title>
5902 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5903 quantification (using <literal>forall</literal>) brings into scope the
5904 explicitly-quantified
5905 type variables, in the definition of the named function. For example:
5907 f :: forall a. [a] -> [a]
5908 f (x:xs) = xs ++ [ x :: a ]
5910 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5911 the definition of "<literal>f</literal>".
5913 <para>This only happens if:
5915 <listitem><para> The quantification in <literal>f</literal>'s type
5916 signature is explicit. For example:
5919 g (x:xs) = xs ++ [ x :: a ]
5921 This program will be rejected, because "<literal>a</literal>" does not scope
5922 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5923 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5924 quantification rules.
5926 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5927 not a pattern binding.
5930 f1 :: forall a. [a] -> [a]
5931 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5933 f2 :: forall a. [a] -> [a]
5934 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5936 f3 :: forall a. [a] -> [a]
5937 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5939 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5940 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5941 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5942 the type signature brings <literal>a</literal> into scope.
5948 <sect3 id="exp-type-sigs">
5949 <title>Expression type signatures</title>
5951 <para>An expression type signature that has <emphasis>explicit</emphasis>
5952 quantification (using <literal>forall</literal>) brings into scope the
5953 explicitly-quantified
5954 type variables, in the annotated expression. For example:
5956 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5958 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5959 type variable <literal>s</literal> into scope, in the annotated expression
5960 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5965 <sect3 id="pattern-type-sigs">
5966 <title>Pattern type signatures</title>
5968 A type signature may occur in any pattern; this is a <emphasis>pattern type
5969 signature</emphasis>.
5972 -- f and g assume that 'a' is already in scope
5973 f = \(x::Int, y::a) -> x
5975 h ((x,y) :: (Int,Bool)) = (y,x)
5977 In the case where all the type variables in the pattern type signature are
5978 already in scope (i.e. bound by the enclosing context), matters are simple: the
5979 signature simply constrains the type of the pattern in the obvious way.
5982 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5983 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5984 that are already in scope. For example:
5986 f :: forall a. [a] -> (Int, [a])
5989 (ys::[a], n) = (reverse xs, length xs) -- OK
5990 zs::[a] = xs ++ ys -- OK
5992 Just (v::b) = ... -- Not OK; b is not in scope
5994 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5995 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5999 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
6000 type signature may mention a type variable that is not in scope; in this case,
6001 <emphasis>the signature brings that type variable into scope</emphasis>.
6002 This is particularly important for existential data constructors. For example:
6004 data T = forall a. MkT [a]
6007 k (MkT [t::a]) = MkT t3
6011 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
6012 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
6013 because it is bound by the pattern match. GHC's rule is that in this situation
6014 (and only then), a pattern type signature can mention a type variable that is
6015 not already in scope; the effect is to bring it into scope, standing for the
6016 existentially-bound type variable.
6019 When a pattern type signature binds a type variable in this way, GHC insists that the
6020 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
6021 This means that any user-written type signature always stands for a completely known type.
6024 If all this seems a little odd, we think so too. But we must have
6025 <emphasis>some</emphasis> way to bring such type variables into scope, else we
6026 could not name existentially-bound type variables in subsequent type signatures.
6029 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
6030 signature is allowed to mention a lexical variable that is not already in
6032 For example, both <literal>f</literal> and <literal>g</literal> would be
6033 illegal if <literal>a</literal> was not already in scope.
6039 <!-- ==================== Commented out part about result type signatures
6041 <sect3 id="result-type-sigs">
6042 <title>Result type signatures</title>
6045 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
6048 {- f assumes that 'a' is already in scope -}
6049 f x y :: [a] = [x,y,x]
6051 g = \ x :: [Int] -> [3,4]
6053 h :: forall a. [a] -> a
6057 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
6058 the result of the function. Similarly, the body of the lambda in the RHS of
6059 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
6060 alternative in <literal>h</literal> is <literal>a</literal>.
6062 <para> A result type signature never brings new type variables into scope.</para>
6064 There are a couple of syntactic wrinkles. First, notice that all three
6065 examples would parse quite differently with parentheses:
6067 {- f assumes that 'a' is already in scope -}
6068 f x (y :: [a]) = [x,y,x]
6070 g = \ (x :: [Int]) -> [3,4]
6072 h :: forall a. [a] -> a
6076 Now the signature is on the <emphasis>pattern</emphasis>; and
6077 <literal>h</literal> would certainly be ill-typed (since the pattern
6078 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
6080 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
6081 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
6082 token or a parenthesised type of some sort). To see why,
6083 consider how one would parse this:
6092 <sect3 id="cls-inst-scoped-tyvars">
6093 <title>Class and instance declarations</title>
6096 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
6097 scope over the methods defined in the <literal>where</literal> part. For example:
6115 <sect2 id="typing-binds">
6116 <title>Generalised typing of mutually recursive bindings</title>
6119 The Haskell Report specifies that a group of bindings (at top level, or in a
6120 <literal>let</literal> or <literal>where</literal>) should be sorted into
6121 strongly-connected components, and then type-checked in dependency order
6122 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6123 Report, Section 4.5.1</ulink>).
6124 As each group is type-checked, any binders of the group that
6126 an explicit type signature are put in the type environment with the specified
6128 and all others are monomorphic until the group is generalised
6129 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6132 <para>Following a suggestion of Mark Jones, in his paper
6133 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6135 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6137 <emphasis>the dependency analysis ignores references to variables that have an explicit
6138 type signature</emphasis>.
6139 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6140 typecheck. For example, consider:
6142 f :: Eq a => a -> Bool
6143 f x = (x == x) || g True || g "Yes"
6145 g y = (y <= y) || f True
6147 This is rejected by Haskell 98, but under Jones's scheme the definition for
6148 <literal>g</literal> is typechecked first, separately from that for
6149 <literal>f</literal>,
6150 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6151 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6152 type is generalised, to get
6154 g :: Ord a => a -> Bool
6156 Now, the definition for <literal>f</literal> is typechecked, with this type for
6157 <literal>g</literal> in the type environment.
6161 The same refined dependency analysis also allows the type signatures of
6162 mutually-recursive functions to have different contexts, something that is illegal in
6163 Haskell 98 (Section 4.5.2, last sentence). With
6164 <option>-XRelaxedPolyRec</option>
6165 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6166 type signatures; in practice this means that only variables bound by the same
6167 pattern binding must have the same context. For example, this is fine:
6169 f :: Eq a => a -> Bool
6170 f x = (x == x) || g True
6172 g :: Ord a => a -> Bool
6173 g y = (y <= y) || f True
6178 <sect2 id="mono-local-binds">
6179 <title>Monomorphic local bindings</title>
6181 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6182 The rationale is described in the paper
6183 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6186 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6187 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6188 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6189 If you supply a type signature, then the flag has no effect.
6194 <!-- ==================== End of type system extensions ================= -->
6196 <!-- ====================== TEMPLATE HASKELL ======================= -->
6198 <sect1 id="template-haskell">
6199 <title>Template Haskell</title>
6201 <para>Template Haskell allows you to do compile-time meta-programming in
6204 the main technical innovations is discussed in "<ulink
6205 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6206 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6209 There is a Wiki page about
6210 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6211 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6215 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6216 Haskell library reference material</ulink>
6217 (look for module <literal>Language.Haskell.TH</literal>).
6218 Many changes to the original design are described in
6219 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6220 Notes on Template Haskell version 2</ulink>.
6221 Not all of these changes are in GHC, however.
6224 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6225 as a worked example to help get you started.
6229 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6230 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6235 <title>Syntax</title>
6237 <para> Template Haskell has the following new syntactic
6238 constructions. You need to use the flag
6239 <option>-XTemplateHaskell</option>
6240 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6241 </indexterm>to switch these syntactic extensions on
6242 (<option>-XTemplateHaskell</option> is no longer implied by
6243 <option>-fglasgow-exts</option>).</para>
6247 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6248 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6249 There must be no space between the "$" and the identifier or parenthesis. This use
6250 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6251 of "." as an infix operator. If you want the infix operator, put spaces around it.
6253 <para> A splice can occur in place of
6255 <listitem><para> an expression; the spliced expression must
6256 have type <literal>Q Exp</literal></para></listitem>
6257 <listitem><para> an type; the spliced expression must
6258 have type <literal>Q Typ</literal></para></listitem>
6259 <listitem><para> a list of top-level declarations; the spliced expression
6260 must have type <literal>Q [Dec]</literal></para></listitem>
6262 Note that pattern splices are not supported.
6263 Inside a splice you can can only call functions defined in imported modules,
6264 not functions defined elsewhere in the same module.</para></listitem>
6267 A expression quotation is written in Oxford brackets, thus:
6269 <listitem><para> <literal>[| ... |]</literal>, or <literal>[e| ... |]</literal>,
6270 where the "..." is an expression;
6271 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6272 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6273 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6274 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6275 the quotation has type <literal>Q Type</literal>.</para></listitem>
6276 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;
6277 the quotation has type <literal>Q Pat</literal>.</para></listitem>
6278 </itemizedlist></para></listitem>
6281 A quasi-quotation can appear in either a pattern context or an
6282 expression context and is also written in Oxford brackets:
6284 <listitem><para> <literal>[<replaceable>varid</replaceable>| ... |]</literal>,
6285 where the "..." is an arbitrary string; a full description of the
6286 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6287 </itemizedlist></para></listitem>
6290 A name can be quoted with either one or two prefix single quotes:
6292 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6293 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6294 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6296 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6297 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6300 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6301 may also be given as an argument to the <literal>reify</literal> function.
6305 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6306 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6313 $(deriveStuff 'f) -- Uses the $(...) notation
6317 deriveStuff 'g -- Omits the $(...)
6321 This abbreviation makes top-level declaration slices quieter and less intimidating.
6326 (Compared to the original paper, there are many differences of detail.
6327 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6328 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6329 Pattern splices and quotations are not implemented.)
6333 <sect2> <title> Using Template Haskell </title>
6337 The data types and monadic constructor functions for Template Haskell are in the library
6338 <literal>Language.Haskell.THSyntax</literal>.
6342 You can only run a function at compile time if it is imported from another module. That is,
6343 you can't define a function in a module, and call it from within a splice in the same module.
6344 (It would make sense to do so, but it's hard to implement.)
6348 You can only run a function at compile time if it is imported
6349 from another module <emphasis>that is not part of a mutually-recursive group of modules
6350 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6351 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6352 splice is to be run.</para>
6354 For example, when compiling module A,
6355 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6356 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6360 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6363 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6364 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6365 compiles and runs a program, and then looks at the result. So it's important that
6366 the program it compiles produces results whose representations are identical to
6367 those of the compiler itself.
6371 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6372 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6377 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6378 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6379 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6386 -- Import our template "pr"
6387 import Printf ( pr )
6389 -- The splice operator $ takes the Haskell source code
6390 -- generated at compile time by "pr" and splices it into
6391 -- the argument of "putStrLn".
6392 main = putStrLn ( $(pr "Hello") )
6398 -- Skeletal printf from the paper.
6399 -- It needs to be in a separate module to the one where
6400 -- you intend to use it.
6402 -- Import some Template Haskell syntax
6403 import Language.Haskell.TH
6405 -- Describe a format string
6406 data Format = D | S | L String
6408 -- Parse a format string. This is left largely to you
6409 -- as we are here interested in building our first ever
6410 -- Template Haskell program and not in building printf.
6411 parse :: String -> [Format]
6414 -- Generate Haskell source code from a parsed representation
6415 -- of the format string. This code will be spliced into
6416 -- the module which calls "pr", at compile time.
6417 gen :: [Format] -> Q Exp
6418 gen [D] = [| \n -> show n |]
6419 gen [S] = [| \s -> s |]
6420 gen [L s] = stringE s
6422 -- Here we generate the Haskell code for the splice
6423 -- from an input format string.
6424 pr :: String -> Q Exp
6425 pr s = gen (parse s)
6428 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6431 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6434 <para>Run "main.exe" and here is your output:</para>
6444 <title>Using Template Haskell with Profiling</title>
6445 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6447 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6448 interpreter to run the splice expressions. The bytecode interpreter
6449 runs the compiled expression on top of the same runtime on which GHC
6450 itself is running; this means that the compiled code referred to by
6451 the interpreted expression must be compatible with this runtime, and
6452 in particular this means that object code that is compiled for
6453 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6454 expression, because profiled object code is only compatible with the
6455 profiling version of the runtime.</para>
6457 <para>This causes difficulties if you have a multi-module program
6458 containing Template Haskell code and you need to compile it for
6459 profiling, because GHC cannot load the profiled object code and use it
6460 when executing the splices. Fortunately GHC provides a workaround.
6461 The basic idea is to compile the program twice:</para>
6465 <para>Compile the program or library first the normal way, without
6466 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6469 <para>Then compile it again with <option>-prof</option>, and
6470 additionally use <option>-osuf
6471 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6472 to name the object files differently (you can choose any suffix
6473 that isn't the normal object suffix here). GHC will automatically
6474 load the object files built in the first step when executing splice
6475 expressions. If you omit the <option>-osuf</option> flag when
6476 building with <option>-prof</option> and Template Haskell is used,
6477 GHC will emit an error message. </para>
6482 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6483 <para>Quasi-quotation allows patterns and expressions to be written using
6484 programmer-defined concrete syntax; the motivation behind the extension and
6485 several examples are documented in
6486 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6487 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6488 2007). The example below shows how to write a quasiquoter for a simple
6489 expression language.</para>
6491 Here are the salient features
6494 A quasi-quote has the form
6495 <literal>[<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6498 The <replaceable>quoter</replaceable> must be the (unqualified) name of an imported
6499 quoter; it cannot be an arbitrary expression.
6502 The <replaceable>quoter</replaceable> cannot be "<literal>e</literal>",
6503 "<literal>t</literal>", "<literal>d</literal>", or "<literal>p</literal>", since
6504 those overlap with Template Haskell quotations.
6507 There must be no spaces in the token
6508 <literal>[<replaceable>quoter</replaceable>|</literal>.
6511 The quoted <replaceable>string</replaceable>
6512 can be arbitrary, and may contain newlines.
6518 A quasiquote may appear in place of
6520 <listitem><para>An expression</para></listitem>
6521 <listitem><para>A pattern</para></listitem>
6522 <listitem><para>A type</para></listitem>
6523 <listitem><para>A top-level declaration</para></listitem>
6525 (Only the first two are described in the paper.)
6529 A quoter is a value of type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal>,
6530 which is defined thus:
6532 data QuasiQuoter = QuasiQuoter { quoteExp :: String -> Q Exp,
6533 quotePat :: String -> Q Pat,
6534 quoteType :: String -> Q Type,
6535 quoteDec :: String -> Q [Dec] }
6537 That is, a quoter is a tuple of four parsers, one for each of the contexts
6538 in which a quasi-quote can occur.
6541 A quasi-quote is expanded by applying the appropriate parser to the string
6542 enclosed by the Oxford brackets. The context of the quasi-quote (expression, pattern,
6543 type, declaration) determines which of the parsers is called.
6548 The example below shows quasi-quotation in action. The quoter <literal>expr</literal>
6549 is bound to a value of type <literal>QuasiQuoter</literal> defined in module <literal>Expr</literal>.
6550 The example makes use of an antiquoted
6551 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6552 (this syntax for anti-quotation was defined by the parser's
6553 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6554 integer value argument of the constructor <literal>IntExpr</literal> when
6555 pattern matching. Please see the referenced paper for further details regarding
6556 anti-quotation as well as the description of a technique that uses SYB to
6557 leverage a single parser of type <literal>String -> a</literal> to generate both
6558 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6559 pattern parser that returns a value of type <literal>Q Pat</literal>.
6563 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6564 the example, <literal>expr</literal> cannot be defined
6565 in <literal>Main.hs</literal> where it is used, but must be imported.
6569 {- ------------- file Main.hs --------------- -}
6575 main = do { print $ eval [expr|1 + 2|]
6577 { [expr|'int:n|] -> print n
6583 {- ------------- file Expr.hs --------------- -}
6586 import qualified Language.Haskell.TH as TH
6587 import Language.Haskell.TH.Quote
6589 data Expr = IntExpr Integer
6590 | AntiIntExpr String
6591 | BinopExpr BinOp Expr Expr
6593 deriving(Show, Typeable, Data)
6599 deriving(Show, Typeable, Data)
6601 eval :: Expr -> Integer
6602 eval (IntExpr n) = n
6603 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6610 expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
6612 -- Parse an Expr, returning its representation as
6613 -- either a Q Exp or a Q Pat. See the referenced paper
6614 -- for how to use SYB to do this by writing a single
6615 -- parser of type String -> Expr instead of two
6616 -- separate parsers.
6618 parseExprExp :: String -> Q Exp
6621 parseExprPat :: String -> Q Pat
6625 <para>Now run the compiler:
6627 $ ghc --make -XQuasiQuotes Main.hs -o main
6631 <para>Run "main" and here is your output:
6642 <!-- ===================== Arrow notation =================== -->
6644 <sect1 id="arrow-notation">
6645 <title>Arrow notation
6648 <para>Arrows are a generalization of monads introduced by John Hughes.
6649 For more details, see
6654 “Generalising Monads to Arrows”,
6655 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6656 pp67–111, May 2000.
6657 The paper that introduced arrows: a friendly introduction, motivated with
6658 programming examples.
6664 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6665 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6666 Introduced the notation described here.
6672 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6673 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6680 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6681 John Hughes, in <citetitle>5th International Summer School on
6682 Advanced Functional Programming</citetitle>,
6683 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6685 This paper includes another introduction to the notation,
6686 with practical examples.
6692 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6693 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6694 A terse enumeration of the formal rules used
6695 (extracted from comments in the source code).
6701 The arrows web page at
6702 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6707 With the <option>-XArrows</option> flag, GHC supports the arrow
6708 notation described in the second of these papers,
6709 translating it using combinators from the
6710 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6712 What follows is a brief introduction to the notation;
6713 it won't make much sense unless you've read Hughes's paper.
6716 <para>The extension adds a new kind of expression for defining arrows:
6718 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6719 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6721 where <literal>proc</literal> is a new keyword.
6722 The variables of the pattern are bound in the body of the
6723 <literal>proc</literal>-expression,
6724 which is a new sort of thing called a <firstterm>command</firstterm>.
6725 The syntax of commands is as follows:
6727 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6728 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6729 | <replaceable>cmd</replaceable><superscript>0</superscript>
6731 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6732 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6733 infix operators as for expressions, and
6735 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6736 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6737 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6738 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6739 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6740 | <replaceable>fcmd</replaceable>
6742 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6743 | ( <replaceable>cmd</replaceable> )
6744 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6746 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6747 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6748 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6749 | <replaceable>cmd</replaceable>
6751 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6752 except that the bodies are commands instead of expressions.
6756 Commands produce values, but (like monadic computations)
6757 may yield more than one value,
6758 or none, and may do other things as well.
6759 For the most part, familiarity with monadic notation is a good guide to
6761 However the values of expressions, even monadic ones,
6762 are determined by the values of the variables they contain;
6763 this is not necessarily the case for commands.
6767 A simple example of the new notation is the expression
6769 proc x -> f -< x+1
6771 We call this a <firstterm>procedure</firstterm> or
6772 <firstterm>arrow abstraction</firstterm>.
6773 As with a lambda expression, the variable <literal>x</literal>
6774 is a new variable bound within the <literal>proc</literal>-expression.
6775 It refers to the input to the arrow.
6776 In the above example, <literal>-<</literal> is not an identifier but an
6777 new reserved symbol used for building commands from an expression of arrow
6778 type and an expression to be fed as input to that arrow.
6779 (The weird look will make more sense later.)
6780 It may be read as analogue of application for arrows.
6781 The above example is equivalent to the Haskell expression
6783 arr (\ x -> x+1) >>> f
6785 That would make no sense if the expression to the left of
6786 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6787 More generally, the expression to the left of <literal>-<</literal>
6788 may not involve any <firstterm>local variable</firstterm>,
6789 i.e. a variable bound in the current arrow abstraction.
6790 For such a situation there is a variant <literal>-<<</literal>, as in
6792 proc x -> f x -<< x+1
6794 which is equivalent to
6796 arr (\ x -> (f x, x+1)) >>> app
6798 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6800 Such an arrow is equivalent to a monad, so if you're using this form
6801 you may find a monadic formulation more convenient.
6805 <title>do-notation for commands</title>
6808 Another form of command is a form of <literal>do</literal>-notation.
6809 For example, you can write
6818 You can read this much like ordinary <literal>do</literal>-notation,
6819 but with commands in place of monadic expressions.
6820 The first line sends the value of <literal>x+1</literal> as an input to
6821 the arrow <literal>f</literal>, and matches its output against
6822 <literal>y</literal>.
6823 In the next line, the output is discarded.
6824 The arrow <function>returnA</function> is defined in the
6825 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6826 module as <literal>arr id</literal>.
6827 The above example is treated as an abbreviation for
6829 arr (\ x -> (x, x)) >>>
6830 first (arr (\ x -> x+1) >>> f) >>>
6831 arr (\ (y, x) -> (y, (x, y))) >>>
6832 first (arr (\ y -> 2*y) >>> g) >>>
6834 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6835 first (arr (\ (x, z) -> x*z) >>> h) >>>
6836 arr (\ (t, z) -> t+z) >>>
6839 Note that variables not used later in the composition are projected out.
6840 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6842 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6843 module, this reduces to
6845 arr (\ x -> (x+1, x)) >>>
6847 arr (\ (y, x) -> (2*y, (x, y))) >>>
6849 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6851 arr (\ (t, z) -> t+z)
6853 which is what you might have written by hand.
6854 With arrow notation, GHC keeps track of all those tuples of variables for you.
6858 Note that although the above translation suggests that
6859 <literal>let</literal>-bound variables like <literal>z</literal> must be
6860 monomorphic, the actual translation produces Core,
6861 so polymorphic variables are allowed.
6865 It's also possible to have mutually recursive bindings,
6866 using the new <literal>rec</literal> keyword, as in the following example:
6868 counter :: ArrowCircuit a => a Bool Int
6869 counter = proc reset -> do
6870 rec output <- returnA -< if reset then 0 else next
6871 next <- delay 0 -< output+1
6872 returnA -< output
6874 The translation of such forms uses the <function>loop</function> combinator,
6875 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6881 <title>Conditional commands</title>
6884 In the previous example, we used a conditional expression to construct the
6886 Sometimes we want to conditionally execute different commands, as in
6893 which is translated to
6895 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6896 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6898 Since the translation uses <function>|||</function>,
6899 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6903 There are also <literal>case</literal> commands, like
6909 y <- h -< (x1, x2)
6913 The syntax is the same as for <literal>case</literal> expressions,
6914 except that the bodies of the alternatives are commands rather than expressions.
6915 The translation is similar to that of <literal>if</literal> commands.
6921 <title>Defining your own control structures</title>
6924 As we're seen, arrow notation provides constructs,
6925 modelled on those for expressions,
6926 for sequencing, value recursion and conditionals.
6927 But suitable combinators,
6928 which you can define in ordinary Haskell,
6929 may also be used to build new commands out of existing ones.
6930 The basic idea is that a command defines an arrow from environments to values.
6931 These environments assign values to the free local variables of the command.
6932 Thus combinators that produce arrows from arrows
6933 may also be used to build commands from commands.
6934 For example, the <literal>ArrowChoice</literal> class includes a combinator
6936 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6938 so we can use it to build commands:
6940 expr' = proc x -> do
6943 symbol Plus -< ()
6944 y <- term -< ()
6947 symbol Minus -< ()
6948 y <- term -< ()
6951 (The <literal>do</literal> on the first line is needed to prevent the first
6952 <literal><+> ...</literal> from being interpreted as part of the
6953 expression on the previous line.)
6954 This is equivalent to
6956 expr' = (proc x -> returnA -< x)
6957 <+> (proc x -> do
6958 symbol Plus -< ()
6959 y <- term -< ()
6961 <+> (proc x -> do
6962 symbol Minus -< ()
6963 y <- term -< ()
6966 It is essential that this operator be polymorphic in <literal>e</literal>
6967 (representing the environment input to the command
6968 and thence to its subcommands)
6969 and satisfy the corresponding naturality property
6971 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6973 at least for strict <literal>k</literal>.
6974 (This should be automatic if you're not using <function>seq</function>.)
6975 This ensures that environments seen by the subcommands are environments
6976 of the whole command,
6977 and also allows the translation to safely trim these environments.
6978 The operator must also not use any variable defined within the current
6983 We could define our own operator
6985 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6986 untilA body cond = proc x ->
6987 b <- cond -< x
6988 if b then returnA -< ()
6991 untilA body cond -< x
6993 and use it in the same way.
6994 Of course this infix syntax only makes sense for binary operators;
6995 there is also a more general syntax involving special brackets:
6999 (|untilA (increment -< x+y) (within 0.5 -< x)|)
7006 <title>Primitive constructs</title>
7009 Some operators will need to pass additional inputs to their subcommands.
7010 For example, in an arrow type supporting exceptions,
7011 the operator that attaches an exception handler will wish to pass the
7012 exception that occurred to the handler.
7013 Such an operator might have a type
7015 handleA :: ... => a e c -> a (e,Ex) c -> a e c
7017 where <literal>Ex</literal> is the type of exceptions handled.
7018 You could then use this with arrow notation by writing a command
7020 body `handleA` \ ex -> handler
7022 so that if an exception is raised in the command <literal>body</literal>,
7023 the variable <literal>ex</literal> is bound to the value of the exception
7024 and the command <literal>handler</literal>,
7025 which typically refers to <literal>ex</literal>, is entered.
7026 Though the syntax here looks like a functional lambda,
7027 we are talking about commands, and something different is going on.
7028 The input to the arrow represented by a command consists of values for
7029 the free local variables in the command, plus a stack of anonymous values.
7030 In all the prior examples, this stack was empty.
7031 In the second argument to <function>handleA</function>,
7032 this stack consists of one value, the value of the exception.
7033 The command form of lambda merely gives this value a name.
7038 the values on the stack are paired to the right of the environment.
7039 So operators like <function>handleA</function> that pass
7040 extra inputs to their subcommands can be designed for use with the notation
7041 by pairing the values with the environment in this way.
7042 More precisely, the type of each argument of the operator (and its result)
7043 should have the form
7045 a (...(e,t1), ... tn) t
7047 where <replaceable>e</replaceable> is a polymorphic variable
7048 (representing the environment)
7049 and <replaceable>ti</replaceable> are the types of the values on the stack,
7050 with <replaceable>t1</replaceable> being the <quote>top</quote>.
7051 The polymorphic variable <replaceable>e</replaceable> must not occur in
7052 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
7053 <replaceable>t</replaceable>.
7054 However the arrows involved need not be the same.
7055 Here are some more examples of suitable operators:
7057 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
7058 runReader :: ... => a e c -> a' (e,State) c
7059 runState :: ... => a e c -> a' (e,State) (c,State)
7061 We can supply the extra input required by commands built with the last two
7062 by applying them to ordinary expressions, as in
7066 (|runReader (do { ... })|) s
7068 which adds <literal>s</literal> to the stack of inputs to the command
7069 built using <function>runReader</function>.
7073 The command versions of lambda abstraction and application are analogous to
7074 the expression versions.
7075 In particular, the beta and eta rules describe equivalences of commands.
7076 These three features (operators, lambda abstraction and application)
7077 are the core of the notation; everything else can be built using them,
7078 though the results would be somewhat clumsy.
7079 For example, we could simulate <literal>do</literal>-notation by defining
7081 bind :: Arrow a => a e b -> a (e,b) c -> a e c
7082 u `bind` f = returnA &&& u >>> f
7084 bind_ :: Arrow a => a e b -> a e c -> a e c
7085 u `bind_` f = u `bind` (arr fst >>> f)
7087 We could simulate <literal>if</literal> by defining
7089 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
7090 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
7097 <title>Differences with the paper</title>
7102 <para>Instead of a single form of arrow application (arrow tail) with two
7103 translations, the implementation provides two forms
7104 <quote><literal>-<</literal></quote> (first-order)
7105 and <quote><literal>-<<</literal></quote> (higher-order).
7110 <para>User-defined operators are flagged with banana brackets instead of
7111 a new <literal>form</literal> keyword.
7120 <title>Portability</title>
7123 Although only GHC implements arrow notation directly,
7124 there is also a preprocessor
7126 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
7127 that translates arrow notation into Haskell 98
7128 for use with other Haskell systems.
7129 You would still want to check arrow programs with GHC;
7130 tracing type errors in the preprocessor output is not easy.
7131 Modules intended for both GHC and the preprocessor must observe some
7132 additional restrictions:
7137 The module must import
7138 <ulink url="&libraryBaseLocation;/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
7144 The preprocessor cannot cope with other Haskell extensions.
7145 These would have to go in separate modules.
7151 Because the preprocessor targets Haskell (rather than Core),
7152 <literal>let</literal>-bound variables are monomorphic.
7163 <!-- ==================== BANG PATTERNS ================= -->
7165 <sect1 id="bang-patterns">
7166 <title>Bang patterns
7167 <indexterm><primary>Bang patterns</primary></indexterm>
7169 <para>GHC supports an extension of pattern matching called <emphasis>bang
7170 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7171 Bang patterns are under consideration for Haskell Prime.
7173 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7174 prime feature description</ulink> contains more discussion and examples
7175 than the material below.
7178 The key change is the addition of a new rule to the
7179 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7180 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7181 against a value <replaceable>v</replaceable> behaves as follows:
7183 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7184 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7188 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7191 <sect2 id="bang-patterns-informal">
7192 <title>Informal description of bang patterns
7195 The main idea is to add a single new production to the syntax of patterns:
7199 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7200 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7205 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7206 whereas without the bang it would be lazy.
7207 Bang patterns can be nested of course:
7211 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7212 <literal>y</literal>.
7213 A bang only really has an effect if it precedes a variable or wild-card pattern:
7218 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7219 putting a bang before a pattern that
7220 forces evaluation anyway does nothing.
7223 There is one (apparent) exception to this general rule that a bang only
7224 makes a difference when it precedes a variable or wild-card: a bang at the
7225 top level of a <literal>let</literal> or <literal>where</literal>
7226 binding makes the binding strict, regardless of the pattern. For example:
7230 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7231 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7232 (We say "apparent" exception because the Right Way to think of it is that the bang
7233 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7234 is part of the syntax of the <emphasis>binding</emphasis>.)
7235 Nested bangs in a pattern binding behave uniformly with all other forms of
7236 pattern matching. For example
7238 let (!x,[y]) = e in b
7240 is equivalent to this:
7242 let { t = case e of (x,[y]) -> x `seq` (x,y)
7247 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7248 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7249 evaluation of <literal>x</literal>.
7252 Bang patterns work in <literal>case</literal> expressions too, of course:
7254 g5 x = let y = f x in body
7255 g6 x = case f x of { y -> body }
7256 g7 x = case f x of { !y -> body }
7258 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7259 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7260 result, and then evaluates <literal>body</literal>.
7265 <sect2 id="bang-patterns-sem">
7266 <title>Syntax and semantics
7270 We add a single new production to the syntax of patterns:
7274 There is one problem with syntactic ambiguity. Consider:
7278 Is this a definition of the infix function "<literal>(!)</literal>",
7279 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7280 ambiguity in favour of the latter. If you want to define
7281 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7286 The semantics of Haskell pattern matching is described in <ulink
7287 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7288 Section 3.17.2</ulink> of the Haskell Report. To this description add
7289 one extra item 10, saying:
7290 <itemizedlist><listitem><para>Matching
7291 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7292 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7293 <listitem><para>otherwise, <literal>pat</literal> is matched against
7294 <literal>v</literal></para></listitem>
7296 </para></listitem></itemizedlist>
7297 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7298 Section 3.17.3</ulink>, add a new case (t):
7300 case v of { !pat -> e; _ -> e' }
7301 = v `seq` case v of { pat -> e; _ -> e' }
7304 That leaves let expressions, whose translation is given in
7305 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7307 of the Haskell Report.
7308 In the translation box, first apply
7309 the following transformation: for each pattern <literal>pi</literal> that is of
7310 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7311 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7312 have a bang at the top, apply the rules in the existing box.
7314 <para>The effect of the let rule is to force complete matching of the pattern
7315 <literal>qi</literal> before evaluation of the body is begun. The bang is
7316 retained in the translated form in case <literal>qi</literal> is a variable,
7324 The let-binding can be recursive. However, it is much more common for
7325 the let-binding to be non-recursive, in which case the following law holds:
7326 <literal>(let !p = rhs in body)</literal>
7328 <literal>(case rhs of !p -> body)</literal>
7331 A pattern with a bang at the outermost level is not allowed at the top level of
7337 <!-- ==================== ASSERTIONS ================= -->
7339 <sect1 id="assertions">
7341 <indexterm><primary>Assertions</primary></indexterm>
7345 If you want to make use of assertions in your standard Haskell code, you
7346 could define a function like the following:
7352 assert :: Bool -> a -> a
7353 assert False x = error "assertion failed!"
7360 which works, but gives you back a less than useful error message --
7361 an assertion failed, but which and where?
7365 One way out is to define an extended <function>assert</function> function which also
7366 takes a descriptive string to include in the error message and
7367 perhaps combine this with the use of a pre-processor which inserts
7368 the source location where <function>assert</function> was used.
7372 Ghc offers a helping hand here, doing all of this for you. For every
7373 use of <function>assert</function> in the user's source:
7379 kelvinToC :: Double -> Double
7380 kelvinToC k = assert (k >= 0.0) (k+273.15)
7386 Ghc will rewrite this to also include the source location where the
7393 assert pred val ==> assertError "Main.hs|15" pred val
7399 The rewrite is only performed by the compiler when it spots
7400 applications of <function>Control.Exception.assert</function>, so you
7401 can still define and use your own versions of
7402 <function>assert</function>, should you so wish. If not, import
7403 <literal>Control.Exception</literal> to make use
7404 <function>assert</function> in your code.
7408 GHC ignores assertions when optimisation is turned on with the
7409 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7410 <literal>assert pred e</literal> will be rewritten to
7411 <literal>e</literal>. You can also disable assertions using the
7412 <option>-fignore-asserts</option>
7413 option<indexterm><primary><option>-fignore-asserts</option></primary>
7414 </indexterm>.</para>
7417 Assertion failures can be caught, see the documentation for the
7418 <literal>Control.Exception</literal> library for the details.
7424 <!-- =============================== PRAGMAS =========================== -->
7426 <sect1 id="pragmas">
7427 <title>Pragmas</title>
7429 <indexterm><primary>pragma</primary></indexterm>
7431 <para>GHC supports several pragmas, or instructions to the
7432 compiler placed in the source code. Pragmas don't normally affect
7433 the meaning of the program, but they might affect the efficiency
7434 of the generated code.</para>
7436 <para>Pragmas all take the form
7438 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7440 where <replaceable>word</replaceable> indicates the type of
7441 pragma, and is followed optionally by information specific to that
7442 type of pragma. Case is ignored in
7443 <replaceable>word</replaceable>. The various values for
7444 <replaceable>word</replaceable> that GHC understands are described
7445 in the following sections; any pragma encountered with an
7446 unrecognised <replaceable>word</replaceable> is
7447 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7448 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7450 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7454 pragma must precede the <literal>module</literal> keyword in the file.
7457 There can be as many file-header pragmas as you please, and they can be
7458 preceded or followed by comments.
7461 File-header pragmas are read once only, before
7462 pre-processing the file (e.g. with cpp).
7465 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7466 <literal>{-# OPTIONS_GHC #-}</literal>, and
7467 <literal>{-# INCLUDE #-}</literal>.
7472 <sect2 id="language-pragma">
7473 <title>LANGUAGE pragma</title>
7475 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7476 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7478 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7480 It is the intention that all Haskell compilers support the
7481 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7482 all extensions are supported by all compilers, of
7483 course. The <literal>LANGUAGE</literal> pragma should be used instead
7484 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7486 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7488 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7490 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7492 <para>Every language extension can also be turned into a command-line flag
7493 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7494 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7497 <para>A list of all supported language extensions can be obtained by invoking
7498 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7500 <para>Any extension from the <literal>Extension</literal> type defined in
7502 url="&libraryCabalLocation;/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7503 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7507 <sect2 id="options-pragma">
7508 <title>OPTIONS_GHC pragma</title>
7509 <indexterm><primary>OPTIONS_GHC</primary>
7511 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7514 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7515 additional options that are given to the compiler when compiling
7516 this source file. See <xref linkend="source-file-options"/> for
7519 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7520 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7523 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7525 <sect2 id="include-pragma">
7526 <title>INCLUDE pragma</title>
7528 <para>The <literal>INCLUDE</literal> used to be necessary for
7529 specifying header files to be included when using the FFI and
7530 compiling via C. It is no longer required for GHC, but is
7531 accepted (and ignored) for compatibility with other
7535 <sect2 id="warning-deprecated-pragma">
7536 <title>WARNING and DEPRECATED pragmas</title>
7537 <indexterm><primary>WARNING</primary></indexterm>
7538 <indexterm><primary>DEPRECATED</primary></indexterm>
7540 <para>The WARNING pragma allows you to attach an arbitrary warning
7541 to a particular function, class, or type.
7542 A DEPRECATED pragma lets you specify that
7543 a particular function, class, or type is deprecated.
7544 There are two ways of using these pragmas.
7548 <para>You can work on an entire module thus:</para>
7550 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7555 module Wibble {-# WARNING "This is an unstable interface." #-} where
7558 <para>When you compile any module that import
7559 <literal>Wibble</literal>, GHC will print the specified
7564 <para>You can attach a warning to a function, class, type, or data constructor, with the
7565 following top-level declarations:</para>
7567 {-# DEPRECATED f, C, T "Don't use these" #-}
7568 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7570 <para>When you compile any module that imports and uses any
7571 of the specified entities, GHC will print the specified
7573 <para> You can only attach to entities declared at top level in the module
7574 being compiled, and you can only use unqualified names in the list of
7575 entities. A capitalised name, such as <literal>T</literal>
7576 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7577 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7578 both are in scope. If both are in scope, there is currently no way to
7579 specify one without the other (c.f. fixities
7580 <xref linkend="infix-tycons"/>).</para>
7583 Warnings and deprecations are not reported for
7584 (a) uses within the defining module, and
7585 (b) uses in an export list.
7586 The latter reduces spurious complaints within a library
7587 in which one module gathers together and re-exports
7588 the exports of several others.
7590 <para>You can suppress the warnings with the flag
7591 <option>-fno-warn-warnings-deprecations</option>.</para>
7594 <sect2 id="inline-noinline-pragma">
7595 <title>INLINE and NOINLINE pragmas</title>
7597 <para>These pragmas control the inlining of function
7600 <sect3 id="inline-pragma">
7601 <title>INLINE pragma</title>
7602 <indexterm><primary>INLINE</primary></indexterm>
7604 <para>GHC (with <option>-O</option>, as always) tries to
7605 inline (or “unfold”) functions/values that are
7606 “small enough,” thus avoiding the call overhead
7607 and possibly exposing other more-wonderful optimisations.
7608 Normally, if GHC decides a function is “too
7609 expensive” to inline, it will not do so, nor will it
7610 export that unfolding for other modules to use.</para>
7612 <para>The sledgehammer you can bring to bear is the
7613 <literal>INLINE</literal><indexterm><primary>INLINE
7614 pragma</primary></indexterm> pragma, used thusly:</para>
7617 key_function :: Int -> String -> (Bool, Double)
7618 {-# INLINE key_function #-}
7621 <para>The major effect of an <literal>INLINE</literal> pragma
7622 is to declare a function's “cost” to be very low.
7623 The normal unfolding machinery will then be very keen to
7624 inline it. However, an <literal>INLINE</literal> pragma for a
7625 function "<literal>f</literal>" has a number of other effects:
7628 No functions are inlined into <literal>f</literal>. Otherwise
7629 GHC might inline a big function into <literal>f</literal>'s right hand side,
7630 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7633 The float-in, float-out, and common-sub-expression transformations are not
7634 applied to the body of <literal>f</literal>.
7637 An INLINE function is not worker/wrappered by strictness analysis.
7638 It's going to be inlined wholesale instead.
7641 All of these effects are aimed at ensuring that what gets inlined is
7642 exactly what you asked for, no more and no less.
7644 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7645 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7646 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7647 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7648 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7649 when there is no choice even an INLINE function can be selected, in which case
7650 the INLINE pragma is ignored.
7651 For example, for a self-recursive function, the loop breaker can only be the function
7652 itself, so an INLINE pragma is always ignored.</para>
7654 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7655 function can be put anywhere its type signature could be
7658 <para><literal>INLINE</literal> pragmas are a particularly
7660 <literal>then</literal>/<literal>return</literal> (or
7661 <literal>bind</literal>/<literal>unit</literal>) functions in
7662 a monad. For example, in GHC's own
7663 <literal>UniqueSupply</literal> monad code, we have:</para>
7666 {-# INLINE thenUs #-}
7667 {-# INLINE returnUs #-}
7670 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7671 linkend="noinline-pragma"/>).</para>
7673 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7674 so if you want your code to be HBC-compatible you'll have to surround
7675 the pragma with C pre-processor directives
7676 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7680 <sect3 id="noinline-pragma">
7681 <title>NOINLINE pragma</title>
7683 <indexterm><primary>NOINLINE</primary></indexterm>
7684 <indexterm><primary>NOTINLINE</primary></indexterm>
7686 <para>The <literal>NOINLINE</literal> pragma does exactly what
7687 you'd expect: it stops the named function from being inlined
7688 by the compiler. You shouldn't ever need to do this, unless
7689 you're very cautious about code size.</para>
7691 <para><literal>NOTINLINE</literal> is a synonym for
7692 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7693 specified by Haskell 98 as the standard way to disable
7694 inlining, so it should be used if you want your code to be
7698 <sect3 id="conlike-pragma">
7699 <title>CONLIKE modifier</title>
7700 <indexterm><primary>CONLIKE</primary></indexterm>
7701 <para>An INLINE or NOINLINE pragma may have a CONLIKE modifier,
7702 which affects matching in RULEs (only). See <xref linkend="conlike"/>.
7706 <sect3 id="phase-control">
7707 <title>Phase control</title>
7709 <para> Sometimes you want to control exactly when in GHC's
7710 pipeline the INLINE pragma is switched on. Inlining happens
7711 only during runs of the <emphasis>simplifier</emphasis>. Each
7712 run of the simplifier has a different <emphasis>phase
7713 number</emphasis>; the phase number decreases towards zero.
7714 If you use <option>-dverbose-core2core</option> you'll see the
7715 sequence of phase numbers for successive runs of the
7716 simplifier. In an INLINE pragma you can optionally specify a
7720 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7721 <literal>f</literal>
7722 until phase <literal>k</literal>, but from phase
7723 <literal>k</literal> onwards be very keen to inline it.
7726 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7727 <literal>f</literal>
7728 until phase <literal>k</literal>, but from phase
7729 <literal>k</literal> onwards do not inline it.
7732 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7733 <literal>f</literal>
7734 until phase <literal>k</literal>, but from phase
7735 <literal>k</literal> onwards be willing to inline it (as if
7736 there was no pragma).
7739 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7740 <literal>f</literal>
7741 until phase <literal>k</literal>, but from phase
7742 <literal>k</literal> onwards do not inline it.
7745 The same information is summarised here:
7747 -- Before phase 2 Phase 2 and later
7748 {-# INLINE [2] f #-} -- No Yes
7749 {-# INLINE [~2] f #-} -- Yes No
7750 {-# NOINLINE [2] f #-} -- No Maybe
7751 {-# NOINLINE [~2] f #-} -- Maybe No
7753 {-# INLINE f #-} -- Yes Yes
7754 {-# NOINLINE f #-} -- No No
7756 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7757 function body is small, or it is applied to interesting-looking arguments etc).
7758 Another way to understand the semantics is this:
7760 <listitem><para>For both INLINE and NOINLINE, the phase number says
7761 when inlining is allowed at all.</para></listitem>
7762 <listitem><para>The INLINE pragma has the additional effect of making the
7763 function body look small, so that when inlining is allowed it is very likely to
7768 <para>The same phase-numbering control is available for RULES
7769 (<xref linkend="rewrite-rules"/>).</para>
7773 <sect2 id="annotation-pragmas">
7774 <title>ANN pragmas</title>
7776 <para>GHC offers the ability to annotate various code constructs with additional
7777 data by using three pragmas. This data can then be inspected at a later date by
7778 using GHC-as-a-library.</para>
7780 <sect3 id="ann-pragma">
7781 <title>Annotating values</title>
7783 <indexterm><primary>ANN</primary></indexterm>
7785 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7786 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7787 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7788 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7789 you would do this:</para>
7792 {-# ANN foo (Just "Hello") #-}
7797 A number of restrictions apply to use of annotations:
7799 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7800 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7801 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7802 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7803 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7805 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7806 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7809 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7810 please give the GHC team a shout</ulink>.
7813 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7814 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7817 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7822 <sect3 id="typeann-pragma">
7823 <title>Annotating types</title>
7825 <indexterm><primary>ANN type</primary></indexterm>
7826 <indexterm><primary>ANN</primary></indexterm>
7828 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7831 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7836 <sect3 id="modann-pragma">
7837 <title>Annotating modules</title>
7839 <indexterm><primary>ANN module</primary></indexterm>
7840 <indexterm><primary>ANN</primary></indexterm>
7842 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7845 {-# ANN module (Just "A `Maybe String' annotation") #-}
7850 <sect2 id="line-pragma">
7851 <title>LINE pragma</title>
7853 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7854 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7855 <para>This pragma is similar to C's <literal>#line</literal>
7856 pragma, and is mainly for use in automatically generated Haskell
7857 code. It lets you specify the line number and filename of the
7858 original code; for example</para>
7860 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7862 <para>if you'd generated the current file from something called
7863 <filename>Foo.vhs</filename> and this line corresponds to line
7864 42 in the original. GHC will adjust its error messages to refer
7865 to the line/file named in the <literal>LINE</literal>
7870 <title>RULES pragma</title>
7872 <para>The RULES pragma lets you specify rewrite rules. It is
7873 described in <xref linkend="rewrite-rules"/>.</para>
7876 <sect2 id="specialize-pragma">
7877 <title>SPECIALIZE pragma</title>
7879 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7880 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7881 <indexterm><primary>overloading, death to</primary></indexterm>
7883 <para>(UK spelling also accepted.) For key overloaded
7884 functions, you can create extra versions (NB: more code space)
7885 specialised to particular types. Thus, if you have an
7886 overloaded function:</para>
7889 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7892 <para>If it is heavily used on lists with
7893 <literal>Widget</literal> keys, you could specialise it as
7897 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7900 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7901 be put anywhere its type signature could be put.</para>
7903 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7904 (a) a specialised version of the function and (b) a rewrite rule
7905 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7906 un-specialised function into a call to the specialised one.</para>
7908 <para>The type in a SPECIALIZE pragma can be any type that is less
7909 polymorphic than the type of the original function. In concrete terms,
7910 if the original function is <literal>f</literal> then the pragma
7912 {-# SPECIALIZE f :: <type> #-}
7914 is valid if and only if the definition
7916 f_spec :: <type>
7919 is valid. Here are some examples (where we only give the type signature
7920 for the original function, not its code):
7922 f :: Eq a => a -> b -> b
7923 {-# SPECIALISE f :: Int -> b -> b #-}
7925 g :: (Eq a, Ix b) => a -> b -> b
7926 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7928 h :: Eq a => a -> a -> a
7929 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7931 The last of these examples will generate a
7932 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7933 well. If you use this kind of specialisation, let us know how well it works.
7936 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7937 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7938 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7939 The <literal>INLINE</literal> pragma affects the specialised version of the
7940 function (only), and applies even if the function is recursive. The motivating
7943 -- A GADT for arrays with type-indexed representation
7945 ArrInt :: !Int -> ByteArray# -> Arr Int
7946 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7948 (!:) :: Arr e -> Int -> e
7949 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7950 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7951 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7952 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7954 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7955 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7956 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7957 the specialised function will be inlined. It has two calls to
7958 <literal>(!:)</literal>,
7959 both at type <literal>Int</literal>. Both these calls fire the first
7960 specialisation, whose body is also inlined. The result is a type-based
7961 unrolling of the indexing function.</para>
7962 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7963 on an ordinarily-recursive function.</para>
7965 <para>Note: In earlier versions of GHC, it was possible to provide your own
7966 specialised function for a given type:
7969 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7972 This feature has been removed, as it is now subsumed by the
7973 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7977 <sect2 id="specialize-instance-pragma">
7978 <title>SPECIALIZE instance pragma
7982 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7983 <indexterm><primary>overloading, death to</primary></indexterm>
7984 Same idea, except for instance declarations. For example:
7987 instance (Eq a) => Eq (Foo a) where {
7988 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7992 The pragma must occur inside the <literal>where</literal> part
7993 of the instance declaration.
7996 Compatible with HBC, by the way, except perhaps in the placement
8002 <sect2 id="unpack-pragma">
8003 <title>UNPACK pragma</title>
8005 <indexterm><primary>UNPACK</primary></indexterm>
8007 <para>The <literal>UNPACK</literal> indicates to the compiler
8008 that it should unpack the contents of a constructor field into
8009 the constructor itself, removing a level of indirection. For
8013 data T = T {-# UNPACK #-} !Float
8014 {-# UNPACK #-} !Float
8017 <para>will create a constructor <literal>T</literal> containing
8018 two unboxed floats. This may not always be an optimisation: if
8019 the <function>T</function> constructor is scrutinised and the
8020 floats passed to a non-strict function for example, they will
8021 have to be reboxed (this is done automatically by the
8024 <para>Unpacking constructor fields should only be used in
8025 conjunction with <option>-O</option>, in order to expose
8026 unfoldings to the compiler so the reboxing can be removed as
8027 often as possible. For example:</para>
8031 f (T f1 f2) = f1 + f2
8034 <para>The compiler will avoid reboxing <function>f1</function>
8035 and <function>f2</function> by inlining <function>+</function>
8036 on floats, but only when <option>-O</option> is on.</para>
8038 <para>Any single-constructor data is eligible for unpacking; for
8042 data T = T {-# UNPACK #-} !(Int,Int)
8045 <para>will store the two <literal>Int</literal>s directly in the
8046 <function>T</function> constructor, by flattening the pair.
8047 Multi-level unpacking is also supported:
8050 data T = T {-# UNPACK #-} !S
8051 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
8054 will store two unboxed <literal>Int#</literal>s
8055 directly in the <function>T</function> constructor. The
8056 unpacker can see through newtypes, too.</para>
8058 <para>If a field cannot be unpacked, you will not get a warning,
8059 so it might be an idea to check the generated code with
8060 <option>-ddump-simpl</option>.</para>
8062 <para>See also the <option>-funbox-strict-fields</option> flag,
8063 which essentially has the effect of adding
8064 <literal>{-# UNPACK #-}</literal> to every strict
8065 constructor field.</para>
8068 <sect2 id="source-pragma">
8069 <title>SOURCE pragma</title>
8071 <indexterm><primary>SOURCE</primary></indexterm>
8072 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
8073 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
8079 <!-- ======================= REWRITE RULES ======================== -->
8081 <sect1 id="rewrite-rules">
8082 <title>Rewrite rules
8084 <indexterm><primary>RULES pragma</primary></indexterm>
8085 <indexterm><primary>pragma, RULES</primary></indexterm>
8086 <indexterm><primary>rewrite rules</primary></indexterm></title>
8089 The programmer can specify rewrite rules as part of the source program
8095 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8100 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
8101 If you need more information, then <option>-ddump-rule-firings</option> shows you
8102 each individual rule firing in detail.
8106 <title>Syntax</title>
8109 From a syntactic point of view:
8115 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
8116 may be generated by the layout rule).
8122 The layout rule applies in a pragma.
8123 Currently no new indentation level
8124 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
8125 you must lay out the starting in the same column as the enclosing definitions.
8128 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
8129 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
8132 Furthermore, the closing <literal>#-}</literal>
8133 should start in a column to the right of the opening <literal>{-#</literal>.
8139 Each rule has a name, enclosed in double quotes. The name itself has
8140 no significance at all. It is only used when reporting how many times the rule fired.
8146 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
8147 immediately after the name of the rule. Thus:
8150 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
8153 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
8154 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
8163 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
8164 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8165 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8166 by spaces, just like in a type <literal>forall</literal>.
8172 A pattern variable may optionally have a type signature.
8173 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8174 For example, here is the <literal>foldr/build</literal> rule:
8177 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8178 foldr k z (build g) = g k z
8181 Since <function>g</function> has a polymorphic type, it must have a type signature.
8188 The left hand side of a rule must consist of a top-level variable applied
8189 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8192 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8193 "wrong2" forall f. f True = True
8196 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8203 A rule does not need to be in the same module as (any of) the
8204 variables it mentions, though of course they need to be in scope.
8210 All rules are implicitly exported from the module, and are therefore
8211 in force in any module that imports the module that defined the rule, directly
8212 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8213 in force when compiling A.) The situation is very similar to that for instance
8221 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8222 any other flag settings. Furthermore, inside a RULE, the language extension
8223 <option>-XScopedTypeVariables</option> is automatically enabled; see
8224 <xref linkend="scoped-type-variables"/>.
8230 Like other pragmas, RULE pragmas are always checked for scope errors, and
8231 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8232 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8233 if the <option>-fenable-rewrite-rules</option> flag is
8234 on (see <xref linkend="rule-semantics"/>).
8243 <sect2 id="rule-semantics">
8244 <title>Semantics</title>
8247 From a semantic point of view:
8252 Rules are enabled (that is, used during optimisation)
8253 by the <option>-fenable-rewrite-rules</option> flag.
8254 This flag is implied by <option>-O</option>, and may be switched
8255 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8256 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8257 may not do what you expect, though, because without <option>-O</option> GHC
8258 ignores all optimisation information in interface files;
8259 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8260 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8261 has no effect on parsing or typechecking.
8267 Rules are regarded as left-to-right rewrite rules.
8268 When GHC finds an expression that is a substitution instance of the LHS
8269 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8270 By "a substitution instance" we mean that the LHS can be made equal to the
8271 expression by substituting for the pattern variables.
8278 GHC makes absolutely no attempt to verify that the LHS and RHS
8279 of a rule have the same meaning. That is undecidable in general, and
8280 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8287 GHC makes no attempt to make sure that the rules are confluent or
8288 terminating. For example:
8291 "loop" forall x y. f x y = f y x
8294 This rule will cause the compiler to go into an infinite loop.
8301 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8307 GHC currently uses a very simple, syntactic, matching algorithm
8308 for matching a rule LHS with an expression. It seeks a substitution
8309 which makes the LHS and expression syntactically equal modulo alpha
8310 conversion. The pattern (rule), but not the expression, is eta-expanded if
8311 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8312 But not beta conversion (that's called higher-order matching).
8316 Matching is carried out on GHC's intermediate language, which includes
8317 type abstractions and applications. So a rule only matches if the
8318 types match too. See <xref linkend="rule-spec"/> below.
8324 GHC keeps trying to apply the rules as it optimises the program.
8325 For example, consider:
8334 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8335 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8336 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8337 not be substituted, and the rule would not fire.
8347 <sect2 id="conlike">
8348 <title>How rules interact with INLINE/NOINLINE and CONLIKE pragmas</title>
8351 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8352 results. Consider this (artificial) example
8358 {-# RULES "f" f True = False #-}
8360 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8365 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8367 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8368 would have been a better chance that <literal>f</literal>'s RULE might fire.
8371 The way to get predictable behaviour is to use a NOINLINE
8372 pragma, or an INLINE[<replaceable>phase</replaceable>] pragma, on <literal>f</literal>, to ensure
8373 that it is not inlined until its RULEs have had a chance to fire.
8376 GHC is very cautious about duplicating work. For example, consider
8378 f k z xs = let xs = build g
8379 in ...(foldr k z xs)...sum xs...
8380 {-# RULES "foldr/build" forall k z g. foldr k z (build g) = g k z #-}
8382 Since <literal>xs</literal> is used twice, GHC does not fire the foldr/build rule. Rightly
8383 so, because it might take a lot of work to compute <literal>xs</literal>, which would be
8384 duplicated if the rule fired.
8387 Sometimes, however, this approach is over-cautious, and we <emphasis>do</emphasis> want the
8388 rule to fire, even though doing so would duplicate redex. There is no way that GHC can work out
8389 when this is a good idea, so we provide the CONLIKE pragma to declare it, thus:
8391 {-# INLINE[1] CONLIKE f #-}
8392 f x = <replaceable>blah</replaceable>
8394 CONLIKE is a modifier to an INLINE or NOINLINE pragam. It specifies that an application
8395 of f to one argument (in general, the number of arguments to the left of the '=' sign)
8396 should be considered cheap enough to duplicate, if such a duplication would make rule
8397 fire. (The name "CONLIKE" is short for "constructor-like", because constructors certainly
8398 have such a property.)
8399 The CONLIKE pragam is a modifier to INLINE/NOINLINE because it really only makes sense to match
8400 <literal>f</literal> on the LHS of a rule if you are sure that <literal>f</literal> is
8401 not going to be inlined before the rule has a chance to fire.
8406 <title>List fusion</title>
8409 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8410 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8411 intermediate list should be eliminated entirely.
8415 The following are good producers:
8427 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8433 Explicit lists (e.g. <literal>[True, False]</literal>)
8439 The cons constructor (e.g <literal>3:4:[]</literal>)
8445 <function>++</function>
8451 <function>map</function>
8457 <function>take</function>, <function>filter</function>
8463 <function>iterate</function>, <function>repeat</function>
8469 <function>zip</function>, <function>zipWith</function>
8478 The following are good consumers:
8490 <function>array</function> (on its second argument)
8496 <function>++</function> (on its first argument)
8502 <function>foldr</function>
8508 <function>map</function>
8514 <function>take</function>, <function>filter</function>
8520 <function>concat</function>
8526 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8532 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8533 will fuse with one but not the other)
8539 <function>partition</function>
8545 <function>head</function>
8551 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8557 <function>sequence_</function>
8563 <function>msum</function>
8569 <function>sortBy</function>
8578 So, for example, the following should generate no intermediate lists:
8581 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8587 This list could readily be extended; if there are Prelude functions that you use
8588 a lot which are not included, please tell us.
8592 If you want to write your own good consumers or producers, look at the
8593 Prelude definitions of the above functions to see how to do so.
8598 <sect2 id="rule-spec">
8599 <title>Specialisation
8603 Rewrite rules can be used to get the same effect as a feature
8604 present in earlier versions of GHC.
8605 For example, suppose that:
8608 genericLookup :: Ord a => Table a b -> a -> b
8609 intLookup :: Table Int b -> Int -> b
8612 where <function>intLookup</function> is an implementation of
8613 <function>genericLookup</function> that works very fast for
8614 keys of type <literal>Int</literal>. You might wish
8615 to tell GHC to use <function>intLookup</function> instead of
8616 <function>genericLookup</function> whenever the latter was called with
8617 type <literal>Table Int b -> Int -> b</literal>.
8618 It used to be possible to write
8621 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8624 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8627 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8630 This slightly odd-looking rule instructs GHC to replace
8631 <function>genericLookup</function> by <function>intLookup</function>
8632 <emphasis>whenever the types match</emphasis>.
8633 What is more, this rule does not need to be in the same
8634 file as <function>genericLookup</function>, unlike the
8635 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8636 have an original definition available to specialise).
8639 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8640 <function>intLookup</function> really behaves as a specialised version
8641 of <function>genericLookup</function>!!!</para>
8643 <para>An example in which using <literal>RULES</literal> for
8644 specialisation will Win Big:
8647 toDouble :: Real a => a -> Double
8648 toDouble = fromRational . toRational
8650 {-# RULES "toDouble/Int" toDouble = i2d #-}
8651 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8654 The <function>i2d</function> function is virtually one machine
8655 instruction; the default conversion—via an intermediate
8656 <literal>Rational</literal>—is obscenely expensive by
8662 <sect2 id="controlling-rules">
8663 <title>Controlling what's going on in rewrite rules</title>
8671 Use <option>-ddump-rules</option> to see the rules that are defined
8672 <emphasis>in this module</emphasis>.
8673 This includes rules generated by the specialisation pass, but excludes
8674 rules imported from other modules.
8680 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8681 If you add <option>-dppr-debug</option> you get a more detailed listing.
8687 Use <option>-ddump-rule-firings</option> to see in great detail what rules are being fired.
8688 If you add <option>-dppr-debug</option> you get a still more detailed listing.
8694 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8697 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8698 {-# INLINE build #-}
8702 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8703 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8704 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8705 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8712 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8713 see how to write rules that will do fusion and yet give an efficient
8714 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8724 <sect2 id="core-pragma">
8725 <title>CORE pragma</title>
8727 <indexterm><primary>CORE pragma</primary></indexterm>
8728 <indexterm><primary>pragma, CORE</primary></indexterm>
8729 <indexterm><primary>core, annotation</primary></indexterm>
8732 The external core format supports <quote>Note</quote> annotations;
8733 the <literal>CORE</literal> pragma gives a way to specify what these
8734 should be in your Haskell source code. Syntactically, core
8735 annotations are attached to expressions and take a Haskell string
8736 literal as an argument. The following function definition shows an
8740 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8743 Semantically, this is equivalent to:
8751 However, when external core is generated (via
8752 <option>-fext-core</option>), there will be Notes attached to the
8753 expressions <function>show</function> and <varname>x</varname>.
8754 The core function declaration for <function>f</function> is:
8758 f :: %forall a . GHCziShow.ZCTShow a ->
8759 a -> GHCziBase.ZMZN GHCziBase.Char =
8760 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8762 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8764 (tpl1::GHCziBase.Int ->
8766 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8768 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8769 (tpl3::GHCziBase.ZMZN a ->
8770 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8778 Here, we can see that the function <function>show</function> (which
8779 has been expanded out to a case expression over the Show dictionary)
8780 has a <literal>%note</literal> attached to it, as does the
8781 expression <varname>eta</varname> (which used to be called
8782 <varname>x</varname>).
8789 <sect1 id="special-ids">
8790 <title>Special built-in functions</title>
8791 <para>GHC has a few built-in functions with special behaviour. These
8792 are now described in the module <ulink
8793 url="&libraryGhcPrimLocation;/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8794 in the library documentation.</para>
8798 <sect1 id="generic-classes">
8799 <title>Generic classes</title>
8802 The ideas behind this extension are described in detail in "Derivable type classes",
8803 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8804 An example will give the idea:
8812 fromBin :: [Int] -> (a, [Int])
8814 toBin {| Unit |} Unit = []
8815 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8816 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8817 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8819 fromBin {| Unit |} bs = (Unit, bs)
8820 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8821 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8822 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8823 (y,bs'') = fromBin bs'
8826 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8827 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8828 which are defined thus in the library module <literal>Generics</literal>:
8832 data a :+: b = Inl a | Inr b
8833 data a :*: b = a :*: b
8836 Now you can make a data type into an instance of Bin like this:
8838 instance (Bin a, Bin b) => Bin (a,b)
8839 instance Bin a => Bin [a]
8841 That is, just leave off the "where" clause. Of course, you can put in the
8842 where clause and over-ride whichever methods you please.
8846 <title> Using generics </title>
8847 <para>To use generics you need to</para>
8850 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8851 <option>-XGenerics</option> (to generate extra per-data-type code),
8852 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8856 <para>Import the module <literal>Generics</literal> from the
8857 <literal>lang</literal> package. This import brings into
8858 scope the data types <literal>Unit</literal>,
8859 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8860 don't need this import if you don't mention these types
8861 explicitly; for example, if you are simply giving instance
8862 declarations.)</para>
8867 <sect2> <title> Changes wrt the paper </title>
8869 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8870 can be written infix (indeed, you can now use
8871 any operator starting in a colon as an infix type constructor). Also note that
8872 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8873 Finally, note that the syntax of the type patterns in the class declaration
8874 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8875 alone would ambiguous when they appear on right hand sides (an extension we
8876 anticipate wanting).
8880 <sect2> <title>Terminology and restrictions</title>
8882 Terminology. A "generic default method" in a class declaration
8883 is one that is defined using type patterns as above.
8884 A "polymorphic default method" is a default method defined as in Haskell 98.
8885 A "generic class declaration" is a class declaration with at least one
8886 generic default method.
8894 Alas, we do not yet implement the stuff about constructor names and
8901 A generic class can have only one parameter; you can't have a generic
8902 multi-parameter class.
8908 A default method must be defined entirely using type patterns, or entirely
8909 without. So this is illegal:
8912 op :: a -> (a, Bool)
8913 op {| Unit |} Unit = (Unit, True)
8916 However it is perfectly OK for some methods of a generic class to have
8917 generic default methods and others to have polymorphic default methods.
8923 The type variable(s) in the type pattern for a generic method declaration
8924 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:
8928 op {| p :*: q |} (x :*: y) = op (x :: p)
8936 The type patterns in a generic default method must take one of the forms:
8942 where "a" and "b" are type variables. Furthermore, all the type patterns for
8943 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8944 must use the same type variables. So this is illegal:
8948 op {| a :+: b |} (Inl x) = True
8949 op {| p :+: q |} (Inr y) = False
8951 The type patterns must be identical, even in equations for different methods of the class.
8952 So this too is illegal:
8956 op1 {| a :*: b |} (x :*: y) = True
8959 op2 {| p :*: q |} (x :*: y) = False
8961 (The reason for this restriction is that we gather all the equations for a particular type constructor
8962 into a single generic instance declaration.)
8968 A generic method declaration must give a case for each of the three type constructors.
8974 The type for a generic method can be built only from:
8976 <listitem> <para> Function arrows </para> </listitem>
8977 <listitem> <para> Type variables </para> </listitem>
8978 <listitem> <para> Tuples </para> </listitem>
8979 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8981 Here are some example type signatures for generic methods:
8984 op2 :: Bool -> (a,Bool)
8985 op3 :: [Int] -> a -> a
8988 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8992 This restriction is an implementation restriction: we just haven't got around to
8993 implementing the necessary bidirectional maps over arbitrary type constructors.
8994 It would be relatively easy to add specific type constructors, such as Maybe and list,
8995 to the ones that are allowed.</para>
9000 In an instance declaration for a generic class, the idea is that the compiler
9001 will fill in the methods for you, based on the generic templates. However it can only
9006 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
9011 No constructor of the instance type has unboxed fields.
9015 (Of course, these things can only arise if you are already using GHC extensions.)
9016 However, you can still give an instance declarations for types which break these rules,
9017 provided you give explicit code to override any generic default methods.
9025 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
9026 what the compiler does with generic declarations.
9031 <sect2> <title> Another example </title>
9033 Just to finish with, here's another example I rather like:
9037 nCons {| Unit |} _ = 1
9038 nCons {| a :*: b |} _ = 1
9039 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
9042 tag {| Unit |} _ = 1
9043 tag {| a :*: b |} _ = 1
9044 tag {| a :+: b |} (Inl x) = tag x
9045 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
9051 <sect1 id="monomorphism">
9052 <title>Control over monomorphism</title>
9054 <para>GHC supports two flags that control the way in which generalisation is
9055 carried out at let and where bindings.
9059 <title>Switching off the dreaded Monomorphism Restriction</title>
9060 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
9062 <para>Haskell's monomorphism restriction (see
9063 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
9065 of the Haskell Report)
9066 can be completely switched off by
9067 <option>-XNoMonomorphismRestriction</option>.
9072 <title>Monomorphic pattern bindings</title>
9073 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
9074 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
9076 <para> As an experimental change, we are exploring the possibility of
9077 making pattern bindings monomorphic; that is, not generalised at all.
9078 A pattern binding is a binding whose LHS has no function arguments,
9079 and is not a simple variable. For example:
9081 f x = x -- Not a pattern binding
9082 f = \x -> x -- Not a pattern binding
9083 f :: Int -> Int = \x -> x -- Not a pattern binding
9085 (g,h) = e -- A pattern binding
9086 (f) = e -- A pattern binding
9087 [x] = e -- A pattern binding
9089 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
9090 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
9099 ;;; Local Variables: ***
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