1 <?xml version="1.0" encoding="iso-8859-1"?>
3 <indexterm><primary>language, GHC</primary></indexterm>
4 <indexterm><primary>extensions, GHC</primary></indexterm>
5 As with all known Haskell systems, GHC implements some extensions to
6 the language. They are all enabled by options; by default GHC
7 understands only plain Haskell 98.
11 Some of the Glasgow extensions serve to give you access to the
12 underlying facilities with which we implement Haskell. Thus, you can
13 get at the Raw Iron, if you are willing to write some non-portable
14 code at a more primitive level. You need not be “stuck”
15 on performance because of the implementation costs of Haskell's
16 “high-level” features—you can always code
17 “under” them. In an extreme case, you can write all your
18 time-critical code in C, and then just glue it together with Haskell!
22 Before you get too carried away working at the lowest level (e.g.,
23 sloshing <literal>MutableByteArray#</literal>s around your
24 program), you may wish to check if there are libraries that provide a
25 “Haskellised veneer” over the features you want. The
26 separate <ulink url="../libraries/index.html">libraries
27 documentation</ulink> describes all the libraries that come with GHC.
30 <!-- LANGUAGE OPTIONS -->
31 <sect1 id="options-language">
32 <title>Language options</title>
34 <indexterm><primary>language</primary><secondary>option</secondary>
36 <indexterm><primary>options</primary><secondary>language</secondary>
38 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
41 <para>The language option flags control what variation of the language are
42 permitted. Leaving out all of them gives you standard Haskell
45 <para>Language options can be controlled in two ways:
47 <listitem><para>Every language option can switched on by a command-line flag "<option>-X...</option>"
48 (e.g. <option>-XTemplateHaskell</option>), and switched off by the flag "<option>-XNo...</option>";
49 (e.g. <option>-XNoTemplateHaskell</option>).</para></listitem>
51 Language options recognised by Cabal can also be enabled using the <literal>LANGUAGE</literal> pragma,
52 thus <literal>{-# LANGUAGE TemplateHaskell #-}</literal> (see <xref linkend="language-pragma"/>). </para>
54 </itemizedlist></para>
56 <para>The flag <option>-fglasgow-exts</option>
57 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
58 is equivalent to enabling the following extensions:
59 <option>-XPrintExplicitForalls</option>,
60 <option>-XForeignFunctionInterface</option>,
61 <option>-XUnliftedFFITypes</option>,
62 <option>-XGADTs</option>,
63 <option>-XImplicitParams</option>,
64 <option>-XScopedTypeVariables</option>,
65 <option>-XUnboxedTuples</option>,
66 <option>-XTypeSynonymInstances</option>,
67 <option>-XStandaloneDeriving</option>,
68 <option>-XDeriveDataTypeable</option>,
69 <option>-XFlexibleContexts</option>,
70 <option>-XFlexibleInstances</option>,
71 <option>-XConstrainedClassMethods</option>,
72 <option>-XMultiParamTypeClasses</option>,
73 <option>-XFunctionalDependencies</option>,
74 <option>-XMagicHash</option>,
75 <option>-XPolymorphicComponents</option>,
76 <option>-XExistentialQuantification</option>,
77 <option>-XUnicodeSyntax</option>,
78 <option>-XPostfixOperators</option>,
79 <option>-XPatternGuards</option>,
80 <option>-XLiberalTypeSynonyms</option>,
81 <option>-XExplicitForAll</option>,
82 <option>-XRankNTypes</option>,
83 <option>-XImpredicativeTypes</option>,
84 <option>-XTypeOperators</option>,
85 <option>-XDoRec</option>,
86 <option>-XParallelListComp</option>,
87 <option>-XEmptyDataDecls</option>,
88 <option>-XKindSignatures</option>,
89 <option>-XGeneralizedNewtypeDeriving</option>,
90 <option>-XTypeFamilies</option>.
91 Enabling these options is the <emphasis>only</emphasis>
92 effect of <option>-fglasgow-exts</option>.
93 We are trying to move away from this portmanteau flag,
94 and towards enabling features individually.</para>
98 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
99 <sect1 id="primitives">
100 <title>Unboxed types and primitive operations</title>
102 <para>GHC is built on a raft of primitive data types and operations;
103 "primitive" in the sense that they cannot be defined in Haskell itself.
104 While you really can use this stuff to write fast code,
105 we generally find it a lot less painful, and more satisfying in the
106 long run, to use higher-level language features and libraries. With
107 any luck, the code you write will be optimised to the efficient
108 unboxed version in any case. And if it isn't, we'd like to know
111 <para>All these primitive data types and operations are exported by the
112 library <literal>GHC.Prim</literal>, for which there is
113 <ulink url="../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
864 The do-notation of Haskell 98 does not allow <emphasis>recursive bindings</emphasis>,
865 that is, the variables bound in a do-expression are visible only in the textually following
866 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
867 group. It turns out that several applications can benefit from recursive bindings in
868 the do-notation. The <option>-XDoRec</option> flag provides the necessary syntactic support.
871 Here is a simple (albeit contrived) example:
873 {-# LANGUAGE DoRec #-}
874 justOnes = do { rec { xs <- Just (1:xs) }
875 ; return (map negate xs) }
877 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
880 The background and motivation for recusrive do-notation is described in
881 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
882 by Levent Erkok, John Launchbury,
883 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
884 The theory behind monadic value recursion is explained further in Erkok's thesis
885 <ulink url="http://sites.google.com/site/leventerkok/erkok-thesis.pdf">Value Recursion in Monadic Computations</ulink>.
886 However, note that GHC uses a different syntax than the one described in these documents.
890 <title>Details of recursive do-notation</title>
892 The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
893 the LANGUAGE pragma <option>DoRec</option>. It introduces the single new keyword "<literal>rec</literal>",
894 which wraps a mutually-recursive group of monadic statements,
895 producing a single statement.
897 <para>Similar to a <literal>let</literal>
898 statement, the variables bound in the <literal>rec</literal> are
899 visible throughout the <literal>rec</literal> group, and below it.
902 do { a <- getChar do { a <- getChar
903 ; let { r1 = f a r2 ; rec { r1 <- f a r2
904 ; r2 = g r1 } ; r2 <- g r1 }
905 ; return (r1 ++ r2) } ; return (r1 ++ r2) }
907 In both cases, <literal>r1</literal> and <literal>r2</literal> are
908 available both throughout the <literal>let</literal> or <literal>rec</literal> block, and
909 in the statements that follow it. The difference is that <literal>let</literal> is non-monadic,
910 while <literal>rec</literal> is monadic. (In Haskell <literal>let</literal> is
911 really <literal>letrec</literal>, of course.)
914 The static and dynamic semantics of <literal>rec</literal> can be described as follows:
918 similar to let-bindings, the <literal>rec</literal> is broken into
919 minimal recursive groups, a process known as <emphasis>segmentation</emphasis>.
922 rec { a <- getChar ===> a <- getChar
923 ; b <- f a c rec { b <- f a c
924 ; c <- f b a ; c <- f b a }
925 ; putChar c } putChar c
927 The details of segmentation are described in Section 3.2 of
928 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>.
929 Segmentation improves polymorphism, reduces the size of the recursive "knot", and, as the paper
930 describes, also has a semantic effect (unless the monad satisfies the right-shrinking law).
933 Then each resulting <literal>rec</literal> is desugared, using a call to <literal>Control.Monad.Fix.mfix</literal>.
934 For example, the <literal>rec</literal> group in the preceding example is desugared like this:
936 rec { b <- f a c ===> (b,c) <- mfix (\~(b,c) -> do { b <- f a c
937 ; c <- f b a } ; c <- f b a
940 In general, the statment <literal>rec <replaceable>ss</replaceable></literal>
941 is desugared to the statement
943 <replaceable>vs</replaceable> <- mfix (\~<replaceable>vs</replaceable> -> do { <replaceable>ss</replaceable>; return <replaceable>vs</replaceable> })
945 where <replaceable>vs</replaceable> is a tuple of the variables bound by <replaceable>ss</replaceable>.
947 The original <literal>rec</literal> typechecks exactly
948 when the above desugared version would do so. For example, this means that
949 the variables <replaceable>vs</replaceable> are all monomorphic in the statements
950 following the <literal>rec</literal>, because they are bound by a lambda.
953 The <literal>mfix</literal> function is defined in the <literal>MonadFix</literal>
954 class, in <literal>Control.Monad.Fix</literal>, thus:
956 class Monad m => MonadFix m where
957 mfix :: (a -> m a) -> m a
964 Here are some other important points in using the recursive-do notation:
967 It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
968 <literal>-fglasgow-exts</literal>.
972 If recursive bindings are required for a monad,
973 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
977 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
978 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
979 for Haskell's internal state monad (strict and lazy, respectively).
983 Like <literal>let</literal> and <literal>where</literal> bindings,
984 name shadowing is not allowed within a <literal>rec</literal>;
985 that is, all the names bound in a single <literal>rec</literal> must
986 be distinct (Section 3.3 of the paper).
989 It supports rebindable syntax (see <xref linkend="rebindable-syntax"/>).
995 <sect3> <title> Mdo-notation (deprecated) </title>
997 <para> GHC used to support the flag <option>-XREecursiveDo</option>,
998 which enabled the keyword <literal>mdo</literal>, precisely as described in
999 <ulink url="http://sites.google.com/site/leventerkok/">A recursive do for Haskell</ulink>,
1000 but this is now deprecated. Instead of <literal>mdo { Q; e }</literal>, write
1001 <literal>do { rec Q; e }</literal>.
1004 Historical note: The old implementation of the mdo-notation (and most
1005 of the existing documents) used the name
1006 <literal>MonadRec</literal> for the class and the corresponding library.
1007 This name is not supported by GHC.
1014 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
1016 <sect2 id="parallel-list-comprehensions">
1017 <title>Parallel List Comprehensions</title>
1018 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
1020 <indexterm><primary>parallel list comprehensions</primary>
1023 <para>Parallel list comprehensions are a natural extension to list
1024 comprehensions. List comprehensions can be thought of as a nice
1025 syntax for writing maps and filters. Parallel comprehensions
1026 extend this to include the zipWith family.</para>
1028 <para>A parallel list comprehension has multiple independent
1029 branches of qualifier lists, each separated by a `|' symbol. For
1030 example, the following zips together two lists:</para>
1033 [ (x, y) | x <- xs | y <- ys ]
1036 <para>The behavior of parallel list comprehensions follows that of
1037 zip, in that the resulting list will have the same length as the
1038 shortest branch.</para>
1040 <para>We can define parallel list comprehensions by translation to
1041 regular comprehensions. Here's the basic idea:</para>
1043 <para>Given a parallel comprehension of the form: </para>
1046 [ e | p1 <- e11, p2 <- e12, ...
1047 | q1 <- e21, q2 <- e22, ...
1052 <para>This will be translated to: </para>
1055 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1056 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1061 <para>where `zipN' is the appropriate zip for the given number of
1066 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1068 <sect2 id="generalised-list-comprehensions">
1069 <title>Generalised (SQL-Like) List Comprehensions</title>
1070 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1072 <indexterm><primary>extended list comprehensions</primary>
1074 <indexterm><primary>group</primary></indexterm>
1075 <indexterm><primary>sql</primary></indexterm>
1078 <para>Generalised list comprehensions are a further enhancement to the
1079 list comprehension syntactic sugar to allow operations such as sorting
1080 and grouping which are familiar from SQL. They are fully described in the
1081 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1082 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1083 except that the syntax we use differs slightly from the paper.</para>
1084 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1085 <para>Here is an example:
1087 employees = [ ("Simon", "MS", 80)
1088 , ("Erik", "MS", 100)
1089 , ("Phil", "Ed", 40)
1090 , ("Gordon", "Ed", 45)
1091 , ("Paul", "Yale", 60)]
1093 output = [ (the dept, sum salary)
1094 | (name, dept, salary) <- employees
1095 , then group by dept
1096 , then sortWith by (sum salary)
1099 In this example, the list <literal>output</literal> would take on
1103 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1106 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1107 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1108 function that is exported by <literal>GHC.Exts</literal>.)</para>
1110 <para>There are five new forms of comprehension qualifier,
1111 all introduced by the (existing) keyword <literal>then</literal>:
1119 This statement requires that <literal>f</literal> have the type <literal>
1120 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1121 motivating example, as this form is used to apply <literal>take 5</literal>.
1132 This form is similar to the previous one, but allows you to create a function
1133 which will be passed as the first argument to f. As a consequence f must have
1134 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1135 from the type, this function lets f "project out" some information
1136 from the elements of the list it is transforming.</para>
1138 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1139 is supplied with a function that lets it find out the <literal>sum salary</literal>
1140 for any item in the list comprehension it transforms.</para>
1148 then group by e using f
1151 <para>This is the most general of the grouping-type statements. In this form,
1152 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1153 As with the <literal>then f by e</literal> case above, the first argument
1154 is a function supplied to f by the compiler which lets it compute e on every
1155 element of the list being transformed. However, unlike the non-grouping case,
1156 f additionally partitions the list into a number of sublists: this means that
1157 at every point after this statement, binders occurring before it in the comprehension
1158 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1159 this, let's look at an example:</para>
1162 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1163 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1164 groupRuns f = groupBy (\x y -> f x == f y)
1166 output = [ (the x, y)
1167 | x <- ([1..3] ++ [1..2])
1169 , then group by x using groupRuns ]
1172 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1175 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1178 <para>Note that we have used the <literal>the</literal> function to change the type
1179 of x from a list to its original numeric type. The variable y, in contrast, is left
1180 unchanged from the list form introduced by the grouping.</para>
1190 <para>This form of grouping is essentially the same as the one described above. However,
1191 since no function to use for the grouping has been supplied it will fall back on the
1192 <literal>groupWith</literal> function defined in
1193 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1194 is the form of the group statement that we made use of in the opening example.</para>
1205 <para>With this form of the group statement, f is required to simply have the type
1206 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1207 comprehension so far directly. An example of this form is as follows:</para>
1213 , then group using inits]
1216 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1219 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1227 <!-- ===================== REBINDABLE SYNTAX =================== -->
1229 <sect2 id="rebindable-syntax">
1230 <title>Rebindable syntax and the implicit Prelude import</title>
1232 <para><indexterm><primary>-XNoImplicitPrelude
1233 option</primary></indexterm> GHC normally imports
1234 <filename>Prelude.hi</filename> files for you. If you'd
1235 rather it didn't, then give it a
1236 <option>-XNoImplicitPrelude</option> option. The idea is
1237 that you can then import a Prelude of your own. (But don't
1238 call it <literal>Prelude</literal>; the Haskell module
1239 namespace is flat, and you must not conflict with any
1240 Prelude module.)</para>
1242 <para>Suppose you are importing a Prelude of your own
1243 in order to define your own numeric class
1244 hierarchy. It completely defeats that purpose if the
1245 literal "1" means "<literal>Prelude.fromInteger
1246 1</literal>", which is what the Haskell Report specifies.
1247 So the <option>-XNoImplicitPrelude</option>
1248 flag <emphasis>also</emphasis> causes
1249 the following pieces of built-in syntax to refer to
1250 <emphasis>whatever is in scope</emphasis>, not the Prelude
1254 <para>An integer literal <literal>368</literal> means
1255 "<literal>fromInteger (368::Integer)</literal>", rather than
1256 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1259 <listitem><para>Fractional literals are handed in just the same way,
1260 except that the translation is
1261 <literal>fromRational (3.68::Rational)</literal>.
1264 <listitem><para>The equality test in an overloaded numeric pattern
1265 uses whatever <literal>(==)</literal> is in scope.
1268 <listitem><para>The subtraction operation, and the
1269 greater-than-or-equal test, in <literal>n+k</literal> patterns
1270 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1274 <para>Negation (e.g. "<literal>- (f x)</literal>")
1275 means "<literal>negate (f x)</literal>", both in numeric
1276 patterns, and expressions.
1280 <para>"Do" notation is translated using whatever
1281 functions <literal>(>>=)</literal>,
1282 <literal>(>>)</literal>, and <literal>fail</literal>,
1283 are in scope (not the Prelude
1284 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1285 comprehensions, are unaffected. </para></listitem>
1289 notation (see <xref linkend="arrow-notation"/>)
1290 uses whatever <literal>arr</literal>,
1291 <literal>(>>>)</literal>, <literal>first</literal>,
1292 <literal>app</literal>, <literal>(|||)</literal> and
1293 <literal>loop</literal> functions are in scope. But unlike the
1294 other constructs, the types of these functions must match the
1295 Prelude types very closely. Details are in flux; if you want
1299 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1300 even if that is a little unexpected. For example, the
1301 static semantics of the literal <literal>368</literal>
1302 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1303 <literal>fromInteger</literal> to have any of the types:
1305 fromInteger :: Integer -> Integer
1306 fromInteger :: forall a. Foo a => Integer -> a
1307 fromInteger :: Num a => a -> Integer
1308 fromInteger :: Integer -> Bool -> Bool
1312 <para>Be warned: this is an experimental facility, with
1313 fewer checks than usual. Use <literal>-dcore-lint</literal>
1314 to typecheck the desugared program. If Core Lint is happy
1315 you should be all right.</para>
1319 <sect2 id="postfix-operators">
1320 <title>Postfix operators</title>
1323 The <option>-XPostfixOperators</option> flag enables a small
1324 extension to the syntax of left operator sections, which allows you to
1325 define postfix operators. The extension is this: the left section
1329 is equivalent (from the point of view of both type checking and execution) to the expression
1333 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1334 The strict Haskell 98 interpretation is that the section is equivalent to
1338 That is, the operator must be a function of two arguments. GHC allows it to
1339 take only one argument, and that in turn allows you to write the function
1342 <para>The extension does not extend to the left-hand side of function
1343 definitions; you must define such a function in prefix form.</para>
1347 <sect2 id="tuple-sections">
1348 <title>Tuple sections</title>
1351 The <option>-XTupleSections</option> flag enables Python-style partially applied
1352 tuple constructors. For example, the following program
1356 is considered to be an alternative notation for the more unwieldy alternative
1360 You can omit any combination of arguments to the tuple, as in the following
1362 (, "I", , , "Love", , 1337)
1366 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1371 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1372 will also be available for them, like so
1376 Because there is no unboxed unit tuple, the following expression
1380 continues to stand for the unboxed singleton tuple data constructor.
1385 <sect2 id="disambiguate-fields">
1386 <title>Record field disambiguation</title>
1388 In record construction and record pattern matching
1389 it is entirely unambiguous which field is referred to, even if there are two different
1390 data types in scope with a common field name. For example:
1393 data S = MkS { x :: Int, y :: Bool }
1398 data T = MkT { x :: Int }
1400 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1401 ok2 n = MkT { x = n+1 } -- Unambiguous
1403 bad1 k = k { x = 3 } -- Ambiguous
1404 bad2 k = x k -- Ambiguous
1406 Even though there are two <literal>x</literal>'s in scope,
1407 it is clear that the <literal>x</literal> in the pattern in the
1408 definition of <literal>ok1</literal> can only mean the field
1409 <literal>x</literal> from type <literal>S</literal>. Similarly for
1410 the function <literal>ok2</literal>. However, in the record update
1411 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1412 it is not clear which of the two types is intended.
1415 Haskell 98 regards all four as ambiguous, but with the
1416 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1417 the former two. The rules are precisely the same as those for instance
1418 declarations in Haskell 98, where the method names on the left-hand side
1419 of the method bindings in an instance declaration refer unambiguously
1420 to the method of that class (provided they are in scope at all), even
1421 if there are other variables in scope with the same name.
1422 This reduces the clutter of qualified names when you import two
1423 records from different modules that use the same field name.
1429 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1434 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1439 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1440 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1441 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1444 import qualified M -- Note qualified
1446 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1448 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1449 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1450 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1451 is not. (In effect, it is qualified by the constructor.)
1458 <!-- ===================== Record puns =================== -->
1460 <sect2 id="record-puns">
1465 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1469 When using records, it is common to write a pattern that binds a
1470 variable with the same name as a record field, such as:
1473 data C = C {a :: Int}
1479 Record punning permits the variable name to be elided, so one can simply
1486 to mean the same pattern as above. That is, in a record pattern, the
1487 pattern <literal>a</literal> expands into the pattern <literal>a =
1488 a</literal> for the same name <literal>a</literal>.
1495 Record punning can also be used in an expression, writing, for example,
1501 let a = 1 in C {a = a}
1503 The expansion is purely syntactic, so the expanded right-hand side
1504 expression refers to the nearest enclosing variable that is spelled the
1505 same as the field name.
1509 Puns and other patterns can be mixed in the same record:
1511 data C = C {a :: Int, b :: Int}
1512 f (C {a, b = 4}) = a
1517 Puns can be used wherever record patterns occur (e.g. in
1518 <literal>let</literal> bindings or at the top-level).
1522 A pun on a qualified field name is expanded by stripping off the module qualifier.
1529 f (M.C {M.a = a}) = a
1531 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1532 is only in scope in qualified form.)
1540 <!-- ===================== Record wildcards =================== -->
1542 <sect2 id="record-wildcards">
1543 <title>Record wildcards
1547 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1548 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1552 For records with many fields, it can be tiresome to write out each field
1553 individually in a record pattern, as in
1555 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1556 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1561 Record wildcard syntax permits a "<literal>..</literal>" in a record
1562 pattern, where each elided field <literal>f</literal> is replaced by the
1563 pattern <literal>f = f</literal>. For example, the above pattern can be
1566 f (C {a = 1, ..}) = b + c + d
1574 Wildcards can be mixed with other patterns, including puns
1575 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1576 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1577 wherever record patterns occur, including in <literal>let</literal>
1578 bindings and at the top-level. For example, the top-level binding
1582 defines <literal>b</literal>, <literal>c</literal>, and
1583 <literal>d</literal>.
1587 Record wildcards can also be used in expressions, writing, for example,
1589 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1593 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1595 The expansion is purely syntactic, so the record wildcard
1596 expression refers to the nearest enclosing variables that are spelled
1597 the same as the omitted field names.
1601 The "<literal>..</literal>" expands to the missing
1602 <emphasis>in-scope</emphasis> record fields, where "in scope"
1603 includes both unqualified and qualified-only.
1604 Any fields that are not in scope are not filled in. For example
1607 data R = R { a,b,c :: Int }
1609 import qualified M( R(a,b) )
1612 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1613 omitting <literal>c</literal> since it is not in scope at all.
1620 <!-- ===================== Local fixity declarations =================== -->
1622 <sect2 id="local-fixity-declarations">
1623 <title>Local Fixity Declarations
1626 <para>A careful reading of the Haskell 98 Report reveals that fixity
1627 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1628 <literal>infixr</literal>) are permitted to appear inside local bindings
1629 such those introduced by <literal>let</literal> and
1630 <literal>where</literal>. However, the Haskell Report does not specify
1631 the semantics of such bindings very precisely.
1634 <para>In GHC, a fixity declaration may accompany a local binding:
1641 and the fixity declaration applies wherever the binding is in scope.
1642 For example, in a <literal>let</literal>, it applies in the right-hand
1643 sides of other <literal>let</literal>-bindings and the body of the
1644 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1645 expressions (<xref linkend="mdo-notation"/>), the local fixity
1646 declarations of a <literal>let</literal> statement scope over other
1647 statements in the group, just as the bound name does.
1651 Moreover, a local fixity declaration *must* accompany a local binding of
1652 that name: it is not possible to revise the fixity of name bound
1655 let infixr 9 $ in ...
1658 Because local fixity declarations are technically Haskell 98, no flag is
1659 necessary to enable them.
1663 <sect2 id="package-imports">
1664 <title>Package-qualified imports</title>
1666 <para>With the <option>-XPackageImports</option> flag, GHC allows
1667 import declarations to be qualified by the package name that the
1668 module is intended to be imported from. For example:</para>
1671 import "network" Network.Socket
1674 <para>would import the module <literal>Network.Socket</literal> from
1675 the package <literal>network</literal> (any version). This may
1676 be used to disambiguate an import when the same module is
1677 available from multiple packages, or is present in both the
1678 current package being built and an external package.</para>
1680 <para>Note: you probably don't need to use this feature, it was
1681 added mainly so that we can build backwards-compatible versions of
1682 packages when APIs change. It can lead to fragile dependencies in
1683 the common case: modules occasionally move from one package to
1684 another, rendering any package-qualified imports broken.</para>
1687 <sect2 id="syntax-stolen">
1688 <title>Summary of stolen syntax</title>
1690 <para>Turning on an option that enables special syntax
1691 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1692 to compile, perhaps because it uses a variable name which has
1693 become a reserved word. This section lists the syntax that is
1694 "stolen" by language extensions.
1696 notation and nonterminal names from the Haskell 98 lexical syntax
1697 (see the Haskell 98 Report).
1698 We only list syntax changes here that might affect
1699 existing working programs (i.e. "stolen" syntax). Many of these
1700 extensions will also enable new context-free syntax, but in all
1701 cases programs written to use the new syntax would not be
1702 compilable without the option enabled.</para>
1704 <para>There are two classes of special
1709 <para>New reserved words and symbols: character sequences
1710 which are no longer available for use as identifiers in the
1714 <para>Other special syntax: sequences of characters that have
1715 a different meaning when this particular option is turned
1720 The following syntax is stolen:
1725 <literal>forall</literal>
1726 <indexterm><primary><literal>forall</literal></primary></indexterm>
1729 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1730 <option>-XScopedTypeVariables</option>,
1731 <option>-XLiberalTypeSynonyms</option>,
1732 <option>-XRank2Types</option>,
1733 <option>-XRankNTypes</option>,
1734 <option>-XPolymorphicComponents</option>,
1735 <option>-XExistentialQuantification</option>
1741 <literal>mdo</literal>
1742 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1745 Stolen by: <option>-XRecursiveDo</option>,
1751 <literal>foreign</literal>
1752 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1755 Stolen by: <option>-XForeignFunctionInterface</option>,
1761 <literal>rec</literal>,
1762 <literal>proc</literal>, <literal>-<</literal>,
1763 <literal>>-</literal>, <literal>-<<</literal>,
1764 <literal>>>-</literal>, and <literal>(|</literal>,
1765 <literal>|)</literal> brackets
1766 <indexterm><primary><literal>proc</literal></primary></indexterm>
1769 Stolen by: <option>-XArrows</option>,
1775 <literal>?<replaceable>varid</replaceable></literal>,
1776 <literal>%<replaceable>varid</replaceable></literal>
1777 <indexterm><primary>implicit parameters</primary></indexterm>
1780 Stolen by: <option>-XImplicitParams</option>,
1786 <literal>[|</literal>,
1787 <literal>[e|</literal>, <literal>[p|</literal>,
1788 <literal>[d|</literal>, <literal>[t|</literal>,
1789 <literal>$(</literal>,
1790 <literal>$<replaceable>varid</replaceable></literal>
1791 <indexterm><primary>Template Haskell</primary></indexterm>
1794 Stolen by: <option>-XTemplateHaskell</option>,
1800 <literal>[:<replaceable>varid</replaceable>|</literal>
1801 <indexterm><primary>quasi-quotation</primary></indexterm>
1804 Stolen by: <option>-XQuasiQuotes</option>,
1810 <replaceable>varid</replaceable>{<literal>#</literal>},
1811 <replaceable>char</replaceable><literal>#</literal>,
1812 <replaceable>string</replaceable><literal>#</literal>,
1813 <replaceable>integer</replaceable><literal>#</literal>,
1814 <replaceable>float</replaceable><literal>#</literal>,
1815 <replaceable>float</replaceable><literal>##</literal>,
1816 <literal>(#</literal>, <literal>#)</literal>,
1819 Stolen by: <option>-XMagicHash</option>,
1828 <!-- TYPE SYSTEM EXTENSIONS -->
1829 <sect1 id="data-type-extensions">
1830 <title>Extensions to data types and type synonyms</title>
1832 <sect2 id="nullary-types">
1833 <title>Data types with no constructors</title>
1835 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1836 a data type with no constructors. For example:</para>
1840 data T a -- T :: * -> *
1843 <para>Syntactically, the declaration lacks the "= constrs" part. The
1844 type can be parameterised over types of any kind, but if the kind is
1845 not <literal>*</literal> then an explicit kind annotation must be used
1846 (see <xref linkend="kinding"/>).</para>
1848 <para>Such data types have only one value, namely bottom.
1849 Nevertheless, they can be useful when defining "phantom types".</para>
1852 <sect2 id="infix-tycons">
1853 <title>Infix type constructors, classes, and type variables</title>
1856 GHC allows type constructors, classes, and type variables to be operators, and
1857 to be written infix, very much like expressions. More specifically:
1860 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1861 The lexical syntax is the same as that for data constructors.
1864 Data type and type-synonym declarations can be written infix, parenthesised
1865 if you want further arguments. E.g.
1867 data a :*: b = Foo a b
1868 type a :+: b = Either a b
1869 class a :=: b where ...
1871 data (a :**: b) x = Baz a b x
1872 type (a :++: b) y = Either (a,b) y
1876 Types, and class constraints, can be written infix. For example
1879 f :: (a :=: b) => a -> b
1883 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1884 The lexical syntax is the same as that for variable operators, excluding "(.)",
1885 "(!)", and "(*)". In a binding position, the operator must be
1886 parenthesised. For example:
1888 type T (+) = Int + Int
1892 liftA2 :: Arrow (~>)
1893 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1899 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1900 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1903 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1904 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1905 sets the fixity for a data constructor and the corresponding type constructor. For example:
1909 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1910 and similarly for <literal>:*:</literal>.
1911 <literal>Int `a` Bool</literal>.
1914 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1921 <sect2 id="type-synonyms">
1922 <title>Liberalised type synonyms</title>
1925 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1926 on individual synonym declarations.
1927 With the <option>-XLiberalTypeSynonyms</option> extension,
1928 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1929 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1932 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1933 in a type synonym, thus:
1935 type Discard a = forall b. Show b => a -> b -> (a, String)
1940 g :: Discard Int -> (Int,String) -- A rank-2 type
1947 If you also use <option>-XUnboxedTuples</option>,
1948 you can write an unboxed tuple in a type synonym:
1950 type Pr = (# Int, Int #)
1958 You can apply a type synonym to a forall type:
1960 type Foo a = a -> a -> Bool
1962 f :: Foo (forall b. b->b)
1964 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1966 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1971 You can apply a type synonym to a partially applied type synonym:
1973 type Generic i o = forall x. i x -> o x
1976 foo :: Generic Id []
1978 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1980 foo :: forall x. x -> [x]
1988 GHC currently does kind checking before expanding synonyms (though even that
1992 After expanding type synonyms, GHC does validity checking on types, looking for
1993 the following mal-formedness which isn't detected simply by kind checking:
1996 Type constructor applied to a type involving for-alls.
1999 Unboxed tuple on left of an arrow.
2002 Partially-applied type synonym.
2006 this will be rejected:
2008 type Pr = (# Int, Int #)
2013 because GHC does not allow unboxed tuples on the left of a function arrow.
2018 <sect2 id="existential-quantification">
2019 <title>Existentially quantified data constructors
2023 The idea of using existential quantification in data type declarations
2024 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
2025 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
2026 London, 1991). It was later formalised by Laufer and Odersky
2027 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
2028 TOPLAS, 16(5), pp1411-1430, 1994).
2029 It's been in Lennart
2030 Augustsson's <command>hbc</command> Haskell compiler for several years, and
2031 proved very useful. Here's the idea. Consider the declaration:
2037 data Foo = forall a. MkFoo a (a -> Bool)
2044 The data type <literal>Foo</literal> has two constructors with types:
2050 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2057 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2058 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2059 For example, the following expression is fine:
2065 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2071 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2072 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2073 isUpper</function> packages a character with a compatible function. These
2074 two things are each of type <literal>Foo</literal> and can be put in a list.
2078 What can we do with a value of type <literal>Foo</literal>?. In particular,
2079 what happens when we pattern-match on <function>MkFoo</function>?
2085 f (MkFoo val fn) = ???
2091 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2092 are compatible, the only (useful) thing we can do with them is to
2093 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2100 f (MkFoo val fn) = fn val
2106 What this allows us to do is to package heterogeneous values
2107 together with a bunch of functions that manipulate them, and then treat
2108 that collection of packages in a uniform manner. You can express
2109 quite a bit of object-oriented-like programming this way.
2112 <sect3 id="existential">
2113 <title>Why existential?
2117 What has this to do with <emphasis>existential</emphasis> quantification?
2118 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2124 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2130 But Haskell programmers can safely think of the ordinary
2131 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2132 adding a new existential quantification construct.
2137 <sect3 id="existential-with-context">
2138 <title>Existentials and type classes</title>
2141 An easy extension is to allow
2142 arbitrary contexts before the constructor. For example:
2148 data Baz = forall a. Eq a => Baz1 a a
2149 | forall b. Show b => Baz2 b (b -> b)
2155 The two constructors have the types you'd expect:
2161 Baz1 :: forall a. Eq a => a -> a -> Baz
2162 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2168 But when pattern matching on <function>Baz1</function> the matched values can be compared
2169 for equality, and when pattern matching on <function>Baz2</function> the first matched
2170 value can be converted to a string (as well as applying the function to it).
2171 So this program is legal:
2178 f (Baz1 p q) | p == q = "Yes"
2180 f (Baz2 v fn) = show (fn v)
2186 Operationally, in a dictionary-passing implementation, the
2187 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2188 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2189 extract it on pattern matching.
2194 <sect3 id="existential-records">
2195 <title>Record Constructors</title>
2198 GHC allows existentials to be used with records syntax as well. For example:
2201 data Counter a = forall self. NewCounter
2203 , _inc :: self -> self
2204 , _display :: self -> IO ()
2208 Here <literal>tag</literal> is a public field, with a well-typed selector
2209 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2210 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2211 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2212 compile-time error. In other words, <emphasis>GHC defines a record selector function
2213 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2214 (This example used an underscore in the fields for which record selectors
2215 will not be defined, but that is only programming style; GHC ignores them.)
2219 To make use of these hidden fields, we need to create some helper functions:
2222 inc :: Counter a -> Counter a
2223 inc (NewCounter x i d t) = NewCounter
2224 { _this = i x, _inc = i, _display = d, tag = t }
2226 display :: Counter a -> IO ()
2227 display NewCounter{ _this = x, _display = d } = d x
2230 Now we can define counters with different underlying implementations:
2233 counterA :: Counter String
2234 counterA = NewCounter
2235 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2237 counterB :: Counter String
2238 counterB = NewCounter
2239 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2242 display (inc counterA) -- prints "1"
2243 display (inc (inc counterB)) -- prints "##"
2246 Record update syntax is supported for existentials (and GADTs):
2248 setTag :: Counter a -> a -> Counter a
2249 setTag obj t = obj{ tag = t }
2251 The rule for record update is this: <emphasis>
2252 the types of the updated fields may
2253 mention only the universally-quantified type variables
2254 of the data constructor. For GADTs, the field may mention only types
2255 that appear as a simple type-variable argument in the constructor's result
2256 type</emphasis>. For example:
2258 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2259 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2260 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2261 -- existentially quantified)
2263 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2264 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2265 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2266 -- type-variable argument in G1's result type)
2274 <title>Restrictions</title>
2277 There are several restrictions on the ways in which existentially-quantified
2278 constructors can be use.
2287 When pattern matching, each pattern match introduces a new,
2288 distinct, type for each existential type variable. These types cannot
2289 be unified with any other type, nor can they escape from the scope of
2290 the pattern match. For example, these fragments are incorrect:
2298 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2299 is the result of <function>f1</function>. One way to see why this is wrong is to
2300 ask what type <function>f1</function> has:
2304 f1 :: Foo -> a -- Weird!
2308 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2313 f1 :: forall a. Foo -> a -- Wrong!
2317 The original program is just plain wrong. Here's another sort of error
2321 f2 (Baz1 a b) (Baz1 p q) = a==q
2325 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2326 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2327 from the two <function>Baz1</function> constructors.
2335 You can't pattern-match on an existentially quantified
2336 constructor in a <literal>let</literal> or <literal>where</literal> group of
2337 bindings. So this is illegal:
2341 f3 x = a==b where { Baz1 a b = x }
2344 Instead, use a <literal>case</literal> expression:
2347 f3 x = case x of Baz1 a b -> a==b
2350 In general, you can only pattern-match
2351 on an existentially-quantified constructor in a <literal>case</literal> expression or
2352 in the patterns of a function definition.
2354 The reason for this restriction is really an implementation one.
2355 Type-checking binding groups is already a nightmare without
2356 existentials complicating the picture. Also an existential pattern
2357 binding at the top level of a module doesn't make sense, because it's
2358 not clear how to prevent the existentially-quantified type "escaping".
2359 So for now, there's a simple-to-state restriction. We'll see how
2367 You can't use existential quantification for <literal>newtype</literal>
2368 declarations. So this is illegal:
2372 newtype T = forall a. Ord a => MkT a
2376 Reason: a value of type <literal>T</literal> must be represented as a
2377 pair of a dictionary for <literal>Ord t</literal> and a value of type
2378 <literal>t</literal>. That contradicts the idea that
2379 <literal>newtype</literal> should have no concrete representation.
2380 You can get just the same efficiency and effect by using
2381 <literal>data</literal> instead of <literal>newtype</literal>. If
2382 there is no overloading involved, then there is more of a case for
2383 allowing an existentially-quantified <literal>newtype</literal>,
2384 because the <literal>data</literal> version does carry an
2385 implementation cost, but single-field existentially quantified
2386 constructors aren't much use. So the simple restriction (no
2387 existential stuff on <literal>newtype</literal>) stands, unless there
2388 are convincing reasons to change it.
2396 You can't use <literal>deriving</literal> to define instances of a
2397 data type with existentially quantified data constructors.
2399 Reason: in most cases it would not make sense. For example:;
2402 data T = forall a. MkT [a] deriving( Eq )
2405 To derive <literal>Eq</literal> in the standard way we would need to have equality
2406 between the single component of two <function>MkT</function> constructors:
2410 (MkT a) == (MkT b) = ???
2413 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2414 It's just about possible to imagine examples in which the derived instance
2415 would make sense, but it seems altogether simpler simply to prohibit such
2416 declarations. Define your own instances!
2427 <!-- ====================== Generalised algebraic data types ======================= -->
2429 <sect2 id="gadt-style">
2430 <title>Declaring data types with explicit constructor signatures</title>
2432 <para>GHC allows you to declare an algebraic data type by
2433 giving the type signatures of constructors explicitly. For example:
2437 Just :: a -> Maybe a
2439 The form is called a "GADT-style declaration"
2440 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2441 can only be declared using this form.</para>
2442 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2443 For example, these two declarations are equivalent:
2445 data Foo = forall a. MkFoo a (a -> Bool)
2446 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2449 <para>Any data type that can be declared in standard Haskell-98 syntax
2450 can also be declared using GADT-style syntax.
2451 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2452 they treat class constraints on the data constructors differently.
2453 Specifically, if the constructor is given a type-class context, that
2454 context is made available by pattern matching. For example:
2457 MkSet :: Eq a => [a] -> Set a
2459 makeSet :: Eq a => [a] -> Set a
2460 makeSet xs = MkSet (nub xs)
2462 insert :: a -> Set a -> Set a
2463 insert a (MkSet as) | a `elem` as = MkSet as
2464 | otherwise = MkSet (a:as)
2466 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2467 gives rise to a <literal>(Eq a)</literal>
2468 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2469 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2470 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2471 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2472 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2473 In the example, the equality dictionary is used to satisfy the equality constraint
2474 generated by the call to <literal>elem</literal>, so that the type of
2475 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2478 For example, one possible application is to reify dictionaries:
2480 data NumInst a where
2481 MkNumInst :: Num a => NumInst a
2483 intInst :: NumInst Int
2486 plus :: NumInst a -> a -> a -> a
2487 plus MkNumInst p q = p + q
2489 Here, a value of type <literal>NumInst a</literal> is equivalent
2490 to an explicit <literal>(Num a)</literal> dictionary.
2493 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2494 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2498 = Num a => MkNumInst (NumInst a)
2500 Notice that, unlike the situation when declaring an existential, there is
2501 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2502 data type's universally quantified type variable <literal>a</literal>.
2503 A constructor may have both universal and existential type variables: for example,
2504 the following two declarations are equivalent:
2507 = forall b. (Num a, Eq b) => MkT1 a b
2509 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2512 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2513 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2514 In Haskell 98 the definition
2516 data Eq a => Set' a = MkSet' [a]
2518 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2519 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2520 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2521 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2522 GHC's behaviour is much more useful, as well as much more intuitive.
2526 The rest of this section gives further details about GADT-style data
2531 The result type of each data constructor must begin with the type constructor being defined.
2532 If the result type of all constructors
2533 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2534 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2535 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2539 As with other type signatures, you can give a single signature for several data constructors.
2540 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2549 The type signature of
2550 each constructor is independent, and is implicitly universally quantified as usual.
2551 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2552 have no scope, and different constructors may have different universally-quantified type variables:
2554 data T a where -- The 'a' has no scope
2555 T1,T2 :: b -> T b -- Means forall b. b -> T b
2556 T3 :: T a -- Means forall a. T a
2561 A constructor signature may mention type class constraints, which can differ for
2562 different constructors. For example, this is fine:
2565 T1 :: Eq b => b -> b -> T b
2566 T2 :: (Show c, Ix c) => c -> [c] -> T c
2568 When patten matching, these constraints are made available to discharge constraints
2569 in the body of the match. For example:
2572 f (T1 x y) | x==y = "yes"
2576 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2577 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2578 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2582 Unlike a Haskell-98-style
2583 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2584 have no scope. Indeed, one can write a kind signature instead:
2586 data Set :: * -> * where ...
2588 or even a mixture of the two:
2590 data Bar a :: (* -> *) -> * where ...
2592 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2595 data Bar a (b :: * -> *) where ...
2601 You can use strictness annotations, in the obvious places
2602 in the constructor type:
2605 Lit :: !Int -> Term Int
2606 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2607 Pair :: Term a -> Term b -> Term (a,b)
2612 You can use a <literal>deriving</literal> clause on a GADT-style data type
2613 declaration. For example, these two declarations are equivalent
2615 data Maybe1 a where {
2616 Nothing1 :: Maybe1 a ;
2617 Just1 :: a -> Maybe1 a
2618 } deriving( Eq, Ord )
2620 data Maybe2 a = Nothing2 | Just2 a
2626 The type signature may have quantified type variables that do not appear
2630 MkFoo :: a -> (a->Bool) -> Foo
2633 Here the type variable <literal>a</literal> does not appear in the result type
2634 of either constructor.
2635 Although it is universally quantified in the type of the constructor, such
2636 a type variable is often called "existential".
2637 Indeed, the above declaration declares precisely the same type as
2638 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2640 The type may contain a class context too, of course:
2643 MkShowable :: Show a => a -> Showable
2648 You can use record syntax on a GADT-style data type declaration:
2652 Adult :: { name :: String, children :: [Person] } -> Person
2653 Child :: Show a => { name :: !String, funny :: a } -> Person
2655 As usual, for every constructor that has a field <literal>f</literal>, the type of
2656 field <literal>f</literal> must be the same (modulo alpha conversion).
2657 The <literal>Child</literal> constructor above shows that the signature
2658 may have a context, existentially-quantified variables, and strictness annotations,
2659 just as in the non-record case. (NB: the "type" that follows the double-colon
2660 is not really a type, because of the record syntax and strictness annotations.
2661 A "type" of this form can appear only in a constructor signature.)
2665 Record updates are allowed with GADT-style declarations,
2666 only fields that have the following property: the type of the field
2667 mentions no existential type variables.
2671 As in the case of existentials declared using the Haskell-98-like record syntax
2672 (<xref linkend="existential-records"/>),
2673 record-selector functions are generated only for those fields that have well-typed
2675 Here is the example of that section, in GADT-style syntax:
2677 data Counter a where
2678 NewCounter { _this :: self
2679 , _inc :: self -> self
2680 , _display :: self -> IO ()
2685 As before, only one selector function is generated here, that for <literal>tag</literal>.
2686 Nevertheless, you can still use all the field names in pattern matching and record construction.
2688 </itemizedlist></para>
2692 <title>Generalised Algebraic Data Types (GADTs)</title>
2694 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2695 by allowing constructors to have richer return types. Here is an example:
2698 Lit :: Int -> Term Int
2699 Succ :: Term Int -> Term Int
2700 IsZero :: Term Int -> Term Bool
2701 If :: Term Bool -> Term a -> Term a -> Term a
2702 Pair :: Term a -> Term b -> Term (a,b)
2704 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2705 case with ordinary data types. This generality allows us to
2706 write a well-typed <literal>eval</literal> function
2707 for these <literal>Terms</literal>:
2711 eval (Succ t) = 1 + eval t
2712 eval (IsZero t) = eval t == 0
2713 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2714 eval (Pair e1 e2) = (eval e1, eval e2)
2716 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2717 For example, in the right hand side of the equation
2722 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2723 A precise specification of the type rules is beyond what this user manual aspires to,
2724 but the design closely follows that described in
2726 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2727 unification-based type inference for GADTs</ulink>,
2729 The general principle is this: <emphasis>type refinement is only carried out
2730 based on user-supplied type annotations</emphasis>.
2731 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2732 and lots of obscure error messages will
2733 occur. However, the refinement is quite general. For example, if we had:
2735 eval :: Term a -> a -> a
2736 eval (Lit i) j = i+j
2738 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2739 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2740 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2743 These and many other examples are given in papers by Hongwei Xi, and
2744 Tim Sheard. There is a longer introduction
2745 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2747 <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
2748 may use different notation to that implemented in GHC.
2751 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2752 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2755 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2756 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2757 The result type of each constructor must begin with the type constructor being defined,
2758 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2759 For example, in the <literal>Term</literal> data
2760 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2761 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2766 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2767 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2768 whose result type is not just <literal>T a b</literal>.
2772 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2773 an ordinary data type.
2777 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2781 Lit { val :: Int } :: Term Int
2782 Succ { num :: Term Int } :: Term Int
2783 Pred { num :: Term Int } :: Term Int
2784 IsZero { arg :: Term Int } :: Term Bool
2785 Pair { arg1 :: Term a
2788 If { cnd :: Term Bool
2793 However, for GADTs there is the following additional constraint:
2794 every constructor that has a field <literal>f</literal> must have
2795 the same result type (modulo alpha conversion)
2796 Hence, in the above example, we cannot merge the <literal>num</literal>
2797 and <literal>arg</literal> fields above into a
2798 single name. Although their field types are both <literal>Term Int</literal>,
2799 their selector functions actually have different types:
2802 num :: Term Int -> Term Int
2803 arg :: Term Bool -> Term Int
2808 When pattern-matching against data constructors drawn from a GADT,
2809 for example in a <literal>case</literal> expression, the following rules apply:
2811 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2812 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2813 <listitem><para>The type of any free variable mentioned in any of
2814 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2816 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2817 way to ensure that a variable a rigid type is to give it a type signature.
2818 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2819 Simple unification-based type inference for GADTs
2820 </ulink>. The criteria implemented by GHC are given in the Appendix.
2830 <!-- ====================== End of Generalised algebraic data types ======================= -->
2832 <sect1 id="deriving">
2833 <title>Extensions to the "deriving" mechanism</title>
2835 <sect2 id="deriving-inferred">
2836 <title>Inferred context for deriving clauses</title>
2839 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2842 data T0 f a = MkT0 a deriving( Eq )
2843 data T1 f a = MkT1 (f a) deriving( Eq )
2844 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2846 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2848 instance Eq a => Eq (T0 f a) where ...
2849 instance Eq (f a) => Eq (T1 f a) where ...
2850 instance Eq (f (f a)) => Eq (T2 f a) where ...
2852 The first of these is obviously fine. The second is still fine, although less obviously.
2853 The third is not Haskell 98, and risks losing termination of instances.
2856 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2857 each constraint in the inferred instance context must consist only of type variables,
2858 with no repetitions.
2861 This rule is applied regardless of flags. If you want a more exotic context, you can write
2862 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2866 <sect2 id="stand-alone-deriving">
2867 <title>Stand-alone deriving declarations</title>
2870 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2872 data Foo a = Bar a | Baz String
2874 deriving instance Eq a => Eq (Foo a)
2876 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2877 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2878 Note the following points:
2881 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2882 exactly as you would in an ordinary instance declaration.
2883 (In contrast, in a <literal>deriving</literal> clause
2884 attached to a data type declaration, the context is inferred.)
2888 A <literal>deriving instance</literal> declaration
2889 must obey the same rules concerning form and termination as ordinary instance declarations,
2890 controlled by the same flags; see <xref linkend="instance-decls"/>.
2894 Unlike a <literal>deriving</literal>
2895 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2896 than the data type (assuming you also use
2897 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2900 data Foo a = Bar a | Baz String
2902 deriving instance Eq a => Eq (Foo [a])
2903 deriving instance Eq a => Eq (Foo (Maybe a))
2905 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2906 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2910 Unlike a <literal>deriving</literal>
2911 declaration attached to a <literal>data</literal> declaration,
2912 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2913 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2914 your problem. (GHC will show you the offending code if it has a type error.)
2915 The merit of this is that you can derive instances for GADTs and other exotic
2916 data types, providing only that the boilerplate code does indeed typecheck. For example:
2922 deriving instance Show (T a)
2924 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2925 data type declaration for <literal>T</literal>,
2926 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2927 the instance declaration using stand-alone deriving.
2932 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2933 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2936 newtype Foo a = MkFoo (State Int a)
2938 deriving instance MonadState Int Foo
2940 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2941 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2943 </itemizedlist></para>
2948 <sect2 id="deriving-typeable">
2949 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2952 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2953 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2954 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2955 classes <literal>Eq</literal>, <literal>Ord</literal>,
2956 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2959 GHC extends this list with several more classes that may be automatically derived:
2961 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2962 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2963 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2965 <para>An instance of <literal>Typeable</literal> can only be derived if the
2966 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2967 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2969 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2970 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2972 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2973 are used, and only <literal>Typeable1</literal> up to
2974 <literal>Typeable7</literal> are provided in the library.)
2975 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2976 class, whose kind suits that of the data type constructor, and
2977 then writing the data type instance by hand.
2981 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2982 the class <literal>Functor</literal>,
2983 defined in <literal>GHC.Base</literal>.
2986 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2987 the class <literal>Foldable</literal>,
2988 defined in <literal>Data.Foldable</literal>.
2991 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2992 the class <literal>Traversable</literal>,
2993 defined in <literal>Data.Traversable</literal>.
2996 In each case the appropriate class must be in scope before it
2997 can be mentioned in the <literal>deriving</literal> clause.
3001 <sect2 id="newtype-deriving">
3002 <title>Generalised derived instances for newtypes</title>
3005 When you define an abstract type using <literal>newtype</literal>, you may want
3006 the new type to inherit some instances from its representation. In
3007 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3008 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3009 other classes you have to write an explicit instance declaration. For
3010 example, if you define
3013 newtype Dollars = Dollars Int
3016 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3017 explicitly define an instance of <literal>Num</literal>:
3020 instance Num Dollars where
3021 Dollars a + Dollars b = Dollars (a+b)
3024 All the instance does is apply and remove the <literal>newtype</literal>
3025 constructor. It is particularly galling that, since the constructor
3026 doesn't appear at run-time, this instance declaration defines a
3027 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3028 dictionary, only slower!
3032 <sect3> <title> Generalising the deriving clause </title>
3034 GHC now permits such instances to be derived instead,
3035 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3038 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3041 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3042 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3043 derives an instance declaration of the form
3046 instance Num Int => Num Dollars
3049 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3053 We can also derive instances of constructor classes in a similar
3054 way. For example, suppose we have implemented state and failure monad
3055 transformers, such that
3058 instance Monad m => Monad (State s m)
3059 instance Monad m => Monad (Failure m)
3061 In Haskell 98, we can define a parsing monad by
3063 type Parser tok m a = State [tok] (Failure m) a
3066 which is automatically a monad thanks to the instance declarations
3067 above. With the extension, we can make the parser type abstract,
3068 without needing to write an instance of class <literal>Monad</literal>, via
3071 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3074 In this case the derived instance declaration is of the form
3076 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3079 Notice that, since <literal>Monad</literal> is a constructor class, the
3080 instance is a <emphasis>partial application</emphasis> of the new type, not the
3081 entire left hand side. We can imagine that the type declaration is
3082 "eta-converted" to generate the context of the instance
3087 We can even derive instances of multi-parameter classes, provided the
3088 newtype is the last class parameter. In this case, a ``partial
3089 application'' of the class appears in the <literal>deriving</literal>
3090 clause. For example, given the class
3093 class StateMonad s m | m -> s where ...
3094 instance Monad m => StateMonad s (State s m) where ...
3096 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3098 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3099 deriving (Monad, StateMonad [tok])
3102 The derived instance is obtained by completing the application of the
3103 class to the new type:
3106 instance StateMonad [tok] (State [tok] (Failure m)) =>
3107 StateMonad [tok] (Parser tok m)
3112 As a result of this extension, all derived instances in newtype
3113 declarations are treated uniformly (and implemented just by reusing
3114 the dictionary for the representation type), <emphasis>except</emphasis>
3115 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3116 the newtype and its representation.
3120 <sect3> <title> A more precise specification </title>
3122 Derived instance declarations are constructed as follows. Consider the
3123 declaration (after expansion of any type synonyms)
3126 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3132 The <literal>ci</literal> are partial applications of
3133 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3134 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3137 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3140 The type <literal>t</literal> is an arbitrary type.
3143 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3144 nor in the <literal>ci</literal>, and
3147 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3148 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3149 should not "look through" the type or its constructor. You can still
3150 derive these classes for a newtype, but it happens in the usual way, not
3151 via this new mechanism.
3154 Then, for each <literal>ci</literal>, the derived instance
3157 instance ci t => ci (T v1...vk)
3159 As an example which does <emphasis>not</emphasis> work, consider
3161 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3163 Here we cannot derive the instance
3165 instance Monad (State s m) => Monad (NonMonad m)
3168 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3169 and so cannot be "eta-converted" away. It is a good thing that this
3170 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3171 not, in fact, a monad --- for the same reason. Try defining
3172 <literal>>>=</literal> with the correct type: you won't be able to.
3176 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3177 important, since we can only derive instances for the last one. If the
3178 <literal>StateMonad</literal> class above were instead defined as
3181 class StateMonad m s | m -> s where ...
3184 then we would not have been able to derive an instance for the
3185 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3186 classes usually have one "main" parameter for which deriving new
3187 instances is most interesting.
3189 <para>Lastly, all of this applies only for classes other than
3190 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3191 and <literal>Data</literal>, for which the built-in derivation applies (section
3192 4.3.3. of the Haskell Report).
3193 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3194 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3195 the standard method is used or the one described here.)
3202 <!-- TYPE SYSTEM EXTENSIONS -->
3203 <sect1 id="type-class-extensions">
3204 <title>Class and instances declarations</title>
3206 <sect2 id="multi-param-type-classes">
3207 <title>Class declarations</title>
3210 This section, and the next one, documents GHC's type-class extensions.
3211 There's lots of background in the paper <ulink
3212 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3213 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3214 Jones, Erik Meijer).
3217 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3221 <title>Multi-parameter type classes</title>
3223 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3228 class Collection c a where
3229 union :: c a -> c a -> c a
3236 <sect3 id="superclass-rules">
3237 <title>The superclasses of a class declaration</title>
3240 In Haskell 98 the context of a class declaration (which introduces superclasses)
3241 must be simple; that is, each predicate must consist of a class applied to
3242 type variables. The flag <option>-XFlexibleContexts</option>
3243 (<xref linkend="flexible-contexts"/>)
3244 lifts this restriction,
3245 so that the only restriction on the context in a class declaration is
3246 that the class hierarchy must be acyclic. So these class declarations are OK:
3250 class Functor (m k) => FiniteMap m k where
3253 class (Monad m, Monad (t m)) => Transform t m where
3254 lift :: m a -> (t m) a
3260 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3261 of "acyclic" involves only the superclass relationships. For example,
3267 op :: D b => a -> b -> b
3270 class C a => D a where { ... }
3274 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3275 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3276 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3283 <sect3 id="class-method-types">
3284 <title>Class method types</title>
3287 Haskell 98 prohibits class method types to mention constraints on the
3288 class type variable, thus:
3291 fromList :: [a] -> s a
3292 elem :: Eq a => a -> s a -> Bool
3294 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3295 contains the constraint <literal>Eq a</literal>, constrains only the
3296 class type variable (in this case <literal>a</literal>).
3297 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3304 <sect2 id="functional-dependencies">
3305 <title>Functional dependencies
3308 <para> Functional dependencies are implemented as described by Mark Jones
3309 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3310 In Proceedings of the 9th European Symposium on Programming,
3311 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3315 Functional dependencies are introduced by a vertical bar in the syntax of a
3316 class declaration; e.g.
3318 class (Monad m) => MonadState s m | m -> s where ...
3320 class Foo a b c | a b -> c where ...
3322 There should be more documentation, but there isn't (yet). Yell if you need it.
3325 <sect3><title>Rules for functional dependencies </title>
3327 In a class declaration, all of the class type variables must be reachable (in the sense
3328 mentioned in <xref linkend="flexible-contexts"/>)
3329 from the free variables of each method type.
3333 class Coll s a where
3335 insert :: s -> a -> s
3338 is not OK, because the type of <literal>empty</literal> doesn't mention
3339 <literal>a</literal>. Functional dependencies can make the type variable
3342 class Coll s a | s -> a where
3344 insert :: s -> a -> s
3347 Alternatively <literal>Coll</literal> might be rewritten
3350 class Coll s a where
3352 insert :: s a -> a -> s a
3356 which makes the connection between the type of a collection of
3357 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3358 Occasionally this really doesn't work, in which case you can split the
3366 class CollE s => Coll s a where
3367 insert :: s -> a -> s
3374 <title>Background on functional dependencies</title>
3376 <para>The following description of the motivation and use of functional dependencies is taken
3377 from the Hugs user manual, reproduced here (with minor changes) by kind
3378 permission of Mark Jones.
3381 Consider the following class, intended as part of a
3382 library for collection types:
3384 class Collects e ce where
3386 insert :: e -> ce -> ce
3387 member :: e -> ce -> Bool
3389 The type variable e used here represents the element type, while ce is the type
3390 of the container itself. Within this framework, we might want to define
3391 instances of this class for lists or characteristic functions (both of which
3392 can be used to represent collections of any equality type), bit sets (which can
3393 be used to represent collections of characters), or hash tables (which can be
3394 used to represent any collection whose elements have a hash function). Omitting
3395 standard implementation details, this would lead to the following declarations:
3397 instance Eq e => Collects e [e] where ...
3398 instance Eq e => Collects e (e -> Bool) where ...
3399 instance Collects Char BitSet where ...
3400 instance (Hashable e, Collects a ce)
3401 => Collects e (Array Int ce) where ...
3403 All this looks quite promising; we have a class and a range of interesting
3404 implementations. Unfortunately, there are some serious problems with the class
3405 declaration. First, the empty function has an ambiguous type:
3407 empty :: Collects e ce => ce
3409 By "ambiguous" we mean that there is a type variable e that appears on the left
3410 of the <literal>=></literal> symbol, but not on the right. The problem with
3411 this is that, according to the theoretical foundations of Haskell overloading,
3412 we cannot guarantee a well-defined semantics for any term with an ambiguous
3416 We can sidestep this specific problem by removing the empty member from the
3417 class declaration. However, although the remaining members, insert and member,
3418 do not have ambiguous types, we still run into problems when we try to use
3419 them. For example, consider the following two functions:
3421 f x y = insert x . insert y
3424 for which GHC infers the following types:
3426 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3427 g :: (Collects Bool c, Collects Char c) => c -> c
3429 Notice that the type for f allows the two parameters x and y to be assigned
3430 different types, even though it attempts to insert each of the two values, one
3431 after the other, into the same collection. If we're trying to model collections
3432 that contain only one type of value, then this is clearly an inaccurate
3433 type. Worse still, the definition for g is accepted, without causing a type
3434 error. As a result, the error in this code will not be flagged at the point
3435 where it appears. Instead, it will show up only when we try to use g, which
3436 might even be in a different module.
3439 <sect4><title>An attempt to use constructor classes</title>
3442 Faced with the problems described above, some Haskell programmers might be
3443 tempted to use something like the following version of the class declaration:
3445 class Collects e c where
3447 insert :: e -> c e -> c e
3448 member :: e -> c e -> Bool
3450 The key difference here is that we abstract over the type constructor c that is
3451 used to form the collection type c e, and not over that collection type itself,
3452 represented by ce in the original class declaration. This avoids the immediate
3453 problems that we mentioned above: empty has type <literal>Collects e c => c
3454 e</literal>, which is not ambiguous.
3457 The function f from the previous section has a more accurate type:
3459 f :: (Collects e c) => e -> e -> c e -> c e
3461 The function g from the previous section is now rejected with a type error as
3462 we would hope because the type of f does not allow the two arguments to have
3464 This, then, is an example of a multiple parameter class that does actually work
3465 quite well in practice, without ambiguity problems.
3466 There is, however, a catch. This version of the Collects class is nowhere near
3467 as general as the original class seemed to be: only one of the four instances
3468 for <literal>Collects</literal>
3469 given above can be used with this version of Collects because only one of
3470 them---the instance for lists---has a collection type that can be written in
3471 the form c e, for some type constructor c, and element type e.
3475 <sect4><title>Adding functional dependencies</title>
3478 To get a more useful version of the Collects class, Hugs provides a mechanism
3479 that allows programmers to specify dependencies between the parameters of a
3480 multiple parameter class (For readers with an interest in theoretical
3481 foundations and previous work: The use of dependency information can be seen
3482 both as a generalization of the proposal for `parametric type classes' that was
3483 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3484 later framework for "improvement" of qualified types. The
3485 underlying ideas are also discussed in a more theoretical and abstract setting
3486 in a manuscript [implparam], where they are identified as one point in a
3487 general design space for systems of implicit parameterization.).
3489 To start with an abstract example, consider a declaration such as:
3491 class C a b where ...
3493 which tells us simply that C can be thought of as a binary relation on types
3494 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3495 included in the definition of classes to add information about dependencies
3496 between parameters, as in the following examples:
3498 class D a b | a -> b where ...
3499 class E a b | a -> b, b -> a where ...
3501 The notation <literal>a -> b</literal> used here between the | and where
3502 symbols --- not to be
3503 confused with a function type --- indicates that the a parameter uniquely
3504 determines the b parameter, and might be read as "a determines b." Thus D is
3505 not just a relation, but actually a (partial) function. Similarly, from the two
3506 dependencies that are included in the definition of E, we can see that E
3507 represents a (partial) one-one mapping between types.
3510 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3511 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3512 m>=0, meaning that the y parameters are uniquely determined by the x
3513 parameters. Spaces can be used as separators if more than one variable appears
3514 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3515 annotated with multiple dependencies using commas as separators, as in the
3516 definition of E above. Some dependencies that we can write in this notation are
3517 redundant, and will be rejected because they don't serve any useful
3518 purpose, and may instead indicate an error in the program. Examples of
3519 dependencies like this include <literal>a -> a </literal>,
3520 <literal>a -> a a </literal>,
3521 <literal>a -> </literal>, etc. There can also be
3522 some redundancy if multiple dependencies are given, as in
3523 <literal>a->b</literal>,
3524 <literal>b->c </literal>, <literal>a->c </literal>, and
3525 in which some subset implies the remaining dependencies. Examples like this are
3526 not treated as errors. Note that dependencies appear only in class
3527 declarations, and not in any other part of the language. In particular, the
3528 syntax for instance declarations, class constraints, and types is completely
3532 By including dependencies in a class declaration, we provide a mechanism for
3533 the programmer to specify each multiple parameter class more precisely. The
3534 compiler, on the other hand, is responsible for ensuring that the set of
3535 instances that are in scope at any given point in the program is consistent
3536 with any declared dependencies. For example, the following pair of instance
3537 declarations cannot appear together in the same scope because they violate the
3538 dependency for D, even though either one on its own would be acceptable:
3540 instance D Bool Int where ...
3541 instance D Bool Char where ...
3543 Note also that the following declaration is not allowed, even by itself:
3545 instance D [a] b where ...
3547 The problem here is that this instance would allow one particular choice of [a]
3548 to be associated with more than one choice for b, which contradicts the
3549 dependency specified in the definition of D. More generally, this means that,
3550 in any instance of the form:
3552 instance D t s where ...
3554 for some particular types t and s, the only variables that can appear in s are
3555 the ones that appear in t, and hence, if the type t is known, then s will be
3556 uniquely determined.
3559 The benefit of including dependency information is that it allows us to define
3560 more general multiple parameter classes, without ambiguity problems, and with
3561 the benefit of more accurate types. To illustrate this, we return to the
3562 collection class example, and annotate the original definition of <literal>Collects</literal>
3563 with a simple dependency:
3565 class Collects e ce | ce -> e where
3567 insert :: e -> ce -> ce
3568 member :: e -> ce -> Bool
3570 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3571 determined by the type of the collection ce. Note that both parameters of
3572 Collects are of kind *; there are no constructor classes here. Note too that
3573 all of the instances of Collects that we gave earlier can be used
3574 together with this new definition.
3577 What about the ambiguity problems that we encountered with the original
3578 definition? The empty function still has type Collects e ce => ce, but it is no
3579 longer necessary to regard that as an ambiguous type: Although the variable e
3580 does not appear on the right of the => symbol, the dependency for class
3581 Collects tells us that it is uniquely determined by ce, which does appear on
3582 the right of the => symbol. Hence the context in which empty is used can still
3583 give enough information to determine types for both ce and e, without
3584 ambiguity. More generally, we need only regard a type as ambiguous if it
3585 contains a variable on the left of the => that is not uniquely determined
3586 (either directly or indirectly) by the variables on the right.
3589 Dependencies also help to produce more accurate types for user defined
3590 functions, and hence to provide earlier detection of errors, and less cluttered
3591 types for programmers to work with. Recall the previous definition for a
3594 f x y = insert x y = insert x . insert y
3596 for which we originally obtained a type:
3598 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3600 Given the dependency information that we have for Collects, however, we can
3601 deduce that a and b must be equal because they both appear as the second
3602 parameter in a Collects constraint with the same first parameter c. Hence we
3603 can infer a shorter and more accurate type for f:
3605 f :: (Collects a c) => a -> a -> c -> c
3607 In a similar way, the earlier definition of g will now be flagged as a type error.
3610 Although we have given only a few examples here, it should be clear that the
3611 addition of dependency information can help to make multiple parameter classes
3612 more useful in practice, avoiding ambiguity problems, and allowing more general
3613 sets of instance declarations.
3619 <sect2 id="instance-decls">
3620 <title>Instance declarations</title>
3622 <para>An instance declaration has the form
3624 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 ...
3626 The part before the "<literal>=></literal>" is the
3627 <emphasis>context</emphasis>, while the part after the
3628 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3631 <sect3 id="flexible-instance-head">
3632 <title>Relaxed rules for the instance head</title>
3635 In Haskell 98 the head of an instance declaration
3636 must be of the form <literal>C (T a1 ... an)</literal>, where
3637 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3638 and the <literal>a1 ... an</literal> are distinct type variables.
3639 GHC relaxes these rules in two ways.
3643 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3644 declaration to mention arbitrary nested types.
3645 For example, this becomes a legal instance declaration
3647 instance C (Maybe Int) where ...
3649 See also the <link linkend="instance-overlap">rules on overlap</link>.
3652 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3653 synonyms. As always, using a type synonym is just shorthand for
3654 writing the RHS of the type synonym definition. For example:
3658 type Point = (Int,Int)
3659 instance C Point where ...
3660 instance C [Point] where ...
3664 is legal. However, if you added
3668 instance C (Int,Int) where ...
3672 as well, then the compiler will complain about the overlapping
3673 (actually, identical) instance declarations. As always, type synonyms
3674 must be fully applied. You cannot, for example, write:
3678 instance Monad P where ...
3686 <sect3 id="instance-rules">
3687 <title>Relaxed rules for instance contexts</title>
3689 <para>In Haskell 98, the assertions in the context of the instance declaration
3690 must be of the form <literal>C a</literal> where <literal>a</literal>
3691 is a type variable that occurs in the head.
3695 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3696 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3697 With this flag the context of the instance declaration can each consist of arbitrary
3698 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3702 The Paterson Conditions: for each assertion in the context
3704 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3705 <listitem><para>The assertion has fewer constructors and variables (taken together
3706 and counting repetitions) than the head</para></listitem>
3710 <listitem><para>The Coverage Condition. For each functional dependency,
3711 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3712 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3713 every type variable in
3714 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3715 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3716 substitution mapping each type variable in the class declaration to the
3717 corresponding type in the instance declaration.
3720 These restrictions ensure that context reduction terminates: each reduction
3721 step makes the problem smaller by at least one
3722 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3723 if you give the <option>-XUndecidableInstances</option>
3724 flag (<xref linkend="undecidable-instances"/>).
3725 You can find lots of background material about the reason for these
3726 restrictions in the paper <ulink
3727 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3728 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3731 For example, these are OK:
3733 instance C Int [a] -- Multiple parameters
3734 instance Eq (S [a]) -- Structured type in head
3736 -- Repeated type variable in head
3737 instance C4 a a => C4 [a] [a]
3738 instance Stateful (ST s) (MutVar s)
3740 -- Head can consist of type variables only
3742 instance (Eq a, Show b) => C2 a b
3744 -- Non-type variables in context
3745 instance Show (s a) => Show (Sized s a)
3746 instance C2 Int a => C3 Bool [a]
3747 instance C2 Int a => C3 [a] b
3751 -- Context assertion no smaller than head
3752 instance C a => C a where ...
3753 -- (C b b) has more more occurrences of b than the head
3754 instance C b b => Foo [b] where ...
3759 The same restrictions apply to instances generated by
3760 <literal>deriving</literal> clauses. Thus the following is accepted:
3762 data MinHeap h a = H a (h a)
3765 because the derived instance
3767 instance (Show a, Show (h a)) => Show (MinHeap h a)
3769 conforms to the above rules.
3773 A useful idiom permitted by the above rules is as follows.
3774 If one allows overlapping instance declarations then it's quite
3775 convenient to have a "default instance" declaration that applies if
3776 something more specific does not:
3784 <sect3 id="undecidable-instances">
3785 <title>Undecidable instances</title>
3788 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3789 For example, sometimes you might want to use the following to get the
3790 effect of a "class synonym":
3792 class (C1 a, C2 a, C3 a) => C a where { }
3794 instance (C1 a, C2 a, C3 a) => C a where { }
3796 This allows you to write shorter signatures:
3802 f :: (C1 a, C2 a, C3 a) => ...
3804 The restrictions on functional dependencies (<xref
3805 linkend="functional-dependencies"/>) are particularly troublesome.
3806 It is tempting to introduce type variables in the context that do not appear in
3807 the head, something that is excluded by the normal rules. For example:
3809 class HasConverter a b | a -> b where
3812 data Foo a = MkFoo a
3814 instance (HasConverter a b,Show b) => Show (Foo a) where
3815 show (MkFoo value) = show (convert value)
3817 This is dangerous territory, however. Here, for example, is a program that would make the
3822 instance F [a] [[a]]
3823 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3825 Similarly, it can be tempting to lift the coverage condition:
3827 class Mul a b c | a b -> c where
3828 (.*.) :: a -> b -> c
3830 instance Mul Int Int Int where (.*.) = (*)
3831 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3832 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3834 The third instance declaration does not obey the coverage condition;
3835 and indeed the (somewhat strange) definition:
3837 f = \ b x y -> if b then x .*. [y] else y
3839 makes instance inference go into a loop, because it requires the constraint
3840 <literal>(Mul a [b] b)</literal>.
3843 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3844 the experimental flag <option>-XUndecidableInstances</option>
3845 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3846 both the Paterson Conditions and the Coverage Condition
3847 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3848 fixed-depth recursion stack. If you exceed the stack depth you get a
3849 sort of backtrace, and the opportunity to increase the stack depth
3850 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3856 <sect3 id="instance-overlap">
3857 <title>Overlapping instances</title>
3859 In general, <emphasis>GHC requires that that it be unambiguous which instance
3861 should be used to resolve a type-class constraint</emphasis>. This behaviour
3862 can be modified by two flags: <option>-XOverlappingInstances</option>
3863 <indexterm><primary>-XOverlappingInstances
3864 </primary></indexterm>
3865 and <option>-XIncoherentInstances</option>
3866 <indexterm><primary>-XIncoherentInstances
3867 </primary></indexterm>, as this section discusses. Both these
3868 flags are dynamic flags, and can be set on a per-module basis, using
3869 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3871 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3872 it tries to match every instance declaration against the
3874 by instantiating the head of the instance declaration. For example, consider
3877 instance context1 => C Int a where ... -- (A)
3878 instance context2 => C a Bool where ... -- (B)
3879 instance context3 => C Int [a] where ... -- (C)
3880 instance context4 => C Int [Int] where ... -- (D)
3882 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3883 but (C) and (D) do not. When matching, GHC takes
3884 no account of the context of the instance declaration
3885 (<literal>context1</literal> etc).
3886 GHC's default behaviour is that <emphasis>exactly one instance must match the
3887 constraint it is trying to resolve</emphasis>.
3888 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3889 including both declarations (A) and (B), say); an error is only reported if a
3890 particular constraint matches more than one.
3894 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3895 more than one instance to match, provided there is a most specific one. For
3896 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3897 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3898 most-specific match, the program is rejected.
3901 However, GHC is conservative about committing to an overlapping instance. For example:
3906 Suppose that from the RHS of <literal>f</literal> we get the constraint
3907 <literal>C Int [b]</literal>. But
3908 GHC does not commit to instance (C), because in a particular
3909 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3910 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3911 So GHC rejects the program.
3912 (If you add the flag <option>-XIncoherentInstances</option>,
3913 GHC will instead pick (C), without complaining about
3914 the problem of subsequent instantiations.)
3917 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3918 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3919 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3920 it instead. In this case, GHC will refrain from
3921 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3922 as before) but, rather than rejecting the program, it will infer the type
3924 f :: C Int [b] => [b] -> [b]
3926 That postpones the question of which instance to pick to the
3927 call site for <literal>f</literal>
3928 by which time more is known about the type <literal>b</literal>.
3929 You can write this type signature yourself if you use the
3930 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3934 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3938 instance Foo [b] where
3941 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3942 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3943 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3944 declaration. The solution is to postpone the choice by adding the constraint to the context
3945 of the instance declaration, thus:
3947 instance C Int [b] => Foo [b] where
3950 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3953 The willingness to be overlapped or incoherent is a property of
3954 the <emphasis>instance declaration</emphasis> itself, controlled by the
3955 presence or otherwise of the <option>-XOverlappingInstances</option>
3956 and <option>-XIncoherentInstances</option> flags when that module is
3957 being defined. Neither flag is required in a module that imports and uses the
3958 instance declaration. Specifically, during the lookup process:
3961 An instance declaration is ignored during the lookup process if (a) a more specific
3962 match is found, and (b) the instance declaration was compiled with
3963 <option>-XOverlappingInstances</option>. The flag setting for the
3964 more-specific instance does not matter.
3967 Suppose an instance declaration does not match the constraint being looked up, but
3968 does unify with it, so that it might match when the constraint is further
3969 instantiated. Usually GHC will regard this as a reason for not committing to
3970 some other constraint. But if the instance declaration was compiled with
3971 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3972 check for that declaration.
3975 These rules make it possible for a library author to design a library that relies on
3976 overlapping instances without the library client having to know.
3979 If an instance declaration is compiled without
3980 <option>-XOverlappingInstances</option>,
3981 then that instance can never be overlapped. This could perhaps be
3982 inconvenient. Perhaps the rule should instead say that the
3983 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3984 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3985 at a usage site should be permitted regardless of how the instance declarations
3986 are compiled, if the <option>-XOverlappingInstances</option> flag is
3987 used at the usage site. (Mind you, the exact usage site can occasionally be
3988 hard to pin down.) We are interested to receive feedback on these points.
3990 <para>The <option>-XIncoherentInstances</option> flag implies the
3991 <option>-XOverlappingInstances</option> flag, but not vice versa.
3999 <sect2 id="overloaded-strings">
4000 <title>Overloaded string literals
4004 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
4005 string literal has type <literal>String</literal>, but with overloaded string
4006 literals enabled (with <literal>-XOverloadedStrings</literal>)
4007 a string literal has type <literal>(IsString a) => a</literal>.
4010 This means that the usual string syntax can be used, e.g., for packed strings
4011 and other variations of string like types. String literals behave very much
4012 like integer literals, i.e., they can be used in both expressions and patterns.
4013 If used in a pattern the literal with be replaced by an equality test, in the same
4014 way as an integer literal is.
4017 The class <literal>IsString</literal> is defined as:
4019 class IsString a where
4020 fromString :: String -> a
4022 The only predefined instance is the obvious one to make strings work as usual:
4024 instance IsString [Char] where
4027 The class <literal>IsString</literal> is not in scope by default. If you want to mention
4028 it explicitly (for example, to give an instance declaration for it), you can import it
4029 from module <literal>GHC.Exts</literal>.
4032 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4036 Each type in a default declaration must be an
4037 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4041 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4042 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4043 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4044 <emphasis>or</emphasis> <literal>IsString</literal>.
4053 import GHC.Exts( IsString(..) )
4055 newtype MyString = MyString String deriving (Eq, Show)
4056 instance IsString MyString where
4057 fromString = MyString
4059 greet :: MyString -> MyString
4060 greet "hello" = "world"
4064 print $ greet "hello"
4065 print $ greet "fool"
4069 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4070 to work since it gets translated into an equality comparison.
4076 <sect1 id="type-families">
4077 <title>Type families</title>
4080 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4081 facilitate type-level
4082 programming. Type families are a generalisation of <firstterm>associated
4083 data types</firstterm>
4084 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4085 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4086 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4087 Symposium on Principles of Programming Languages (POPL'05)”, pages
4088 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4089 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4090 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4092 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4093 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4094 themselves are described in the paper “<ulink
4095 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4096 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4098 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4099 13th ACM SIGPLAN International Conference on Functional
4100 Programming”, ACM Press, pages 51-62, 2008. Type families
4101 essentially provide type-indexed data types and named functions on types,
4102 which are useful for generic programming and highly parameterised library
4103 interfaces as well as interfaces with enhanced static information, much like
4104 dependent types. They might also be regarded as an alternative to functional
4105 dependencies, but provide a more functional style of type-level programming
4106 than the relational style of functional dependencies.
4109 Indexed type families, or type families for short, are type constructors that
4110 represent sets of types. Set members are denoted by supplying the type family
4111 constructor with type parameters, which are called <firstterm>type
4112 indices</firstterm>. The
4113 difference between vanilla parametrised type constructors and family
4114 constructors is much like between parametrically polymorphic functions and
4115 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4116 behave the same at all type instances, whereas class methods can change their
4117 behaviour in dependence on the class type parameters. Similarly, vanilla type
4118 constructors imply the same data representation for all type instances, but
4119 family constructors can have varying representation types for varying type
4123 Indexed type families come in two flavours: <firstterm>data
4124 families</firstterm> and <firstterm>type synonym
4125 families</firstterm>. They are the indexed family variants of algebraic
4126 data types and type synonyms, respectively. The instances of data families
4127 can be data types and newtypes.
4130 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4131 Additional information on the use of type families in GHC is available on
4132 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4133 Haskell wiki page on type families</ulink>.
4136 <sect2 id="data-families">
4137 <title>Data families</title>
4140 Data families appear in two flavours: (1) they can be defined on the
4142 or (2) they can appear inside type classes (in which case they are known as
4143 associated types). The former is the more general variant, as it lacks the
4144 requirement for the type-indexes to coincide with the class
4145 parameters. However, the latter can lead to more clearly structured code and
4146 compiler warnings if some type instances were - possibly accidentally -
4147 omitted. In the following, we always discuss the general toplevel form first
4148 and then cover the additional constraints placed on associated types.
4151 <sect3 id="data-family-declarations">
4152 <title>Data family declarations</title>
4155 Indexed data families are introduced by a signature, such as
4157 data family GMap k :: * -> *
4159 The special <literal>family</literal> distinguishes family from standard
4160 data declarations. The result kind annotation is optional and, as
4161 usual, defaults to <literal>*</literal> if omitted. An example is
4165 Named arguments can also be given explicit kind signatures if needed.
4167 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4168 declarations] named arguments are entirely optional, so that we can
4169 declare <literal>Array</literal> alternatively with
4171 data family Array :: * -> *
4175 <sect4 id="assoc-data-family-decl">
4176 <title>Associated data family declarations</title>
4178 When a data family is declared as part of a type class, we drop
4179 the <literal>family</literal> special. The <literal>GMap</literal>
4180 declaration takes the following form
4182 class GMapKey k where
4183 data GMap k :: * -> *
4186 In contrast to toplevel declarations, named arguments must be used for
4187 all type parameters that are to be used as type-indexes. Moreover,
4188 the argument names must be class parameters. Each class parameter may
4189 only be used at most once per associated type, but some may be omitted
4190 and they may be in an order other than in the class head. Hence, the
4191 following contrived example is admissible:
4200 <sect3 id="data-instance-declarations">
4201 <title>Data instance declarations</title>
4204 Instance declarations of data and newtype families are very similar to
4205 standard data and newtype declarations. The only two differences are
4206 that the keyword <literal>data</literal> or <literal>newtype</literal>
4207 is followed by <literal>instance</literal> and that some or all of the
4208 type arguments can be non-variable types, but may not contain forall
4209 types or type synonym families. However, data families are generally
4210 allowed in type parameters, and type synonyms are allowed as long as
4211 they are fully applied and expand to a type that is itself admissible -
4212 exactly as this is required for occurrences of type synonyms in class
4213 instance parameters. For example, the <literal>Either</literal>
4214 instance for <literal>GMap</literal> is
4216 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4218 In this example, the declaration has only one variant. In general, it
4222 Data and newtype instance declarations are only permitted when an
4223 appropriate family declaration is in scope - just as a class instance declaratoin
4224 requires the class declaration to be visible. Moreover, each instance
4225 declaration has to conform to the kind determined by its family
4226 declaration. This implies that the number of parameters of an instance
4227 declaration matches the arity determined by the kind of the family.
4230 A data family instance declaration can use the full exprssiveness of
4231 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4233 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4234 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4235 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4238 data instance T Int = T1 Int | T2 Bool
4239 newtype instance T Char = TC Bool
4242 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4243 and indeed can define a GADT. For example:
4246 data instance G [a] b where
4247 G1 :: c -> G [Int] b
4251 <listitem><para> You can use a <literal>deriving</literal> clause on a
4252 <literal>data instance</literal> or <literal>newtype instance</literal>
4259 Even if type families are defined as toplevel declarations, functions
4260 that perform different computations for different family instances may still
4261 need to be defined as methods of type classes. In particular, the
4262 following is not possible:
4265 data instance T Int = A
4266 data instance T Char = B
4268 foo A = 1 -- WRONG: These two equations together...
4269 foo B = 2 -- ...will produce a type error.
4271 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4275 instance Foo Int where
4277 instance Foo Char where
4280 (Given the functionality provided by GADTs (Generalised Algebraic Data
4281 Types), it might seem as if a definition, such as the above, should be
4282 feasible. However, type families are - in contrast to GADTs - are
4283 <emphasis>open;</emphasis> i.e., new instances can always be added,
4285 modules. Supporting pattern matching across different data instances
4286 would require a form of extensible case construct.)
4289 <sect4 id="assoc-data-inst">
4290 <title>Associated data instances</title>
4292 When an associated data family instance is declared within a type
4293 class instance, we drop the <literal>instance</literal> keyword in the
4294 family instance. So, the <literal>Either</literal> instance
4295 for <literal>GMap</literal> becomes:
4297 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4298 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4301 The most important point about associated family instances is that the
4302 type indexes corresponding to class parameters must be identical to
4303 the type given in the instance head; here this is the first argument
4304 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4305 which coincides with the only class parameter. Any parameters to the
4306 family constructor that do not correspond to class parameters, need to
4307 be variables in every instance; here this is the
4308 variable <literal>v</literal>.
4311 Instances for an associated family can only appear as part of
4312 instances declarations of the class in which the family was declared -
4313 just as with the equations of the methods of a class. Also in
4314 correspondence to how methods are handled, declarations of associated
4315 types can be omitted in class instances. If an associated family
4316 instance is omitted, the corresponding instance type is not inhabited;
4317 i.e., only diverging expressions, such
4318 as <literal>undefined</literal>, can assume the type.
4322 <sect4 id="scoping-class-params">
4323 <title>Scoping of class parameters</title>
4325 In the case of multi-parameter type classes, the visibility of class
4326 parameters in the right-hand side of associated family instances
4327 depends <emphasis>solely</emphasis> on the parameters of the data
4328 family. As an example, consider the simple class declaration
4333 Only one of the two class parameters is a parameter to the data
4334 family. Hence, the following instance declaration is invalid:
4336 instance C [c] d where
4337 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4339 Here, the right-hand side of the data instance mentions the type
4340 variable <literal>d</literal> that does not occur in its left-hand
4341 side. We cannot admit such data instances as they would compromise
4346 <sect4 id="family-class-inst">
4347 <title>Type class instances of family instances</title>
4349 Type class instances of instances of data families can be defined as
4350 usual, and in particular data instance declarations can
4351 have <literal>deriving</literal> clauses. For example, we can write
4353 data GMap () v = GMapUnit (Maybe v)
4356 which implicitly defines an instance of the form
4358 instance Show v => Show (GMap () v) where ...
4362 Note that class instances are always for
4363 particular <emphasis>instances</emphasis> of a data family and never
4364 for an entire family as a whole. This is for essentially the same
4365 reasons that we cannot define a toplevel function that performs
4366 pattern matching on the data constructors
4367 of <emphasis>different</emphasis> instances of a single type family.
4368 It would require a form of extensible case construct.
4372 <sect4 id="data-family-overlap">
4373 <title>Overlap of data instances</title>
4375 The instance declarations of a data family used in a single program
4376 may not overlap at all, independent of whether they are associated or
4377 not. In contrast to type class instances, this is not only a matter
4378 of consistency, but one of type safety.
4384 <sect3 id="data-family-import-export">
4385 <title>Import and export</title>
4388 The association of data constructors with type families is more dynamic
4389 than that is the case with standard data and newtype declarations. In
4390 the standard case, the notation <literal>T(..)</literal> in an import or
4391 export list denotes the type constructor and all the data constructors
4392 introduced in its declaration. However, a family declaration never
4393 introduces any data constructors; instead, data constructors are
4394 introduced by family instances. As a result, which data constructors
4395 are associated with a type family depends on the currently visible
4396 instance declarations for that family. Consequently, an import or
4397 export item of the form <literal>T(..)</literal> denotes the family
4398 constructor and all currently visible data constructors - in the case of
4399 an export item, these may be either imported or defined in the current
4400 module. The treatment of import and export items that explicitly list
4401 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4405 <sect4 id="data-family-impexp-assoc">
4406 <title>Associated families</title>
4408 As expected, an import or export item of the
4409 form <literal>C(..)</literal> denotes all of the class' methods and
4410 associated types. However, when associated types are explicitly
4411 listed as subitems of a class, we need some new syntax, as uppercase
4412 identifiers as subitems are usually data constructors, not type
4413 constructors. To clarify that we denote types here, each associated
4414 type name needs to be prefixed by the keyword <literal>type</literal>.
4415 So for example, when explicitly listing the components of
4416 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4417 GMap, empty, lookup, insert)</literal>.
4421 <sect4 id="data-family-impexp-examples">
4422 <title>Examples</title>
4424 Assuming our running <literal>GMapKey</literal> class example, let us
4425 look at some export lists and their meaning:
4428 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4429 just the class name.</para>
4432 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4433 Exports the class, the associated type <literal>GMap</literal>
4435 functions <literal>empty</literal>, <literal>lookup</literal>,
4436 and <literal>insert</literal>. None of the data constructors is
4440 <para><literal>module GMap (GMapKey(..), GMap(..))
4441 where...</literal>: As before, but also exports all the data
4442 constructors <literal>GMapInt</literal>,
4443 <literal>GMapChar</literal>,
4444 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4445 and <literal>GMapUnit</literal>.</para>
4448 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4449 GMap(..)) where...</literal>: As before.</para>
4452 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4453 where...</literal>: As before.</para>
4458 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4459 both the class <literal>GMapKey</literal> as well as its associated
4460 type <literal>GMap</literal>. However, you cannot
4461 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4462 sub-component specifications cannot be nested. To
4463 specify <literal>GMap</literal>'s data constructors, you have to list
4468 <sect4 id="data-family-impexp-instances">
4469 <title>Instances</title>
4471 Family instances are implicitly exported, just like class instances.
4472 However, this applies only to the heads of instances, not to the data
4473 constructors an instance defines.
4481 <sect2 id="synonym-families">
4482 <title>Synonym families</title>
4485 Type families appear in two flavours: (1) they can be defined on the
4486 toplevel or (2) they can appear inside type classes (in which case they
4487 are known as associated type synonyms). The former is the more general
4488 variant, as it lacks the requirement for the type-indexes to coincide with
4489 the class parameters. However, the latter can lead to more clearly
4490 structured code and compiler warnings if some type instances were -
4491 possibly accidentally - omitted. In the following, we always discuss the
4492 general toplevel form first and then cover the additional constraints
4493 placed on associated types.
4496 <sect3 id="type-family-declarations">
4497 <title>Type family declarations</title>
4500 Indexed type families are introduced by a signature, such as
4502 type family Elem c :: *
4504 The special <literal>family</literal> distinguishes family from standard
4505 type declarations. The result kind annotation is optional and, as
4506 usual, defaults to <literal>*</literal> if omitted. An example is
4510 Parameters can also be given explicit kind signatures if needed. We
4511 call the number of parameters in a type family declaration, the family's
4512 arity, and all applications of a type family must be fully saturated
4513 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4514 and it implies that the kind of a type family is not sufficient to
4515 determine a family's arity, and hence in general, also insufficient to
4516 determine whether a type family application is well formed. As an
4517 example, consider the following declaration:
4519 type family F a b :: * -> * -- F's arity is 2,
4520 -- although its overall kind is * -> * -> * -> *
4522 Given this declaration the following are examples of well-formed and
4525 F Char [Int] -- OK! Kind: * -> *
4526 F Char [Int] Bool -- OK! Kind: *
4527 F IO Bool -- WRONG: kind mismatch in the first argument
4528 F Bool -- WRONG: unsaturated application
4532 <sect4 id="assoc-type-family-decl">
4533 <title>Associated type family declarations</title>
4535 When a type family is declared as part of a type class, we drop
4536 the <literal>family</literal> special. The <literal>Elem</literal>
4537 declaration takes the following form
4539 class Collects ce where
4543 The argument names of the type family must be class parameters. Each
4544 class parameter may only be used at most once per associated type, but
4545 some may be omitted and they may be in an order other than in the
4546 class head. Hence, the following contrived example is admissible:
4551 These rules are exactly as for associated data families.
4556 <sect3 id="type-instance-declarations">
4557 <title>Type instance declarations</title>
4559 Instance declarations of type families are very similar to standard type
4560 synonym declarations. The only two differences are that the
4561 keyword <literal>type</literal> is followed
4562 by <literal>instance</literal> and that some or all of the type
4563 arguments can be non-variable types, but may not contain forall types or
4564 type synonym families. However, data families are generally allowed, and
4565 type synonyms are allowed as long as they are fully applied and expand
4566 to a type that is admissible - these are the exact same requirements as
4567 for data instances. For example, the <literal>[e]</literal> instance
4568 for <literal>Elem</literal> is
4570 type instance Elem [e] = e
4574 Type family instance declarations are only legitimate when an
4575 appropriate family declaration is in scope - just like class instances
4576 require the class declaration to be visible. Moreover, each instance
4577 declaration has to conform to the kind determined by its family
4578 declaration, and the number of type parameters in an instance
4579 declaration must match the number of type parameters in the family
4580 declaration. Finally, the right-hand side of a type instance must be a
4581 monotype (i.e., it may not include foralls) and after the expansion of
4582 all saturated vanilla type synonyms, no synonyms, except family synonyms
4583 may remain. Here are some examples of admissible and illegal type
4586 type family F a :: *
4587 type instance F [Int] = Int -- OK!
4588 type instance F String = Char -- OK!
4589 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4590 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4591 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4593 type family G a b :: * -> *
4594 type instance G Int = (,) -- WRONG: must be two type parameters
4595 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4599 <sect4 id="assoc-type-instance">
4600 <title>Associated type instance declarations</title>
4602 When an associated family instance is declared within a type class
4603 instance, we drop the <literal>instance</literal> keyword in the family
4604 instance. So, the <literal>[e]</literal> instance
4605 for <literal>Elem</literal> becomes:
4607 instance (Eq (Elem [e])) => Collects ([e]) where
4611 The most important point about associated family instances is that the
4612 type indexes corresponding to class parameters must be identical to the
4613 type given in the instance head; here this is <literal>[e]</literal>,
4614 which coincides with the only class parameter.
4617 Instances for an associated family can only appear as part of instances
4618 declarations of the class in which the family was declared - just as
4619 with the equations of the methods of a class. Also in correspondence to
4620 how methods are handled, declarations of associated types can be omitted
4621 in class instances. If an associated family instance is omitted, the
4622 corresponding instance type is not inhabited; i.e., only diverging
4623 expressions, such as <literal>undefined</literal>, can assume the type.
4627 <sect4 id="type-family-overlap">
4628 <title>Overlap of type synonym instances</title>
4630 The instance declarations of a type family used in a single program
4631 may only overlap if the right-hand sides of the overlapping instances
4632 coincide for the overlapping types. More formally, two instance
4633 declarations overlap if there is a substitution that makes the
4634 left-hand sides of the instances syntactically the same. Whenever
4635 that is the case, the right-hand sides of the instances must also be
4636 syntactically equal under the same substitution. This condition is
4637 independent of whether the type family is associated or not, and it is
4638 not only a matter of consistency, but one of type safety.
4641 Here are two example to illustrate the condition under which overlap
4644 type instance F (a, Int) = [a]
4645 type instance F (Int, b) = [b] -- overlap permitted
4647 type instance G (a, Int) = [a]
4648 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4653 <sect4 id="type-family-decidability">
4654 <title>Decidability of type synonym instances</title>
4656 In order to guarantee that type inference in the presence of type
4657 families decidable, we need to place a number of additional
4658 restrictions on the formation of type instance declarations (c.f.,
4659 Definition 5 (Relaxed Conditions) of “<ulink
4660 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4661 Checking with Open Type Functions</ulink>”). Instance
4662 declarations have the general form
4664 type instance F t1 .. tn = t
4666 where we require that for every type family application <literal>(G s1
4667 .. sm)</literal> in <literal>t</literal>,
4670 <para><literal>s1 .. sm</literal> do not contain any type family
4671 constructors,</para>
4674 <para>the total number of symbols (data type constructors and type
4675 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4676 in <literal>t1 .. tn</literal>, and</para>
4679 <para>for every type
4680 variable <literal>a</literal>, <literal>a</literal> occurs
4681 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4682 .. tn</literal>.</para>
4685 These restrictions are easily verified and ensure termination of type
4686 inference. However, they are not sufficient to guarantee completeness
4687 of type inference in the presence of, so called, ''loopy equalities'',
4688 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4689 a type variable is underneath a family application and data
4690 constructor application - see the above mentioned paper for details.
4693 If the option <option>-XUndecidableInstances</option> is passed to the
4694 compiler, the above restrictions are not enforced and it is on the
4695 programmer to ensure termination of the normalisation of type families
4696 during type inference.
4701 <sect3 id-="equality-constraints">
4702 <title>Equality constraints</title>
4704 Type context can include equality constraints of the form <literal>t1 ~
4705 t2</literal>, which denote that the types <literal>t1</literal>
4706 and <literal>t2</literal> need to be the same. In the presence of type
4707 families, whether two types are equal cannot generally be decided
4708 locally. Hence, the contexts of function signatures may include
4709 equality constraints, as in the following example:
4711 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4713 where we require that the element type of <literal>c1</literal>
4714 and <literal>c2</literal> are the same. In general, the
4715 types <literal>t1</literal> and <literal>t2</literal> of an equality
4716 constraint may be arbitrary monotypes; i.e., they may not contain any
4717 quantifiers, independent of whether higher-rank types are otherwise
4721 Equality constraints can also appear in class and instance contexts.
4722 The former enable a simple translation of programs using functional
4723 dependencies into programs using family synonyms instead. The general
4724 idea is to rewrite a class declaration of the form
4726 class C a b | a -> b
4730 class (F a ~ b) => C a b where
4733 That is, we represent every functional dependency (FD) <literal>a1 .. an
4734 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4735 superclass context equality <literal>F a1 .. an ~ b</literal>,
4736 essentially giving a name to the functional dependency. In class
4737 instances, we define the type instances of FD families in accordance
4738 with the class head. Method signatures are not affected by that
4742 NB: Equalities in superclass contexts are not fully implemented in
4747 <sect3 id-="ty-fams-in-instances">
4748 <title>Type families and instance declarations</title>
4749 <para>Type families require us to extend the rules for
4750 the form of instance heads, which are given
4751 in <xref linkend="flexible-instance-head"/>.
4754 <listitem><para>Data type families may appear in an instance head</para></listitem>
4755 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4757 The reason for the latter restriction is that there is no way to check for. Consider
4760 type instance F Bool = Int
4767 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4768 The situation is especially bad because the type instance for <literal>F Bool</literal>
4769 might be in another module, or even in a module that is not yet written.
4776 <sect1 id="other-type-extensions">
4777 <title>Other type system extensions</title>
4779 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4781 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4782 is used, the keyword <literal>forall</literal>
4783 allows us to say exactly what this means. For example:
4791 g :: forall b. (b -> b)
4793 The two are treated identically.
4796 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4797 a type variable any more!
4802 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4804 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4805 that the type-class constraints in a type signature must have the
4806 form <emphasis>(class type-variable)</emphasis> or
4807 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4808 With <option>-XFlexibleContexts</option>
4809 these type signatures are perfectly OK
4812 g :: Ord (T a ()) => ...
4814 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4815 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4816 (<xref linkend="instance-rules"/>).
4820 GHC imposes the following restrictions on the constraints in a type signature.
4824 forall tv1..tvn (c1, ...,cn) => type
4827 (Here, we write the "foralls" explicitly, although the Haskell source
4828 language omits them; in Haskell 98, all the free type variables of an
4829 explicit source-language type signature are universally quantified,
4830 except for the class type variables in a class declaration. However,
4831 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4840 <emphasis>Each universally quantified type variable
4841 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4843 A type variable <literal>a</literal> is "reachable" if it appears
4844 in the same constraint as either a type variable free in
4845 <literal>type</literal>, or another reachable type variable.
4846 A value with a type that does not obey
4847 this reachability restriction cannot be used without introducing
4848 ambiguity; that is why the type is rejected.
4849 Here, for example, is an illegal type:
4853 forall a. Eq a => Int
4857 When a value with this type was used, the constraint <literal>Eq tv</literal>
4858 would be introduced where <literal>tv</literal> is a fresh type variable, and
4859 (in the dictionary-translation implementation) the value would be
4860 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4861 can never know which instance of <literal>Eq</literal> to use because we never
4862 get any more information about <literal>tv</literal>.
4866 that the reachability condition is weaker than saying that <literal>a</literal> is
4867 functionally dependent on a type variable free in
4868 <literal>type</literal> (see <xref
4869 linkend="functional-dependencies"/>). The reason for this is there
4870 might be a "hidden" dependency, in a superclass perhaps. So
4871 "reachable" is a conservative approximation to "functionally dependent".
4872 For example, consider:
4874 class C a b | a -> b where ...
4875 class C a b => D a b where ...
4876 f :: forall a b. D a b => a -> a
4878 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4879 but that is not immediately apparent from <literal>f</literal>'s type.
4885 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4886 universally quantified type variables <literal>tvi</literal></emphasis>.
4888 For example, this type is OK because <literal>C a b</literal> mentions the
4889 universally quantified type variable <literal>b</literal>:
4893 forall a. C a b => burble
4897 The next type is illegal because the constraint <literal>Eq b</literal> does not
4898 mention <literal>a</literal>:
4902 forall a. Eq b => burble
4906 The reason for this restriction is milder than the other one. The
4907 excluded types are never useful or necessary (because the offending
4908 context doesn't need to be witnessed at this point; it can be floated
4909 out). Furthermore, floating them out increases sharing. Lastly,
4910 excluding them is a conservative choice; it leaves a patch of
4911 territory free in case we need it later.
4922 <sect2 id="implicit-parameters">
4923 <title>Implicit parameters</title>
4925 <para> Implicit parameters are implemented as described in
4926 "Implicit parameters: dynamic scoping with static types",
4927 J Lewis, MB Shields, E Meijer, J Launchbury,
4928 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4932 <para>(Most of the following, still rather incomplete, documentation is
4933 due to Jeff Lewis.)</para>
4935 <para>Implicit parameter support is enabled with the option
4936 <option>-XImplicitParams</option>.</para>
4939 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4940 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4941 context. In Haskell, all variables are statically bound. Dynamic
4942 binding of variables is a notion that goes back to Lisp, but was later
4943 discarded in more modern incarnations, such as Scheme. Dynamic binding
4944 can be very confusing in an untyped language, and unfortunately, typed
4945 languages, in particular Hindley-Milner typed languages like Haskell,
4946 only support static scoping of variables.
4949 However, by a simple extension to the type class system of Haskell, we
4950 can support dynamic binding. Basically, we express the use of a
4951 dynamically bound variable as a constraint on the type. These
4952 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4953 function uses a dynamically-bound variable <literal>?x</literal>
4954 of type <literal>t'</literal>". For
4955 example, the following expresses the type of a sort function,
4956 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4958 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4960 The dynamic binding constraints are just a new form of predicate in the type class system.
4963 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4964 where <literal>x</literal> is
4965 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4966 Use of this construct also introduces a new
4967 dynamic-binding constraint in the type of the expression.
4968 For example, the following definition
4969 shows how we can define an implicitly parameterized sort function in
4970 terms of an explicitly parameterized <literal>sortBy</literal> function:
4972 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4974 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4980 <title>Implicit-parameter type constraints</title>
4982 Dynamic binding constraints behave just like other type class
4983 constraints in that they are automatically propagated. Thus, when a
4984 function is used, its implicit parameters are inherited by the
4985 function that called it. For example, our <literal>sort</literal> function might be used
4986 to pick out the least value in a list:
4988 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4989 least xs = head (sort xs)
4991 Without lifting a finger, the <literal>?cmp</literal> parameter is
4992 propagated to become a parameter of <literal>least</literal> as well. With explicit
4993 parameters, the default is that parameters must always be explicit
4994 propagated. With implicit parameters, the default is to always
4998 An implicit-parameter type constraint differs from other type class constraints in the
4999 following way: All uses of a particular implicit parameter must have
5000 the same type. This means that the type of <literal>(?x, ?x)</literal>
5001 is <literal>(?x::a) => (a,a)</literal>, and not
5002 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
5006 <para> You can't have an implicit parameter in the context of a class or instance
5007 declaration. For example, both these declarations are illegal:
5009 class (?x::Int) => C a where ...
5010 instance (?x::a) => Foo [a] where ...
5012 Reason: exactly which implicit parameter you pick up depends on exactly where
5013 you invoke a function. But the ``invocation'' of instance declarations is done
5014 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
5015 Easiest thing is to outlaw the offending types.</para>
5017 Implicit-parameter constraints do not cause ambiguity. For example, consider:
5019 f :: (?x :: [a]) => Int -> Int
5022 g :: (Read a, Show a) => String -> String
5025 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
5026 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
5027 quite unambiguous, and fixes the type <literal>a</literal>.
5032 <title>Implicit-parameter bindings</title>
5035 An implicit parameter is <emphasis>bound</emphasis> using the standard
5036 <literal>let</literal> or <literal>where</literal> binding forms.
5037 For example, we define the <literal>min</literal> function by binding
5038 <literal>cmp</literal>.
5041 min = let ?cmp = (<=) in least
5045 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5046 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5047 (including in a list comprehension, or do-notation, or pattern guards),
5048 or a <literal>where</literal> clause.
5049 Note the following points:
5052 An implicit-parameter binding group must be a
5053 collection of simple bindings to implicit-style variables (no
5054 function-style bindings, and no type signatures); these bindings are
5055 neither polymorphic or recursive.
5058 You may not mix implicit-parameter bindings with ordinary bindings in a
5059 single <literal>let</literal>
5060 expression; use two nested <literal>let</literal>s instead.
5061 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5065 You may put multiple implicit-parameter bindings in a
5066 single binding group; but they are <emphasis>not</emphasis> treated
5067 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5068 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5069 parameter. The bindings are not nested, and may be re-ordered without changing
5070 the meaning of the program.
5071 For example, consider:
5073 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5075 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5076 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5078 f :: (?x::Int) => Int -> Int
5086 <sect3><title>Implicit parameters and polymorphic recursion</title>
5089 Consider these two definitions:
5092 len1 xs = let ?acc = 0 in len_acc1 xs
5095 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5100 len2 xs = let ?acc = 0 in len_acc2 xs
5102 len_acc2 :: (?acc :: Int) => [a] -> Int
5104 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5106 The only difference between the two groups is that in the second group
5107 <literal>len_acc</literal> is given a type signature.
5108 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5109 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5110 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5111 has a type signature, the recursive call is made to the
5112 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5113 as an implicit parameter. So we get the following results in GHCi:
5120 Adding a type signature dramatically changes the result! This is a rather
5121 counter-intuitive phenomenon, worth watching out for.
5125 <sect3><title>Implicit parameters and monomorphism</title>
5127 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5128 Haskell Report) to implicit parameters. For example, consider:
5136 Since the binding for <literal>y</literal> falls under the Monomorphism
5137 Restriction it is not generalised, so the type of <literal>y</literal> is
5138 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5139 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5140 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5141 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5142 <literal>y</literal> in the body of the <literal>let</literal> will see the
5143 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5144 <literal>14</literal>.
5149 <!-- ======================= COMMENTED OUT ========================
5151 We intend to remove linear implicit parameters, so I'm at least removing
5152 them from the 6.6 user manual
5154 <sect2 id="linear-implicit-parameters">
5155 <title>Linear implicit parameters</title>
5157 Linear implicit parameters are an idea developed by Koen Claessen,
5158 Mark Shields, and Simon PJ. They address the long-standing
5159 problem that monads seem over-kill for certain sorts of problem, notably:
5162 <listitem> <para> distributing a supply of unique names </para> </listitem>
5163 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5164 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5168 Linear implicit parameters are just like ordinary implicit parameters,
5169 except that they are "linear"; that is, they cannot be copied, and
5170 must be explicitly "split" instead. Linear implicit parameters are
5171 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5172 (The '/' in the '%' suggests the split!)
5177 import GHC.Exts( Splittable )
5179 data NameSupply = ...
5181 splitNS :: NameSupply -> (NameSupply, NameSupply)
5182 newName :: NameSupply -> Name
5184 instance Splittable NameSupply where
5188 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5189 f env (Lam x e) = Lam x' (f env e)
5192 env' = extend env x x'
5193 ...more equations for f...
5195 Notice that the implicit parameter %ns is consumed
5197 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5198 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5202 So the translation done by the type checker makes
5203 the parameter explicit:
5205 f :: NameSupply -> Env -> Expr -> Expr
5206 f ns env (Lam x e) = Lam x' (f ns1 env e)
5208 (ns1,ns2) = splitNS ns
5210 env = extend env x x'
5212 Notice the call to 'split' introduced by the type checker.
5213 How did it know to use 'splitNS'? Because what it really did
5214 was to introduce a call to the overloaded function 'split',
5215 defined by the class <literal>Splittable</literal>:
5217 class Splittable a where
5220 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5221 split for name supplies. But we can simply write
5227 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5229 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5230 <literal>GHC.Exts</literal>.
5235 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5236 are entirely distinct implicit parameters: you
5237 can use them together and they won't interfere with each other. </para>
5240 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5242 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5243 in the context of a class or instance declaration. </para></listitem>
5247 <sect3><title>Warnings</title>
5250 The monomorphism restriction is even more important than usual.
5251 Consider the example above:
5253 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5254 f env (Lam x e) = Lam x' (f env e)
5257 env' = extend env x x'
5259 If we replaced the two occurrences of x' by (newName %ns), which is
5260 usually a harmless thing to do, we get:
5262 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5263 f env (Lam x e) = Lam (newName %ns) (f env e)
5265 env' = extend env x (newName %ns)
5267 But now the name supply is consumed in <emphasis>three</emphasis> places
5268 (the two calls to newName,and the recursive call to f), so
5269 the result is utterly different. Urk! We don't even have
5273 Well, this is an experimental change. With implicit
5274 parameters we have already lost beta reduction anyway, and
5275 (as John Launchbury puts it) we can't sensibly reason about
5276 Haskell programs without knowing their typing.
5281 <sect3><title>Recursive functions</title>
5282 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5285 foo :: %x::T => Int -> [Int]
5287 foo n = %x : foo (n-1)
5289 where T is some type in class Splittable.</para>
5291 Do you get a list of all the same T's or all different T's
5292 (assuming that split gives two distinct T's back)?
5294 If you supply the type signature, taking advantage of polymorphic
5295 recursion, you get what you'd probably expect. Here's the
5296 translated term, where the implicit param is made explicit:
5299 foo x n = let (x1,x2) = split x
5300 in x1 : foo x2 (n-1)
5302 But if you don't supply a type signature, GHC uses the Hindley
5303 Milner trick of using a single monomorphic instance of the function
5304 for the recursive calls. That is what makes Hindley Milner type inference
5305 work. So the translation becomes
5309 foom n = x : foom (n-1)
5313 Result: 'x' is not split, and you get a list of identical T's. So the
5314 semantics of the program depends on whether or not foo has a type signature.
5317 You may say that this is a good reason to dislike linear implicit parameters
5318 and you'd be right. That is why they are an experimental feature.
5324 ================ END OF Linear Implicit Parameters commented out -->
5326 <sect2 id="kinding">
5327 <title>Explicitly-kinded quantification</title>
5330 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5331 to give the kind explicitly as (machine-checked) documentation,
5332 just as it is nice to give a type signature for a function. On some occasions,
5333 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5334 John Hughes had to define the data type:
5336 data Set cxt a = Set [a]
5337 | Unused (cxt a -> ())
5339 The only use for the <literal>Unused</literal> constructor was to force the correct
5340 kind for the type variable <literal>cxt</literal>.
5343 GHC now instead allows you to specify the kind of a type variable directly, wherever
5344 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5347 This flag enables kind signatures in the following places:
5349 <listitem><para><literal>data</literal> declarations:
5351 data Set (cxt :: * -> *) a = Set [a]
5352 </screen></para></listitem>
5353 <listitem><para><literal>type</literal> declarations:
5355 type T (f :: * -> *) = f Int
5356 </screen></para></listitem>
5357 <listitem><para><literal>class</literal> declarations:
5359 class (Eq a) => C (f :: * -> *) a where ...
5360 </screen></para></listitem>
5361 <listitem><para><literal>forall</literal>'s in type signatures:
5363 f :: forall (cxt :: * -> *). Set cxt Int
5364 </screen></para></listitem>
5369 The parentheses are required. Some of the spaces are required too, to
5370 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5371 will get a parse error, because "<literal>::*->*</literal>" is a
5372 single lexeme in Haskell.
5376 As part of the same extension, you can put kind annotations in types
5379 f :: (Int :: *) -> Int
5380 g :: forall a. a -> (a :: *)
5384 atype ::= '(' ctype '::' kind ')
5386 The parentheses are required.
5391 <sect2 id="universal-quantification">
5392 <title>Arbitrary-rank polymorphism
5396 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5397 explicit universal quantification in
5399 For example, all the following types are legal:
5401 f1 :: forall a b. a -> b -> a
5402 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5404 f2 :: (forall a. a->a) -> Int -> Int
5405 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5407 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5409 f4 :: Int -> (forall a. a -> a)
5411 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5412 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5413 The <literal>forall</literal> makes explicit the universal quantification that
5414 is implicitly added by Haskell.
5417 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5418 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5419 shows, the polymorphic type on the left of the function arrow can be overloaded.
5422 The function <literal>f3</literal> has a rank-3 type;
5423 it has rank-2 types on the left of a function arrow.
5426 GHC has three flags to control higher-rank types:
5429 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5432 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5435 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5436 That is, you can nest <literal>forall</literal>s
5437 arbitrarily deep in function arrows.
5438 In particular, a forall-type (also called a "type scheme"),
5439 including an operational type class context, is legal:
5441 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5442 of a function arrow </para> </listitem>
5443 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5444 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5445 field type signatures.</para> </listitem>
5446 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5447 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5459 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5460 the types of the constructor arguments. Here are several examples:
5466 data T a = T1 (forall b. b -> b -> b) a
5468 data MonadT m = MkMonad { return :: forall a. a -> m a,
5469 bind :: forall a b. m a -> (a -> m b) -> m b
5472 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5478 The constructors have rank-2 types:
5484 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5485 MkMonad :: forall m. (forall a. a -> m a)
5486 -> (forall a b. m a -> (a -> m b) -> m b)
5488 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5494 Notice that you don't need to use a <literal>forall</literal> if there's an
5495 explicit context. For example in the first argument of the
5496 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5497 prefixed to the argument type. The implicit <literal>forall</literal>
5498 quantifies all type variables that are not already in scope, and are
5499 mentioned in the type quantified over.
5503 As for type signatures, implicit quantification happens for non-overloaded
5504 types too. So if you write this:
5507 data T a = MkT (Either a b) (b -> b)
5510 it's just as if you had written this:
5513 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5516 That is, since the type variable <literal>b</literal> isn't in scope, it's
5517 implicitly universally quantified. (Arguably, it would be better
5518 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5519 where that is what is wanted. Feedback welcomed.)
5523 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5524 the constructor to suitable values, just as usual. For example,
5535 a3 = MkSwizzle reverse
5538 a4 = let r x = Just x
5545 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5546 mkTs f x y = [T1 f x, T1 f y]
5552 The type of the argument can, as usual, be more general than the type
5553 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5554 does not need the <literal>Ord</literal> constraint.)
5558 When you use pattern matching, the bound variables may now have
5559 polymorphic types. For example:
5565 f :: T a -> a -> (a, Char)
5566 f (T1 w k) x = (w k x, w 'c' 'd')
5568 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5569 g (MkSwizzle s) xs f = s (map f (s xs))
5571 h :: MonadT m -> [m a] -> m [a]
5572 h m [] = return m []
5573 h m (x:xs) = bind m x $ \y ->
5574 bind m (h m xs) $ \ys ->
5581 In the function <function>h</function> we use the record selectors <literal>return</literal>
5582 and <literal>bind</literal> to extract the polymorphic bind and return functions
5583 from the <literal>MonadT</literal> data structure, rather than using pattern
5589 <title>Type inference</title>
5592 In general, type inference for arbitrary-rank types is undecidable.
5593 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5594 to get a decidable algorithm by requiring some help from the programmer.
5595 We do not yet have a formal specification of "some help" but the rule is this:
5598 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5599 provides an explicit polymorphic type for x, or GHC's type inference will assume
5600 that x's type has no foralls in it</emphasis>.
5603 What does it mean to "provide" an explicit type for x? You can do that by
5604 giving a type signature for x directly, using a pattern type signature
5605 (<xref linkend="scoped-type-variables"/>), thus:
5607 \ f :: (forall a. a->a) -> (f True, f 'c')
5609 Alternatively, you can give a type signature to the enclosing
5610 context, which GHC can "push down" to find the type for the variable:
5612 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5614 Here the type signature on the expression can be pushed inwards
5615 to give a type signature for f. Similarly, and more commonly,
5616 one can give a type signature for the function itself:
5618 h :: (forall a. a->a) -> (Bool,Char)
5619 h f = (f True, f 'c')
5621 You don't need to give a type signature if the lambda bound variable
5622 is a constructor argument. Here is an example we saw earlier:
5624 f :: T a -> a -> (a, Char)
5625 f (T1 w k) x = (w k x, w 'c' 'd')
5627 Here we do not need to give a type signature to <literal>w</literal>, because
5628 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5635 <sect3 id="implicit-quant">
5636 <title>Implicit quantification</title>
5639 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5640 user-written types, if and only if there is no explicit <literal>forall</literal>,
5641 GHC finds all the type variables mentioned in the type that are not already
5642 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5646 f :: forall a. a -> a
5653 h :: forall b. a -> b -> b
5659 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5662 f :: (a -> a) -> Int
5664 f :: forall a. (a -> a) -> Int
5666 f :: (forall a. a -> a) -> Int
5669 g :: (Ord a => a -> a) -> Int
5670 -- MEANS the illegal type
5671 g :: forall a. (Ord a => a -> a) -> Int
5673 g :: (forall a. Ord a => a -> a) -> Int
5675 The latter produces an illegal type, which you might think is silly,
5676 but at least the rule is simple. If you want the latter type, you
5677 can write your for-alls explicitly. Indeed, doing so is strongly advised
5684 <sect2 id="impredicative-polymorphism">
5685 <title>Impredicative polymorphism
5687 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5688 enabled with <option>-XImpredicativeTypes</option>.
5690 that you can call a polymorphic function at a polymorphic type, and
5691 parameterise data structures over polymorphic types. For example:
5693 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5694 f (Just g) = Just (g [3], g "hello")
5697 Notice here that the <literal>Maybe</literal> type is parameterised by the
5698 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5701 <para>The technical details of this extension are described in the paper
5702 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5703 type inference for higher-rank types and impredicativity</ulink>,
5704 which appeared at ICFP 2006.
5708 <sect2 id="scoped-type-variables">
5709 <title>Lexically scoped type variables
5713 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5714 which some type signatures are simply impossible to write. For example:
5716 f :: forall a. [a] -> [a]
5722 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5723 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5724 The type variables bound by a <literal>forall</literal> scope over
5725 the entire definition of the accompanying value declaration.
5726 In this example, the type variable <literal>a</literal> scopes over the whole
5727 definition of <literal>f</literal>, including over
5728 the type signature for <varname>ys</varname>.
5729 In Haskell 98 it is not possible to declare
5730 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5731 it becomes possible to do so.
5733 <para>Lexically-scoped type variables are enabled by
5734 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5736 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5737 variables work, compared to earlier releases. Read this section
5741 <title>Overview</title>
5743 <para>The design follows the following principles
5745 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5746 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5747 design.)</para></listitem>
5748 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5749 type variables. This means that every programmer-written type signature
5750 (including one that contains free scoped type variables) denotes a
5751 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5752 checker, and no inference is involved.</para></listitem>
5753 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5754 changing the program.</para></listitem>
5758 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5760 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5761 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5762 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5763 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5767 In Haskell, a programmer-written type signature is implicitly quantified over
5768 its free type variables (<ulink
5769 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5771 of the Haskell Report).
5772 Lexically scoped type variables affect this implicit quantification rules
5773 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5774 quantified. For example, if type variable <literal>a</literal> is in scope,
5777 (e :: a -> a) means (e :: a -> a)
5778 (e :: b -> b) means (e :: forall b. b->b)
5779 (e :: a -> b) means (e :: forall b. a->b)
5787 <sect3 id="decl-type-sigs">
5788 <title>Declaration type signatures</title>
5789 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5790 quantification (using <literal>forall</literal>) brings into scope the
5791 explicitly-quantified
5792 type variables, in the definition of the named function. For example:
5794 f :: forall a. [a] -> [a]
5795 f (x:xs) = xs ++ [ x :: a ]
5797 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5798 the definition of "<literal>f</literal>".
5800 <para>This only happens if:
5802 <listitem><para> The quantification in <literal>f</literal>'s type
5803 signature is explicit. For example:
5806 g (x:xs) = xs ++ [ x :: a ]
5808 This program will be rejected, because "<literal>a</literal>" does not scope
5809 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5810 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5811 quantification rules.
5813 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5814 not a pattern binding.
5817 f1 :: forall a. [a] -> [a]
5818 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5820 f2 :: forall a. [a] -> [a]
5821 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5823 f3 :: forall a. [a] -> [a]
5824 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5826 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5827 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5828 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5829 the type signature brings <literal>a</literal> into scope.
5835 <sect3 id="exp-type-sigs">
5836 <title>Expression type signatures</title>
5838 <para>An expression type signature that has <emphasis>explicit</emphasis>
5839 quantification (using <literal>forall</literal>) brings into scope the
5840 explicitly-quantified
5841 type variables, in the annotated expression. For example:
5843 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5845 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5846 type variable <literal>s</literal> into scope, in the annotated expression
5847 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5852 <sect3 id="pattern-type-sigs">
5853 <title>Pattern type signatures</title>
5855 A type signature may occur in any pattern; this is a <emphasis>pattern type
5856 signature</emphasis>.
5859 -- f and g assume that 'a' is already in scope
5860 f = \(x::Int, y::a) -> x
5862 h ((x,y) :: (Int,Bool)) = (y,x)
5864 In the case where all the type variables in the pattern type signature are
5865 already in scope (i.e. bound by the enclosing context), matters are simple: the
5866 signature simply constrains the type of the pattern in the obvious way.
5869 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5870 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5871 that are already in scope. For example:
5873 f :: forall a. [a] -> (Int, [a])
5876 (ys::[a], n) = (reverse xs, length xs) -- OK
5877 zs::[a] = xs ++ ys -- OK
5879 Just (v::b) = ... -- Not OK; b is not in scope
5881 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5882 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5886 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5887 type signature may mention a type variable that is not in scope; in this case,
5888 <emphasis>the signature brings that type variable into scope</emphasis>.
5889 This is particularly important for existential data constructors. For example:
5891 data T = forall a. MkT [a]
5894 k (MkT [t::a]) = MkT t3
5898 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5899 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5900 because it is bound by the pattern match. GHC's rule is that in this situation
5901 (and only then), a pattern type signature can mention a type variable that is
5902 not already in scope; the effect is to bring it into scope, standing for the
5903 existentially-bound type variable.
5906 When a pattern type signature binds a type variable in this way, GHC insists that the
5907 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5908 This means that any user-written type signature always stands for a completely known type.
5911 If all this seems a little odd, we think so too. But we must have
5912 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5913 could not name existentially-bound type variables in subsequent type signatures.
5916 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5917 signature is allowed to mention a lexical variable that is not already in
5919 For example, both <literal>f</literal> and <literal>g</literal> would be
5920 illegal if <literal>a</literal> was not already in scope.
5926 <!-- ==================== Commented out part about result type signatures
5928 <sect3 id="result-type-sigs">
5929 <title>Result type signatures</title>
5932 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5935 {- f assumes that 'a' is already in scope -}
5936 f x y :: [a] = [x,y,x]
5938 g = \ x :: [Int] -> [3,4]
5940 h :: forall a. [a] -> a
5944 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5945 the result of the function. Similarly, the body of the lambda in the RHS of
5946 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5947 alternative in <literal>h</literal> is <literal>a</literal>.
5949 <para> A result type signature never brings new type variables into scope.</para>
5951 There are a couple of syntactic wrinkles. First, notice that all three
5952 examples would parse quite differently with parentheses:
5954 {- f assumes that 'a' is already in scope -}
5955 f x (y :: [a]) = [x,y,x]
5957 g = \ (x :: [Int]) -> [3,4]
5959 h :: forall a. [a] -> a
5963 Now the signature is on the <emphasis>pattern</emphasis>; and
5964 <literal>h</literal> would certainly be ill-typed (since the pattern
5965 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5967 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5968 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5969 token or a parenthesised type of some sort). To see why,
5970 consider how one would parse this:
5979 <sect3 id="cls-inst-scoped-tyvars">
5980 <title>Class and instance declarations</title>
5983 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5984 scope over the methods defined in the <literal>where</literal> part. For example:
6002 <sect2 id="typing-binds">
6003 <title>Generalised typing of mutually recursive bindings</title>
6006 The Haskell Report specifies that a group of bindings (at top level, or in a
6007 <literal>let</literal> or <literal>where</literal>) should be sorted into
6008 strongly-connected components, and then type-checked in dependency order
6009 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
6010 Report, Section 4.5.1</ulink>).
6011 As each group is type-checked, any binders of the group that
6013 an explicit type signature are put in the type environment with the specified
6015 and all others are monomorphic until the group is generalised
6016 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
6019 <para>Following a suggestion of Mark Jones, in his paper
6020 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
6022 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
6024 <emphasis>the dependency analysis ignores references to variables that have an explicit
6025 type signature</emphasis>.
6026 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
6027 typecheck. For example, consider:
6029 f :: Eq a => a -> Bool
6030 f x = (x == x) || g True || g "Yes"
6032 g y = (y <= y) || f True
6034 This is rejected by Haskell 98, but under Jones's scheme the definition for
6035 <literal>g</literal> is typechecked first, separately from that for
6036 <literal>f</literal>,
6037 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6038 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6039 type is generalised, to get
6041 g :: Ord a => a -> Bool
6043 Now, the definition for <literal>f</literal> is typechecked, with this type for
6044 <literal>g</literal> in the type environment.
6048 The same refined dependency analysis also allows the type signatures of
6049 mutually-recursive functions to have different contexts, something that is illegal in
6050 Haskell 98 (Section 4.5.2, last sentence). With
6051 <option>-XRelaxedPolyRec</option>
6052 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6053 type signatures; in practice this means that only variables bound by the same
6054 pattern binding must have the same context. For example, this is fine:
6056 f :: Eq a => a -> Bool
6057 f x = (x == x) || g True
6059 g :: Ord a => a -> Bool
6060 g y = (y <= y) || f True
6065 <sect2 id="mono-local-binds">
6066 <title>Monomorphic local bindings</title>
6068 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6069 The rationale is described in the paper
6070 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6073 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6074 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6075 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6076 If you supply a type signature, then the flag has no effect.
6081 <!-- ==================== End of type system extensions ================= -->
6083 <!-- ====================== TEMPLATE HASKELL ======================= -->
6085 <sect1 id="template-haskell">
6086 <title>Template Haskell</title>
6088 <para>Template Haskell allows you to do compile-time meta-programming in
6091 the main technical innovations is discussed in "<ulink
6092 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6093 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6096 There is a Wiki page about
6097 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6098 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6102 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6103 Haskell library reference material</ulink>
6104 (look for module <literal>Language.Haskell.TH</literal>).
6105 Many changes to the original design are described in
6106 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6107 Notes on Template Haskell version 2</ulink>.
6108 Not all of these changes are in GHC, however.
6111 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6112 as a worked example to help get you started.
6116 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6117 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6122 <title>Syntax</title>
6124 <para> Template Haskell has the following new syntactic
6125 constructions. You need to use the flag
6126 <option>-XTemplateHaskell</option>
6127 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6128 </indexterm>to switch these syntactic extensions on
6129 (<option>-XTemplateHaskell</option> is no longer implied by
6130 <option>-fglasgow-exts</option>).</para>
6134 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6135 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6136 There must be no space between the "$" and the identifier or parenthesis. This use
6137 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6138 of "." as an infix operator. If you want the infix operator, put spaces around it.
6140 <para> A splice can occur in place of
6142 <listitem><para> an expression; the spliced expression must
6143 have type <literal>Q Exp</literal></para></listitem>
6144 <listitem><para> an type; the spliced expression must
6145 have type <literal>Q Typ</literal></para></listitem>
6146 <listitem><para> a list of top-level declarations; the spliced expression
6147 must have type <literal>Q [Dec]</literal></para></listitem>
6149 Inside a splice you can can only call functions defined in imported modules,
6150 not functions defined elsewhere in the same module.</para></listitem>
6153 A expression quotation is written in Oxford brackets, thus:
6155 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6156 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6157 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6158 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6159 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6160 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6161 </itemizedlist></para></listitem>
6164 A quasi-quotation can appear in either a pattern context or an
6165 expression context and is also written in Oxford brackets:
6167 <listitem><para> <literal>[$<replaceable>varid</replaceable>| ... |]</literal>,
6168 where the "..." is an arbitrary string; a full description of the
6169 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6170 </itemizedlist></para></listitem>
6173 A name can be quoted with either one or two prefix single quotes:
6175 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6176 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6177 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6179 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6180 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6183 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6184 may also be given as an argument to the <literal>reify</literal> function.
6188 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6189 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6196 $(deriveStuff 'f) -- Uses the $(...) notation
6200 deriveStuff 'g -- Omits the $(...)
6204 This abbreviation makes top-level declaration slices quieter and less intimidating.
6209 (Compared to the original paper, there are many differences of detail.
6210 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6211 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6212 Pattern splices and quotations are not implemented.)
6216 <sect2> <title> Using Template Haskell </title>
6220 The data types and monadic constructor functions for Template Haskell are in the library
6221 <literal>Language.Haskell.THSyntax</literal>.
6225 You can only run a function at compile time if it is imported from another module. That is,
6226 you can't define a function in a module, and call it from within a splice in the same module.
6227 (It would make sense to do so, but it's hard to implement.)
6231 You can only run a function at compile time if it is imported
6232 from another module <emphasis>that is not part of a mutually-recursive group of modules
6233 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6234 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6235 splice is to be run.</para>
6237 For example, when compiling module A,
6238 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6239 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6243 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6246 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6247 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6248 compiles and runs a program, and then looks at the result. So it's important that
6249 the program it compiles produces results whose representations are identical to
6250 those of the compiler itself.
6254 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6255 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6260 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6261 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6262 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6269 -- Import our template "pr"
6270 import Printf ( pr )
6272 -- The splice operator $ takes the Haskell source code
6273 -- generated at compile time by "pr" and splices it into
6274 -- the argument of "putStrLn".
6275 main = putStrLn ( $(pr "Hello") )
6281 -- Skeletal printf from the paper.
6282 -- It needs to be in a separate module to the one where
6283 -- you intend to use it.
6285 -- Import some Template Haskell syntax
6286 import Language.Haskell.TH
6288 -- Describe a format string
6289 data Format = D | S | L String
6291 -- Parse a format string. This is left largely to you
6292 -- as we are here interested in building our first ever
6293 -- Template Haskell program and not in building printf.
6294 parse :: String -> [Format]
6297 -- Generate Haskell source code from a parsed representation
6298 -- of the format string. This code will be spliced into
6299 -- the module which calls "pr", at compile time.
6300 gen :: [Format] -> Q Exp
6301 gen [D] = [| \n -> show n |]
6302 gen [S] = [| \s -> s |]
6303 gen [L s] = stringE s
6305 -- Here we generate the Haskell code for the splice
6306 -- from an input format string.
6307 pr :: String -> Q Exp
6308 pr s = gen (parse s)
6311 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6314 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6317 <para>Run "main.exe" and here is your output:</para>
6327 <title>Using Template Haskell with Profiling</title>
6328 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6330 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6331 interpreter to run the splice expressions. The bytecode interpreter
6332 runs the compiled expression on top of the same runtime on which GHC
6333 itself is running; this means that the compiled code referred to by
6334 the interpreted expression must be compatible with this runtime, and
6335 in particular this means that object code that is compiled for
6336 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6337 expression, because profiled object code is only compatible with the
6338 profiling version of the runtime.</para>
6340 <para>This causes difficulties if you have a multi-module program
6341 containing Template Haskell code and you need to compile it for
6342 profiling, because GHC cannot load the profiled object code and use it
6343 when executing the splices. Fortunately GHC provides a workaround.
6344 The basic idea is to compile the program twice:</para>
6348 <para>Compile the program or library first the normal way, without
6349 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6352 <para>Then compile it again with <option>-prof</option>, and
6353 additionally use <option>-osuf
6354 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6355 to name the object files differently (you can choose any suffix
6356 that isn't the normal object suffix here). GHC will automatically
6357 load the object files built in the first step when executing splice
6358 expressions. If you omit the <option>-osuf</option> flag when
6359 building with <option>-prof</option> and Template Haskell is used,
6360 GHC will emit an error message. </para>
6365 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6366 <para>Quasi-quotation allows patterns and expressions to be written using
6367 programmer-defined concrete syntax; the motivation behind the extension and
6368 several examples are documented in
6369 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6370 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6371 2007). The example below shows how to write a quasiquoter for a simple
6372 expression language.</para>
6375 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6376 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6377 functions for quoting expressions and patterns, respectively. The first argument
6378 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6379 context of the quasi-quotation statement determines which of the two parsers is
6380 called: if the quasi-quotation occurs in an expression context, the expression
6381 parser is called, and if it occurs in a pattern context, the pattern parser is
6385 Note that in the example we make use of an antiquoted
6386 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6387 (this syntax for anti-quotation was defined by the parser's
6388 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6389 integer value argument of the constructor <literal>IntExpr</literal> when
6390 pattern matching. Please see the referenced paper for further details regarding
6391 anti-quotation as well as the description of a technique that uses SYB to
6392 leverage a single parser of type <literal>String -> a</literal> to generate both
6393 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6394 pattern parser that returns a value of type <literal>Q Pat</literal>.
6397 <para>In general, a quasi-quote has the form
6398 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6399 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6400 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6401 can be arbitrary, and may contain newlines.
6404 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6405 the example, <literal>expr</literal> cannot be defined
6406 in <literal>Main.hs</literal> where it is used, but must be imported.
6417 main = do { print $ eval [$expr|1 + 2|]
6419 { [$expr|'int:n|] -> print n
6428 import qualified Language.Haskell.TH as TH
6429 import Language.Haskell.TH.Quote
6431 data Expr = IntExpr Integer
6432 | AntiIntExpr String
6433 | BinopExpr BinOp Expr Expr
6435 deriving(Show, Typeable, Data)
6441 deriving(Show, Typeable, Data)
6443 eval :: Expr -> Integer
6444 eval (IntExpr n) = n
6445 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6452 expr = QuasiQuoter parseExprExp parseExprPat
6454 -- Parse an Expr, returning its representation as
6455 -- either a Q Exp or a Q Pat. See the referenced paper
6456 -- for how to use SYB to do this by writing a single
6457 -- parser of type String -> Expr instead of two
6458 -- separate parsers.
6460 parseExprExp :: String -> Q Exp
6463 parseExprPat :: String -> Q Pat
6467 <para>Now run the compiler:
6470 $ ghc --make -XQuasiQuotes Main.hs -o main
6473 <para>Run "main" and here is your output:</para>
6485 <!-- ===================== Arrow notation =================== -->
6487 <sect1 id="arrow-notation">
6488 <title>Arrow notation
6491 <para>Arrows are a generalization of monads introduced by John Hughes.
6492 For more details, see
6497 “Generalising Monads to Arrows”,
6498 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6499 pp67–111, May 2000.
6500 The paper that introduced arrows: a friendly introduction, motivated with
6501 programming examples.
6507 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6508 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6509 Introduced the notation described here.
6515 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6516 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6523 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6524 John Hughes, in <citetitle>5th International Summer School on
6525 Advanced Functional Programming</citetitle>,
6526 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6528 This paper includes another introduction to the notation,
6529 with practical examples.
6535 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6536 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6537 A terse enumeration of the formal rules used
6538 (extracted from comments in the source code).
6544 The arrows web page at
6545 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6550 With the <option>-XArrows</option> flag, GHC supports the arrow
6551 notation described in the second of these papers,
6552 translating it using combinators from the
6553 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6555 What follows is a brief introduction to the notation;
6556 it won't make much sense unless you've read Hughes's paper.
6559 <para>The extension adds a new kind of expression for defining arrows:
6561 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6562 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6564 where <literal>proc</literal> is a new keyword.
6565 The variables of the pattern are bound in the body of the
6566 <literal>proc</literal>-expression,
6567 which is a new sort of thing called a <firstterm>command</firstterm>.
6568 The syntax of commands is as follows:
6570 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6571 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6572 | <replaceable>cmd</replaceable><superscript>0</superscript>
6574 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6575 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6576 infix operators as for expressions, and
6578 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6579 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6580 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6581 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6582 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6583 | <replaceable>fcmd</replaceable>
6585 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6586 | ( <replaceable>cmd</replaceable> )
6587 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6589 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6590 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6591 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6592 | <replaceable>cmd</replaceable>
6594 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6595 except that the bodies are commands instead of expressions.
6599 Commands produce values, but (like monadic computations)
6600 may yield more than one value,
6601 or none, and may do other things as well.
6602 For the most part, familiarity with monadic notation is a good guide to
6604 However the values of expressions, even monadic ones,
6605 are determined by the values of the variables they contain;
6606 this is not necessarily the case for commands.
6610 A simple example of the new notation is the expression
6612 proc x -> f -< x+1
6614 We call this a <firstterm>procedure</firstterm> or
6615 <firstterm>arrow abstraction</firstterm>.
6616 As with a lambda expression, the variable <literal>x</literal>
6617 is a new variable bound within the <literal>proc</literal>-expression.
6618 It refers to the input to the arrow.
6619 In the above example, <literal>-<</literal> is not an identifier but an
6620 new reserved symbol used for building commands from an expression of arrow
6621 type and an expression to be fed as input to that arrow.
6622 (The weird look will make more sense later.)
6623 It may be read as analogue of application for arrows.
6624 The above example is equivalent to the Haskell expression
6626 arr (\ x -> x+1) >>> f
6628 That would make no sense if the expression to the left of
6629 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6630 More generally, the expression to the left of <literal>-<</literal>
6631 may not involve any <firstterm>local variable</firstterm>,
6632 i.e. a variable bound in the current arrow abstraction.
6633 For such a situation there is a variant <literal>-<<</literal>, as in
6635 proc x -> f x -<< x+1
6637 which is equivalent to
6639 arr (\ x -> (f x, x+1)) >>> app
6641 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6643 Such an arrow is equivalent to a monad, so if you're using this form
6644 you may find a monadic formulation more convenient.
6648 <title>do-notation for commands</title>
6651 Another form of command is a form of <literal>do</literal>-notation.
6652 For example, you can write
6661 You can read this much like ordinary <literal>do</literal>-notation,
6662 but with commands in place of monadic expressions.
6663 The first line sends the value of <literal>x+1</literal> as an input to
6664 the arrow <literal>f</literal>, and matches its output against
6665 <literal>y</literal>.
6666 In the next line, the output is discarded.
6667 The arrow <function>returnA</function> is defined in the
6668 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6669 module as <literal>arr id</literal>.
6670 The above example is treated as an abbreviation for
6672 arr (\ x -> (x, x)) >>>
6673 first (arr (\ x -> x+1) >>> f) >>>
6674 arr (\ (y, x) -> (y, (x, y))) >>>
6675 first (arr (\ y -> 2*y) >>> g) >>>
6677 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6678 first (arr (\ (x, z) -> x*z) >>> h) >>>
6679 arr (\ (t, z) -> t+z) >>>
6682 Note that variables not used later in the composition are projected out.
6683 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6685 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6686 module, this reduces to
6688 arr (\ x -> (x+1, x)) >>>
6690 arr (\ (y, x) -> (2*y, (x, y))) >>>
6692 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6694 arr (\ (t, z) -> t+z)
6696 which is what you might have written by hand.
6697 With arrow notation, GHC keeps track of all those tuples of variables for you.
6701 Note that although the above translation suggests that
6702 <literal>let</literal>-bound variables like <literal>z</literal> must be
6703 monomorphic, the actual translation produces Core,
6704 so polymorphic variables are allowed.
6708 It's also possible to have mutually recursive bindings,
6709 using the new <literal>rec</literal> keyword, as in the following example:
6711 counter :: ArrowCircuit a => a Bool Int
6712 counter = proc reset -> do
6713 rec output <- returnA -< if reset then 0 else next
6714 next <- delay 0 -< output+1
6715 returnA -< output
6717 The translation of such forms uses the <function>loop</function> combinator,
6718 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6724 <title>Conditional commands</title>
6727 In the previous example, we used a conditional expression to construct the
6729 Sometimes we want to conditionally execute different commands, as in
6736 which is translated to
6738 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6739 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6741 Since the translation uses <function>|||</function>,
6742 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6746 There are also <literal>case</literal> commands, like
6752 y <- h -< (x1, x2)
6756 The syntax is the same as for <literal>case</literal> expressions,
6757 except that the bodies of the alternatives are commands rather than expressions.
6758 The translation is similar to that of <literal>if</literal> commands.
6764 <title>Defining your own control structures</title>
6767 As we're seen, arrow notation provides constructs,
6768 modelled on those for expressions,
6769 for sequencing, value recursion and conditionals.
6770 But suitable combinators,
6771 which you can define in ordinary Haskell,
6772 may also be used to build new commands out of existing ones.
6773 The basic idea is that a command defines an arrow from environments to values.
6774 These environments assign values to the free local variables of the command.
6775 Thus combinators that produce arrows from arrows
6776 may also be used to build commands from commands.
6777 For example, the <literal>ArrowChoice</literal> class includes a combinator
6779 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6781 so we can use it to build commands:
6783 expr' = proc x -> do
6786 symbol Plus -< ()
6787 y <- term -< ()
6790 symbol Minus -< ()
6791 y <- term -< ()
6794 (The <literal>do</literal> on the first line is needed to prevent the first
6795 <literal><+> ...</literal> from being interpreted as part of the
6796 expression on the previous line.)
6797 This is equivalent to
6799 expr' = (proc x -> returnA -< x)
6800 <+> (proc x -> do
6801 symbol Plus -< ()
6802 y <- term -< ()
6804 <+> (proc x -> do
6805 symbol Minus -< ()
6806 y <- term -< ()
6809 It is essential that this operator be polymorphic in <literal>e</literal>
6810 (representing the environment input to the command
6811 and thence to its subcommands)
6812 and satisfy the corresponding naturality property
6814 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6816 at least for strict <literal>k</literal>.
6817 (This should be automatic if you're not using <function>seq</function>.)
6818 This ensures that environments seen by the subcommands are environments
6819 of the whole command,
6820 and also allows the translation to safely trim these environments.
6821 The operator must also not use any variable defined within the current
6826 We could define our own operator
6828 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6829 untilA body cond = proc x ->
6830 b <- cond -< x
6831 if b then returnA -< ()
6834 untilA body cond -< x
6836 and use it in the same way.
6837 Of course this infix syntax only makes sense for binary operators;
6838 there is also a more general syntax involving special brackets:
6842 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6849 <title>Primitive constructs</title>
6852 Some operators will need to pass additional inputs to their subcommands.
6853 For example, in an arrow type supporting exceptions,
6854 the operator that attaches an exception handler will wish to pass the
6855 exception that occurred to the handler.
6856 Such an operator might have a type
6858 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6860 where <literal>Ex</literal> is the type of exceptions handled.
6861 You could then use this with arrow notation by writing a command
6863 body `handleA` \ ex -> handler
6865 so that if an exception is raised in the command <literal>body</literal>,
6866 the variable <literal>ex</literal> is bound to the value of the exception
6867 and the command <literal>handler</literal>,
6868 which typically refers to <literal>ex</literal>, is entered.
6869 Though the syntax here looks like a functional lambda,
6870 we are talking about commands, and something different is going on.
6871 The input to the arrow represented by a command consists of values for
6872 the free local variables in the command, plus a stack of anonymous values.
6873 In all the prior examples, this stack was empty.
6874 In the second argument to <function>handleA</function>,
6875 this stack consists of one value, the value of the exception.
6876 The command form of lambda merely gives this value a name.
6881 the values on the stack are paired to the right of the environment.
6882 So operators like <function>handleA</function> that pass
6883 extra inputs to their subcommands can be designed for use with the notation
6884 by pairing the values with the environment in this way.
6885 More precisely, the type of each argument of the operator (and its result)
6886 should have the form
6888 a (...(e,t1), ... tn) t
6890 where <replaceable>e</replaceable> is a polymorphic variable
6891 (representing the environment)
6892 and <replaceable>ti</replaceable> are the types of the values on the stack,
6893 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6894 The polymorphic variable <replaceable>e</replaceable> must not occur in
6895 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6896 <replaceable>t</replaceable>.
6897 However the arrows involved need not be the same.
6898 Here are some more examples of suitable operators:
6900 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6901 runReader :: ... => a e c -> a' (e,State) c
6902 runState :: ... => a e c -> a' (e,State) (c,State)
6904 We can supply the extra input required by commands built with the last two
6905 by applying them to ordinary expressions, as in
6909 (|runReader (do { ... })|) s
6911 which adds <literal>s</literal> to the stack of inputs to the command
6912 built using <function>runReader</function>.
6916 The command versions of lambda abstraction and application are analogous to
6917 the expression versions.
6918 In particular, the beta and eta rules describe equivalences of commands.
6919 These three features (operators, lambda abstraction and application)
6920 are the core of the notation; everything else can be built using them,
6921 though the results would be somewhat clumsy.
6922 For example, we could simulate <literal>do</literal>-notation by defining
6924 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6925 u `bind` f = returnA &&& u >>> f
6927 bind_ :: Arrow a => a e b -> a e c -> a e c
6928 u `bind_` f = u `bind` (arr fst >>> f)
6930 We could simulate <literal>if</literal> by defining
6932 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6933 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6940 <title>Differences with the paper</title>
6945 <para>Instead of a single form of arrow application (arrow tail) with two
6946 translations, the implementation provides two forms
6947 <quote><literal>-<</literal></quote> (first-order)
6948 and <quote><literal>-<<</literal></quote> (higher-order).
6953 <para>User-defined operators are flagged with banana brackets instead of
6954 a new <literal>form</literal> keyword.
6963 <title>Portability</title>
6966 Although only GHC implements arrow notation directly,
6967 there is also a preprocessor
6969 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6970 that translates arrow notation into Haskell 98
6971 for use with other Haskell systems.
6972 You would still want to check arrow programs with GHC;
6973 tracing type errors in the preprocessor output is not easy.
6974 Modules intended for both GHC and the preprocessor must observe some
6975 additional restrictions:
6980 The module must import
6981 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6987 The preprocessor cannot cope with other Haskell extensions.
6988 These would have to go in separate modules.
6994 Because the preprocessor targets Haskell (rather than Core),
6995 <literal>let</literal>-bound variables are monomorphic.
7006 <!-- ==================== BANG PATTERNS ================= -->
7008 <sect1 id="bang-patterns">
7009 <title>Bang patterns
7010 <indexterm><primary>Bang patterns</primary></indexterm>
7012 <para>GHC supports an extension of pattern matching called <emphasis>bang
7013 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
7014 Bang patterns are under consideration for Haskell Prime.
7016 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
7017 prime feature description</ulink> contains more discussion and examples
7018 than the material below.
7021 The key change is the addition of a new rule to the
7022 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
7023 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
7024 against a value <replaceable>v</replaceable> behaves as follows:
7026 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
7027 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
7031 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7034 <sect2 id="bang-patterns-informal">
7035 <title>Informal description of bang patterns
7038 The main idea is to add a single new production to the syntax of patterns:
7042 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7043 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7048 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7049 whereas without the bang it would be lazy.
7050 Bang patterns can be nested of course:
7054 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7055 <literal>y</literal>.
7056 A bang only really has an effect if it precedes a variable or wild-card pattern:
7061 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7062 putting a bang before a pattern that
7063 forces evaluation anyway does nothing.
7066 There is one (apparent) exception to this general rule that a bang only
7067 makes a difference when it precedes a variable or wild-card: a bang at the
7068 top level of a <literal>let</literal> or <literal>where</literal>
7069 binding makes the binding strict, regardless of the pattern. For example:
7073 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7074 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7075 (We say "apparent" exception because the Right Way to think of it is that the bang
7076 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7077 is part of the syntax of the <emphasis>binding</emphasis>.)
7078 Nested bangs in a pattern binding behave uniformly with all other forms of
7079 pattern matching. For example
7081 let (!x,[y]) = e in b
7083 is equivalent to this:
7085 let { t = case e of (x,[y]) -> x `seq` (x,y)
7090 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7091 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7092 evaluation of <literal>x</literal>.
7095 Bang patterns work in <literal>case</literal> expressions too, of course:
7097 g5 x = let y = f x in body
7098 g6 x = case f x of { y -> body }
7099 g7 x = case f x of { !y -> body }
7101 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7102 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7103 result, and then evaluates <literal>body</literal>.
7108 <sect2 id="bang-patterns-sem">
7109 <title>Syntax and semantics
7113 We add a single new production to the syntax of patterns:
7117 There is one problem with syntactic ambiguity. Consider:
7121 Is this a definition of the infix function "<literal>(!)</literal>",
7122 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7123 ambiguity in favour of the latter. If you want to define
7124 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7129 The semantics of Haskell pattern matching is described in <ulink
7130 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7131 Section 3.17.2</ulink> of the Haskell Report. To this description add
7132 one extra item 10, saying:
7133 <itemizedlist><listitem><para>Matching
7134 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7135 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7136 <listitem><para>otherwise, <literal>pat</literal> is matched against
7137 <literal>v</literal></para></listitem>
7139 </para></listitem></itemizedlist>
7140 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7141 Section 3.17.3</ulink>, add a new case (t):
7143 case v of { !pat -> e; _ -> e' }
7144 = v `seq` case v of { pat -> e; _ -> e' }
7147 That leaves let expressions, whose translation is given in
7148 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7150 of the Haskell Report.
7151 In the translation box, first apply
7152 the following transformation: for each pattern <literal>pi</literal> that is of
7153 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7154 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7155 have a bang at the top, apply the rules in the existing box.
7157 <para>The effect of the let rule is to force complete matching of the pattern
7158 <literal>qi</literal> before evaluation of the body is begun. The bang is
7159 retained in the translated form in case <literal>qi</literal> is a variable,
7167 The let-binding can be recursive. However, it is much more common for
7168 the let-binding to be non-recursive, in which case the following law holds:
7169 <literal>(let !p = rhs in body)</literal>
7171 <literal>(case rhs of !p -> body)</literal>
7174 A pattern with a bang at the outermost level is not allowed at the top level of
7180 <!-- ==================== ASSERTIONS ================= -->
7182 <sect1 id="assertions">
7184 <indexterm><primary>Assertions</primary></indexterm>
7188 If you want to make use of assertions in your standard Haskell code, you
7189 could define a function like the following:
7195 assert :: Bool -> a -> a
7196 assert False x = error "assertion failed!"
7203 which works, but gives you back a less than useful error message --
7204 an assertion failed, but which and where?
7208 One way out is to define an extended <function>assert</function> function which also
7209 takes a descriptive string to include in the error message and
7210 perhaps combine this with the use of a pre-processor which inserts
7211 the source location where <function>assert</function> was used.
7215 Ghc offers a helping hand here, doing all of this for you. For every
7216 use of <function>assert</function> in the user's source:
7222 kelvinToC :: Double -> Double
7223 kelvinToC k = assert (k >= 0.0) (k+273.15)
7229 Ghc will rewrite this to also include the source location where the
7236 assert pred val ==> assertError "Main.hs|15" pred val
7242 The rewrite is only performed by the compiler when it spots
7243 applications of <function>Control.Exception.assert</function>, so you
7244 can still define and use your own versions of
7245 <function>assert</function>, should you so wish. If not, import
7246 <literal>Control.Exception</literal> to make use
7247 <function>assert</function> in your code.
7251 GHC ignores assertions when optimisation is turned on with the
7252 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7253 <literal>assert pred e</literal> will be rewritten to
7254 <literal>e</literal>. You can also disable assertions using the
7255 <option>-fignore-asserts</option>
7256 option<indexterm><primary><option>-fignore-asserts</option></primary>
7257 </indexterm>.</para>
7260 Assertion failures can be caught, see the documentation for the
7261 <literal>Control.Exception</literal> library for the details.
7267 <!-- =============================== PRAGMAS =========================== -->
7269 <sect1 id="pragmas">
7270 <title>Pragmas</title>
7272 <indexterm><primary>pragma</primary></indexterm>
7274 <para>GHC supports several pragmas, or instructions to the
7275 compiler placed in the source code. Pragmas don't normally affect
7276 the meaning of the program, but they might affect the efficiency
7277 of the generated code.</para>
7279 <para>Pragmas all take the form
7281 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7283 where <replaceable>word</replaceable> indicates the type of
7284 pragma, and is followed optionally by information specific to that
7285 type of pragma. Case is ignored in
7286 <replaceable>word</replaceable>. The various values for
7287 <replaceable>word</replaceable> that GHC understands are described
7288 in the following sections; any pragma encountered with an
7289 unrecognised <replaceable>word</replaceable> is
7290 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7291 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7293 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7297 pragma must precede the <literal>module</literal> keyword in the file.
7300 There can be as many file-header pragmas as you please, and they can be
7301 preceded or followed by comments.
7304 File-header pragmas are read once only, before
7305 pre-processing the file (e.g. with cpp).
7308 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7309 <literal>{-# OPTIONS_GHC #-}</literal>, and
7310 <literal>{-# INCLUDE #-}</literal>.
7315 <sect2 id="language-pragma">
7316 <title>LANGUAGE pragma</title>
7318 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7319 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7321 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7323 It is the intention that all Haskell compilers support the
7324 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7325 all extensions are supported by all compilers, of
7326 course. The <literal>LANGUAGE</literal> pragma should be used instead
7327 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7329 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7331 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7333 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7335 <para>Every language extension can also be turned into a command-line flag
7336 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7337 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7340 <para>A list of all supported language extensions can be obtained by invoking
7341 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7343 <para>Any extension from the <literal>Extension</literal> type defined in
7345 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7346 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7350 <sect2 id="options-pragma">
7351 <title>OPTIONS_GHC pragma</title>
7352 <indexterm><primary>OPTIONS_GHC</primary>
7354 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7357 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7358 additional options that are given to the compiler when compiling
7359 this source file. See <xref linkend="source-file-options"/> for
7362 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7363 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7366 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7368 <sect2 id="include-pragma">
7369 <title>INCLUDE pragma</title>
7371 <para>The <literal>INCLUDE</literal> used to be necessary for
7372 specifying header files to be included when using the FFI and
7373 compiling via C. It is no longer required for GHC, but is
7374 accepted (and ignored) for compatibility with other
7378 <sect2 id="warning-deprecated-pragma">
7379 <title>WARNING and DEPRECATED pragmas</title>
7380 <indexterm><primary>WARNING</primary></indexterm>
7381 <indexterm><primary>DEPRECATED</primary></indexterm>
7383 <para>The WARNING pragma allows you to attach an arbitrary warning
7384 to a particular function, class, or type.
7385 A DEPRECATED pragma lets you specify that
7386 a particular function, class, or type is deprecated.
7387 There are two ways of using these pragmas.
7391 <para>You can work on an entire module thus:</para>
7393 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7398 module Wibble {-# WARNING "This is an unstable interface." #-} where
7401 <para>When you compile any module that import
7402 <literal>Wibble</literal>, GHC will print the specified
7407 <para>You can attach a warning to a function, class, type, or data constructor, with the
7408 following top-level declarations:</para>
7410 {-# DEPRECATED f, C, T "Don't use these" #-}
7411 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7413 <para>When you compile any module that imports and uses any
7414 of the specified entities, GHC will print the specified
7416 <para> You can only attach to entities declared at top level in the module
7417 being compiled, and you can only use unqualified names in the list of
7418 entities. A capitalised name, such as <literal>T</literal>
7419 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7420 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7421 both are in scope. If both are in scope, there is currently no way to
7422 specify one without the other (c.f. fixities
7423 <xref linkend="infix-tycons"/>).</para>
7426 Warnings and deprecations are not reported for
7427 (a) uses within the defining module, and
7428 (b) uses in an export list.
7429 The latter reduces spurious complaints within a library
7430 in which one module gathers together and re-exports
7431 the exports of several others.
7433 <para>You can suppress the warnings with the flag
7434 <option>-fno-warn-warnings-deprecations</option>.</para>
7437 <sect2 id="inline-noinline-pragma">
7438 <title>INLINE and NOINLINE pragmas</title>
7440 <para>These pragmas control the inlining of function
7443 <sect3 id="inline-pragma">
7444 <title>INLINE pragma</title>
7445 <indexterm><primary>INLINE</primary></indexterm>
7447 <para>GHC (with <option>-O</option>, as always) tries to
7448 inline (or “unfold”) functions/values that are
7449 “small enough,” thus avoiding the call overhead
7450 and possibly exposing other more-wonderful optimisations.
7451 Normally, if GHC decides a function is “too
7452 expensive” to inline, it will not do so, nor will it
7453 export that unfolding for other modules to use.</para>
7455 <para>The sledgehammer you can bring to bear is the
7456 <literal>INLINE</literal><indexterm><primary>INLINE
7457 pragma</primary></indexterm> pragma, used thusly:</para>
7460 key_function :: Int -> String -> (Bool, Double)
7461 {-# INLINE key_function #-}
7464 <para>The major effect of an <literal>INLINE</literal> pragma
7465 is to declare a function's “cost” to be very low.
7466 The normal unfolding machinery will then be very keen to
7467 inline it. However, an <literal>INLINE</literal> pragma for a
7468 function "<literal>f</literal>" has a number of other effects:
7471 No functions are inlined into <literal>f</literal>. Otherwise
7472 GHC might inline a big function into <literal>f</literal>'s right hand side,
7473 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7476 The float-in, float-out, and common-sub-expression transformations are not
7477 applied to the body of <literal>f</literal>.
7480 An INLINE function is not worker/wrappered by strictness analysis.
7481 It's going to be inlined wholesale instead.
7484 All of these effects are aimed at ensuring that what gets inlined is
7485 exactly what you asked for, no more and no less.
7487 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7488 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7489 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7490 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7491 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7492 when there is no choice even an INLINE function can be selected, in which case
7493 the INLINE pragma is ignored.
7494 For example, for a self-recursive function, the loop breaker can only be the function
7495 itself, so an INLINE pragma is always ignored.</para>
7497 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7498 function can be put anywhere its type signature could be
7501 <para><literal>INLINE</literal> pragmas are a particularly
7503 <literal>then</literal>/<literal>return</literal> (or
7504 <literal>bind</literal>/<literal>unit</literal>) functions in
7505 a monad. For example, in GHC's own
7506 <literal>UniqueSupply</literal> monad code, we have:</para>
7509 {-# INLINE thenUs #-}
7510 {-# INLINE returnUs #-}
7513 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7514 linkend="noinline-pragma"/>).</para>
7516 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7517 so if you want your code to be HBC-compatible you'll have to surround
7518 the pragma with C pre-processor directives
7519 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7523 <sect3 id="noinline-pragma">
7524 <title>NOINLINE pragma</title>
7526 <indexterm><primary>NOINLINE</primary></indexterm>
7527 <indexterm><primary>NOTINLINE</primary></indexterm>
7529 <para>The <literal>NOINLINE</literal> pragma does exactly what
7530 you'd expect: it stops the named function from being inlined
7531 by the compiler. You shouldn't ever need to do this, unless
7532 you're very cautious about code size.</para>
7534 <para><literal>NOTINLINE</literal> is a synonym for
7535 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7536 specified by Haskell 98 as the standard way to disable
7537 inlining, so it should be used if you want your code to be
7541 <sect3 id="phase-control">
7542 <title>Phase control</title>
7544 <para> Sometimes you want to control exactly when in GHC's
7545 pipeline the INLINE pragma is switched on. Inlining happens
7546 only during runs of the <emphasis>simplifier</emphasis>. Each
7547 run of the simplifier has a different <emphasis>phase
7548 number</emphasis>; the phase number decreases towards zero.
7549 If you use <option>-dverbose-core2core</option> you'll see the
7550 sequence of phase numbers for successive runs of the
7551 simplifier. In an INLINE pragma you can optionally specify a
7555 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7556 <literal>f</literal>
7557 until phase <literal>k</literal>, but from phase
7558 <literal>k</literal> onwards be very keen to inline it.
7561 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7562 <literal>f</literal>
7563 until phase <literal>k</literal>, but from phase
7564 <literal>k</literal> onwards do not inline it.
7567 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7568 <literal>f</literal>
7569 until phase <literal>k</literal>, but from phase
7570 <literal>k</literal> onwards be willing to inline it (as if
7571 there was no pragma).
7574 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7575 <literal>f</literal>
7576 until phase <literal>k</literal>, but from phase
7577 <literal>k</literal> onwards do not inline it.
7580 The same information is summarised here:
7582 -- Before phase 2 Phase 2 and later
7583 {-# INLINE [2] f #-} -- No Yes
7584 {-# INLINE [~2] f #-} -- Yes No
7585 {-# NOINLINE [2] f #-} -- No Maybe
7586 {-# NOINLINE [~2] f #-} -- Maybe No
7588 {-# INLINE f #-} -- Yes Yes
7589 {-# NOINLINE f #-} -- No No
7591 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7592 function body is small, or it is applied to interesting-looking arguments etc).
7593 Another way to understand the semantics is this:
7595 <listitem><para>For both INLINE and NOINLINE, the phase number says
7596 when inlining is allowed at all.</para></listitem>
7597 <listitem><para>The INLINE pragma has the additional effect of making the
7598 function body look small, so that when inlining is allowed it is very likely to
7603 <para>The same phase-numbering control is available for RULES
7604 (<xref linkend="rewrite-rules"/>).</para>
7608 <sect2 id="annotation-pragmas">
7609 <title>ANN pragmas</title>
7611 <para>GHC offers the ability to annotate various code constructs with additional
7612 data by using three pragmas. This data can then be inspected at a later date by
7613 using GHC-as-a-library.</para>
7615 <sect3 id="ann-pragma">
7616 <title>Annotating values</title>
7618 <indexterm><primary>ANN</primary></indexterm>
7620 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7621 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7622 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7623 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7624 you would do this:</para>
7627 {-# ANN foo (Just "Hello") #-}
7632 A number of restrictions apply to use of annotations:
7634 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7635 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7636 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7637 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7638 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7640 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7641 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7644 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7645 please give the GHC team a shout</ulink>.
7648 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7649 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7652 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7657 <sect3 id="typeann-pragma">
7658 <title>Annotating types</title>
7660 <indexterm><primary>ANN type</primary></indexterm>
7661 <indexterm><primary>ANN</primary></indexterm>
7663 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7666 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7671 <sect3 id="modann-pragma">
7672 <title>Annotating modules</title>
7674 <indexterm><primary>ANN module</primary></indexterm>
7675 <indexterm><primary>ANN</primary></indexterm>
7677 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7680 {-# ANN module (Just "A `Maybe String' annotation") #-}
7685 <sect2 id="line-pragma">
7686 <title>LINE pragma</title>
7688 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7689 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7690 <para>This pragma is similar to C's <literal>#line</literal>
7691 pragma, and is mainly for use in automatically generated Haskell
7692 code. It lets you specify the line number and filename of the
7693 original code; for example</para>
7695 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7697 <para>if you'd generated the current file from something called
7698 <filename>Foo.vhs</filename> and this line corresponds to line
7699 42 in the original. GHC will adjust its error messages to refer
7700 to the line/file named in the <literal>LINE</literal>
7705 <title>RULES pragma</title>
7707 <para>The RULES pragma lets you specify rewrite rules. It is
7708 described in <xref linkend="rewrite-rules"/>.</para>
7711 <sect2 id="specialize-pragma">
7712 <title>SPECIALIZE pragma</title>
7714 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7715 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7716 <indexterm><primary>overloading, death to</primary></indexterm>
7718 <para>(UK spelling also accepted.) For key overloaded
7719 functions, you can create extra versions (NB: more code space)
7720 specialised to particular types. Thus, if you have an
7721 overloaded function:</para>
7724 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7727 <para>If it is heavily used on lists with
7728 <literal>Widget</literal> keys, you could specialise it as
7732 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7735 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7736 be put anywhere its type signature could be put.</para>
7738 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7739 (a) a specialised version of the function and (b) a rewrite rule
7740 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7741 un-specialised function into a call to the specialised one.</para>
7743 <para>The type in a SPECIALIZE pragma can be any type that is less
7744 polymorphic than the type of the original function. In concrete terms,
7745 if the original function is <literal>f</literal> then the pragma
7747 {-# SPECIALIZE f :: <type> #-}
7749 is valid if and only if the definition
7751 f_spec :: <type>
7754 is valid. Here are some examples (where we only give the type signature
7755 for the original function, not its code):
7757 f :: Eq a => a -> b -> b
7758 {-# SPECIALISE f :: Int -> b -> b #-}
7760 g :: (Eq a, Ix b) => a -> b -> b
7761 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7763 h :: Eq a => a -> a -> a
7764 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7766 The last of these examples will generate a
7767 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7768 well. If you use this kind of specialisation, let us know how well it works.
7771 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7772 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7773 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7774 The <literal>INLINE</literal> pragma affects the specialised version of the
7775 function (only), and applies even if the function is recursive. The motivating
7778 -- A GADT for arrays with type-indexed representation
7780 ArrInt :: !Int -> ByteArray# -> Arr Int
7781 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7783 (!:) :: Arr e -> Int -> e
7784 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7785 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7786 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7787 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7789 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7790 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7791 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7792 the specialised function will be inlined. It has two calls to
7793 <literal>(!:)</literal>,
7794 both at type <literal>Int</literal>. Both these calls fire the first
7795 specialisation, whose body is also inlined. The result is a type-based
7796 unrolling of the indexing function.</para>
7797 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7798 on an ordinarily-recursive function.</para>
7800 <para>Note: In earlier versions of GHC, it was possible to provide your own
7801 specialised function for a given type:
7804 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7807 This feature has been removed, as it is now subsumed by the
7808 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7812 <sect2 id="specialize-instance-pragma">
7813 <title>SPECIALIZE instance pragma
7817 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7818 <indexterm><primary>overloading, death to</primary></indexterm>
7819 Same idea, except for instance declarations. For example:
7822 instance (Eq a) => Eq (Foo a) where {
7823 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7827 The pragma must occur inside the <literal>where</literal> part
7828 of the instance declaration.
7831 Compatible with HBC, by the way, except perhaps in the placement
7837 <sect2 id="unpack-pragma">
7838 <title>UNPACK pragma</title>
7840 <indexterm><primary>UNPACK</primary></indexterm>
7842 <para>The <literal>UNPACK</literal> indicates to the compiler
7843 that it should unpack the contents of a constructor field into
7844 the constructor itself, removing a level of indirection. For
7848 data T = T {-# UNPACK #-} !Float
7849 {-# UNPACK #-} !Float
7852 <para>will create a constructor <literal>T</literal> containing
7853 two unboxed floats. This may not always be an optimisation: if
7854 the <function>T</function> constructor is scrutinised and the
7855 floats passed to a non-strict function for example, they will
7856 have to be reboxed (this is done automatically by the
7859 <para>Unpacking constructor fields should only be used in
7860 conjunction with <option>-O</option>, in order to expose
7861 unfoldings to the compiler so the reboxing can be removed as
7862 often as possible. For example:</para>
7866 f (T f1 f2) = f1 + f2
7869 <para>The compiler will avoid reboxing <function>f1</function>
7870 and <function>f2</function> by inlining <function>+</function>
7871 on floats, but only when <option>-O</option> is on.</para>
7873 <para>Any single-constructor data is eligible for unpacking; for
7877 data T = T {-# UNPACK #-} !(Int,Int)
7880 <para>will store the two <literal>Int</literal>s directly in the
7881 <function>T</function> constructor, by flattening the pair.
7882 Multi-level unpacking is also supported:
7885 data T = T {-# UNPACK #-} !S
7886 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7889 will store two unboxed <literal>Int#</literal>s
7890 directly in the <function>T</function> constructor. The
7891 unpacker can see through newtypes, too.</para>
7893 <para>If a field cannot be unpacked, you will not get a warning,
7894 so it might be an idea to check the generated code with
7895 <option>-ddump-simpl</option>.</para>
7897 <para>See also the <option>-funbox-strict-fields</option> flag,
7898 which essentially has the effect of adding
7899 <literal>{-# UNPACK #-}</literal> to every strict
7900 constructor field.</para>
7903 <sect2 id="source-pragma">
7904 <title>SOURCE pragma</title>
7906 <indexterm><primary>SOURCE</primary></indexterm>
7907 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7908 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7914 <!-- ======================= REWRITE RULES ======================== -->
7916 <sect1 id="rewrite-rules">
7917 <title>Rewrite rules
7919 <indexterm><primary>RULES pragma</primary></indexterm>
7920 <indexterm><primary>pragma, RULES</primary></indexterm>
7921 <indexterm><primary>rewrite rules</primary></indexterm></title>
7924 The programmer can specify rewrite rules as part of the source program
7930 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7935 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7936 If you need more information, then <option>-ddump-rule-firings</option> shows you
7937 each individual rule firing in detail.
7941 <title>Syntax</title>
7944 From a syntactic point of view:
7950 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7951 may be generated by the layout rule).
7957 The layout rule applies in a pragma.
7958 Currently no new indentation level
7959 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7960 you must lay out the starting in the same column as the enclosing definitions.
7963 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7964 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7967 Furthermore, the closing <literal>#-}</literal>
7968 should start in a column to the right of the opening <literal>{-#</literal>.
7974 Each rule has a name, enclosed in double quotes. The name itself has
7975 no significance at all. It is only used when reporting how many times the rule fired.
7981 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7982 immediately after the name of the rule. Thus:
7985 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7988 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7989 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7998 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7999 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
8000 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
8001 by spaces, just like in a type <literal>forall</literal>.
8007 A pattern variable may optionally have a type signature.
8008 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
8009 For example, here is the <literal>foldr/build</literal> rule:
8012 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
8013 foldr k z (build g) = g k z
8016 Since <function>g</function> has a polymorphic type, it must have a type signature.
8023 The left hand side of a rule must consist of a top-level variable applied
8024 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
8027 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
8028 "wrong2" forall f. f True = True
8031 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8038 A rule does not need to be in the same module as (any of) the
8039 variables it mentions, though of course they need to be in scope.
8045 All rules are implicitly exported from the module, and are therefore
8046 in force in any module that imports the module that defined the rule, directly
8047 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8048 in force when compiling A.) The situation is very similar to that for instance
8056 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8057 any other flag settings. Furthermore, inside a RULE, the language extension
8058 <option>-XScopedTypeVariables</option> is automatically enabled; see
8059 <xref linkend="scoped-type-variables"/>.
8065 Like other pragmas, RULE pragmas are always checked for scope errors, and
8066 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8067 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8068 if the <option>-fenable-rewrite-rules</option> flag is
8069 on (see <xref linkend="rule-semantics"/>).
8078 <sect2 id="rule-semantics">
8079 <title>Semantics</title>
8082 From a semantic point of view:
8087 Rules are enabled (that is, used during optimisation)
8088 by the <option>-fenable-rewrite-rules</option> flag.
8089 This flag is implied by <option>-O</option>, and may be switched
8090 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8091 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8092 may not do what you expect, though, because without <option>-O</option> GHC
8093 ignores all optimisation information in interface files;
8094 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8095 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8096 has no effect on parsing or typechecking.
8102 Rules are regarded as left-to-right rewrite rules.
8103 When GHC finds an expression that is a substitution instance of the LHS
8104 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8105 By "a substitution instance" we mean that the LHS can be made equal to the
8106 expression by substituting for the pattern variables.
8113 GHC makes absolutely no attempt to verify that the LHS and RHS
8114 of a rule have the same meaning. That is undecidable in general, and
8115 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8122 GHC makes no attempt to make sure that the rules are confluent or
8123 terminating. For example:
8126 "loop" forall x y. f x y = f y x
8129 This rule will cause the compiler to go into an infinite loop.
8136 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8142 GHC currently uses a very simple, syntactic, matching algorithm
8143 for matching a rule LHS with an expression. It seeks a substitution
8144 which makes the LHS and expression syntactically equal modulo alpha
8145 conversion. The pattern (rule), but not the expression, is eta-expanded if
8146 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8147 But not beta conversion (that's called higher-order matching).
8151 Matching is carried out on GHC's intermediate language, which includes
8152 type abstractions and applications. So a rule only matches if the
8153 types match too. See <xref linkend="rule-spec"/> below.
8159 GHC keeps trying to apply the rules as it optimises the program.
8160 For example, consider:
8169 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8170 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8171 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8172 not be substituted, and the rule would not fire.
8179 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8180 results. Consider this (artificial) example
8183 {-# RULES "f" f True = False #-}
8189 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8194 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8196 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8197 would have been a better chance that <literal>f</literal>'s RULE might fire.
8200 The way to get predictable behaviour is to use a NOINLINE
8201 pragma on <literal>f</literal>, to ensure
8202 that it is not inlined until its RULEs have had a chance to fire.
8212 <title>List fusion</title>
8215 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8216 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8217 intermediate list should be eliminated entirely.
8221 The following are good producers:
8233 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8239 Explicit lists (e.g. <literal>[True, False]</literal>)
8245 The cons constructor (e.g <literal>3:4:[]</literal>)
8251 <function>++</function>
8257 <function>map</function>
8263 <function>take</function>, <function>filter</function>
8269 <function>iterate</function>, <function>repeat</function>
8275 <function>zip</function>, <function>zipWith</function>
8284 The following are good consumers:
8296 <function>array</function> (on its second argument)
8302 <function>++</function> (on its first argument)
8308 <function>foldr</function>
8314 <function>map</function>
8320 <function>take</function>, <function>filter</function>
8326 <function>concat</function>
8332 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8338 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8339 will fuse with one but not the other)
8345 <function>partition</function>
8351 <function>head</function>
8357 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8363 <function>sequence_</function>
8369 <function>msum</function>
8375 <function>sortBy</function>
8384 So, for example, the following should generate no intermediate lists:
8387 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8393 This list could readily be extended; if there are Prelude functions that you use
8394 a lot which are not included, please tell us.
8398 If you want to write your own good consumers or producers, look at the
8399 Prelude definitions of the above functions to see how to do so.
8404 <sect2 id="rule-spec">
8405 <title>Specialisation
8409 Rewrite rules can be used to get the same effect as a feature
8410 present in earlier versions of GHC.
8411 For example, suppose that:
8414 genericLookup :: Ord a => Table a b -> a -> b
8415 intLookup :: Table Int b -> Int -> b
8418 where <function>intLookup</function> is an implementation of
8419 <function>genericLookup</function> that works very fast for
8420 keys of type <literal>Int</literal>. You might wish
8421 to tell GHC to use <function>intLookup</function> instead of
8422 <function>genericLookup</function> whenever the latter was called with
8423 type <literal>Table Int b -> Int -> b</literal>.
8424 It used to be possible to write
8427 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8430 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8433 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8436 This slightly odd-looking rule instructs GHC to replace
8437 <function>genericLookup</function> by <function>intLookup</function>
8438 <emphasis>whenever the types match</emphasis>.
8439 What is more, this rule does not need to be in the same
8440 file as <function>genericLookup</function>, unlike the
8441 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8442 have an original definition available to specialise).
8445 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8446 <function>intLookup</function> really behaves as a specialised version
8447 of <function>genericLookup</function>!!!</para>
8449 <para>An example in which using <literal>RULES</literal> for
8450 specialisation will Win Big:
8453 toDouble :: Real a => a -> Double
8454 toDouble = fromRational . toRational
8456 {-# RULES "toDouble/Int" toDouble = i2d #-}
8457 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8460 The <function>i2d</function> function is virtually one machine
8461 instruction; the default conversion—via an intermediate
8462 <literal>Rational</literal>—is obscenely expensive by
8469 <title>Controlling what's going on</title>
8477 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8483 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8484 If you add <option>-dppr-debug</option> you get a more detailed listing.
8490 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8493 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8494 {-# INLINE build #-}
8498 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8499 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8500 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8501 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8508 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8509 see how to write rules that will do fusion and yet give an efficient
8510 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8520 <sect2 id="core-pragma">
8521 <title>CORE pragma</title>
8523 <indexterm><primary>CORE pragma</primary></indexterm>
8524 <indexterm><primary>pragma, CORE</primary></indexterm>
8525 <indexterm><primary>core, annotation</primary></indexterm>
8528 The external core format supports <quote>Note</quote> annotations;
8529 the <literal>CORE</literal> pragma gives a way to specify what these
8530 should be in your Haskell source code. Syntactically, core
8531 annotations are attached to expressions and take a Haskell string
8532 literal as an argument. The following function definition shows an
8536 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8539 Semantically, this is equivalent to:
8547 However, when external core is generated (via
8548 <option>-fext-core</option>), there will be Notes attached to the
8549 expressions <function>show</function> and <varname>x</varname>.
8550 The core function declaration for <function>f</function> is:
8554 f :: %forall a . GHCziShow.ZCTShow a ->
8555 a -> GHCziBase.ZMZN GHCziBase.Char =
8556 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8558 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8560 (tpl1::GHCziBase.Int ->
8562 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8564 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8565 (tpl3::GHCziBase.ZMZN a ->
8566 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8574 Here, we can see that the function <function>show</function> (which
8575 has been expanded out to a case expression over the Show dictionary)
8576 has a <literal>%note</literal> attached to it, as does the
8577 expression <varname>eta</varname> (which used to be called
8578 <varname>x</varname>).
8585 <sect1 id="special-ids">
8586 <title>Special built-in functions</title>
8587 <para>GHC has a few built-in functions with special behaviour. These
8588 are now described in the module <ulink
8589 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8590 in the library documentation.</para>
8594 <sect1 id="generic-classes">
8595 <title>Generic classes</title>
8598 The ideas behind this extension are described in detail in "Derivable type classes",
8599 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8600 An example will give the idea:
8608 fromBin :: [Int] -> (a, [Int])
8610 toBin {| Unit |} Unit = []
8611 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8612 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8613 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8615 fromBin {| Unit |} bs = (Unit, bs)
8616 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8617 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8618 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8619 (y,bs'') = fromBin bs'
8622 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8623 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8624 which are defined thus in the library module <literal>Generics</literal>:
8628 data a :+: b = Inl a | Inr b
8629 data a :*: b = a :*: b
8632 Now you can make a data type into an instance of Bin like this:
8634 instance (Bin a, Bin b) => Bin (a,b)
8635 instance Bin a => Bin [a]
8637 That is, just leave off the "where" clause. Of course, you can put in the
8638 where clause and over-ride whichever methods you please.
8642 <title> Using generics </title>
8643 <para>To use generics you need to</para>
8646 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8647 <option>-XGenerics</option> (to generate extra per-data-type code),
8648 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8652 <para>Import the module <literal>Generics</literal> from the
8653 <literal>lang</literal> package. This import brings into
8654 scope the data types <literal>Unit</literal>,
8655 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8656 don't need this import if you don't mention these types
8657 explicitly; for example, if you are simply giving instance
8658 declarations.)</para>
8663 <sect2> <title> Changes wrt the paper </title>
8665 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8666 can be written infix (indeed, you can now use
8667 any operator starting in a colon as an infix type constructor). Also note that
8668 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8669 Finally, note that the syntax of the type patterns in the class declaration
8670 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8671 alone would ambiguous when they appear on right hand sides (an extension we
8672 anticipate wanting).
8676 <sect2> <title>Terminology and restrictions</title>
8678 Terminology. A "generic default method" in a class declaration
8679 is one that is defined using type patterns as above.
8680 A "polymorphic default method" is a default method defined as in Haskell 98.
8681 A "generic class declaration" is a class declaration with at least one
8682 generic default method.
8690 Alas, we do not yet implement the stuff about constructor names and
8697 A generic class can have only one parameter; you can't have a generic
8698 multi-parameter class.
8704 A default method must be defined entirely using type patterns, or entirely
8705 without. So this is illegal:
8708 op :: a -> (a, Bool)
8709 op {| Unit |} Unit = (Unit, True)
8712 However it is perfectly OK for some methods of a generic class to have
8713 generic default methods and others to have polymorphic default methods.
8719 The type variable(s) in the type pattern for a generic method declaration
8720 scope over the right hand side. So this is legal (note the use of the type variable ``p'' in a type signature on the right hand side:
8724 op {| p :*: q |} (x :*: y) = op (x :: p)
8732 The type patterns in a generic default method must take one of the forms:
8738 where "a" and "b" are type variables. Furthermore, all the type patterns for
8739 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8740 must use the same type variables. So this is illegal:
8744 op {| a :+: b |} (Inl x) = True
8745 op {| p :+: q |} (Inr y) = False
8747 The type patterns must be identical, even in equations for different methods of the class.
8748 So this too is illegal:
8752 op1 {| a :*: b |} (x :*: y) = True
8755 op2 {| p :*: q |} (x :*: y) = False
8757 (The reason for this restriction is that we gather all the equations for a particular type constructor
8758 into a single generic instance declaration.)
8764 A generic method declaration must give a case for each of the three type constructors.
8770 The type for a generic method can be built only from:
8772 <listitem> <para> Function arrows </para> </listitem>
8773 <listitem> <para> Type variables </para> </listitem>
8774 <listitem> <para> Tuples </para> </listitem>
8775 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8777 Here are some example type signatures for generic methods:
8780 op2 :: Bool -> (a,Bool)
8781 op3 :: [Int] -> a -> a
8784 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8788 This restriction is an implementation restriction: we just haven't got around to
8789 implementing the necessary bidirectional maps over arbitrary type constructors.
8790 It would be relatively easy to add specific type constructors, such as Maybe and list,
8791 to the ones that are allowed.</para>
8796 In an instance declaration for a generic class, the idea is that the compiler
8797 will fill in the methods for you, based on the generic templates. However it can only
8802 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8807 No constructor of the instance type has unboxed fields.
8811 (Of course, these things can only arise if you are already using GHC extensions.)
8812 However, you can still give an instance declarations for types which break these rules,
8813 provided you give explicit code to override any generic default methods.
8821 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8822 what the compiler does with generic declarations.
8827 <sect2> <title> Another example </title>
8829 Just to finish with, here's another example I rather like:
8833 nCons {| Unit |} _ = 1
8834 nCons {| a :*: b |} _ = 1
8835 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8838 tag {| Unit |} _ = 1
8839 tag {| a :*: b |} _ = 1
8840 tag {| a :+: b |} (Inl x) = tag x
8841 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8847 <sect1 id="monomorphism">
8848 <title>Control over monomorphism</title>
8850 <para>GHC supports two flags that control the way in which generalisation is
8851 carried out at let and where bindings.
8855 <title>Switching off the dreaded Monomorphism Restriction</title>
8856 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8858 <para>Haskell's monomorphism restriction (see
8859 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8861 of the Haskell Report)
8862 can be completely switched off by
8863 <option>-XNoMonomorphismRestriction</option>.
8868 <title>Monomorphic pattern bindings</title>
8869 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8870 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8872 <para> As an experimental change, we are exploring the possibility of
8873 making pattern bindings monomorphic; that is, not generalised at all.
8874 A pattern binding is a binding whose LHS has no function arguments,
8875 and is not a simple variable. For example:
8877 f x = x -- Not a pattern binding
8878 f = \x -> x -- Not a pattern binding
8879 f :: Int -> Int = \x -> x -- Not a pattern binding
8881 (g,h) = e -- A pattern binding
8882 (f) = e -- A pattern binding
8883 [x] = e -- A pattern binding
8885 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8886 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8895 ;;; Local Variables: ***
8897 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8898 ;;; ispell-local-dictionary: "british" ***
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