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>-XRecursiveDo</option>,
86 <option>-XParallelListComp</option>,
87 <option>-XEmptyDataDecls</option>,
88 <option>-XKindSignatures</option>,
89 <option>-XGeneralizedNewtypeDeriving</option>,
90 <option>-XTypeFamilies</option>.
91 Enabling these options is the <emphasis>only</emphasis>
92 effect of <option>-fglasgow-exts</option>.
93 We are trying to move away from this portmanteau flag,
94 and towards enabling features individually.</para>
98 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
99 <sect1 id="primitives">
100 <title>Unboxed types and primitive operations</title>
102 <para>GHC is built on a raft of primitive data types and operations;
103 "primitive" in the sense that they cannot be defined in Haskell itself.
104 While you really can use this stuff to write fast code,
105 we generally find it a lot less painful, and more satisfying in the
106 long run, to use higher-level language features and libraries. With
107 any luck, the code you write will be optimised to the efficient
108 unboxed version in any case. And if it isn't, we'd like to know
111 <para>All these primitive data types and operations are exported by the
112 library <literal>GHC.Prim</literal>, for which there is
113 <ulink url="../libraries/ghc-prim/GHC-Prim.html">detailed online documentation</ulink>.
114 (This documentation is generated from the file <filename>compiler/prelude/primops.txt.pp</filename>.)
117 If you want to mention any of the primitive data types or operations in your
118 program, you must first import <literal>GHC.Prim</literal> to bring them
119 into scope. Many of them have names ending in "#", and to mention such
120 names you need the <option>-XMagicHash</option> extension (<xref linkend="magic-hash"/>).
123 <para>The primops make extensive use of <link linkend="glasgow-unboxed">unboxed types</link>
124 and <link linkend="unboxed-tuples">unboxed tuples</link>, which
125 we briefly summarise here. </para>
127 <sect2 id="glasgow-unboxed">
132 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
135 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
136 that values of that type are represented by a pointer to a heap
137 object. The representation of a Haskell <literal>Int</literal>, for
138 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
139 type, however, is represented by the value itself, no pointers or heap
140 allocation are involved.
144 Unboxed types correspond to the “raw machine” types you
145 would use in C: <literal>Int#</literal> (long int),
146 <literal>Double#</literal> (double), <literal>Addr#</literal>
147 (void *), etc. The <emphasis>primitive operations</emphasis>
148 (PrimOps) on these types are what you might expect; e.g.,
149 <literal>(+#)</literal> is addition on
150 <literal>Int#</literal>s, and is the machine-addition that we all
151 know and love—usually one instruction.
155 Primitive (unboxed) types cannot be defined in Haskell, and are
156 therefore built into the language and compiler. Primitive types are
157 always unlifted; that is, a value of a primitive type cannot be
158 bottom. We use the convention (but it is only a convention)
159 that primitive types, values, and
160 operations have a <literal>#</literal> suffix (see <xref linkend="magic-hash"/>).
161 For some primitive types we have special syntax for literals, also
162 described in the <link linkend="magic-hash">same section</link>.
166 Primitive values are often represented by a simple bit-pattern, such
167 as <literal>Int#</literal>, <literal>Float#</literal>,
168 <literal>Double#</literal>. But this is not necessarily the case:
169 a primitive value might be represented by a pointer to a
170 heap-allocated object. Examples include
171 <literal>Array#</literal>, the type of primitive arrays. A
172 primitive array is heap-allocated because it is too big a value to fit
173 in a register, and would be too expensive to copy around; in a sense,
174 it is accidental that it is represented by a pointer. If a pointer
175 represents a primitive value, then it really does point to that value:
176 no unevaluated thunks, no indirections…nothing can be at the
177 other end of the pointer than the primitive value.
178 A numerically-intensive program using unboxed types can
179 go a <emphasis>lot</emphasis> faster than its “standard”
180 counterpart—we saw a threefold speedup on one example.
184 There are some restrictions on the use of primitive types:
186 <listitem><para>The main restriction
187 is that you can't pass a primitive value to a polymorphic
188 function or store one in a polymorphic data type. This rules out
189 things like <literal>[Int#]</literal> (i.e. lists of primitive
190 integers). The reason for this restriction is that polymorphic
191 arguments and constructor fields are assumed to be pointers: if an
192 unboxed integer is stored in one of these, the garbage collector would
193 attempt to follow it, leading to unpredictable space leaks. Or a
194 <function>seq</function> operation on the polymorphic component may
195 attempt to dereference the pointer, with disastrous results. Even
196 worse, the unboxed value might be larger than a pointer
197 (<literal>Double#</literal> for instance).
200 <listitem><para> You cannot define a newtype whose representation type
201 (the argument type of the data constructor) is an unboxed type. Thus,
207 <listitem><para> You cannot bind a variable with an unboxed type
208 in a <emphasis>top-level</emphasis> binding.
210 <listitem><para> You cannot bind a variable with an unboxed type
211 in a <emphasis>recursive</emphasis> binding.
213 <listitem><para> You may bind unboxed variables in a (non-recursive,
214 non-top-level) pattern binding, but you must make any such pattern-match
215 strict. For example, rather than:
217 data Foo = Foo Int Int#
219 f x = let (Foo a b, w) = ..rhs.. in ..body..
223 data Foo = Foo Int Int#
225 f x = let !(Foo a b, w) = ..rhs.. in ..body..
227 since <literal>b</literal> has type <literal>Int#</literal>.
235 <sect2 id="unboxed-tuples">
236 <title>Unboxed Tuples
240 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
241 they're available by default with <option>-fglasgow-exts</option>. An
242 unboxed tuple looks like this:
254 where <literal>e_1..e_n</literal> are expressions of any
255 type (primitive or non-primitive). The type of an unboxed tuple looks
260 Unboxed tuples are used for functions that need to return multiple
261 values, but they avoid the heap allocation normally associated with
262 using fully-fledged tuples. When an unboxed tuple is returned, the
263 components are put directly into registers or on the stack; the
264 unboxed tuple itself does not have a composite representation. Many
265 of the primitive operations listed in <literal>primops.txt.pp</literal> return unboxed
267 In particular, the <literal>IO</literal> and <literal>ST</literal> monads use unboxed
268 tuples to avoid unnecessary allocation during sequences of operations.
272 There are some pretty stringent restrictions on the use of unboxed tuples:
277 Values of unboxed tuple types are subject to the same restrictions as
278 other unboxed types; i.e. they may not be stored in polymorphic data
279 structures or passed to polymorphic functions.
286 No variable can have an unboxed tuple type, nor may a constructor or function
287 argument have an unboxed tuple type. The following are all illegal:
291 data Foo = Foo (# Int, Int #)
293 f :: (# Int, Int #) -> (# Int, Int #)
296 g :: (# Int, Int #) -> Int
299 h x = let y = (# x,x #) in ...
306 The typical use of unboxed tuples is simply to return multiple values,
307 binding those multiple results with a <literal>case</literal> expression, thus:
309 f x y = (# x+1, y-1 #)
310 g x = case f x x of { (# a, b #) -> a + b }
312 You can have an unboxed tuple in a pattern binding, thus
314 f x = let (# p,q #) = h x in ..body..
316 If the types of <literal>p</literal> and <literal>q</literal> are not unboxed,
317 the resulting binding is lazy like any other Haskell pattern binding. The
318 above example desugars like this:
320 f x = let t = case h x o f{ (# p,q #) -> (p,q)
325 Indeed, the bindings can even be recursive.
332 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
334 <sect1 id="syntax-extns">
335 <title>Syntactic extensions</title>
337 <sect2 id="unicode-syntax">
338 <title>Unicode syntax</title>
340 extension <option>-XUnicodeSyntax</option><indexterm><primary><option>-XUnicodeSyntax</option></primary></indexterm>
341 enables Unicode characters to be used to stand for certain ASCII
342 character sequences. The following alternatives are provided:</para>
345 <tgroup cols="2" align="left" colsep="1" rowsep="1">
349 <entry>Unicode alternative</entry>
350 <entry>Code point</entry>
356 <entry><literal>::</literal></entry>
357 <entry>::</entry> <!-- no special char, apparently -->
358 <entry>0x2237</entry>
359 <entry>PROPORTION</entry>
364 <entry><literal>=></literal></entry>
365 <entry>⇒</entry>
366 <entry>0x21D2</entry>
367 <entry>RIGHTWARDS DOUBLE ARROW</entry>
372 <entry><literal>forall</literal></entry>
373 <entry>∀</entry>
374 <entry>0x2200</entry>
375 <entry>FOR ALL</entry>
380 <entry><literal>-></literal></entry>
381 <entry>→</entry>
382 <entry>0x2192</entry>
383 <entry>RIGHTWARDS ARROW</entry>
388 <entry><literal><-</literal></entry>
389 <entry>←</entry>
390 <entry>0x2190</entry>
391 <entry>LEFTWARDS ARROW</entry>
397 <entry>…</entry>
398 <entry>0x22EF</entry>
399 <entry>MIDLINE HORIZONTAL ELLIPSIS</entry>
406 <sect2 id="magic-hash">
407 <title>The magic hash</title>
408 <para>The language extension <option>-XMagicHash</option> allows "#" as a
409 postfix modifier to identifiers. Thus, "x#" is a valid variable, and "T#" is
410 a valid type constructor or data constructor.</para>
412 <para>The hash sign does not change sematics at all. We tend to use variable
413 names ending in "#" for unboxed values or types (e.g. <literal>Int#</literal>),
414 but there is no requirement to do so; they are just plain ordinary variables.
415 Nor does the <option>-XMagicHash</option> extension bring anything into scope.
416 For example, to bring <literal>Int#</literal> into scope you must
417 import <literal>GHC.Prim</literal> (see <xref linkend="primitives"/>);
418 the <option>-XMagicHash</option> extension
419 then allows you to <emphasis>refer</emphasis> to the <literal>Int#</literal>
420 that is now in scope.</para>
421 <para> The <option>-XMagicHash</option> also enables some new forms of literals (see <xref linkend="glasgow-unboxed"/>):
423 <listitem><para> <literal>'x'#</literal> has type <literal>Char#</literal></para> </listitem>
424 <listitem><para> <literal>"foo"#</literal> has type <literal>Addr#</literal></para> </listitem>
425 <listitem><para> <literal>3#</literal> has type <literal>Int#</literal>. In general,
426 any Haskell 98 integer lexeme followed by a <literal>#</literal> is an <literal>Int#</literal> literal, e.g.
427 <literal>-0x3A#</literal> as well as <literal>32#</literal></para>.</listitem>
428 <listitem><para> <literal>3##</literal> has type <literal>Word#</literal>. In general,
429 any non-negative Haskell 98 integer lexeme followed by <literal>##</literal>
430 is a <literal>Word#</literal>. </para> </listitem>
431 <listitem><para> <literal>3.2#</literal> has type <literal>Float#</literal>.</para> </listitem>
432 <listitem><para> <literal>3.2##</literal> has type <literal>Double#</literal></para> </listitem>
437 <sect2 id="new-qualified-operators">
438 <title>New qualified operator syntax</title>
440 <para>A new syntax for referencing qualified operators is
441 planned to be introduced by Haskell', and is enabled in GHC
443 the <option>-XNewQualifiedOperators</option><indexterm><primary><option>-XNewQualifiedOperators</option></primary></indexterm>
444 option. In the new syntax, the prefix form of a qualified
446 written <literal><replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)</literal>
447 (in Haskell 98 this would
448 be <literal>(<replaceable>module</replaceable>.<replaceable>symbol</replaceable>)</literal>),
449 and the infix form is
450 written <literal>`<replaceable>module</replaceable>.(<replaceable>symbol</replaceable>)`</literal>
451 (in Haskell 98 this would
452 be <literal>`<replaceable>module</replaceable>.<replaceable>symbol</replaceable>`</literal>.
455 add x y = Prelude.(+) x y
456 subtract y = (`Prelude.(-)` y)
458 The new form of qualified operators is intended to regularise
459 the syntax by eliminating odd cases
460 like <literal>Prelude..</literal>. For example,
461 when <literal>NewQualifiedOperators</literal> is on, it is possible to
462 write the enumerated sequence <literal>[Monday..]</literal>
463 without spaces, whereas in Haskell 98 this would be a
464 reference to the operator ‘<literal>.</literal>‘
465 from module <literal>Monday</literal>.</para>
467 <para>When <option>-XNewQualifiedOperators</option> is on, the old Haskell
468 98 syntax for qualified operators is not accepted, so this
469 option may cause existing Haskell 98 code to break.</para>
474 <!-- ====================== HIERARCHICAL MODULES ======================= -->
477 <sect2 id="hierarchical-modules">
478 <title>Hierarchical Modules</title>
480 <para>GHC supports a small extension to the syntax of module
481 names: a module name is allowed to contain a dot
482 <literal>‘.’</literal>. This is also known as the
483 “hierarchical module namespace” extension, because
484 it extends the normally flat Haskell module namespace into a
485 more flexible hierarchy of modules.</para>
487 <para>This extension has very little impact on the language
488 itself; modules names are <emphasis>always</emphasis> fully
489 qualified, so you can just think of the fully qualified module
490 name as <quote>the module name</quote>. In particular, this
491 means that the full module name must be given after the
492 <literal>module</literal> keyword at the beginning of the
493 module; for example, the module <literal>A.B.C</literal> must
496 <programlisting>module A.B.C</programlisting>
499 <para>It is a common strategy to use the <literal>as</literal>
500 keyword to save some typing when using qualified names with
501 hierarchical modules. For example:</para>
504 import qualified Control.Monad.ST.Strict as ST
507 <para>For details on how GHC searches for source and interface
508 files in the presence of hierarchical modules, see <xref
509 linkend="search-path"/>.</para>
511 <para>GHC comes with a large collection of libraries arranged
512 hierarchically; see the accompanying <ulink
513 url="../libraries/index.html">library
514 documentation</ulink>. More libraries to install are available
516 url="http://hackage.haskell.org/packages/hackage.html">HackageDB</ulink>.</para>
519 <!-- ====================== PATTERN GUARDS ======================= -->
521 <sect2 id="pattern-guards">
522 <title>Pattern guards</title>
525 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
526 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ulink url="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ulink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
530 Suppose we have an abstract data type of finite maps, with a
534 lookup :: FiniteMap -> Int -> Maybe Int
537 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
538 where <varname>v</varname> is the value that the key maps to. Now consider the following definition:
542 clunky env var1 var2 | ok1 && ok2 = val1 + val2
543 | otherwise = var1 + var2
554 The auxiliary functions are
558 maybeToBool :: Maybe a -> Bool
559 maybeToBool (Just x) = True
560 maybeToBool Nothing = False
562 expectJust :: Maybe a -> a
563 expectJust (Just x) = x
564 expectJust Nothing = error "Unexpected Nothing"
568 What is <function>clunky</function> doing? The guard <literal>ok1 &&
569 ok2</literal> checks that both lookups succeed, using
570 <function>maybeToBool</function> to convert the <function>Maybe</function>
571 types to booleans. The (lazily evaluated) <function>expectJust</function>
572 calls extract the values from the results of the lookups, and binds the
573 returned values to <varname>val1</varname> and <varname>val2</varname>
574 respectively. If either lookup fails, then clunky takes the
575 <literal>otherwise</literal> case and returns the sum of its arguments.
579 This is certainly legal Haskell, but it is a tremendously verbose and
580 un-obvious way to achieve the desired effect. Arguably, a more direct way
581 to write clunky would be to use case expressions:
585 clunky env var1 var2 = case lookup env var1 of
587 Just val1 -> case lookup env var2 of
589 Just val2 -> val1 + val2
595 This is a bit shorter, but hardly better. Of course, we can rewrite any set
596 of pattern-matching, guarded equations as case expressions; that is
597 precisely what the compiler does when compiling equations! The reason that
598 Haskell provides guarded equations is because they allow us to write down
599 the cases we want to consider, one at a time, independently of each other.
600 This structure is hidden in the case version. Two of the right-hand sides
601 are really the same (<function>fail</function>), and the whole expression
602 tends to become more and more indented.
606 Here is how I would write clunky:
611 | Just val1 <- lookup env var1
612 , Just val2 <- lookup env var2
614 ...other equations for clunky...
618 The semantics should be clear enough. The qualifiers are matched in order.
619 For a <literal><-</literal> qualifier, which I call a pattern guard, the
620 right hand side is evaluated and matched against the pattern on the left.
621 If the match fails then the whole guard fails and the next equation is
622 tried. If it succeeds, then the appropriate binding takes place, and the
623 next qualifier is matched, in the augmented environment. Unlike list
624 comprehensions, however, the type of the expression to the right of the
625 <literal><-</literal> is the same as the type of the pattern to its
626 left. The bindings introduced by pattern guards scope over all the
627 remaining guard qualifiers, and over the right hand side of the equation.
631 Just as with list comprehensions, boolean expressions can be freely mixed
632 with among the pattern guards. For example:
643 Haskell's current guards therefore emerge as a special case, in which the
644 qualifier list has just one element, a boolean expression.
648 <!-- ===================== View patterns =================== -->
650 <sect2 id="view-patterns">
655 View patterns are enabled by the flag <literal>-XViewPatterns</literal>.
656 More information and examples of view patterns can be found on the
657 <ulink url="http://hackage.haskell.org/trac/ghc/wiki/ViewPatterns">Wiki
662 View patterns are somewhat like pattern guards that can be nested inside
663 of other patterns. They are a convenient way of pattern-matching
664 against values of abstract types. For example, in a programming language
665 implementation, we might represent the syntax of the types of the
674 view :: Type -> TypeView
676 -- additional operations for constructing Typ's ...
679 The representation of Typ is held abstract, permitting implementations
680 to use a fancy representation (e.g., hash-consing to manage sharing).
682 Without view patterns, using this signature a little inconvenient:
684 size :: Typ -> Integer
685 size t = case view t of
687 Arrow t1 t2 -> size t1 + size t2
690 It is necessary to iterate the case, rather than using an equational
691 function definition. And the situation is even worse when the matching
692 against <literal>t</literal> is buried deep inside another pattern.
696 View patterns permit calling the view function inside the pattern and
697 matching against the result:
699 size (view -> Unit) = 1
700 size (view -> Arrow t1 t2) = size t1 + size t2
703 That is, we add a new form of pattern, written
704 <replaceable>expression</replaceable> <literal>-></literal>
705 <replaceable>pattern</replaceable> that means "apply the expression to
706 whatever we're trying to match against, and then match the result of
707 that application against the pattern". The expression can be any Haskell
708 expression of function type, and view patterns can be used wherever
713 The semantics of a pattern <literal>(</literal>
714 <replaceable>exp</replaceable> <literal>-></literal>
715 <replaceable>pat</replaceable> <literal>)</literal> are as follows:
721 <para>The variables bound by the view pattern are the variables bound by
722 <replaceable>pat</replaceable>.
726 Any variables in <replaceable>exp</replaceable> are bound occurrences,
727 but variables bound "to the left" in a pattern are in scope. This
728 feature permits, for example, one argument to a function to be used in
729 the view of another argument. For example, the function
730 <literal>clunky</literal> from <xref linkend="pattern-guards" /> can be
731 written using view patterns as follows:
734 clunky env (lookup env -> Just val1) (lookup env -> Just val2) = val1 + val2
735 ...other equations for clunky...
740 More precisely, the scoping rules are:
744 In a single pattern, variables bound by patterns to the left of a view
745 pattern expression are in scope. For example:
747 example :: Maybe ((String -> Integer,Integer), String) -> Bool
748 example Just ((f,_), f -> 4) = True
751 Additionally, in function definitions, variables bound by matching earlier curried
752 arguments may be used in view pattern expressions in later arguments:
754 example :: (String -> Integer) -> String -> Bool
755 example f (f -> 4) = True
757 That is, the scoping is the same as it would be if the curried arguments
758 were collected into a tuple.
764 In mutually recursive bindings, such as <literal>let</literal>,
765 <literal>where</literal>, or the top level, view patterns in one
766 declaration may not mention variables bound by other declarations. That
767 is, each declaration must be self-contained. For example, the following
768 program is not allowed:
775 restriction in the future; the only cost is that type checking patterns
776 would get a little more complicated.)
786 <listitem><para> Typing: If <replaceable>exp</replaceable> has type
787 <replaceable>T1</replaceable> <literal>-></literal>
788 <replaceable>T2</replaceable> and <replaceable>pat</replaceable> matches
789 a <replaceable>T2</replaceable>, then the whole view pattern matches a
790 <replaceable>T1</replaceable>.
793 <listitem><para> Matching: To the equations in Section 3.17.3 of the
794 <ulink url="http://www.haskell.org/onlinereport/">Haskell 98
795 Report</ulink>, add the following:
797 case v of { (e -> p) -> e1 ; _ -> e2 }
799 case (e v) of { p -> e1 ; _ -> e2 }
801 That is, to match a variable <replaceable>v</replaceable> against a pattern
802 <literal>(</literal> <replaceable>exp</replaceable>
803 <literal>-></literal> <replaceable>pat</replaceable>
804 <literal>)</literal>, evaluate <literal>(</literal>
805 <replaceable>exp</replaceable> <replaceable> v</replaceable>
806 <literal>)</literal> and match the result against
807 <replaceable>pat</replaceable>.
810 <listitem><para> Efficiency: When the same view function is applied in
811 multiple branches of a function definition or a case expression (e.g.,
812 in <literal>size</literal> above), GHC makes an attempt to collect these
813 applications into a single nested case expression, so that the view
814 function is only applied once. Pattern compilation in GHC follows the
815 matrix algorithm described in Chapter 4 of <ulink
816 url="http://research.microsoft.com/~simonpj/Papers/slpj-book-1987/">The
817 Implementation of Functional Programming Languages</ulink>. When the
818 top rows of the first column of a matrix are all view patterns with the
819 "same" expression, these patterns are transformed into a single nested
820 case. This includes, for example, adjacent view patterns that line up
823 f ((view -> A, p1), p2) = e1
824 f ((view -> B, p3), p4) = e2
828 <para> The current notion of when two view pattern expressions are "the
829 same" is very restricted: it is not even full syntactic equality.
830 However, it does include variables, literals, applications, and tuples;
831 e.g., two instances of <literal>view ("hi", "there")</literal> will be
832 collected. However, the current implementation does not compare up to
833 alpha-equivalence, so two instances of <literal>(x, view x ->
834 y)</literal> will not be coalesced.
844 <!-- ===================== n+k patterns =================== -->
846 <sect2 id="n-k-patterns">
847 <title>n+k patterns</title>
848 <indexterm><primary><option>-XNoNPlusKPatterns</option></primary></indexterm>
851 <literal>n+k</literal> pattern support is enabled by default. To disable
852 it, you can use the <option>-XNoNPlusKPatterns</option> flag.
857 <!-- ===================== Recursive do-notation =================== -->
859 <sect2 id="mdo-notation">
860 <title>The recursive do-notation
863 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
864 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
865 by Levent Erkok, John Launchbury,
866 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
867 This paper is essential reading for anyone making non-trivial use of mdo-notation,
868 and we do not repeat it here.
871 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
872 that is, the variables bound in a do-expression are visible only in the textually following
873 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
874 group. It turns out that several applications can benefit from recursive bindings in
875 the do-notation, and this extension provides the necessary syntactic support.
878 Here is a simple (yet contrived) example:
881 import Control.Monad.Fix
883 justOnes = mdo xs <- Just (1:xs)
887 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
891 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. Its definition is:
894 class Monad m => MonadFix m where
895 mfix :: (a -> m a) -> m a
898 The function <literal>mfix</literal>
899 dictates how the required recursion operation should be performed. For example,
900 <literal>justOnes</literal> desugars as follows:
902 justOnes = mfix (\xs' -> do { xs <- Just (1:xs'); return xs }
904 For full details of the way in which mdo is typechecked and desugared, see
905 the paper <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>.
906 In particular, GHC implements the segmentation technique described in Section 3.2 of the paper.
909 If recursive bindings are required for a monad,
910 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
911 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
912 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
913 for Haskell's internal state monad (strict and lazy, respectively).
916 Here are some important points in using the recursive-do notation:
919 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
920 than <literal>do</literal>).
924 It is enabled with the flag <literal>-XRecursiveDo</literal>, which is in turn implied by
925 <literal>-fglasgow-exts</literal>.
929 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
930 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
931 be distinct (Section 3.3 of the paper).
935 Variables bound by a <literal>let</literal> statement in an <literal>mdo</literal>
936 are monomorphic in the <literal>mdo</literal> (Section 3.1 of the paper). However
937 GHC breaks the <literal>mdo</literal> into segments to enhance polymorphism,
938 and improve termination (Section 3.2 of the paper).
944 Historical note: The old implementation of the mdo-notation (and most
945 of the existing documents) used the name
946 <literal>MonadRec</literal> for the class and the corresponding library.
947 This name is not supported by GHC.
953 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
955 <sect2 id="parallel-list-comprehensions">
956 <title>Parallel List Comprehensions</title>
957 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
959 <indexterm><primary>parallel list comprehensions</primary>
962 <para>Parallel list comprehensions are a natural extension to list
963 comprehensions. List comprehensions can be thought of as a nice
964 syntax for writing maps and filters. Parallel comprehensions
965 extend this to include the zipWith family.</para>
967 <para>A parallel list comprehension has multiple independent
968 branches of qualifier lists, each separated by a `|' symbol. For
969 example, the following zips together two lists:</para>
972 [ (x, y) | x <- xs | y <- ys ]
975 <para>The behavior of parallel list comprehensions follows that of
976 zip, in that the resulting list will have the same length as the
977 shortest branch.</para>
979 <para>We can define parallel list comprehensions by translation to
980 regular comprehensions. Here's the basic idea:</para>
982 <para>Given a parallel comprehension of the form: </para>
985 [ e | p1 <- e11, p2 <- e12, ...
986 | q1 <- e21, q2 <- e22, ...
991 <para>This will be translated to: </para>
994 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
995 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1000 <para>where `zipN' is the appropriate zip for the given number of
1005 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1007 <sect2 id="generalised-list-comprehensions">
1008 <title>Generalised (SQL-Like) List Comprehensions</title>
1009 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1011 <indexterm><primary>extended list comprehensions</primary>
1013 <indexterm><primary>group</primary></indexterm>
1014 <indexterm><primary>sql</primary></indexterm>
1017 <para>Generalised list comprehensions are a further enhancement to the
1018 list comprehension syntactic sugar to allow operations such as sorting
1019 and grouping which are familiar from SQL. They are fully described in the
1020 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1021 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1022 except that the syntax we use differs slightly from the paper.</para>
1023 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1024 <para>Here is an example:
1026 employees = [ ("Simon", "MS", 80)
1027 , ("Erik", "MS", 100)
1028 , ("Phil", "Ed", 40)
1029 , ("Gordon", "Ed", 45)
1030 , ("Paul", "Yale", 60)]
1032 output = [ (the dept, sum salary)
1033 | (name, dept, salary) <- employees
1034 , then group by dept
1035 , then sortWith by (sum salary)
1038 In this example, the list <literal>output</literal> would take on
1042 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1045 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1046 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1047 function that is exported by <literal>GHC.Exts</literal>.)</para>
1049 <para>There are five new forms of comprehension qualifier,
1050 all introduced by the (existing) keyword <literal>then</literal>:
1058 This statement requires that <literal>f</literal> have the type <literal>
1059 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1060 motivating example, as this form is used to apply <literal>take 5</literal>.
1071 This form is similar to the previous one, but allows you to create a function
1072 which will be passed as the first argument to f. As a consequence f must have
1073 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1074 from the type, this function lets f "project out" some information
1075 from the elements of the list it is transforming.</para>
1077 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1078 is supplied with a function that lets it find out the <literal>sum salary</literal>
1079 for any item in the list comprehension it transforms.</para>
1087 then group by e using f
1090 <para>This is the most general of the grouping-type statements. In this form,
1091 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1092 As with the <literal>then f by e</literal> case above, the first argument
1093 is a function supplied to f by the compiler which lets it compute e on every
1094 element of the list being transformed. However, unlike the non-grouping case,
1095 f additionally partitions the list into a number of sublists: this means that
1096 at every point after this statement, binders occurring before it in the comprehension
1097 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1098 this, let's look at an example:</para>
1101 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1102 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1103 groupRuns f = groupBy (\x y -> f x == f y)
1105 output = [ (the x, y)
1106 | x <- ([1..3] ++ [1..2])
1108 , then group by x using groupRuns ]
1111 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1114 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1117 <para>Note that we have used the <literal>the</literal> function to change the type
1118 of x from a list to its original numeric type. The variable y, in contrast, is left
1119 unchanged from the list form introduced by the grouping.</para>
1129 <para>This form of grouping is essentially the same as the one described above. However,
1130 since no function to use for the grouping has been supplied it will fall back on the
1131 <literal>groupWith</literal> function defined in
1132 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1133 is the form of the group statement that we made use of in the opening example.</para>
1144 <para>With this form of the group statement, f is required to simply have the type
1145 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1146 comprehension so far directly. An example of this form is as follows:</para>
1152 , then group using inits]
1155 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1158 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1166 <!-- ===================== REBINDABLE SYNTAX =================== -->
1168 <sect2 id="rebindable-syntax">
1169 <title>Rebindable syntax and the implicit Prelude import</title>
1171 <para><indexterm><primary>-XNoImplicitPrelude
1172 option</primary></indexterm> GHC normally imports
1173 <filename>Prelude.hi</filename> files for you. If you'd
1174 rather it didn't, then give it a
1175 <option>-XNoImplicitPrelude</option> option. The idea is
1176 that you can then import a Prelude of your own. (But don't
1177 call it <literal>Prelude</literal>; the Haskell module
1178 namespace is flat, and you must not conflict with any
1179 Prelude module.)</para>
1181 <para>Suppose you are importing a Prelude of your own
1182 in order to define your own numeric class
1183 hierarchy. It completely defeats that purpose if the
1184 literal "1" means "<literal>Prelude.fromInteger
1185 1</literal>", which is what the Haskell Report specifies.
1186 So the <option>-XNoImplicitPrelude</option>
1187 flag <emphasis>also</emphasis> causes
1188 the following pieces of built-in syntax to refer to
1189 <emphasis>whatever is in scope</emphasis>, not the Prelude
1193 <para>An integer literal <literal>368</literal> means
1194 "<literal>fromInteger (368::Integer)</literal>", rather than
1195 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1198 <listitem><para>Fractional literals are handed in just the same way,
1199 except that the translation is
1200 <literal>fromRational (3.68::Rational)</literal>.
1203 <listitem><para>The equality test in an overloaded numeric pattern
1204 uses whatever <literal>(==)</literal> is in scope.
1207 <listitem><para>The subtraction operation, and the
1208 greater-than-or-equal test, in <literal>n+k</literal> patterns
1209 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1213 <para>Negation (e.g. "<literal>- (f x)</literal>")
1214 means "<literal>negate (f x)</literal>", both in numeric
1215 patterns, and expressions.
1219 <para>"Do" notation is translated using whatever
1220 functions <literal>(>>=)</literal>,
1221 <literal>(>>)</literal>, and <literal>fail</literal>,
1222 are in scope (not the Prelude
1223 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1224 comprehensions, are unaffected. </para></listitem>
1228 notation (see <xref linkend="arrow-notation"/>)
1229 uses whatever <literal>arr</literal>,
1230 <literal>(>>>)</literal>, <literal>first</literal>,
1231 <literal>app</literal>, <literal>(|||)</literal> and
1232 <literal>loop</literal> functions are in scope. But unlike the
1233 other constructs, the types of these functions must match the
1234 Prelude types very closely. Details are in flux; if you want
1238 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1239 even if that is a little unexpected. For example, the
1240 static semantics of the literal <literal>368</literal>
1241 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1242 <literal>fromInteger</literal> to have any of the types:
1244 fromInteger :: Integer -> Integer
1245 fromInteger :: forall a. Foo a => Integer -> a
1246 fromInteger :: Num a => a -> Integer
1247 fromInteger :: Integer -> Bool -> Bool
1251 <para>Be warned: this is an experimental facility, with
1252 fewer checks than usual. Use <literal>-dcore-lint</literal>
1253 to typecheck the desugared program. If Core Lint is happy
1254 you should be all right.</para>
1258 <sect2 id="postfix-operators">
1259 <title>Postfix operators</title>
1262 The <option>-XPostfixOperators</option> flag enables a small
1263 extension to the syntax of left operator sections, which allows you to
1264 define postfix operators. The extension is this: the left section
1268 is equivalent (from the point of view of both type checking and execution) to the expression
1272 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1273 The strict Haskell 98 interpretation is that the section is equivalent to
1277 That is, the operator must be a function of two arguments. GHC allows it to
1278 take only one argument, and that in turn allows you to write the function
1281 <para>The extension does not extend to the left-hand side of function
1282 definitions; you must define such a function in prefix form.</para>
1286 <sect2 id="tuple-sections">
1287 <title>Tuple sections</title>
1290 The <option>-XTupleSections</option> flag enables Python-style partially applied
1291 tuple constructors. For example, the following program
1295 is considered to be an alternative notation for the more unwieldy alternative
1299 You can omit any combination of arguments to the tuple, as in the following
1301 (, "I", , , "Love", , 1337)
1305 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1310 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1311 will also be available for them, like so
1315 Because there is no unboxed unit tuple, the following expression
1319 continues to stand for the unboxed singleton tuple data constructor.
1324 <sect2 id="disambiguate-fields">
1325 <title>Record field disambiguation</title>
1327 In record construction and record pattern matching
1328 it is entirely unambiguous which field is referred to, even if there are two different
1329 data types in scope with a common field name. For example:
1332 data S = MkS { x :: Int, y :: Bool }
1337 data T = MkT { x :: Int }
1339 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1340 ok2 n = MkT { x = n+1 } -- Unambiguous
1342 bad1 k = k { x = 3 } -- Ambiguous
1343 bad2 k = x k -- Ambiguous
1345 Even though there are two <literal>x</literal>'s in scope,
1346 it is clear that the <literal>x</literal> in the pattern in the
1347 definition of <literal>ok1</literal> can only mean the field
1348 <literal>x</literal> from type <literal>S</literal>. Similarly for
1349 the function <literal>ok2</literal>. However, in the record update
1350 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1351 it is not clear which of the two types is intended.
1354 Haskell 98 regards all four as ambiguous, but with the
1355 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1356 the former two. The rules are precisely the same as those for instance
1357 declarations in Haskell 98, where the method names on the left-hand side
1358 of the method bindings in an instance declaration refer unambiguously
1359 to the method of that class (provided they are in scope at all), even
1360 if there are other variables in scope with the same name.
1361 This reduces the clutter of qualified names when you import two
1362 records from different modules that use the same field name.
1368 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1373 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1378 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1379 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1380 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1383 import qualified M -- Note qualified
1385 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1387 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1388 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1389 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1390 is not. (In effect, it is qualified by the constructor.)
1397 <!-- ===================== Record puns =================== -->
1399 <sect2 id="record-puns">
1404 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1408 When using records, it is common to write a pattern that binds a
1409 variable with the same name as a record field, such as:
1412 data C = C {a :: Int}
1418 Record punning permits the variable name to be elided, so one can simply
1425 to mean the same pattern as above. That is, in a record pattern, the
1426 pattern <literal>a</literal> expands into the pattern <literal>a =
1427 a</literal> for the same name <literal>a</literal>.
1434 Record punning can also be used in an expression, writing, for example,
1440 let a = 1 in C {a = a}
1442 The expansion is purely syntactic, so the expanded right-hand side
1443 expression refers to the nearest enclosing variable that is spelled the
1444 same as the field name.
1448 Puns and other patterns can be mixed in the same record:
1450 data C = C {a :: Int, b :: Int}
1451 f (C {a, b = 4}) = a
1456 Puns can be used wherever record patterns occur (e.g. in
1457 <literal>let</literal> bindings or at the top-level).
1461 A pun on a qualified field name is expanded by stripping off the module qualifier.
1468 f (M.C {M.a = a}) = a
1470 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1471 is only in scope in qualified form.)
1479 <!-- ===================== Record wildcards =================== -->
1481 <sect2 id="record-wildcards">
1482 <title>Record wildcards
1486 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1487 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1491 For records with many fields, it can be tiresome to write out each field
1492 individually in a record pattern, as in
1494 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1495 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1500 Record wildcard syntax permits a "<literal>..</literal>" in a record
1501 pattern, where each elided field <literal>f</literal> is replaced by the
1502 pattern <literal>f = f</literal>. For example, the above pattern can be
1505 f (C {a = 1, ..}) = b + c + d
1513 Wildcards can be mixed with other patterns, including puns
1514 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1515 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1516 wherever record patterns occur, including in <literal>let</literal>
1517 bindings and at the top-level. For example, the top-level binding
1521 defines <literal>b</literal>, <literal>c</literal>, and
1522 <literal>d</literal>.
1526 Record wildcards can also be used in expressions, writing, for example,
1528 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1532 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1534 The expansion is purely syntactic, so the record wildcard
1535 expression refers to the nearest enclosing variables that are spelled
1536 the same as the omitted field names.
1540 The "<literal>..</literal>" expands to the missing
1541 <emphasis>in-scope</emphasis> record fields, where "in scope"
1542 includes both unqualified and qualified-only.
1543 Any fields that are not in scope are not filled in. For example
1546 data R = R { a,b,c :: Int }
1548 import qualified M( R(a,b) )
1551 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1552 omitting <literal>c</literal> since it is not in scope at all.
1559 <!-- ===================== Local fixity declarations =================== -->
1561 <sect2 id="local-fixity-declarations">
1562 <title>Local Fixity Declarations
1565 <para>A careful reading of the Haskell 98 Report reveals that fixity
1566 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1567 <literal>infixr</literal>) are permitted to appear inside local bindings
1568 such those introduced by <literal>let</literal> and
1569 <literal>where</literal>. However, the Haskell Report does not specify
1570 the semantics of such bindings very precisely.
1573 <para>In GHC, a fixity declaration may accompany a local binding:
1580 and the fixity declaration applies wherever the binding is in scope.
1581 For example, in a <literal>let</literal>, it applies in the right-hand
1582 sides of other <literal>let</literal>-bindings and the body of the
1583 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1584 expressions (<xref linkend="mdo-notation"/>), the local fixity
1585 declarations of a <literal>let</literal> statement scope over other
1586 statements in the group, just as the bound name does.
1590 Moreover, a local fixity declaration *must* accompany a local binding of
1591 that name: it is not possible to revise the fixity of name bound
1594 let infixr 9 $ in ...
1597 Because local fixity declarations are technically Haskell 98, no flag is
1598 necessary to enable them.
1602 <sect2 id="package-imports">
1603 <title>Package-qualified imports</title>
1605 <para>With the <option>-XPackageImports</option> flag, GHC allows
1606 import declarations to be qualified by the package name that the
1607 module is intended to be imported from. For example:</para>
1610 import "network" Network.Socket
1613 <para>would import the module <literal>Network.Socket</literal> from
1614 the package <literal>network</literal> (any version). This may
1615 be used to disambiguate an import when the same module is
1616 available from multiple packages, or is present in both the
1617 current package being built and an external package.</para>
1619 <para>Note: you probably don't need to use this feature, it was
1620 added mainly so that we can build backwards-compatible versions of
1621 packages when APIs change. It can lead to fragile dependencies in
1622 the common case: modules occasionally move from one package to
1623 another, rendering any package-qualified imports broken.</para>
1626 <sect2 id="syntax-stolen">
1627 <title>Summary of stolen syntax</title>
1629 <para>Turning on an option that enables special syntax
1630 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1631 to compile, perhaps because it uses a variable name which has
1632 become a reserved word. This section lists the syntax that is
1633 "stolen" by language extensions.
1635 notation and nonterminal names from the Haskell 98 lexical syntax
1636 (see the Haskell 98 Report).
1637 We only list syntax changes here that might affect
1638 existing working programs (i.e. "stolen" syntax). Many of these
1639 extensions will also enable new context-free syntax, but in all
1640 cases programs written to use the new syntax would not be
1641 compilable without the option enabled.</para>
1643 <para>There are two classes of special
1648 <para>New reserved words and symbols: character sequences
1649 which are no longer available for use as identifiers in the
1653 <para>Other special syntax: sequences of characters that have
1654 a different meaning when this particular option is turned
1659 The following syntax is stolen:
1664 <literal>forall</literal>
1665 <indexterm><primary><literal>forall</literal></primary></indexterm>
1668 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1669 <option>-XScopedTypeVariables</option>,
1670 <option>-XLiberalTypeSynonyms</option>,
1671 <option>-XRank2Types</option>,
1672 <option>-XRankNTypes</option>,
1673 <option>-XPolymorphicComponents</option>,
1674 <option>-XExistentialQuantification</option>
1680 <literal>mdo</literal>
1681 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1684 Stolen by: <option>-XRecursiveDo</option>,
1690 <literal>foreign</literal>
1691 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1694 Stolen by: <option>-XForeignFunctionInterface</option>,
1700 <literal>rec</literal>,
1701 <literal>proc</literal>, <literal>-<</literal>,
1702 <literal>>-</literal>, <literal>-<<</literal>,
1703 <literal>>>-</literal>, and <literal>(|</literal>,
1704 <literal>|)</literal> brackets
1705 <indexterm><primary><literal>proc</literal></primary></indexterm>
1708 Stolen by: <option>-XArrows</option>,
1714 <literal>?<replaceable>varid</replaceable></literal>,
1715 <literal>%<replaceable>varid</replaceable></literal>
1716 <indexterm><primary>implicit parameters</primary></indexterm>
1719 Stolen by: <option>-XImplicitParams</option>,
1725 <literal>[|</literal>,
1726 <literal>[e|</literal>, <literal>[p|</literal>,
1727 <literal>[d|</literal>, <literal>[t|</literal>,
1728 <literal>$(</literal>,
1729 <literal>$<replaceable>varid</replaceable></literal>
1730 <indexterm><primary>Template Haskell</primary></indexterm>
1733 Stolen by: <option>-XTemplateHaskell</option>,
1739 <literal>[:<replaceable>varid</replaceable>|</literal>
1740 <indexterm><primary>quasi-quotation</primary></indexterm>
1743 Stolen by: <option>-XQuasiQuotes</option>,
1749 <replaceable>varid</replaceable>{<literal>#</literal>},
1750 <replaceable>char</replaceable><literal>#</literal>,
1751 <replaceable>string</replaceable><literal>#</literal>,
1752 <replaceable>integer</replaceable><literal>#</literal>,
1753 <replaceable>float</replaceable><literal>#</literal>,
1754 <replaceable>float</replaceable><literal>##</literal>,
1755 <literal>(#</literal>, <literal>#)</literal>,
1758 Stolen by: <option>-XMagicHash</option>,
1767 <!-- TYPE SYSTEM EXTENSIONS -->
1768 <sect1 id="data-type-extensions">
1769 <title>Extensions to data types and type synonyms</title>
1771 <sect2 id="nullary-types">
1772 <title>Data types with no constructors</title>
1774 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1775 a data type with no constructors. For example:</para>
1779 data T a -- T :: * -> *
1782 <para>Syntactically, the declaration lacks the "= constrs" part. The
1783 type can be parameterised over types of any kind, but if the kind is
1784 not <literal>*</literal> then an explicit kind annotation must be used
1785 (see <xref linkend="kinding"/>).</para>
1787 <para>Such data types have only one value, namely bottom.
1788 Nevertheless, they can be useful when defining "phantom types".</para>
1791 <sect2 id="infix-tycons">
1792 <title>Infix type constructors, classes, and type variables</title>
1795 GHC allows type constructors, classes, and type variables to be operators, and
1796 to be written infix, very much like expressions. More specifically:
1799 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1800 The lexical syntax is the same as that for data constructors.
1803 Data type and type-synonym declarations can be written infix, parenthesised
1804 if you want further arguments. E.g.
1806 data a :*: b = Foo a b
1807 type a :+: b = Either a b
1808 class a :=: b where ...
1810 data (a :**: b) x = Baz a b x
1811 type (a :++: b) y = Either (a,b) y
1815 Types, and class constraints, can be written infix. For example
1818 f :: (a :=: b) => a -> b
1822 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1823 The lexical syntax is the same as that for variable operators, excluding "(.)",
1824 "(!)", and "(*)". In a binding position, the operator must be
1825 parenthesised. For example:
1827 type T (+) = Int + Int
1831 liftA2 :: Arrow (~>)
1832 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1838 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1839 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1842 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1843 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1844 sets the fixity for a data constructor and the corresponding type constructor. For example:
1848 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1849 and similarly for <literal>:*:</literal>.
1850 <literal>Int `a` Bool</literal>.
1853 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1860 <sect2 id="type-synonyms">
1861 <title>Liberalised type synonyms</title>
1864 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1865 on individual synonym declarations.
1866 With the <option>-XLiberalTypeSynonyms</option> extension,
1867 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1868 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1871 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1872 in a type synonym, thus:
1874 type Discard a = forall b. Show b => a -> b -> (a, String)
1879 g :: Discard Int -> (Int,String) -- A rank-2 type
1886 If you also use <option>-XUnboxedTuples</option>,
1887 you can write an unboxed tuple in a type synonym:
1889 type Pr = (# Int, Int #)
1897 You can apply a type synonym to a forall type:
1899 type Foo a = a -> a -> Bool
1901 f :: Foo (forall b. b->b)
1903 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1905 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1910 You can apply a type synonym to a partially applied type synonym:
1912 type Generic i o = forall x. i x -> o x
1915 foo :: Generic Id []
1917 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1919 foo :: forall x. x -> [x]
1927 GHC currently does kind checking before expanding synonyms (though even that
1931 After expanding type synonyms, GHC does validity checking on types, looking for
1932 the following mal-formedness which isn't detected simply by kind checking:
1935 Type constructor applied to a type involving for-alls.
1938 Unboxed tuple on left of an arrow.
1941 Partially-applied type synonym.
1945 this will be rejected:
1947 type Pr = (# Int, Int #)
1952 because GHC does not allow unboxed tuples on the left of a function arrow.
1957 <sect2 id="existential-quantification">
1958 <title>Existentially quantified data constructors
1962 The idea of using existential quantification in data type declarations
1963 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1964 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1965 London, 1991). It was later formalised by Laufer and Odersky
1966 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1967 TOPLAS, 16(5), pp1411-1430, 1994).
1968 It's been in Lennart
1969 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1970 proved very useful. Here's the idea. Consider the declaration:
1976 data Foo = forall a. MkFoo a (a -> Bool)
1983 The data type <literal>Foo</literal> has two constructors with types:
1989 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1996 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1997 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1998 For example, the following expression is fine:
2004 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2010 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2011 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2012 isUpper</function> packages a character with a compatible function. These
2013 two things are each of type <literal>Foo</literal> and can be put in a list.
2017 What can we do with a value of type <literal>Foo</literal>?. In particular,
2018 what happens when we pattern-match on <function>MkFoo</function>?
2024 f (MkFoo val fn) = ???
2030 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2031 are compatible, the only (useful) thing we can do with them is to
2032 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2039 f (MkFoo val fn) = fn val
2045 What this allows us to do is to package heterogeneous values
2046 together with a bunch of functions that manipulate them, and then treat
2047 that collection of packages in a uniform manner. You can express
2048 quite a bit of object-oriented-like programming this way.
2051 <sect3 id="existential">
2052 <title>Why existential?
2056 What has this to do with <emphasis>existential</emphasis> quantification?
2057 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2063 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2069 But Haskell programmers can safely think of the ordinary
2070 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2071 adding a new existential quantification construct.
2076 <sect3 id="existential-with-context">
2077 <title>Existentials and type classes</title>
2080 An easy extension is to allow
2081 arbitrary contexts before the constructor. For example:
2087 data Baz = forall a. Eq a => Baz1 a a
2088 | forall b. Show b => Baz2 b (b -> b)
2094 The two constructors have the types you'd expect:
2100 Baz1 :: forall a. Eq a => a -> a -> Baz
2101 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2107 But when pattern matching on <function>Baz1</function> the matched values can be compared
2108 for equality, and when pattern matching on <function>Baz2</function> the first matched
2109 value can be converted to a string (as well as applying the function to it).
2110 So this program is legal:
2117 f (Baz1 p q) | p == q = "Yes"
2119 f (Baz2 v fn) = show (fn v)
2125 Operationally, in a dictionary-passing implementation, the
2126 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2127 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2128 extract it on pattern matching.
2133 <sect3 id="existential-records">
2134 <title>Record Constructors</title>
2137 GHC allows existentials to be used with records syntax as well. For example:
2140 data Counter a = forall self. NewCounter
2142 , _inc :: self -> self
2143 , _display :: self -> IO ()
2147 Here <literal>tag</literal> is a public field, with a well-typed selector
2148 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2149 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2150 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2151 compile-time error. In other words, <emphasis>GHC defines a record selector function
2152 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2153 (This example used an underscore in the fields for which record selectors
2154 will not be defined, but that is only programming style; GHC ignores them.)
2158 To make use of these hidden fields, we need to create some helper functions:
2161 inc :: Counter a -> Counter a
2162 inc (NewCounter x i d t) = NewCounter
2163 { _this = i x, _inc = i, _display = d, tag = t }
2165 display :: Counter a -> IO ()
2166 display NewCounter{ _this = x, _display = d } = d x
2169 Now we can define counters with different underlying implementations:
2172 counterA :: Counter String
2173 counterA = NewCounter
2174 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2176 counterB :: Counter String
2177 counterB = NewCounter
2178 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2181 display (inc counterA) -- prints "1"
2182 display (inc (inc counterB)) -- prints "##"
2185 Record update syntax is supported for existentials (and GADTs):
2187 setTag :: Counter a -> a -> Counter a
2188 setTag obj t = obj{ tag = t }
2190 The rule for record update is this: <emphasis>
2191 the types of the updated fields may
2192 mention only the universally-quantified type variables
2193 of the data constructor. For GADTs, the field may mention only types
2194 that appear as a simple type-variable argument in the constructor's result
2195 type</emphasis>. For example:
2197 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2198 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2199 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2200 -- existentially quantified)
2202 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2203 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2204 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2205 -- type-variable argument in G1's result type)
2213 <title>Restrictions</title>
2216 There are several restrictions on the ways in which existentially-quantified
2217 constructors can be use.
2226 When pattern matching, each pattern match introduces a new,
2227 distinct, type for each existential type variable. These types cannot
2228 be unified with any other type, nor can they escape from the scope of
2229 the pattern match. For example, these fragments are incorrect:
2237 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2238 is the result of <function>f1</function>. One way to see why this is wrong is to
2239 ask what type <function>f1</function> has:
2243 f1 :: Foo -> a -- Weird!
2247 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2252 f1 :: forall a. Foo -> a -- Wrong!
2256 The original program is just plain wrong. Here's another sort of error
2260 f2 (Baz1 a b) (Baz1 p q) = a==q
2264 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2265 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2266 from the two <function>Baz1</function> constructors.
2274 You can't pattern-match on an existentially quantified
2275 constructor in a <literal>let</literal> or <literal>where</literal> group of
2276 bindings. So this is illegal:
2280 f3 x = a==b where { Baz1 a b = x }
2283 Instead, use a <literal>case</literal> expression:
2286 f3 x = case x of Baz1 a b -> a==b
2289 In general, you can only pattern-match
2290 on an existentially-quantified constructor in a <literal>case</literal> expression or
2291 in the patterns of a function definition.
2293 The reason for this restriction is really an implementation one.
2294 Type-checking binding groups is already a nightmare without
2295 existentials complicating the picture. Also an existential pattern
2296 binding at the top level of a module doesn't make sense, because it's
2297 not clear how to prevent the existentially-quantified type "escaping".
2298 So for now, there's a simple-to-state restriction. We'll see how
2306 You can't use existential quantification for <literal>newtype</literal>
2307 declarations. So this is illegal:
2311 newtype T = forall a. Ord a => MkT a
2315 Reason: a value of type <literal>T</literal> must be represented as a
2316 pair of a dictionary for <literal>Ord t</literal> and a value of type
2317 <literal>t</literal>. That contradicts the idea that
2318 <literal>newtype</literal> should have no concrete representation.
2319 You can get just the same efficiency and effect by using
2320 <literal>data</literal> instead of <literal>newtype</literal>. If
2321 there is no overloading involved, then there is more of a case for
2322 allowing an existentially-quantified <literal>newtype</literal>,
2323 because the <literal>data</literal> version does carry an
2324 implementation cost, but single-field existentially quantified
2325 constructors aren't much use. So the simple restriction (no
2326 existential stuff on <literal>newtype</literal>) stands, unless there
2327 are convincing reasons to change it.
2335 You can't use <literal>deriving</literal> to define instances of a
2336 data type with existentially quantified data constructors.
2338 Reason: in most cases it would not make sense. For example:;
2341 data T = forall a. MkT [a] deriving( Eq )
2344 To derive <literal>Eq</literal> in the standard way we would need to have equality
2345 between the single component of two <function>MkT</function> constructors:
2349 (MkT a) == (MkT b) = ???
2352 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2353 It's just about possible to imagine examples in which the derived instance
2354 would make sense, but it seems altogether simpler simply to prohibit such
2355 declarations. Define your own instances!
2366 <!-- ====================== Generalised algebraic data types ======================= -->
2368 <sect2 id="gadt-style">
2369 <title>Declaring data types with explicit constructor signatures</title>
2371 <para>GHC allows you to declare an algebraic data type by
2372 giving the type signatures of constructors explicitly. For example:
2376 Just :: a -> Maybe a
2378 The form is called a "GADT-style declaration"
2379 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2380 can only be declared using this form.</para>
2381 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2382 For example, these two declarations are equivalent:
2384 data Foo = forall a. MkFoo a (a -> Bool)
2385 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2388 <para>Any data type that can be declared in standard Haskell-98 syntax
2389 can also be declared using GADT-style syntax.
2390 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2391 they treat class constraints on the data constructors differently.
2392 Specifically, if the constructor is given a type-class context, that
2393 context is made available by pattern matching. For example:
2396 MkSet :: Eq a => [a] -> Set a
2398 makeSet :: Eq a => [a] -> Set a
2399 makeSet xs = MkSet (nub xs)
2401 insert :: a -> Set a -> Set a
2402 insert a (MkSet as) | a `elem` as = MkSet as
2403 | otherwise = MkSet (a:as)
2405 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2406 gives rise to a <literal>(Eq a)</literal>
2407 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2408 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2409 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2410 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2411 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2412 In the example, the equality dictionary is used to satisfy the equality constraint
2413 generated by the call to <literal>elem</literal>, so that the type of
2414 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2417 For example, one possible application is to reify dictionaries:
2419 data NumInst a where
2420 MkNumInst :: Num a => NumInst a
2422 intInst :: NumInst Int
2425 plus :: NumInst a -> a -> a -> a
2426 plus MkNumInst p q = p + q
2428 Here, a value of type <literal>NumInst a</literal> is equivalent
2429 to an explicit <literal>(Num a)</literal> dictionary.
2432 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2433 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2437 = Num a => MkNumInst (NumInst a)
2439 Notice that, unlike the situation when declaring an existential, there is
2440 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2441 data type's universally quantified type variable <literal>a</literal>.
2442 A constructor may have both universal and existential type variables: for example,
2443 the following two declarations are equivalent:
2446 = forall b. (Num a, Eq b) => MkT1 a b
2448 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2451 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2452 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2453 In Haskell 98 the definition
2455 data Eq a => Set' a = MkSet' [a]
2457 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2458 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2459 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2460 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2461 GHC's behaviour is much more useful, as well as much more intuitive.
2465 The rest of this section gives further details about GADT-style data
2470 The result type of each data constructor must begin with the type constructor being defined.
2471 If the result type of all constructors
2472 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2473 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2474 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2478 As with other type signatures, you can give a single signature for several data constructors.
2479 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2488 The type signature of
2489 each constructor is independent, and is implicitly universally quantified as usual.
2490 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2491 have no scope, and different constructors may have different universally-quantified type variables:
2493 data T a where -- The 'a' has no scope
2494 T1,T2 :: b -> T b -- Means forall b. b -> T b
2495 T3 :: T a -- Means forall a. T a
2500 A constructor signature may mention type class constraints, which can differ for
2501 different constructors. For example, this is fine:
2504 T1 :: Eq b => b -> b -> T b
2505 T2 :: (Show c, Ix c) => c -> [c] -> T c
2507 When patten matching, these constraints are made available to discharge constraints
2508 in the body of the match. For example:
2511 f (T1 x y) | x==y = "yes"
2515 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2516 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2517 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2521 Unlike a Haskell-98-style
2522 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2523 have no scope. Indeed, one can write a kind signature instead:
2525 data Set :: * -> * where ...
2527 or even a mixture of the two:
2529 data Bar a :: (* -> *) -> * where ...
2531 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2534 data Bar a (b :: * -> *) where ...
2540 You can use strictness annotations, in the obvious places
2541 in the constructor type:
2544 Lit :: !Int -> Term Int
2545 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2546 Pair :: Term a -> Term b -> Term (a,b)
2551 You can use a <literal>deriving</literal> clause on a GADT-style data type
2552 declaration. For example, these two declarations are equivalent
2554 data Maybe1 a where {
2555 Nothing1 :: Maybe1 a ;
2556 Just1 :: a -> Maybe1 a
2557 } deriving( Eq, Ord )
2559 data Maybe2 a = Nothing2 | Just2 a
2565 The type signature may have quantified type variables that do not appear
2569 MkFoo :: a -> (a->Bool) -> Foo
2572 Here the type variable <literal>a</literal> does not appear in the result type
2573 of either constructor.
2574 Although it is universally quantified in the type of the constructor, such
2575 a type variable is often called "existential".
2576 Indeed, the above declaration declares precisely the same type as
2577 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2579 The type may contain a class context too, of course:
2582 MkShowable :: Show a => a -> Showable
2587 You can use record syntax on a GADT-style data type declaration:
2591 Adult :: { name :: String, children :: [Person] } -> Person
2592 Child :: Show a => { name :: !String, funny :: a } -> Person
2594 As usual, for every constructor that has a field <literal>f</literal>, the type of
2595 field <literal>f</literal> must be the same (modulo alpha conversion).
2596 The <literal>Child</literal> constructor above shows that the signature
2597 may have a context, existentially-quantified variables, and strictness annotations,
2598 just as in the non-record case. (NB: the "type" that follows the double-colon
2599 is not really a type, because of the record syntax and strictness annotations.
2600 A "type" of this form can appear only in a constructor signature.)
2604 Record updates are allowed with GADT-style declarations,
2605 only fields that have the following property: the type of the field
2606 mentions no existential type variables.
2610 As in the case of existentials declared using the Haskell-98-like record syntax
2611 (<xref linkend="existential-records"/>),
2612 record-selector functions are generated only for those fields that have well-typed
2614 Here is the example of that section, in GADT-style syntax:
2616 data Counter a where
2617 NewCounter { _this :: self
2618 , _inc :: self -> self
2619 , _display :: self -> IO ()
2624 As before, only one selector function is generated here, that for <literal>tag</literal>.
2625 Nevertheless, you can still use all the field names in pattern matching and record construction.
2627 </itemizedlist></para>
2631 <title>Generalised Algebraic Data Types (GADTs)</title>
2633 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2634 by allowing constructors to have richer return types. Here is an example:
2637 Lit :: Int -> Term Int
2638 Succ :: Term Int -> Term Int
2639 IsZero :: Term Int -> Term Bool
2640 If :: Term Bool -> Term a -> Term a -> Term a
2641 Pair :: Term a -> Term b -> Term (a,b)
2643 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2644 case with ordinary data types. This generality allows us to
2645 write a well-typed <literal>eval</literal> function
2646 for these <literal>Terms</literal>:
2650 eval (Succ t) = 1 + eval t
2651 eval (IsZero t) = eval t == 0
2652 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2653 eval (Pair e1 e2) = (eval e1, eval e2)
2655 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2656 For example, in the right hand side of the equation
2661 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2662 A precise specification of the type rules is beyond what this user manual aspires to,
2663 but the design closely follows that described in
2665 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2666 unification-based type inference for GADTs</ulink>,
2668 The general principle is this: <emphasis>type refinement is only carried out
2669 based on user-supplied type annotations</emphasis>.
2670 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2671 and lots of obscure error messages will
2672 occur. However, the refinement is quite general. For example, if we had:
2674 eval :: Term a -> a -> a
2675 eval (Lit i) j = i+j
2677 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2678 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2679 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2682 These and many other examples are given in papers by Hongwei Xi, and
2683 Tim Sheard. There is a longer introduction
2684 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2686 <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
2687 may use different notation to that implemented in GHC.
2690 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2691 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2694 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2695 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2696 The result type of each constructor must begin with the type constructor being defined,
2697 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2698 For example, in the <literal>Term</literal> data
2699 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2700 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2705 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2706 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2707 whose result type is not just <literal>T a b</literal>.
2711 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2712 an ordinary data type.
2716 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2720 Lit { val :: Int } :: Term Int
2721 Succ { num :: Term Int } :: Term Int
2722 Pred { num :: Term Int } :: Term Int
2723 IsZero { arg :: Term Int } :: Term Bool
2724 Pair { arg1 :: Term a
2727 If { cnd :: Term Bool
2732 However, for GADTs there is the following additional constraint:
2733 every constructor that has a field <literal>f</literal> must have
2734 the same result type (modulo alpha conversion)
2735 Hence, in the above example, we cannot merge the <literal>num</literal>
2736 and <literal>arg</literal> fields above into a
2737 single name. Although their field types are both <literal>Term Int</literal>,
2738 their selector functions actually have different types:
2741 num :: Term Int -> Term Int
2742 arg :: Term Bool -> Term Int
2747 When pattern-matching against data constructors drawn from a GADT,
2748 for example in a <literal>case</literal> expression, the following rules apply:
2750 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2751 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2752 <listitem><para>The type of any free variable mentioned in any of
2753 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2755 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2756 way to ensure that a variable a rigid type is to give it a type signature.
2757 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2758 Simple unification-based type inference for GADTs
2759 </ulink>. The criteria implemented by GHC are given in the Appendix.
2769 <!-- ====================== End of Generalised algebraic data types ======================= -->
2771 <sect1 id="deriving">
2772 <title>Extensions to the "deriving" mechanism</title>
2774 <sect2 id="deriving-inferred">
2775 <title>Inferred context for deriving clauses</title>
2778 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2781 data T0 f a = MkT0 a deriving( Eq )
2782 data T1 f a = MkT1 (f a) deriving( Eq )
2783 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2785 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2787 instance Eq a => Eq (T0 f a) where ...
2788 instance Eq (f a) => Eq (T1 f a) where ...
2789 instance Eq (f (f a)) => Eq (T2 f a) where ...
2791 The first of these is obviously fine. The second is still fine, although less obviously.
2792 The third is not Haskell 98, and risks losing termination of instances.
2795 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2796 each constraint in the inferred instance context must consist only of type variables,
2797 with no repetitions.
2800 This rule is applied regardless of flags. If you want a more exotic context, you can write
2801 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2805 <sect2 id="stand-alone-deriving">
2806 <title>Stand-alone deriving declarations</title>
2809 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2811 data Foo a = Bar a | Baz String
2813 deriving instance Eq a => Eq (Foo a)
2815 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2816 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2817 Note the following points:
2820 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2821 exactly as you would in an ordinary instance declaration.
2822 (In contrast, in a <literal>deriving</literal> clause
2823 attached to a data type declaration, the context is inferred.)
2827 A <literal>deriving instance</literal> declaration
2828 must obey the same rules concerning form and termination as ordinary instance declarations,
2829 controlled by the same flags; see <xref linkend="instance-decls"/>.
2833 Unlike a <literal>deriving</literal>
2834 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2835 than the data type (assuming you also use
2836 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2839 data Foo a = Bar a | Baz String
2841 deriving instance Eq a => Eq (Foo [a])
2842 deriving instance Eq a => Eq (Foo (Maybe a))
2844 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2845 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2849 Unlike a <literal>deriving</literal>
2850 declaration attached to a <literal>data</literal> declaration,
2851 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2852 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2853 your problem. (GHC will show you the offending code if it has a type error.)
2854 The merit of this is that you can derive instances for GADTs and other exotic
2855 data types, providing only that the boilerplate code does indeed typecheck. For example:
2861 deriving instance Show (T a)
2863 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2864 data type declaration for <literal>T</literal>,
2865 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2866 the instance declaration using stand-alone deriving.
2871 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2872 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2875 newtype Foo a = MkFoo (State Int a)
2877 deriving instance MonadState Int Foo
2879 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2880 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2882 </itemizedlist></para>
2887 <sect2 id="deriving-typeable">
2888 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2891 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2892 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2893 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2894 classes <literal>Eq</literal>, <literal>Ord</literal>,
2895 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2898 GHC extends this list with several more classes that may be automatically derived:
2900 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2901 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2902 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2904 <para>An instance of <literal>Typeable</literal> can only be derived if the
2905 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2906 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2908 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2909 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2911 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2912 are used, and only <literal>Typeable1</literal> up to
2913 <literal>Typeable7</literal> are provided in the library.)
2914 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2915 class, whose kind suits that of the data type constructor, and
2916 then writing the data type instance by hand.
2920 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2921 the class <literal>Functor</literal>,
2922 defined in <literal>GHC.Base</literal>.
2925 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2926 the class <literal>Foldable</literal>,
2927 defined in <literal>Data.Foldable</literal>.
2930 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2931 the class <literal>Traversable</literal>,
2932 defined in <literal>Data.Traversable</literal>.
2935 In each case the appropriate class must be in scope before it
2936 can be mentioned in the <literal>deriving</literal> clause.
2940 <sect2 id="newtype-deriving">
2941 <title>Generalised derived instances for newtypes</title>
2944 When you define an abstract type using <literal>newtype</literal>, you may want
2945 the new type to inherit some instances from its representation. In
2946 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2947 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2948 other classes you have to write an explicit instance declaration. For
2949 example, if you define
2952 newtype Dollars = Dollars Int
2955 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2956 explicitly define an instance of <literal>Num</literal>:
2959 instance Num Dollars where
2960 Dollars a + Dollars b = Dollars (a+b)
2963 All the instance does is apply and remove the <literal>newtype</literal>
2964 constructor. It is particularly galling that, since the constructor
2965 doesn't appear at run-time, this instance declaration defines a
2966 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2967 dictionary, only slower!
2971 <sect3> <title> Generalising the deriving clause </title>
2973 GHC now permits such instances to be derived instead,
2974 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
2977 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2980 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2981 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2982 derives an instance declaration of the form
2985 instance Num Int => Num Dollars
2988 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2992 We can also derive instances of constructor classes in a similar
2993 way. For example, suppose we have implemented state and failure monad
2994 transformers, such that
2997 instance Monad m => Monad (State s m)
2998 instance Monad m => Monad (Failure m)
3000 In Haskell 98, we can define a parsing monad by
3002 type Parser tok m a = State [tok] (Failure m) a
3005 which is automatically a monad thanks to the instance declarations
3006 above. With the extension, we can make the parser type abstract,
3007 without needing to write an instance of class <literal>Monad</literal>, via
3010 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3013 In this case the derived instance declaration is of the form
3015 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3018 Notice that, since <literal>Monad</literal> is a constructor class, the
3019 instance is a <emphasis>partial application</emphasis> of the new type, not the
3020 entire left hand side. We can imagine that the type declaration is
3021 "eta-converted" to generate the context of the instance
3026 We can even derive instances of multi-parameter classes, provided the
3027 newtype is the last class parameter. In this case, a ``partial
3028 application'' of the class appears in the <literal>deriving</literal>
3029 clause. For example, given the class
3032 class StateMonad s m | m -> s where ...
3033 instance Monad m => StateMonad s (State s m) where ...
3035 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3037 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3038 deriving (Monad, StateMonad [tok])
3041 The derived instance is obtained by completing the application of the
3042 class to the new type:
3045 instance StateMonad [tok] (State [tok] (Failure m)) =>
3046 StateMonad [tok] (Parser tok m)
3051 As a result of this extension, all derived instances in newtype
3052 declarations are treated uniformly (and implemented just by reusing
3053 the dictionary for the representation type), <emphasis>except</emphasis>
3054 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3055 the newtype and its representation.
3059 <sect3> <title> A more precise specification </title>
3061 Derived instance declarations are constructed as follows. Consider the
3062 declaration (after expansion of any type synonyms)
3065 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3071 The <literal>ci</literal> are partial applications of
3072 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3073 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3076 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3079 The type <literal>t</literal> is an arbitrary type.
3082 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3083 nor in the <literal>ci</literal>, and
3086 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3087 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3088 should not "look through" the type or its constructor. You can still
3089 derive these classes for a newtype, but it happens in the usual way, not
3090 via this new mechanism.
3093 Then, for each <literal>ci</literal>, the derived instance
3096 instance ci t => ci (T v1...vk)
3098 As an example which does <emphasis>not</emphasis> work, consider
3100 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3102 Here we cannot derive the instance
3104 instance Monad (State s m) => Monad (NonMonad m)
3107 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3108 and so cannot be "eta-converted" away. It is a good thing that this
3109 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3110 not, in fact, a monad --- for the same reason. Try defining
3111 <literal>>>=</literal> with the correct type: you won't be able to.
3115 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3116 important, since we can only derive instances for the last one. If the
3117 <literal>StateMonad</literal> class above were instead defined as
3120 class StateMonad m s | m -> s where ...
3123 then we would not have been able to derive an instance for the
3124 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3125 classes usually have one "main" parameter for which deriving new
3126 instances is most interesting.
3128 <para>Lastly, all of this applies only for classes other than
3129 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3130 and <literal>Data</literal>, for which the built-in derivation applies (section
3131 4.3.3. of the Haskell Report).
3132 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3133 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3134 the standard method is used or the one described here.)
3141 <!-- TYPE SYSTEM EXTENSIONS -->
3142 <sect1 id="type-class-extensions">
3143 <title>Class and instances declarations</title>
3145 <sect2 id="multi-param-type-classes">
3146 <title>Class declarations</title>
3149 This section, and the next one, documents GHC's type-class extensions.
3150 There's lots of background in the paper <ulink
3151 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3152 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3153 Jones, Erik Meijer).
3156 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3160 <title>Multi-parameter type classes</title>
3162 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3167 class Collection c a where
3168 union :: c a -> c a -> c a
3175 <sect3 id="superclass-rules">
3176 <title>The superclasses of a class declaration</title>
3179 In Haskell 98 the context of a class declaration (which introduces superclasses)
3180 must be simple; that is, each predicate must consist of a class applied to
3181 type variables. The flag <option>-XFlexibleContexts</option>
3182 (<xref linkend="flexible-contexts"/>)
3183 lifts this restriction,
3184 so that the only restriction on the context in a class declaration is
3185 that the class hierarchy must be acyclic. So these class declarations are OK:
3189 class Functor (m k) => FiniteMap m k where
3192 class (Monad m, Monad (t m)) => Transform t m where
3193 lift :: m a -> (t m) a
3199 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3200 of "acyclic" involves only the superclass relationships. For example,
3206 op :: D b => a -> b -> b
3209 class C a => D a where { ... }
3213 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3214 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3215 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3222 <sect3 id="class-method-types">
3223 <title>Class method types</title>
3226 Haskell 98 prohibits class method types to mention constraints on the
3227 class type variable, thus:
3230 fromList :: [a] -> s a
3231 elem :: Eq a => a -> s a -> Bool
3233 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3234 contains the constraint <literal>Eq a</literal>, constrains only the
3235 class type variable (in this case <literal>a</literal>).
3236 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3243 <sect2 id="functional-dependencies">
3244 <title>Functional dependencies
3247 <para> Functional dependencies are implemented as described by Mark Jones
3248 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3249 In Proceedings of the 9th European Symposium on Programming,
3250 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3254 Functional dependencies are introduced by a vertical bar in the syntax of a
3255 class declaration; e.g.
3257 class (Monad m) => MonadState s m | m -> s where ...
3259 class Foo a b c | a b -> c where ...
3261 There should be more documentation, but there isn't (yet). Yell if you need it.
3264 <sect3><title>Rules for functional dependencies </title>
3266 In a class declaration, all of the class type variables must be reachable (in the sense
3267 mentioned in <xref linkend="flexible-contexts"/>)
3268 from the free variables of each method type.
3272 class Coll s a where
3274 insert :: s -> a -> s
3277 is not OK, because the type of <literal>empty</literal> doesn't mention
3278 <literal>a</literal>. Functional dependencies can make the type variable
3281 class Coll s a | s -> a where
3283 insert :: s -> a -> s
3286 Alternatively <literal>Coll</literal> might be rewritten
3289 class Coll s a where
3291 insert :: s a -> a -> s a
3295 which makes the connection between the type of a collection of
3296 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3297 Occasionally this really doesn't work, in which case you can split the
3305 class CollE s => Coll s a where
3306 insert :: s -> a -> s
3313 <title>Background on functional dependencies</title>
3315 <para>The following description of the motivation and use of functional dependencies is taken
3316 from the Hugs user manual, reproduced here (with minor changes) by kind
3317 permission of Mark Jones.
3320 Consider the following class, intended as part of a
3321 library for collection types:
3323 class Collects e ce where
3325 insert :: e -> ce -> ce
3326 member :: e -> ce -> Bool
3328 The type variable e used here represents the element type, while ce is the type
3329 of the container itself. Within this framework, we might want to define
3330 instances of this class for lists or characteristic functions (both of which
3331 can be used to represent collections of any equality type), bit sets (which can
3332 be used to represent collections of characters), or hash tables (which can be
3333 used to represent any collection whose elements have a hash function). Omitting
3334 standard implementation details, this would lead to the following declarations:
3336 instance Eq e => Collects e [e] where ...
3337 instance Eq e => Collects e (e -> Bool) where ...
3338 instance Collects Char BitSet where ...
3339 instance (Hashable e, Collects a ce)
3340 => Collects e (Array Int ce) where ...
3342 All this looks quite promising; we have a class and a range of interesting
3343 implementations. Unfortunately, there are some serious problems with the class
3344 declaration. First, the empty function has an ambiguous type:
3346 empty :: Collects e ce => ce
3348 By "ambiguous" we mean that there is a type variable e that appears on the left
3349 of the <literal>=></literal> symbol, but not on the right. The problem with
3350 this is that, according to the theoretical foundations of Haskell overloading,
3351 we cannot guarantee a well-defined semantics for any term with an ambiguous
3355 We can sidestep this specific problem by removing the empty member from the
3356 class declaration. However, although the remaining members, insert and member,
3357 do not have ambiguous types, we still run into problems when we try to use
3358 them. For example, consider the following two functions:
3360 f x y = insert x . insert y
3363 for which GHC infers the following types:
3365 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3366 g :: (Collects Bool c, Collects Char c) => c -> c
3368 Notice that the type for f allows the two parameters x and y to be assigned
3369 different types, even though it attempts to insert each of the two values, one
3370 after the other, into the same collection. If we're trying to model collections
3371 that contain only one type of value, then this is clearly an inaccurate
3372 type. Worse still, the definition for g is accepted, without causing a type
3373 error. As a result, the error in this code will not be flagged at the point
3374 where it appears. Instead, it will show up only when we try to use g, which
3375 might even be in a different module.
3378 <sect4><title>An attempt to use constructor classes</title>
3381 Faced with the problems described above, some Haskell programmers might be
3382 tempted to use something like the following version of the class declaration:
3384 class Collects e c where
3386 insert :: e -> c e -> c e
3387 member :: e -> c e -> Bool
3389 The key difference here is that we abstract over the type constructor c that is
3390 used to form the collection type c e, and not over that collection type itself,
3391 represented by ce in the original class declaration. This avoids the immediate
3392 problems that we mentioned above: empty has type <literal>Collects e c => c
3393 e</literal>, which is not ambiguous.
3396 The function f from the previous section has a more accurate type:
3398 f :: (Collects e c) => e -> e -> c e -> c e
3400 The function g from the previous section is now rejected with a type error as
3401 we would hope because the type of f does not allow the two arguments to have
3403 This, then, is an example of a multiple parameter class that does actually work
3404 quite well in practice, without ambiguity problems.
3405 There is, however, a catch. This version of the Collects class is nowhere near
3406 as general as the original class seemed to be: only one of the four instances
3407 for <literal>Collects</literal>
3408 given above can be used with this version of Collects because only one of
3409 them---the instance for lists---has a collection type that can be written in
3410 the form c e, for some type constructor c, and element type e.
3414 <sect4><title>Adding functional dependencies</title>
3417 To get a more useful version of the Collects class, Hugs provides a mechanism
3418 that allows programmers to specify dependencies between the parameters of a
3419 multiple parameter class (For readers with an interest in theoretical
3420 foundations and previous work: The use of dependency information can be seen
3421 both as a generalization of the proposal for `parametric type classes' that was
3422 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3423 later framework for "improvement" of qualified types. The
3424 underlying ideas are also discussed in a more theoretical and abstract setting
3425 in a manuscript [implparam], where they are identified as one point in a
3426 general design space for systems of implicit parameterization.).
3428 To start with an abstract example, consider a declaration such as:
3430 class C a b where ...
3432 which tells us simply that C can be thought of as a binary relation on types
3433 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3434 included in the definition of classes to add information about dependencies
3435 between parameters, as in the following examples:
3437 class D a b | a -> b where ...
3438 class E a b | a -> b, b -> a where ...
3440 The notation <literal>a -> b</literal> used here between the | and where
3441 symbols --- not to be
3442 confused with a function type --- indicates that the a parameter uniquely
3443 determines the b parameter, and might be read as "a determines b." Thus D is
3444 not just a relation, but actually a (partial) function. Similarly, from the two
3445 dependencies that are included in the definition of E, we can see that E
3446 represents a (partial) one-one mapping between types.
3449 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3450 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3451 m>=0, meaning that the y parameters are uniquely determined by the x
3452 parameters. Spaces can be used as separators if more than one variable appears
3453 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3454 annotated with multiple dependencies using commas as separators, as in the
3455 definition of E above. Some dependencies that we can write in this notation are
3456 redundant, and will be rejected because they don't serve any useful
3457 purpose, and may instead indicate an error in the program. Examples of
3458 dependencies like this include <literal>a -> a </literal>,
3459 <literal>a -> a a </literal>,
3460 <literal>a -> </literal>, etc. There can also be
3461 some redundancy if multiple dependencies are given, as in
3462 <literal>a->b</literal>,
3463 <literal>b->c </literal>, <literal>a->c </literal>, and
3464 in which some subset implies the remaining dependencies. Examples like this are
3465 not treated as errors. Note that dependencies appear only in class
3466 declarations, and not in any other part of the language. In particular, the
3467 syntax for instance declarations, class constraints, and types is completely
3471 By including dependencies in a class declaration, we provide a mechanism for
3472 the programmer to specify each multiple parameter class more precisely. The
3473 compiler, on the other hand, is responsible for ensuring that the set of
3474 instances that are in scope at any given point in the program is consistent
3475 with any declared dependencies. For example, the following pair of instance
3476 declarations cannot appear together in the same scope because they violate the
3477 dependency for D, even though either one on its own would be acceptable:
3479 instance D Bool Int where ...
3480 instance D Bool Char where ...
3482 Note also that the following declaration is not allowed, even by itself:
3484 instance D [a] b where ...
3486 The problem here is that this instance would allow one particular choice of [a]
3487 to be associated with more than one choice for b, which contradicts the
3488 dependency specified in the definition of D. More generally, this means that,
3489 in any instance of the form:
3491 instance D t s where ...
3493 for some particular types t and s, the only variables that can appear in s are
3494 the ones that appear in t, and hence, if the type t is known, then s will be
3495 uniquely determined.
3498 The benefit of including dependency information is that it allows us to define
3499 more general multiple parameter classes, without ambiguity problems, and with
3500 the benefit of more accurate types. To illustrate this, we return to the
3501 collection class example, and annotate the original definition of <literal>Collects</literal>
3502 with a simple dependency:
3504 class Collects e ce | ce -> e where
3506 insert :: e -> ce -> ce
3507 member :: e -> ce -> Bool
3509 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3510 determined by the type of the collection ce. Note that both parameters of
3511 Collects are of kind *; there are no constructor classes here. Note too that
3512 all of the instances of Collects that we gave earlier can be used
3513 together with this new definition.
3516 What about the ambiguity problems that we encountered with the original
3517 definition? The empty function still has type Collects e ce => ce, but it is no
3518 longer necessary to regard that as an ambiguous type: Although the variable e
3519 does not appear on the right of the => symbol, the dependency for class
3520 Collects tells us that it is uniquely determined by ce, which does appear on
3521 the right of the => symbol. Hence the context in which empty is used can still
3522 give enough information to determine types for both ce and e, without
3523 ambiguity. More generally, we need only regard a type as ambiguous if it
3524 contains a variable on the left of the => that is not uniquely determined
3525 (either directly or indirectly) by the variables on the right.
3528 Dependencies also help to produce more accurate types for user defined
3529 functions, and hence to provide earlier detection of errors, and less cluttered
3530 types for programmers to work with. Recall the previous definition for a
3533 f x y = insert x y = insert x . insert y
3535 for which we originally obtained a type:
3537 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3539 Given the dependency information that we have for Collects, however, we can
3540 deduce that a and b must be equal because they both appear as the second
3541 parameter in a Collects constraint with the same first parameter c. Hence we
3542 can infer a shorter and more accurate type for f:
3544 f :: (Collects a c) => a -> a -> c -> c
3546 In a similar way, the earlier definition of g will now be flagged as a type error.
3549 Although we have given only a few examples here, it should be clear that the
3550 addition of dependency information can help to make multiple parameter classes
3551 more useful in practice, avoiding ambiguity problems, and allowing more general
3552 sets of instance declarations.
3558 <sect2 id="instance-decls">
3559 <title>Instance declarations</title>
3561 <para>An instance declaration has the form
3563 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 ...
3565 The part before the "<literal>=></literal>" is the
3566 <emphasis>context</emphasis>, while the part after the
3567 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3570 <sect3 id="flexible-instance-head">
3571 <title>Relaxed rules for the instance head</title>
3574 In Haskell 98 the head of an instance declaration
3575 must be of the form <literal>C (T a1 ... an)</literal>, where
3576 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3577 and the <literal>a1 ... an</literal> are distinct type variables.
3578 GHC relaxes these rules in two ways.
3582 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3583 declaration to mention arbitrary nested types.
3584 For example, this becomes a legal instance declaration
3586 instance C (Maybe Int) where ...
3588 See also the <link linkend="instance-overlap">rules on overlap</link>.
3591 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3592 synonyms. As always, using a type synonym is just shorthand for
3593 writing the RHS of the type synonym definition. For example:
3597 type Point = (Int,Int)
3598 instance C Point where ...
3599 instance C [Point] where ...
3603 is legal. However, if you added
3607 instance C (Int,Int) where ...
3611 as well, then the compiler will complain about the overlapping
3612 (actually, identical) instance declarations. As always, type synonyms
3613 must be fully applied. You cannot, for example, write:
3617 instance Monad P where ...
3625 <sect3 id="instance-rules">
3626 <title>Relaxed rules for instance contexts</title>
3628 <para>In Haskell 98, the assertions in the context of the instance declaration
3629 must be of the form <literal>C a</literal> where <literal>a</literal>
3630 is a type variable that occurs in the head.
3634 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3635 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3636 With this flag the context of the instance declaration can each consist of arbitrary
3637 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3641 The Paterson Conditions: for each assertion in the context
3643 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3644 <listitem><para>The assertion has fewer constructors and variables (taken together
3645 and counting repetitions) than the head</para></listitem>
3649 <listitem><para>The Coverage Condition. For each functional dependency,
3650 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3651 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3652 every type variable in
3653 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3654 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3655 substitution mapping each type variable in the class declaration to the
3656 corresponding type in the instance declaration.
3659 These restrictions ensure that context reduction terminates: each reduction
3660 step makes the problem smaller by at least one
3661 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3662 if you give the <option>-XUndecidableInstances</option>
3663 flag (<xref linkend="undecidable-instances"/>).
3664 You can find lots of background material about the reason for these
3665 restrictions in the paper <ulink
3666 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3667 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3670 For example, these are OK:
3672 instance C Int [a] -- Multiple parameters
3673 instance Eq (S [a]) -- Structured type in head
3675 -- Repeated type variable in head
3676 instance C4 a a => C4 [a] [a]
3677 instance Stateful (ST s) (MutVar s)
3679 -- Head can consist of type variables only
3681 instance (Eq a, Show b) => C2 a b
3683 -- Non-type variables in context
3684 instance Show (s a) => Show (Sized s a)
3685 instance C2 Int a => C3 Bool [a]
3686 instance C2 Int a => C3 [a] b
3690 -- Context assertion no smaller than head
3691 instance C a => C a where ...
3692 -- (C b b) has more more occurrences of b than the head
3693 instance C b b => Foo [b] where ...
3698 The same restrictions apply to instances generated by
3699 <literal>deriving</literal> clauses. Thus the following is accepted:
3701 data MinHeap h a = H a (h a)
3704 because the derived instance
3706 instance (Show a, Show (h a)) => Show (MinHeap h a)
3708 conforms to the above rules.
3712 A useful idiom permitted by the above rules is as follows.
3713 If one allows overlapping instance declarations then it's quite
3714 convenient to have a "default instance" declaration that applies if
3715 something more specific does not:
3723 <sect3 id="undecidable-instances">
3724 <title>Undecidable instances</title>
3727 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3728 For example, sometimes you might want to use the following to get the
3729 effect of a "class synonym":
3731 class (C1 a, C2 a, C3 a) => C a where { }
3733 instance (C1 a, C2 a, C3 a) => C a where { }
3735 This allows you to write shorter signatures:
3741 f :: (C1 a, C2 a, C3 a) => ...
3743 The restrictions on functional dependencies (<xref
3744 linkend="functional-dependencies"/>) are particularly troublesome.
3745 It is tempting to introduce type variables in the context that do not appear in
3746 the head, something that is excluded by the normal rules. For example:
3748 class HasConverter a b | a -> b where
3751 data Foo a = MkFoo a
3753 instance (HasConverter a b,Show b) => Show (Foo a) where
3754 show (MkFoo value) = show (convert value)
3756 This is dangerous territory, however. Here, for example, is a program that would make the
3761 instance F [a] [[a]]
3762 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3764 Similarly, it can be tempting to lift the coverage condition:
3766 class Mul a b c | a b -> c where
3767 (.*.) :: a -> b -> c
3769 instance Mul Int Int Int where (.*.) = (*)
3770 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3771 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3773 The third instance declaration does not obey the coverage condition;
3774 and indeed the (somewhat strange) definition:
3776 f = \ b x y -> if b then x .*. [y] else y
3778 makes instance inference go into a loop, because it requires the constraint
3779 <literal>(Mul a [b] b)</literal>.
3782 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3783 the experimental flag <option>-XUndecidableInstances</option>
3784 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3785 both the Paterson Conditions and the Coverage Condition
3786 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3787 fixed-depth recursion stack. If you exceed the stack depth you get a
3788 sort of backtrace, and the opportunity to increase the stack depth
3789 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3795 <sect3 id="instance-overlap">
3796 <title>Overlapping instances</title>
3798 In general, <emphasis>GHC requires that that it be unambiguous which instance
3800 should be used to resolve a type-class constraint</emphasis>. This behaviour
3801 can be modified by two flags: <option>-XOverlappingInstances</option>
3802 <indexterm><primary>-XOverlappingInstances
3803 </primary></indexterm>
3804 and <option>-XIncoherentInstances</option>
3805 <indexterm><primary>-XIncoherentInstances
3806 </primary></indexterm>, as this section discusses. Both these
3807 flags are dynamic flags, and can be set on a per-module basis, using
3808 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3810 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3811 it tries to match every instance declaration against the
3813 by instantiating the head of the instance declaration. For example, consider
3816 instance context1 => C Int a where ... -- (A)
3817 instance context2 => C a Bool where ... -- (B)
3818 instance context3 => C Int [a] where ... -- (C)
3819 instance context4 => C Int [Int] where ... -- (D)
3821 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3822 but (C) and (D) do not. When matching, GHC takes
3823 no account of the context of the instance declaration
3824 (<literal>context1</literal> etc).
3825 GHC's default behaviour is that <emphasis>exactly one instance must match the
3826 constraint it is trying to resolve</emphasis>.
3827 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3828 including both declarations (A) and (B), say); an error is only reported if a
3829 particular constraint matches more than one.
3833 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3834 more than one instance to match, provided there is a most specific one. For
3835 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3836 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3837 most-specific match, the program is rejected.
3840 However, GHC is conservative about committing to an overlapping instance. For example:
3845 Suppose that from the RHS of <literal>f</literal> we get the constraint
3846 <literal>C Int [b]</literal>. But
3847 GHC does not commit to instance (C), because in a particular
3848 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3849 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3850 So GHC rejects the program.
3851 (If you add the flag <option>-XIncoherentInstances</option>,
3852 GHC will instead pick (C), without complaining about
3853 the problem of subsequent instantiations.)
3856 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3857 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3858 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3859 it instead. In this case, GHC will refrain from
3860 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3861 as before) but, rather than rejecting the program, it will infer the type
3863 f :: C Int [b] => [b] -> [b]
3865 That postpones the question of which instance to pick to the
3866 call site for <literal>f</literal>
3867 by which time more is known about the type <literal>b</literal>.
3868 You can write this type signature yourself if you use the
3869 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3873 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3877 instance Foo [b] where
3880 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3881 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3882 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3883 declaration. The solution is to postpone the choice by adding the constraint to the context
3884 of the instance declaration, thus:
3886 instance C Int [b] => Foo [b] where
3889 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3892 The willingness to be overlapped or incoherent is a property of
3893 the <emphasis>instance declaration</emphasis> itself, controlled by the
3894 presence or otherwise of the <option>-XOverlappingInstances</option>
3895 and <option>-XIncoherentInstances</option> flags when that module is
3896 being defined. Neither flag is required in a module that imports and uses the
3897 instance declaration. Specifically, during the lookup process:
3900 An instance declaration is ignored during the lookup process if (a) a more specific
3901 match is found, and (b) the instance declaration was compiled with
3902 <option>-XOverlappingInstances</option>. The flag setting for the
3903 more-specific instance does not matter.
3906 Suppose an instance declaration does not match the constraint being looked up, but
3907 does unify with it, so that it might match when the constraint is further
3908 instantiated. Usually GHC will regard this as a reason for not committing to
3909 some other constraint. But if the instance declaration was compiled with
3910 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3911 check for that declaration.
3914 These rules make it possible for a library author to design a library that relies on
3915 overlapping instances without the library client having to know.
3918 If an instance declaration is compiled without
3919 <option>-XOverlappingInstances</option>,
3920 then that instance can never be overlapped. This could perhaps be
3921 inconvenient. Perhaps the rule should instead say that the
3922 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3923 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3924 at a usage site should be permitted regardless of how the instance declarations
3925 are compiled, if the <option>-XOverlappingInstances</option> flag is
3926 used at the usage site. (Mind you, the exact usage site can occasionally be
3927 hard to pin down.) We are interested to receive feedback on these points.
3929 <para>The <option>-XIncoherentInstances</option> flag implies the
3930 <option>-XOverlappingInstances</option> flag, but not vice versa.
3938 <sect2 id="overloaded-strings">
3939 <title>Overloaded string literals
3943 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3944 string literal has type <literal>String</literal>, but with overloaded string
3945 literals enabled (with <literal>-XOverloadedStrings</literal>)
3946 a string literal has type <literal>(IsString a) => a</literal>.
3949 This means that the usual string syntax can be used, e.g., for packed strings
3950 and other variations of string like types. String literals behave very much
3951 like integer literals, i.e., they can be used in both expressions and patterns.
3952 If used in a pattern the literal with be replaced by an equality test, in the same
3953 way as an integer literal is.
3956 The class <literal>IsString</literal> is defined as:
3958 class IsString a where
3959 fromString :: String -> a
3961 The only predefined instance is the obvious one to make strings work as usual:
3963 instance IsString [Char] where
3966 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3967 it explicitly (for example, to give an instance declaration for it), you can import it
3968 from module <literal>GHC.Exts</literal>.
3971 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
3975 Each type in a default declaration must be an
3976 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
3980 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
3981 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
3982 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
3983 <emphasis>or</emphasis> <literal>IsString</literal>.
3992 import GHC.Exts( IsString(..) )
3994 newtype MyString = MyString String deriving (Eq, Show)
3995 instance IsString MyString where
3996 fromString = MyString
3998 greet :: MyString -> MyString
3999 greet "hello" = "world"
4003 print $ greet "hello"
4004 print $ greet "fool"
4008 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4009 to work since it gets translated into an equality comparison.
4015 <sect1 id="type-families">
4016 <title>Type families</title>
4019 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4020 facilitate type-level
4021 programming. Type families are a generalisation of <firstterm>associated
4022 data types</firstterm>
4023 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4024 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4025 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4026 Symposium on Principles of Programming Languages (POPL'05)”, pages
4027 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4028 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4029 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4031 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4032 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4033 themselves are described in the paper “<ulink
4034 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4035 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4037 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4038 13th ACM SIGPLAN International Conference on Functional
4039 Programming”, ACM Press, pages 51-62, 2008. Type families
4040 essentially provide type-indexed data types and named functions on types,
4041 which are useful for generic programming and highly parameterised library
4042 interfaces as well as interfaces with enhanced static information, much like
4043 dependent types. They might also be regarded as an alternative to functional
4044 dependencies, but provide a more functional style of type-level programming
4045 than the relational style of functional dependencies.
4048 Indexed type families, or type families for short, are type constructors that
4049 represent sets of types. Set members are denoted by supplying the type family
4050 constructor with type parameters, which are called <firstterm>type
4051 indices</firstterm>. The
4052 difference between vanilla parametrised type constructors and family
4053 constructors is much like between parametrically polymorphic functions and
4054 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4055 behave the same at all type instances, whereas class methods can change their
4056 behaviour in dependence on the class type parameters. Similarly, vanilla type
4057 constructors imply the same data representation for all type instances, but
4058 family constructors can have varying representation types for varying type
4062 Indexed type families come in two flavours: <firstterm>data
4063 families</firstterm> and <firstterm>type synonym
4064 families</firstterm>. They are the indexed family variants of algebraic
4065 data types and type synonyms, respectively. The instances of data families
4066 can be data types and newtypes.
4069 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4070 Additional information on the use of type families in GHC is available on
4071 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4072 Haskell wiki page on type families</ulink>.
4075 <sect2 id="data-families">
4076 <title>Data families</title>
4079 Data families appear in two flavours: (1) they can be defined on the
4081 or (2) they can appear inside type classes (in which case they are known as
4082 associated types). The former is the more general variant, as it lacks the
4083 requirement for the type-indexes to coincide with the class
4084 parameters. However, the latter can lead to more clearly structured code and
4085 compiler warnings if some type instances were - possibly accidentally -
4086 omitted. In the following, we always discuss the general toplevel form first
4087 and then cover the additional constraints placed on associated types.
4090 <sect3 id="data-family-declarations">
4091 <title>Data family declarations</title>
4094 Indexed data families are introduced by a signature, such as
4096 data family GMap k :: * -> *
4098 The special <literal>family</literal> distinguishes family from standard
4099 data declarations. The result kind annotation is optional and, as
4100 usual, defaults to <literal>*</literal> if omitted. An example is
4104 Named arguments can also be given explicit kind signatures if needed.
4106 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4107 declarations] named arguments are entirely optional, so that we can
4108 declare <literal>Array</literal> alternatively with
4110 data family Array :: * -> *
4114 <sect4 id="assoc-data-family-decl">
4115 <title>Associated data family declarations</title>
4117 When a data family is declared as part of a type class, we drop
4118 the <literal>family</literal> special. The <literal>GMap</literal>
4119 declaration takes the following form
4121 class GMapKey k where
4122 data GMap k :: * -> *
4125 In contrast to toplevel declarations, named arguments must be used for
4126 all type parameters that are to be used as type-indexes. Moreover,
4127 the argument names must be class parameters. Each class parameter may
4128 only be used at most once per associated type, but some may be omitted
4129 and they may be in an order other than in the class head. Hence, the
4130 following contrived example is admissible:
4139 <sect3 id="data-instance-declarations">
4140 <title>Data instance declarations</title>
4143 Instance declarations of data and newtype families are very similar to
4144 standard data and newtype declarations. The only two differences are
4145 that the keyword <literal>data</literal> or <literal>newtype</literal>
4146 is followed by <literal>instance</literal> and that some or all of the
4147 type arguments can be non-variable types, but may not contain forall
4148 types or type synonym families. However, data families are generally
4149 allowed in type parameters, and type synonyms are allowed as long as
4150 they are fully applied and expand to a type that is itself admissible -
4151 exactly as this is required for occurrences of type synonyms in class
4152 instance parameters. For example, the <literal>Either</literal>
4153 instance for <literal>GMap</literal> is
4155 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4157 In this example, the declaration has only one variant. In general, it
4161 Data and newtype instance declarations are only permitted when an
4162 appropriate family declaration is in scope - just as a class instance declaratoin
4163 requires the class declaration to be visible. Moreover, each instance
4164 declaration has to conform to the kind determined by its family
4165 declaration. This implies that the number of parameters of an instance
4166 declaration matches the arity determined by the kind of the family.
4169 A data family instance declaration can use the full exprssiveness of
4170 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4172 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with