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 import Control.Monad.Fix
876 justOnes = do { rec { xs <- Just (1:xs) }
877 ; return (map negate xs) }
879 The <literal>rec</literal>
880 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [-1,-1,-1,...</literal>.
883 The background and motivation for recusrive do-notation is described in
884 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
885 by Levent Erkok, John Launchbury,
886 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
887 This paper is essential reading for anyone making non-trivial use of mdo-notation,
888 and we do not repeat it here. However, note that GHC uses a different syntax than the one
893 <title>Details of recursive do-notation</title>
895 The recursive do-notation is enabled with the flag <option>-XDoRec</option> or, equivalently,
896 the LANGUAGE pragma <option>DoRec</option>. It introduces the single new keyword "<literal>rec</literal>",
897 which wraps a mutually-recusrive group of monadic statements,
898 producing a single statement. Similar to a <literal>let</literal>
899 statement, the variables bound in the <literal>rec</literal> are
900 visible throughout the <literal>rec</literal> group, and below it.
903 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. Its definition is:
906 class Monad m => MonadFix m where
907 mfix :: (a -> m a) -> m a
910 The function <literal>mfix</literal>
911 dictates how the required recursion operation should be performed. For example,
912 <literal>justOnes</literal> desugars as follows:
914 justOnes = do { xs <- mfix (\xs' -> do { xs <- Just (1:xs'); return xs })
915 ; return (map negate xs) }
917 In general, a <literal>rec</literal> statment <literal>rec <replaceable>ss</replaceable></literal>
918 is desugared to the statement
920 <replaceable>vs</replaceable> <- mfix (\~<replaceable>vs</replaceable> -> do { <replaceable>ss</replaceable>
921 ; return <replaceable>vs</replaceable> })
923 where <replaceable>vs</replaceable> is a tuple of the varaibles bound by <replaceable>ss</replaceable>.
924 Moreover, the original <literal>rec</literal> typechecks exactly
925 when the above desugared version would do so. (For example, this means that
926 the variables <replaceable>vs</replaceable> are all monomorphic in the statements
927 following the <literal>rec</literal>, because they are bound by a lambda.)
930 Here are some other important points in using the recursive-do notation:
933 It is enabled with the flag <literal>-XDoRec</literal>, which is in turn implied by
934 <literal>-fglasgow-exts</literal>.
938 If recursive bindings are required for a monad,
939 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
940 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
941 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
942 for Haskell's internal state monad (strict and lazy, respectively).
946 Unlike ordinary do-notation, but like <literal>let</literal> and <literal>where</literal> bindings,
947 name shadowing is not allowed; that is, all the names bound in a single <literal>mdo</literal> must
948 be distinct (Section 3.3 of the paper).
952 Similar to let-bindings, GHC implements the segmentation technique described in Section 3.2 of
953 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
954 to break up a single <literal>rec</literal> statement into a sequenc e of statements with
955 <literal>rec</literal> groups of minimal size. This
956 improves polymorphism, and reduces the size of the recursive "knot".
962 <sect3> <title Mdo-notation (deprecated) </title>
964 <para> GHC used to support the flag <option>-XREecursiveDo</option>,
965 which enabled the keyword <literal>mdo</literal>, precisely as described in
966 <ulink url="http://citeseer.ist.psu.edu/erk02recursive.html">A recursive do for Haskell</ulink>,
967 but this is now deprecated. Instead of <literal>mdo { Q; e }</literal>, write
968 <literal>do { rec Q; e }</literal>.
971 Historical note: The old implementation of the mdo-notation (and most
972 of the existing documents) used the name
973 <literal>MonadRec</literal> for the class and the corresponding library.
974 This name is not supported by GHC.
981 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
983 <sect2 id="parallel-list-comprehensions">
984 <title>Parallel List Comprehensions</title>
985 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
987 <indexterm><primary>parallel list comprehensions</primary>
990 <para>Parallel list comprehensions are a natural extension to list
991 comprehensions. List comprehensions can be thought of as a nice
992 syntax for writing maps and filters. Parallel comprehensions
993 extend this to include the zipWith family.</para>
995 <para>A parallel list comprehension has multiple independent
996 branches of qualifier lists, each separated by a `|' symbol. For
997 example, the following zips together two lists:</para>
1000 [ (x, y) | x <- xs | y <- ys ]
1003 <para>The behavior of parallel list comprehensions follows that of
1004 zip, in that the resulting list will have the same length as the
1005 shortest branch.</para>
1007 <para>We can define parallel list comprehensions by translation to
1008 regular comprehensions. Here's the basic idea:</para>
1010 <para>Given a parallel comprehension of the form: </para>
1013 [ e | p1 <- e11, p2 <- e12, ...
1014 | q1 <- e21, q2 <- e22, ...
1019 <para>This will be translated to: </para>
1022 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
1023 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
1028 <para>where `zipN' is the appropriate zip for the given number of
1033 <!-- ===================== TRANSFORM LIST COMPREHENSIONS =================== -->
1035 <sect2 id="generalised-list-comprehensions">
1036 <title>Generalised (SQL-Like) List Comprehensions</title>
1037 <indexterm><primary>list comprehensions</primary><secondary>generalised</secondary>
1039 <indexterm><primary>extended list comprehensions</primary>
1041 <indexterm><primary>group</primary></indexterm>
1042 <indexterm><primary>sql</primary></indexterm>
1045 <para>Generalised list comprehensions are a further enhancement to the
1046 list comprehension syntactic sugar to allow operations such as sorting
1047 and grouping which are familiar from SQL. They are fully described in the
1048 paper <ulink url="http://research.microsoft.com/~simonpj/papers/list-comp">
1049 Comprehensive comprehensions: comprehensions with "order by" and "group by"</ulink>,
1050 except that the syntax we use differs slightly from the paper.</para>
1051 <para>The extension is enabled with the flag <option>-XTransformListComp</option>.</para>
1052 <para>Here is an example:
1054 employees = [ ("Simon", "MS", 80)
1055 , ("Erik", "MS", 100)
1056 , ("Phil", "Ed", 40)
1057 , ("Gordon", "Ed", 45)
1058 , ("Paul", "Yale", 60)]
1060 output = [ (the dept, sum salary)
1061 | (name, dept, salary) <- employees
1062 , then group by dept
1063 , then sortWith by (sum salary)
1066 In this example, the list <literal>output</literal> would take on
1070 [("Yale", 60), ("Ed", 85), ("MS", 180)]
1073 <para>There are three new keywords: <literal>group</literal>, <literal>by</literal>, and <literal>using</literal>.
1074 (The function <literal>sortWith</literal> is not a keyword; it is an ordinary
1075 function that is exported by <literal>GHC.Exts</literal>.)</para>
1077 <para>There are five new forms of comprehension qualifier,
1078 all introduced by the (existing) keyword <literal>then</literal>:
1086 This statement requires that <literal>f</literal> have the type <literal>
1087 forall a. [a] -> [a]</literal>. You can see an example of its use in the
1088 motivating example, as this form is used to apply <literal>take 5</literal>.
1099 This form is similar to the previous one, but allows you to create a function
1100 which will be passed as the first argument to f. As a consequence f must have
1101 the type <literal>forall a. (a -> t) -> [a] -> [a]</literal>. As you can see
1102 from the type, this function lets f "project out" some information
1103 from the elements of the list it is transforming.</para>
1105 <para>An example is shown in the opening example, where <literal>sortWith</literal>
1106 is supplied with a function that lets it find out the <literal>sum salary</literal>
1107 for any item in the list comprehension it transforms.</para>
1115 then group by e using f
1118 <para>This is the most general of the grouping-type statements. In this form,
1119 f is required to have type <literal>forall a. (a -> t) -> [a] -> [[a]]</literal>.
1120 As with the <literal>then f by e</literal> case above, the first argument
1121 is a function supplied to f by the compiler which lets it compute e on every
1122 element of the list being transformed. However, unlike the non-grouping case,
1123 f additionally partitions the list into a number of sublists: this means that
1124 at every point after this statement, binders occurring before it in the comprehension
1125 refer to <emphasis>lists</emphasis> of possible values, not single values. To help understand
1126 this, let's look at an example:</para>
1129 -- This works similarly to groupWith in GHC.Exts, but doesn't sort its input first
1130 groupRuns :: Eq b => (a -> b) -> [a] -> [[a]]
1131 groupRuns f = groupBy (\x y -> f x == f y)
1133 output = [ (the x, y)
1134 | x <- ([1..3] ++ [1..2])
1136 , then group by x using groupRuns ]
1139 <para>This results in the variable <literal>output</literal> taking on the value below:</para>
1142 [(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
1145 <para>Note that we have used the <literal>the</literal> function to change the type
1146 of x from a list to its original numeric type. The variable y, in contrast, is left
1147 unchanged from the list form introduced by the grouping.</para>
1157 <para>This form of grouping is essentially the same as the one described above. However,
1158 since no function to use for the grouping has been supplied it will fall back on the
1159 <literal>groupWith</literal> function defined in
1160 <ulink url="../libraries/base/GHC-Exts.html"><literal>GHC.Exts</literal></ulink>. This
1161 is the form of the group statement that we made use of in the opening example.</para>
1172 <para>With this form of the group statement, f is required to simply have the type
1173 <literal>forall a. [a] -> [[a]]</literal>, which will be used to group up the
1174 comprehension so far directly. An example of this form is as follows:</para>
1180 , then group using inits]
1183 <para>This will yield a list containing every prefix of the word "hello" written out 5 times:</para>
1186 ["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
1194 <!-- ===================== REBINDABLE SYNTAX =================== -->
1196 <sect2 id="rebindable-syntax">
1197 <title>Rebindable syntax and the implicit Prelude import</title>
1199 <para><indexterm><primary>-XNoImplicitPrelude
1200 option</primary></indexterm> GHC normally imports
1201 <filename>Prelude.hi</filename> files for you. If you'd
1202 rather it didn't, then give it a
1203 <option>-XNoImplicitPrelude</option> option. The idea is
1204 that you can then import a Prelude of your own. (But don't
1205 call it <literal>Prelude</literal>; the Haskell module
1206 namespace is flat, and you must not conflict with any
1207 Prelude module.)</para>
1209 <para>Suppose you are importing a Prelude of your own
1210 in order to define your own numeric class
1211 hierarchy. It completely defeats that purpose if the
1212 literal "1" means "<literal>Prelude.fromInteger
1213 1</literal>", which is what the Haskell Report specifies.
1214 So the <option>-XNoImplicitPrelude</option>
1215 flag <emphasis>also</emphasis> causes
1216 the following pieces of built-in syntax to refer to
1217 <emphasis>whatever is in scope</emphasis>, not the Prelude
1221 <para>An integer literal <literal>368</literal> means
1222 "<literal>fromInteger (368::Integer)</literal>", rather than
1223 "<literal>Prelude.fromInteger (368::Integer)</literal>".
1226 <listitem><para>Fractional literals are handed in just the same way,
1227 except that the translation is
1228 <literal>fromRational (3.68::Rational)</literal>.
1231 <listitem><para>The equality test in an overloaded numeric pattern
1232 uses whatever <literal>(==)</literal> is in scope.
1235 <listitem><para>The subtraction operation, and the
1236 greater-than-or-equal test, in <literal>n+k</literal> patterns
1237 use whatever <literal>(-)</literal> and <literal>(>=)</literal> are in scope.
1241 <para>Negation (e.g. "<literal>- (f x)</literal>")
1242 means "<literal>negate (f x)</literal>", both in numeric
1243 patterns, and expressions.
1247 <para>"Do" notation is translated using whatever
1248 functions <literal>(>>=)</literal>,
1249 <literal>(>>)</literal>, and <literal>fail</literal>,
1250 are in scope (not the Prelude
1251 versions). List comprehensions, mdo (<xref linkend="mdo-notation"/>), and parallel array
1252 comprehensions, are unaffected. </para></listitem>
1256 notation (see <xref linkend="arrow-notation"/>)
1257 uses whatever <literal>arr</literal>,
1258 <literal>(>>>)</literal>, <literal>first</literal>,
1259 <literal>app</literal>, <literal>(|||)</literal> and
1260 <literal>loop</literal> functions are in scope. But unlike the
1261 other constructs, the types of these functions must match the
1262 Prelude types very closely. Details are in flux; if you want
1266 In all cases (apart from arrow notation), the static semantics should be that of the desugared form,
1267 even if that is a little unexpected. For example, the
1268 static semantics of the literal <literal>368</literal>
1269 is exactly that of <literal>fromInteger (368::Integer)</literal>; it's fine for
1270 <literal>fromInteger</literal> to have any of the types:
1272 fromInteger :: Integer -> Integer
1273 fromInteger :: forall a. Foo a => Integer -> a
1274 fromInteger :: Num a => a -> Integer
1275 fromInteger :: Integer -> Bool -> Bool
1279 <para>Be warned: this is an experimental facility, with
1280 fewer checks than usual. Use <literal>-dcore-lint</literal>
1281 to typecheck the desugared program. If Core Lint is happy
1282 you should be all right.</para>
1286 <sect2 id="postfix-operators">
1287 <title>Postfix operators</title>
1290 The <option>-XPostfixOperators</option> flag enables a small
1291 extension to the syntax of left operator sections, which allows you to
1292 define postfix operators. The extension is this: the left section
1296 is equivalent (from the point of view of both type checking and execution) to the expression
1300 (for any expression <literal>e</literal> and operator <literal>(!)</literal>.
1301 The strict Haskell 98 interpretation is that the section is equivalent to
1305 That is, the operator must be a function of two arguments. GHC allows it to
1306 take only one argument, and that in turn allows you to write the function
1309 <para>The extension does not extend to the left-hand side of function
1310 definitions; you must define such a function in prefix form.</para>
1314 <sect2 id="tuple-sections">
1315 <title>Tuple sections</title>
1318 The <option>-XTupleSections</option> flag enables Python-style partially applied
1319 tuple constructors. For example, the following program
1323 is considered to be an alternative notation for the more unwieldy alternative
1327 You can omit any combination of arguments to the tuple, as in the following
1329 (, "I", , , "Love", , 1337)
1333 \a b c d -> (a, "I", b, c, "Love", d, 1337)
1338 If you have <link linkend="unboxed-tuples">unboxed tuples</link> enabled, tuple sections
1339 will also be available for them, like so
1343 Because there is no unboxed unit tuple, the following expression
1347 continues to stand for the unboxed singleton tuple data constructor.
1352 <sect2 id="disambiguate-fields">
1353 <title>Record field disambiguation</title>
1355 In record construction and record pattern matching
1356 it is entirely unambiguous which field is referred to, even if there are two different
1357 data types in scope with a common field name. For example:
1360 data S = MkS { x :: Int, y :: Bool }
1365 data T = MkT { x :: Int }
1367 ok1 (MkS { x = n }) = n+1 -- Unambiguous
1368 ok2 n = MkT { x = n+1 } -- Unambiguous
1370 bad1 k = k { x = 3 } -- Ambiguous
1371 bad2 k = x k -- Ambiguous
1373 Even though there are two <literal>x</literal>'s in scope,
1374 it is clear that the <literal>x</literal> in the pattern in the
1375 definition of <literal>ok1</literal> can only mean the field
1376 <literal>x</literal> from type <literal>S</literal>. Similarly for
1377 the function <literal>ok2</literal>. However, in the record update
1378 in <literal>bad1</literal> and the record selection in <literal>bad2</literal>
1379 it is not clear which of the two types is intended.
1382 Haskell 98 regards all four as ambiguous, but with the
1383 <option>-XDisambiguateRecordFields</option> flag, GHC will accept
1384 the former two. The rules are precisely the same as those for instance
1385 declarations in Haskell 98, where the method names on the left-hand side
1386 of the method bindings in an instance declaration refer unambiguously
1387 to the method of that class (provided they are in scope at all), even
1388 if there are other variables in scope with the same name.
1389 This reduces the clutter of qualified names when you import two
1390 records from different modules that use the same field name.
1396 Field disambiguation can be combined with punning (see <xref linkend="record-puns"/>). For exampe:
1401 ok3 (MkS { x }) = x+1 -- Uses both disambiguation and punning
1406 With <option>-XDisambiguateRecordFields</option> you can use <emphasis>unqualifed</emphasis>
1407 field names even if the correponding selector is only in scope <emphasis>qualified</emphasis>
1408 For example, assuming the same module <literal>M</literal> as in our earlier example, this is legal:
1411 import qualified M -- Note qualified
1413 ok4 (M.MkS { x = n }) = n+1 -- Unambiguous
1415 Since the constructore <literal>MkS</literal> is only in scope qualified, you must
1416 name it <literal>M.MkS</literal>, but the field <literal>x</literal> does not need
1417 to be qualified even though <literal>M.x</literal> is in scope but <literal>x</literal>
1418 is not. (In effect, it is qualified by the constructor.)
1425 <!-- ===================== Record puns =================== -->
1427 <sect2 id="record-puns">
1432 Record puns are enabled by the flag <literal>-XNamedFieldPuns</literal>.
1436 When using records, it is common to write a pattern that binds a
1437 variable with the same name as a record field, such as:
1440 data C = C {a :: Int}
1446 Record punning permits the variable name to be elided, so one can simply
1453 to mean the same pattern as above. That is, in a record pattern, the
1454 pattern <literal>a</literal> expands into the pattern <literal>a =
1455 a</literal> for the same name <literal>a</literal>.
1462 Record punning can also be used in an expression, writing, for example,
1468 let a = 1 in C {a = a}
1470 The expansion is purely syntactic, so the expanded right-hand side
1471 expression refers to the nearest enclosing variable that is spelled the
1472 same as the field name.
1476 Puns and other patterns can be mixed in the same record:
1478 data C = C {a :: Int, b :: Int}
1479 f (C {a, b = 4}) = a
1484 Puns can be used wherever record patterns occur (e.g. in
1485 <literal>let</literal> bindings or at the top-level).
1489 A pun on a qualified field name is expanded by stripping off the module qualifier.
1496 f (M.C {M.a = a}) = a
1498 (This is useful if the field selector <literal>a</literal> for constructor <literal>M.C</literal>
1499 is only in scope in qualified form.)
1507 <!-- ===================== Record wildcards =================== -->
1509 <sect2 id="record-wildcards">
1510 <title>Record wildcards
1514 Record wildcards are enabled by the flag <literal>-XRecordWildCards</literal>.
1515 This flag implies <literal>-XDisambiguateRecordFields</literal>.
1519 For records with many fields, it can be tiresome to write out each field
1520 individually in a record pattern, as in
1522 data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
1523 f (C {a = 1, b = b, c = c, d = d}) = b + c + d
1528 Record wildcard syntax permits a "<literal>..</literal>" in a record
1529 pattern, where each elided field <literal>f</literal> is replaced by the
1530 pattern <literal>f = f</literal>. For example, the above pattern can be
1533 f (C {a = 1, ..}) = b + c + d
1541 Wildcards can be mixed with other patterns, including puns
1542 (<xref linkend="record-puns"/>); for example, in a pattern <literal>C {a
1543 = 1, b, ..})</literal>. Additionally, record wildcards can be used
1544 wherever record patterns occur, including in <literal>let</literal>
1545 bindings and at the top-level. For example, the top-level binding
1549 defines <literal>b</literal>, <literal>c</literal>, and
1550 <literal>d</literal>.
1554 Record wildcards can also be used in expressions, writing, for example,
1556 let {a = 1; b = 2; c = 3; d = 4} in C {..}
1560 let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
1562 The expansion is purely syntactic, so the record wildcard
1563 expression refers to the nearest enclosing variables that are spelled
1564 the same as the omitted field names.
1568 The "<literal>..</literal>" expands to the missing
1569 <emphasis>in-scope</emphasis> record fields, where "in scope"
1570 includes both unqualified and qualified-only.
1571 Any fields that are not in scope are not filled in. For example
1574 data R = R { a,b,c :: Int }
1576 import qualified M( R(a,b) )
1579 The <literal>{..}</literal> expands to <literal>{M.a=a,M.b=b}</literal>,
1580 omitting <literal>c</literal> since it is not in scope at all.
1587 <!-- ===================== Local fixity declarations =================== -->
1589 <sect2 id="local-fixity-declarations">
1590 <title>Local Fixity Declarations
1593 <para>A careful reading of the Haskell 98 Report reveals that fixity
1594 declarations (<literal>infix</literal>, <literal>infixl</literal>, and
1595 <literal>infixr</literal>) are permitted to appear inside local bindings
1596 such those introduced by <literal>let</literal> and
1597 <literal>where</literal>. However, the Haskell Report does not specify
1598 the semantics of such bindings very precisely.
1601 <para>In GHC, a fixity declaration may accompany a local binding:
1608 and the fixity declaration applies wherever the binding is in scope.
1609 For example, in a <literal>let</literal>, it applies in the right-hand
1610 sides of other <literal>let</literal>-bindings and the body of the
1611 <literal>let</literal>C. Or, in recursive <literal>do</literal>
1612 expressions (<xref linkend="mdo-notation"/>), the local fixity
1613 declarations of a <literal>let</literal> statement scope over other
1614 statements in the group, just as the bound name does.
1618 Moreover, a local fixity declaration *must* accompany a local binding of
1619 that name: it is not possible to revise the fixity of name bound
1622 let infixr 9 $ in ...
1625 Because local fixity declarations are technically Haskell 98, no flag is
1626 necessary to enable them.
1630 <sect2 id="package-imports">
1631 <title>Package-qualified imports</title>
1633 <para>With the <option>-XPackageImports</option> flag, GHC allows
1634 import declarations to be qualified by the package name that the
1635 module is intended to be imported from. For example:</para>
1638 import "network" Network.Socket
1641 <para>would import the module <literal>Network.Socket</literal> from
1642 the package <literal>network</literal> (any version). This may
1643 be used to disambiguate an import when the same module is
1644 available from multiple packages, or is present in both the
1645 current package being built and an external package.</para>
1647 <para>Note: you probably don't need to use this feature, it was
1648 added mainly so that we can build backwards-compatible versions of
1649 packages when APIs change. It can lead to fragile dependencies in
1650 the common case: modules occasionally move from one package to
1651 another, rendering any package-qualified imports broken.</para>
1654 <sect2 id="syntax-stolen">
1655 <title>Summary of stolen syntax</title>
1657 <para>Turning on an option that enables special syntax
1658 <emphasis>might</emphasis> cause working Haskell 98 code to fail
1659 to compile, perhaps because it uses a variable name which has
1660 become a reserved word. This section lists the syntax that is
1661 "stolen" by language extensions.
1663 notation and nonterminal names from the Haskell 98 lexical syntax
1664 (see the Haskell 98 Report).
1665 We only list syntax changes here that might affect
1666 existing working programs (i.e. "stolen" syntax). Many of these
1667 extensions will also enable new context-free syntax, but in all
1668 cases programs written to use the new syntax would not be
1669 compilable without the option enabled.</para>
1671 <para>There are two classes of special
1676 <para>New reserved words and symbols: character sequences
1677 which are no longer available for use as identifiers in the
1681 <para>Other special syntax: sequences of characters that have
1682 a different meaning when this particular option is turned
1687 The following syntax is stolen:
1692 <literal>forall</literal>
1693 <indexterm><primary><literal>forall</literal></primary></indexterm>
1696 Stolen (in types) by: <option>-XExplicitForAll</option>, and hence by
1697 <option>-XScopedTypeVariables</option>,
1698 <option>-XLiberalTypeSynonyms</option>,
1699 <option>-XRank2Types</option>,
1700 <option>-XRankNTypes</option>,
1701 <option>-XPolymorphicComponents</option>,
1702 <option>-XExistentialQuantification</option>
1708 <literal>mdo</literal>
1709 <indexterm><primary><literal>mdo</literal></primary></indexterm>
1712 Stolen by: <option>-XRecursiveDo</option>,
1718 <literal>foreign</literal>
1719 <indexterm><primary><literal>foreign</literal></primary></indexterm>
1722 Stolen by: <option>-XForeignFunctionInterface</option>,
1728 <literal>rec</literal>,
1729 <literal>proc</literal>, <literal>-<</literal>,
1730 <literal>>-</literal>, <literal>-<<</literal>,
1731 <literal>>>-</literal>, and <literal>(|</literal>,
1732 <literal>|)</literal> brackets
1733 <indexterm><primary><literal>proc</literal></primary></indexterm>
1736 Stolen by: <option>-XArrows</option>,
1742 <literal>?<replaceable>varid</replaceable></literal>,
1743 <literal>%<replaceable>varid</replaceable></literal>
1744 <indexterm><primary>implicit parameters</primary></indexterm>
1747 Stolen by: <option>-XImplicitParams</option>,
1753 <literal>[|</literal>,
1754 <literal>[e|</literal>, <literal>[p|</literal>,
1755 <literal>[d|</literal>, <literal>[t|</literal>,
1756 <literal>$(</literal>,
1757 <literal>$<replaceable>varid</replaceable></literal>
1758 <indexterm><primary>Template Haskell</primary></indexterm>
1761 Stolen by: <option>-XTemplateHaskell</option>,
1767 <literal>[:<replaceable>varid</replaceable>|</literal>
1768 <indexterm><primary>quasi-quotation</primary></indexterm>
1771 Stolen by: <option>-XQuasiQuotes</option>,
1777 <replaceable>varid</replaceable>{<literal>#</literal>},
1778 <replaceable>char</replaceable><literal>#</literal>,
1779 <replaceable>string</replaceable><literal>#</literal>,
1780 <replaceable>integer</replaceable><literal>#</literal>,
1781 <replaceable>float</replaceable><literal>#</literal>,
1782 <replaceable>float</replaceable><literal>##</literal>,
1783 <literal>(#</literal>, <literal>#)</literal>,
1786 Stolen by: <option>-XMagicHash</option>,
1795 <!-- TYPE SYSTEM EXTENSIONS -->
1796 <sect1 id="data-type-extensions">
1797 <title>Extensions to data types and type synonyms</title>
1799 <sect2 id="nullary-types">
1800 <title>Data types with no constructors</title>
1802 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
1803 a data type with no constructors. For example:</para>
1807 data T a -- T :: * -> *
1810 <para>Syntactically, the declaration lacks the "= constrs" part. The
1811 type can be parameterised over types of any kind, but if the kind is
1812 not <literal>*</literal> then an explicit kind annotation must be used
1813 (see <xref linkend="kinding"/>).</para>
1815 <para>Such data types have only one value, namely bottom.
1816 Nevertheless, they can be useful when defining "phantom types".</para>
1819 <sect2 id="infix-tycons">
1820 <title>Infix type constructors, classes, and type variables</title>
1823 GHC allows type constructors, classes, and type variables to be operators, and
1824 to be written infix, very much like expressions. More specifically:
1827 A type constructor or class can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
1828 The lexical syntax is the same as that for data constructors.
1831 Data type and type-synonym declarations can be written infix, parenthesised
1832 if you want further arguments. E.g.
1834 data a :*: b = Foo a b
1835 type a :+: b = Either a b
1836 class a :=: b where ...
1838 data (a :**: b) x = Baz a b x
1839 type (a :++: b) y = Either (a,b) y
1843 Types, and class constraints, can be written infix. For example
1846 f :: (a :=: b) => a -> b
1850 A type variable can be an (unqualified) operator e.g. <literal>+</literal>.
1851 The lexical syntax is the same as that for variable operators, excluding "(.)",
1852 "(!)", and "(*)". In a binding position, the operator must be
1853 parenthesised. For example:
1855 type T (+) = Int + Int
1859 liftA2 :: Arrow (~>)
1860 => (a -> b -> c) -> (e ~> a) -> (e ~> b) -> (e ~> c)
1866 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
1867 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
1870 Fixities may be declared for type constructors, or classes, just as for data constructors. However,
1871 one cannot distinguish between the two in a fixity declaration; a fixity declaration
1872 sets the fixity for a data constructor and the corresponding type constructor. For example:
1876 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
1877 and similarly for <literal>:*:</literal>.
1878 <literal>Int `a` Bool</literal>.
1881 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
1888 <sect2 id="type-synonyms">
1889 <title>Liberalised type synonyms</title>
1892 Type synonyms are like macros at the type level, but Haskell 98 imposes many rules
1893 on individual synonym declarations.
1894 With the <option>-XLiberalTypeSynonyms</option> extension,
1895 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1896 That means that GHC can be very much more liberal about type synonyms than Haskell 98.
1899 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1900 in a type synonym, thus:
1902 type Discard a = forall b. Show b => a -> b -> (a, String)
1907 g :: Discard Int -> (Int,String) -- A rank-2 type
1914 If you also use <option>-XUnboxedTuples</option>,
1915 you can write an unboxed tuple in a type synonym:
1917 type Pr = (# Int, Int #)
1925 You can apply a type synonym to a forall type:
1927 type Foo a = a -> a -> Bool
1929 f :: Foo (forall b. b->b)
1931 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1933 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1938 You can apply a type synonym to a partially applied type synonym:
1940 type Generic i o = forall x. i x -> o x
1943 foo :: Generic Id []
1945 After expanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1947 foo :: forall x. x -> [x]
1955 GHC currently does kind checking before expanding synonyms (though even that
1959 After expanding type synonyms, GHC does validity checking on types, looking for
1960 the following mal-formedness which isn't detected simply by kind checking:
1963 Type constructor applied to a type involving for-alls.
1966 Unboxed tuple on left of an arrow.
1969 Partially-applied type synonym.
1973 this will be rejected:
1975 type Pr = (# Int, Int #)
1980 because GHC does not allow unboxed tuples on the left of a function arrow.
1985 <sect2 id="existential-quantification">
1986 <title>Existentially quantified data constructors
1990 The idea of using existential quantification in data type declarations
1991 was suggested by Perry, and implemented in Hope+ (Nigel Perry, <emphasis>The Implementation
1992 of Practical Functional Programming Languages</emphasis>, PhD Thesis, University of
1993 London, 1991). It was later formalised by Laufer and Odersky
1994 (<emphasis>Polymorphic type inference and abstract data types</emphasis>,
1995 TOPLAS, 16(5), pp1411-1430, 1994).
1996 It's been in Lennart
1997 Augustsson's <command>hbc</command> Haskell compiler for several years, and
1998 proved very useful. Here's the idea. Consider the declaration:
2004 data Foo = forall a. MkFoo a (a -> Bool)
2011 The data type <literal>Foo</literal> has two constructors with types:
2017 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2024 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2025 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2026 For example, the following expression is fine:
2032 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2038 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2039 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2040 isUpper</function> packages a character with a compatible function. These
2041 two things are each of type <literal>Foo</literal> and can be put in a list.
2045 What can we do with a value of type <literal>Foo</literal>?. In particular,
2046 what happens when we pattern-match on <function>MkFoo</function>?
2052 f (MkFoo val fn) = ???
2058 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2059 are compatible, the only (useful) thing we can do with them is to
2060 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2067 f (MkFoo val fn) = fn val
2073 What this allows us to do is to package heterogeneous values
2074 together with a bunch of functions that manipulate them, and then treat
2075 that collection of packages in a uniform manner. You can express
2076 quite a bit of object-oriented-like programming this way.
2079 <sect3 id="existential">
2080 <title>Why existential?
2084 What has this to do with <emphasis>existential</emphasis> quantification?
2085 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2091 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2097 But Haskell programmers can safely think of the ordinary
2098 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2099 adding a new existential quantification construct.
2104 <sect3 id="existential-with-context">
2105 <title>Existentials and type classes</title>
2108 An easy extension is to allow
2109 arbitrary contexts before the constructor. For example:
2115 data Baz = forall a. Eq a => Baz1 a a
2116 | forall b. Show b => Baz2 b (b -> b)
2122 The two constructors have the types you'd expect:
2128 Baz1 :: forall a. Eq a => a -> a -> Baz
2129 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2135 But when pattern matching on <function>Baz1</function> the matched values can be compared
2136 for equality, and when pattern matching on <function>Baz2</function> the first matched
2137 value can be converted to a string (as well as applying the function to it).
2138 So this program is legal:
2145 f (Baz1 p q) | p == q = "Yes"
2147 f (Baz2 v fn) = show (fn v)
2153 Operationally, in a dictionary-passing implementation, the
2154 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2155 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2156 extract it on pattern matching.
2161 <sect3 id="existential-records">
2162 <title>Record Constructors</title>
2165 GHC allows existentials to be used with records syntax as well. For example:
2168 data Counter a = forall self. NewCounter
2170 , _inc :: self -> self
2171 , _display :: self -> IO ()
2175 Here <literal>tag</literal> is a public field, with a well-typed selector
2176 function <literal>tag :: Counter a -> a</literal>. The <literal>self</literal>
2177 type is hidden from the outside; any attempt to apply <literal>_this</literal>,
2178 <literal>_inc</literal> or <literal>_display</literal> as functions will raise a
2179 compile-time error. In other words, <emphasis>GHC defines a record selector function
2180 only for fields whose type does not mention the existentially-quantified variables</emphasis>.
2181 (This example used an underscore in the fields for which record selectors
2182 will not be defined, but that is only programming style; GHC ignores them.)
2186 To make use of these hidden fields, we need to create some helper functions:
2189 inc :: Counter a -> Counter a
2190 inc (NewCounter x i d t) = NewCounter
2191 { _this = i x, _inc = i, _display = d, tag = t }
2193 display :: Counter a -> IO ()
2194 display NewCounter{ _this = x, _display = d } = d x
2197 Now we can define counters with different underlying implementations:
2200 counterA :: Counter String
2201 counterA = NewCounter
2202 { _this = 0, _inc = (1+), _display = print, tag = "A" }
2204 counterB :: Counter String
2205 counterB = NewCounter
2206 { _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
2209 display (inc counterA) -- prints "1"
2210 display (inc (inc counterB)) -- prints "##"
2213 Record update syntax is supported for existentials (and GADTs):
2215 setTag :: Counter a -> a -> Counter a
2216 setTag obj t = obj{ tag = t }
2218 The rule for record update is this: <emphasis>
2219 the types of the updated fields may
2220 mention only the universally-quantified type variables
2221 of the data constructor. For GADTs, the field may mention only types
2222 that appear as a simple type-variable argument in the constructor's result
2223 type</emphasis>. For example:
2225 data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b } -- c is existential
2226 upd1 t x = t { f1=x } -- OK: upd1 :: T a b -> a' -> T a' b
2227 upd2 t x = t { f3=x } -- BAD (f3's type mentions c, which is
2228 -- existentially quantified)
2230 data G a b where { G1 { g1::a, g2::c } :: G a [c] }
2231 upd3 g x = g { g1=x } -- OK: upd3 :: G a b -> c -> G c b
2232 upd4 g x = g { g2=x } -- BAD (f2's type mentions c, which is not a simple
2233 -- type-variable argument in G1's result type)
2241 <title>Restrictions</title>
2244 There are several restrictions on the ways in which existentially-quantified
2245 constructors can be use.
2254 When pattern matching, each pattern match introduces a new,
2255 distinct, type for each existential type variable. These types cannot
2256 be unified with any other type, nor can they escape from the scope of
2257 the pattern match. For example, these fragments are incorrect:
2265 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2266 is the result of <function>f1</function>. One way to see why this is wrong is to
2267 ask what type <function>f1</function> has:
2271 f1 :: Foo -> a -- Weird!
2275 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2280 f1 :: forall a. Foo -> a -- Wrong!
2284 The original program is just plain wrong. Here's another sort of error
2288 f2 (Baz1 a b) (Baz1 p q) = a==q
2292 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2293 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2294 from the two <function>Baz1</function> constructors.
2302 You can't pattern-match on an existentially quantified
2303 constructor in a <literal>let</literal> or <literal>where</literal> group of
2304 bindings. So this is illegal:
2308 f3 x = a==b where { Baz1 a b = x }
2311 Instead, use a <literal>case</literal> expression:
2314 f3 x = case x of Baz1 a b -> a==b
2317 In general, you can only pattern-match
2318 on an existentially-quantified constructor in a <literal>case</literal> expression or
2319 in the patterns of a function definition.
2321 The reason for this restriction is really an implementation one.
2322 Type-checking binding groups is already a nightmare without
2323 existentials complicating the picture. Also an existential pattern
2324 binding at the top level of a module doesn't make sense, because it's
2325 not clear how to prevent the existentially-quantified type "escaping".
2326 So for now, there's a simple-to-state restriction. We'll see how
2334 You can't use existential quantification for <literal>newtype</literal>
2335 declarations. So this is illegal:
2339 newtype T = forall a. Ord a => MkT a
2343 Reason: a value of type <literal>T</literal> must be represented as a
2344 pair of a dictionary for <literal>Ord t</literal> and a value of type
2345 <literal>t</literal>. That contradicts the idea that
2346 <literal>newtype</literal> should have no concrete representation.
2347 You can get just the same efficiency and effect by using
2348 <literal>data</literal> instead of <literal>newtype</literal>. If
2349 there is no overloading involved, then there is more of a case for
2350 allowing an existentially-quantified <literal>newtype</literal>,
2351 because the <literal>data</literal> version does carry an
2352 implementation cost, but single-field existentially quantified
2353 constructors aren't much use. So the simple restriction (no
2354 existential stuff on <literal>newtype</literal>) stands, unless there
2355 are convincing reasons to change it.
2363 You can't use <literal>deriving</literal> to define instances of a
2364 data type with existentially quantified data constructors.
2366 Reason: in most cases it would not make sense. For example:;
2369 data T = forall a. MkT [a] deriving( Eq )
2372 To derive <literal>Eq</literal> in the standard way we would need to have equality
2373 between the single component of two <function>MkT</function> constructors:
2377 (MkT a) == (MkT b) = ???
2380 But <varname>a</varname> and <varname>b</varname> have distinct types, and so can't be compared.
2381 It's just about possible to imagine examples in which the derived instance
2382 would make sense, but it seems altogether simpler simply to prohibit such
2383 declarations. Define your own instances!
2394 <!-- ====================== Generalised algebraic data types ======================= -->
2396 <sect2 id="gadt-style">
2397 <title>Declaring data types with explicit constructor signatures</title>
2399 <para>GHC allows you to declare an algebraic data type by
2400 giving the type signatures of constructors explicitly. For example:
2404 Just :: a -> Maybe a
2406 The form is called a "GADT-style declaration"
2407 because Generalised Algebraic Data Types, described in <xref linkend="gadt"/>,
2408 can only be declared using this form.</para>
2409 <para>Notice that GADT-style syntax generalises existential types (<xref linkend="existential-quantification"/>).
2410 For example, these two declarations are equivalent:
2412 data Foo = forall a. MkFoo a (a -> Bool)
2413 data Foo' where { MKFoo :: a -> (a->Bool) -> Foo' }
2416 <para>Any data type that can be declared in standard Haskell-98 syntax
2417 can also be declared using GADT-style syntax.
2418 The choice is largely stylistic, but GADT-style declarations differ in one important respect:
2419 they treat class constraints on the data constructors differently.
2420 Specifically, if the constructor is given a type-class context, that
2421 context is made available by pattern matching. For example:
2424 MkSet :: Eq a => [a] -> Set a
2426 makeSet :: Eq a => [a] -> Set a
2427 makeSet xs = MkSet (nub xs)
2429 insert :: a -> Set a -> Set a
2430 insert a (MkSet as) | a `elem` as = MkSet as
2431 | otherwise = MkSet (a:as)
2433 A use of <literal>MkSet</literal> as a constructor (e.g. in the definition of <literal>makeSet</literal>)
2434 gives rise to a <literal>(Eq a)</literal>
2435 constraint, as you would expect. The new feature is that pattern-matching on <literal>MkSet</literal>
2436 (as in the definition of <literal>insert</literal>) makes <emphasis>available</emphasis> an <literal>(Eq a)</literal>
2437 context. In implementation terms, the <literal>MkSet</literal> constructor has a hidden field that stores
2438 the <literal>(Eq a)</literal> dictionary that is passed to <literal>MkSet</literal>; so
2439 when pattern-matching that dictionary becomes available for the right-hand side of the match.
2440 In the example, the equality dictionary is used to satisfy the equality constraint
2441 generated by the call to <literal>elem</literal>, so that the type of
2442 <literal>insert</literal> itself has no <literal>Eq</literal> constraint.
2445 For example, one possible application is to reify dictionaries:
2447 data NumInst a where
2448 MkNumInst :: Num a => NumInst a
2450 intInst :: NumInst Int
2453 plus :: NumInst a -> a -> a -> a
2454 plus MkNumInst p q = p + q
2456 Here, a value of type <literal>NumInst a</literal> is equivalent
2457 to an explicit <literal>(Num a)</literal> dictionary.
2460 All this applies to constructors declared using the syntax of <xref linkend="existential-with-context"/>.
2461 For example, the <literal>NumInst</literal> data type above could equivalently be declared
2465 = Num a => MkNumInst (NumInst a)
2467 Notice that, unlike the situation when declaring an existential, there is
2468 no <literal>forall</literal>, because the <literal>Num</literal> constrains the
2469 data type's universally quantified type variable <literal>a</literal>.
2470 A constructor may have both universal and existential type variables: for example,
2471 the following two declarations are equivalent:
2474 = forall b. (Num a, Eq b) => MkT1 a b
2476 MkT2 :: (Num a, Eq b) => a -> b -> T2 a
2479 <para>All this behaviour contrasts with Haskell 98's peculiar treatment of
2480 contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report).
2481 In Haskell 98 the definition
2483 data Eq a => Set' a = MkSet' [a]
2485 gives <literal>MkSet'</literal> the same type as <literal>MkSet</literal> above. But instead of
2486 <emphasis>making available</emphasis> an <literal>(Eq a)</literal> constraint, pattern-matching
2487 on <literal>MkSet'</literal> <emphasis>requires</emphasis> an <literal>(Eq a)</literal> constraint!
2488 GHC faithfully implements this behaviour, odd though it is. But for GADT-style declarations,
2489 GHC's behaviour is much more useful, as well as much more intuitive.
2493 The rest of this section gives further details about GADT-style data
2498 The result type of each data constructor must begin with the type constructor being defined.
2499 If the result type of all constructors
2500 has the form <literal>T a1 ... an</literal>, where <literal>a1 ... an</literal>
2501 are distinct type variables, then the data type is <emphasis>ordinary</emphasis>;
2502 otherwise is a <emphasis>generalised</emphasis> data type (<xref linkend="gadt"/>).
2506 As with other type signatures, you can give a single signature for several data constructors.
2507 In this example we give a single signature for <literal>T1</literal> and <literal>T2</literal>:
2516 The type signature of
2517 each constructor is independent, and is implicitly universally quantified as usual.
2518 In particular, the type variable(s) in the "<literal>data T a where</literal>" header
2519 have no scope, and different constructors may have different universally-quantified type variables:
2521 data T a where -- The 'a' has no scope
2522 T1,T2 :: b -> T b -- Means forall b. b -> T b
2523 T3 :: T a -- Means forall a. T a
2528 A constructor signature may mention type class constraints, which can differ for
2529 different constructors. For example, this is fine:
2532 T1 :: Eq b => b -> b -> T b
2533 T2 :: (Show c, Ix c) => c -> [c] -> T c
2535 When patten matching, these constraints are made available to discharge constraints
2536 in the body of the match. For example:
2539 f (T1 x y) | x==y = "yes"
2543 Note that <literal>f</literal> is not overloaded; the <literal>Eq</literal> constraint arising
2544 from the use of <literal>==</literal> is discharged by the pattern match on <literal>T1</literal>
2545 and similarly the <literal>Show</literal> constraint arising from the use of <literal>show</literal>.
2549 Unlike a Haskell-98-style
2550 data type declaration, the type variable(s) in the "<literal>data Set a where</literal>" header
2551 have no scope. Indeed, one can write a kind signature instead:
2553 data Set :: * -> * where ...
2555 or even a mixture of the two:
2557 data Bar a :: (* -> *) -> * where ...
2559 The type variables (if given) may be explicitly kinded, so we could also write the header for <literal>Foo</literal>
2562 data Bar a (b :: * -> *) where ...
2568 You can use strictness annotations, in the obvious places
2569 in the constructor type:
2572 Lit :: !Int -> Term Int
2573 If :: Term Bool -> !(Term a) -> !(Term a) -> Term a
2574 Pair :: Term a -> Term b -> Term (a,b)
2579 You can use a <literal>deriving</literal> clause on a GADT-style data type
2580 declaration. For example, these two declarations are equivalent
2582 data Maybe1 a where {
2583 Nothing1 :: Maybe1 a ;
2584 Just1 :: a -> Maybe1 a
2585 } deriving( Eq, Ord )
2587 data Maybe2 a = Nothing2 | Just2 a
2593 The type signature may have quantified type variables that do not appear
2597 MkFoo :: a -> (a->Bool) -> Foo
2600 Here the type variable <literal>a</literal> does not appear in the result type
2601 of either constructor.
2602 Although it is universally quantified in the type of the constructor, such
2603 a type variable is often called "existential".
2604 Indeed, the above declaration declares precisely the same type as
2605 the <literal>data Foo</literal> in <xref linkend="existential-quantification"/>.
2607 The type may contain a class context too, of course:
2610 MkShowable :: Show a => a -> Showable
2615 You can use record syntax on a GADT-style data type declaration:
2619 Adult :: { name :: String, children :: [Person] } -> Person
2620 Child :: Show a => { name :: !String, funny :: a } -> Person
2622 As usual, for every constructor that has a field <literal>f</literal>, the type of
2623 field <literal>f</literal> must be the same (modulo alpha conversion).
2624 The <literal>Child</literal> constructor above shows that the signature
2625 may have a context, existentially-quantified variables, and strictness annotations,
2626 just as in the non-record case. (NB: the "type" that follows the double-colon
2627 is not really a type, because of the record syntax and strictness annotations.
2628 A "type" of this form can appear only in a constructor signature.)
2632 Record updates are allowed with GADT-style declarations,
2633 only fields that have the following property: the type of the field
2634 mentions no existential type variables.
2638 As in the case of existentials declared using the Haskell-98-like record syntax
2639 (<xref linkend="existential-records"/>),
2640 record-selector functions are generated only for those fields that have well-typed
2642 Here is the example of that section, in GADT-style syntax:
2644 data Counter a where
2645 NewCounter { _this :: self
2646 , _inc :: self -> self
2647 , _display :: self -> IO ()
2652 As before, only one selector function is generated here, that for <literal>tag</literal>.
2653 Nevertheless, you can still use all the field names in pattern matching and record construction.
2655 </itemizedlist></para>
2659 <title>Generalised Algebraic Data Types (GADTs)</title>
2661 <para>Generalised Algebraic Data Types generalise ordinary algebraic data types
2662 by allowing constructors to have richer return types. Here is an example:
2665 Lit :: Int -> Term Int
2666 Succ :: Term Int -> Term Int
2667 IsZero :: Term Int -> Term Bool
2668 If :: Term Bool -> Term a -> Term a -> Term a
2669 Pair :: Term a -> Term b -> Term (a,b)
2671 Notice that the return type of the constructors is not always <literal>Term a</literal>, as is the
2672 case with ordinary data types. This generality allows us to
2673 write a well-typed <literal>eval</literal> function
2674 for these <literal>Terms</literal>:
2678 eval (Succ t) = 1 + eval t
2679 eval (IsZero t) = eval t == 0
2680 eval (If b e1 e2) = if eval b then eval e1 else eval e2
2681 eval (Pair e1 e2) = (eval e1, eval e2)
2683 The key point about GADTs is that <emphasis>pattern matching causes type refinement</emphasis>.
2684 For example, in the right hand side of the equation
2689 the type <literal>a</literal> is refined to <literal>Int</literal>. That's the whole point!
2690 A precise specification of the type rules is beyond what this user manual aspires to,
2691 but the design closely follows that described in
2693 url="http://research.microsoft.com/%7Esimonpj/papers/gadt/">Simple
2694 unification-based type inference for GADTs</ulink>,
2696 The general principle is this: <emphasis>type refinement is only carried out
2697 based on user-supplied type annotations</emphasis>.
2698 So if no type signature is supplied for <literal>eval</literal>, no type refinement happens,
2699 and lots of obscure error messages will
2700 occur. However, the refinement is quite general. For example, if we had:
2702 eval :: Term a -> a -> a
2703 eval (Lit i) j = i+j
2705 the pattern match causes the type <literal>a</literal> to be refined to <literal>Int</literal> (because of the type
2706 of the constructor <literal>Lit</literal>), and that refinement also applies to the type of <literal>j</literal>, and
2707 the result type of the <literal>case</literal> expression. Hence the addition <literal>i+j</literal> is legal.
2710 These and many other examples are given in papers by Hongwei Xi, and
2711 Tim Sheard. There is a longer introduction
2712 <ulink url="http://www.haskell.org/haskellwiki/GADT">on the wiki</ulink>,
2714 <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
2715 may use different notation to that implemented in GHC.
2718 The rest of this section outlines the extensions to GHC that support GADTs. The extension is enabled with
2719 <option>-XGADTs</option>. The <option>-XGADTs</option> flag also sets <option>-XRelaxedPolyRec</option>.
2722 A GADT can only be declared using GADT-style syntax (<xref linkend="gadt-style"/>);
2723 the old Haskell-98 syntax for data declarations always declares an ordinary data type.
2724 The result type of each constructor must begin with the type constructor being defined,
2725 but for a GADT the arguments to the type constructor can be arbitrary monotypes.
2726 For example, in the <literal>Term</literal> data
2727 type above, the type of each constructor must end with <literal>Term ty</literal>, but
2728 the <literal>ty</literal> need not be a type variable (e.g. the <literal>Lit</literal>
2733 It is permitted to declare an ordinary algebraic data type using GADT-style syntax.
2734 What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors
2735 whose result type is not just <literal>T a b</literal>.
2739 You cannot use a <literal>deriving</literal> clause for a GADT; only for
2740 an ordinary data type.
2744 As mentioned in <xref linkend="gadt-style"/>, record syntax is supported.
2748 Lit { val :: Int } :: Term Int
2749 Succ { num :: Term Int } :: Term Int
2750 Pred { num :: Term Int } :: Term Int
2751 IsZero { arg :: Term Int } :: Term Bool
2752 Pair { arg1 :: Term a
2755 If { cnd :: Term Bool
2760 However, for GADTs there is the following additional constraint:
2761 every constructor that has a field <literal>f</literal> must have
2762 the same result type (modulo alpha conversion)
2763 Hence, in the above example, we cannot merge the <literal>num</literal>
2764 and <literal>arg</literal> fields above into a
2765 single name. Although their field types are both <literal>Term Int</literal>,
2766 their selector functions actually have different types:
2769 num :: Term Int -> Term Int
2770 arg :: Term Bool -> Term Int
2775 When pattern-matching against data constructors drawn from a GADT,
2776 for example in a <literal>case</literal> expression, the following rules apply:
2778 <listitem><para>The type of the scrutinee must be rigid.</para></listitem>
2779 <listitem><para>The type of the entire <literal>case</literal> expression must be rigid.</para></listitem>
2780 <listitem><para>The type of any free variable mentioned in any of
2781 the <literal>case</literal> alternatives must be rigid.</para></listitem>
2783 A type is "rigid" if it is completely known to the compiler at its binding site. The easiest
2784 way to ensure that a variable a rigid type is to give it a type signature.
2785 For more precise details see <ulink url="http://research.microsoft.com/%7Esimonpj/papers/gadt">
2786 Simple unification-based type inference for GADTs
2787 </ulink>. The criteria implemented by GHC are given in the Appendix.
2797 <!-- ====================== End of Generalised algebraic data types ======================= -->
2799 <sect1 id="deriving">
2800 <title>Extensions to the "deriving" mechanism</title>
2802 <sect2 id="deriving-inferred">
2803 <title>Inferred context for deriving clauses</title>
2806 The Haskell Report is vague about exactly when a <literal>deriving</literal> clause is
2809 data T0 f a = MkT0 a deriving( Eq )
2810 data T1 f a = MkT1 (f a) deriving( Eq )
2811 data T2 f a = MkT2 (f (f a)) deriving( Eq )
2813 The natural generated <literal>Eq</literal> code would result in these instance declarations:
2815 instance Eq a => Eq (T0 f a) where ...
2816 instance Eq (f a) => Eq (T1 f a) where ...
2817 instance Eq (f (f a)) => Eq (T2 f a) where ...
2819 The first of these is obviously fine. The second is still fine, although less obviously.
2820 The third is not Haskell 98, and risks losing termination of instances.
2823 GHC takes a conservative position: it accepts the first two, but not the third. The rule is this:
2824 each constraint in the inferred instance context must consist only of type variables,
2825 with no repetitions.
2828 This rule is applied regardless of flags. If you want a more exotic context, you can write
2829 it yourself, using the <link linkend="stand-alone-deriving">standalone deriving mechanism</link>.
2833 <sect2 id="stand-alone-deriving">
2834 <title>Stand-alone deriving declarations</title>
2837 GHC now allows stand-alone <literal>deriving</literal> declarations, enabled by <literal>-XStandaloneDeriving</literal>:
2839 data Foo a = Bar a | Baz String
2841 deriving instance Eq a => Eq (Foo a)
2843 The syntax is identical to that of an ordinary instance declaration apart from (a) the keyword
2844 <literal>deriving</literal>, and (b) the absence of the <literal>where</literal> part.
2845 Note the following points:
2848 You must supply an explicit context (in the example the context is <literal>(Eq a)</literal>),
2849 exactly as you would in an ordinary instance declaration.
2850 (In contrast, in a <literal>deriving</literal> clause
2851 attached to a data type declaration, the context is inferred.)
2855 A <literal>deriving instance</literal> declaration
2856 must obey the same rules concerning form and termination as ordinary instance declarations,
2857 controlled by the same flags; see <xref linkend="instance-decls"/>.
2861 Unlike a <literal>deriving</literal>
2862 declaration attached to a <literal>data</literal> declaration, the instance can be more specific
2863 than the data type (assuming you also use
2864 <literal>-XFlexibleInstances</literal>, <xref linkend="instance-rules"/>). Consider
2867 data Foo a = Bar a | Baz String
2869 deriving instance Eq a => Eq (Foo [a])
2870 deriving instance Eq a => Eq (Foo (Maybe a))
2872 This will generate a derived instance for <literal>(Foo [a])</literal> and <literal>(Foo (Maybe a))</literal>,
2873 but other types such as <literal>(Foo (Int,Bool))</literal> will not be an instance of <literal>Eq</literal>.
2877 Unlike a <literal>deriving</literal>
2878 declaration attached to a <literal>data</literal> declaration,
2879 GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate
2880 boilerplate code for the specified class, and typechecks it. If there is a type error, it is
2881 your problem. (GHC will show you the offending code if it has a type error.)
2882 The merit of this is that you can derive instances for GADTs and other exotic
2883 data types, providing only that the boilerplate code does indeed typecheck. For example:
2889 deriving instance Show (T a)
2891 In this example, you cannot say <literal>... deriving( Show )</literal> on the
2892 data type declaration for <literal>T</literal>,
2893 because <literal>T</literal> is a GADT, but you <emphasis>can</emphasis> generate
2894 the instance declaration using stand-alone deriving.
2899 <para>The stand-alone syntax is generalised for newtypes in exactly the same
2900 way that ordinary <literal>deriving</literal> clauses are generalised (<xref linkend="newtype-deriving"/>).
2903 newtype Foo a = MkFoo (State Int a)
2905 deriving instance MonadState Int Foo
2907 GHC always treats the <emphasis>last</emphasis> parameter of the instance
2908 (<literal>Foo</literal> in this example) as the type whose instance is being derived.
2910 </itemizedlist></para>
2915 <sect2 id="deriving-typeable">
2916 <title>Deriving clause for extra classes (<literal>Typeable</literal>, <literal>Data</literal>, etc)</title>
2919 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2920 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2921 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2922 classes <literal>Eq</literal>, <literal>Ord</literal>,
2923 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2926 GHC extends this list with several more classes that may be automatically derived:
2928 <listitem><para> With <option>-XDeriveDataTypeable</option>, you can derive instances of the classes
2929 <literal>Typeable</literal>, and <literal>Data</literal>, defined in the library
2930 modules <literal>Data.Typeable</literal> and <literal>Data.Generics</literal> respectively.
2932 <para>An instance of <literal>Typeable</literal> can only be derived if the
2933 data type has seven or fewer type parameters, all of kind <literal>*</literal>.
2934 The reason for this is that the <literal>Typeable</literal> class is derived using the scheme
2936 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/hmap/gmap2.ps">
2937 Scrap More Boilerplate: Reflection, Zips, and Generalised Casts
2939 (Section 7.4 of the paper describes the multiple <literal>Typeable</literal> classes that
2940 are used, and only <literal>Typeable1</literal> up to
2941 <literal>Typeable7</literal> are provided in the library.)
2942 In other cases, there is nothing to stop the programmer writing a <literal>TypableX</literal>
2943 class, whose kind suits that of the data type constructor, and
2944 then writing the data type instance by hand.
2948 <listitem><para> With <option>-XDeriveFunctor</option>, you can derive instances of
2949 the class <literal>Functor</literal>,
2950 defined in <literal>GHC.Base</literal>.
2953 <listitem><para> With <option>-XDeriveFoldable</option>, you can derive instances of
2954 the class <literal>Foldable</literal>,
2955 defined in <literal>Data.Foldable</literal>.
2958 <listitem><para> With <option>-XDeriveTraversable</option>, you can derive instances of
2959 the class <literal>Traversable</literal>,
2960 defined in <literal>Data.Traversable</literal>.
2963 In each case the appropriate class must be in scope before it
2964 can be mentioned in the <literal>deriving</literal> clause.
2968 <sect2 id="newtype-deriving">
2969 <title>Generalised derived instances for newtypes</title>
2972 When you define an abstract type using <literal>newtype</literal>, you may want
2973 the new type to inherit some instances from its representation. In
2974 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2975 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2976 other classes you have to write an explicit instance declaration. For
2977 example, if you define
2980 newtype Dollars = Dollars Int
2983 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2984 explicitly define an instance of <literal>Num</literal>:
2987 instance Num Dollars where
2988 Dollars a + Dollars b = Dollars (a+b)
2991 All the instance does is apply and remove the <literal>newtype</literal>
2992 constructor. It is particularly galling that, since the constructor
2993 doesn't appear at run-time, this instance declaration defines a
2994 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2995 dictionary, only slower!
2999 <sect3> <title> Generalising the deriving clause </title>
3001 GHC now permits such instances to be derived instead,
3002 using the flag <option>-XGeneralizedNewtypeDeriving</option>,
3005 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3008 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3009 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3010 derives an instance declaration of the form
3013 instance Num Int => Num Dollars
3016 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3020 We can also derive instances of constructor classes in a similar
3021 way. For example, suppose we have implemented state and failure monad
3022 transformers, such that
3025 instance Monad m => Monad (State s m)
3026 instance Monad m => Monad (Failure m)
3028 In Haskell 98, we can define a parsing monad by
3030 type Parser tok m a = State [tok] (Failure m) a
3033 which is automatically a monad thanks to the instance declarations
3034 above. With the extension, we can make the parser type abstract,
3035 without needing to write an instance of class <literal>Monad</literal>, via
3038 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3041 In this case the derived instance declaration is of the form
3043 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3046 Notice that, since <literal>Monad</literal> is a constructor class, the
3047 instance is a <emphasis>partial application</emphasis> of the new type, not the
3048 entire left hand side. We can imagine that the type declaration is
3049 "eta-converted" to generate the context of the instance
3054 We can even derive instances of multi-parameter classes, provided the
3055 newtype is the last class parameter. In this case, a ``partial
3056 application'' of the class appears in the <literal>deriving</literal>
3057 clause. For example, given the class
3060 class StateMonad s m | m -> s where ...
3061 instance Monad m => StateMonad s (State s m) where ...
3063 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3065 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3066 deriving (Monad, StateMonad [tok])
3069 The derived instance is obtained by completing the application of the
3070 class to the new type:
3073 instance StateMonad [tok] (State [tok] (Failure m)) =>
3074 StateMonad [tok] (Parser tok m)
3079 As a result of this extension, all derived instances in newtype
3080 declarations are treated uniformly (and implemented just by reusing
3081 the dictionary for the representation type), <emphasis>except</emphasis>
3082 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3083 the newtype and its representation.
3087 <sect3> <title> A more precise specification </title>
3089 Derived instance declarations are constructed as follows. Consider the
3090 declaration (after expansion of any type synonyms)
3093 newtype T v1...vn = T' (t vk+1...vn) deriving (c1...cm)
3099 The <literal>ci</literal> are partial applications of
3100 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3101 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3104 The <literal>k</literal> is chosen so that <literal>ci (T v1...vk)</literal> is well-kinded.
3107 The type <literal>t</literal> is an arbitrary type.
3110 The type variables <literal>vk+1...vn</literal> do not occur in <literal>t</literal>,
3111 nor in the <literal>ci</literal>, and
3114 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3115 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3116 should not "look through" the type or its constructor. You can still
3117 derive these classes for a newtype, but it happens in the usual way, not
3118 via this new mechanism.
3121 Then, for each <literal>ci</literal>, the derived instance
3124 instance ci t => ci (T v1...vk)
3126 As an example which does <emphasis>not</emphasis> work, consider
3128 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3130 Here we cannot derive the instance
3132 instance Monad (State s m) => Monad (NonMonad m)
3135 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3136 and so cannot be "eta-converted" away. It is a good thing that this
3137 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3138 not, in fact, a monad --- for the same reason. Try defining
3139 <literal>>>=</literal> with the correct type: you won't be able to.
3143 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3144 important, since we can only derive instances for the last one. If the
3145 <literal>StateMonad</literal> class above were instead defined as
3148 class StateMonad m s | m -> s where ...
3151 then we would not have been able to derive an instance for the
3152 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3153 classes usually have one "main" parameter for which deriving new
3154 instances is most interesting.
3156 <para>Lastly, all of this applies only for classes other than
3157 <literal>Read</literal>, <literal>Show</literal>, <literal>Typeable</literal>,
3158 and <literal>Data</literal>, for which the built-in derivation applies (section
3159 4.3.3. of the Haskell Report).
3160 (For the standard classes <literal>Eq</literal>, <literal>Ord</literal>,
3161 <literal>Ix</literal>, and <literal>Bounded</literal> it is immaterial whether
3162 the standard method is used or the one described here.)
3169 <!-- TYPE SYSTEM EXTENSIONS -->
3170 <sect1 id="type-class-extensions">
3171 <title>Class and instances declarations</title>
3173 <sect2 id="multi-param-type-classes">
3174 <title>Class declarations</title>
3177 This section, and the next one, documents GHC's type-class extensions.
3178 There's lots of background in the paper <ulink
3179 url="http://research.microsoft.com/~simonpj/Papers/type-class-design-space/">Type
3180 classes: exploring the design space</ulink> (Simon Peyton Jones, Mark
3181 Jones, Erik Meijer).
3184 All the extensions are enabled by the <option>-fglasgow-exts</option> flag.
3188 <title>Multi-parameter type classes</title>
3190 Multi-parameter type classes are permitted, with flag <option>-XMultiParamTypeClasses</option>.
3195 class Collection c a where
3196 union :: c a -> c a -> c a
3203 <sect3 id="superclass-rules">
3204 <title>The superclasses of a class declaration</title>
3207 In Haskell 98 the context of a class declaration (which introduces superclasses)
3208 must be simple; that is, each predicate must consist of a class applied to
3209 type variables. The flag <option>-XFlexibleContexts</option>
3210 (<xref linkend="flexible-contexts"/>)
3211 lifts this restriction,
3212 so that the only restriction on the context in a class declaration is
3213 that the class hierarchy must be acyclic. So these class declarations are OK:
3217 class Functor (m k) => FiniteMap m k where
3220 class (Monad m, Monad (t m)) => Transform t m where
3221 lift :: m a -> (t m) a
3227 As in Haskell 98, The class hierarchy must be acyclic. However, the definition
3228 of "acyclic" involves only the superclass relationships. For example,
3234 op :: D b => a -> b -> b
3237 class C a => D a where { ... }
3241 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
3242 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
3243 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
3250 <sect3 id="class-method-types">
3251 <title>Class method types</title>
3254 Haskell 98 prohibits class method types to mention constraints on the
3255 class type variable, thus:
3258 fromList :: [a] -> s a
3259 elem :: Eq a => a -> s a -> Bool
3261 The type of <literal>elem</literal> is illegal in Haskell 98, because it
3262 contains the constraint <literal>Eq a</literal>, constrains only the
3263 class type variable (in this case <literal>a</literal>).
3264 GHC lifts this restriction (flag <option>-XConstrainedClassMethods</option>).
3271 <sect2 id="functional-dependencies">
3272 <title>Functional dependencies
3275 <para> Functional dependencies are implemented as described by Mark Jones
3276 in “<ulink url="http://citeseer.ist.psu.edu/jones00type.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
3277 In Proceedings of the 9th European Symposium on Programming,
3278 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
3282 Functional dependencies are introduced by a vertical bar in the syntax of a
3283 class declaration; e.g.
3285 class (Monad m) => MonadState s m | m -> s where ...
3287 class Foo a b c | a b -> c where ...
3289 There should be more documentation, but there isn't (yet). Yell if you need it.
3292 <sect3><title>Rules for functional dependencies </title>
3294 In a class declaration, all of the class type variables must be reachable (in the sense
3295 mentioned in <xref linkend="flexible-contexts"/>)
3296 from the free variables of each method type.
3300 class Coll s a where
3302 insert :: s -> a -> s
3305 is not OK, because the type of <literal>empty</literal> doesn't mention
3306 <literal>a</literal>. Functional dependencies can make the type variable
3309 class Coll s a | s -> a where
3311 insert :: s -> a -> s
3314 Alternatively <literal>Coll</literal> might be rewritten
3317 class Coll s a where
3319 insert :: s a -> a -> s a
3323 which makes the connection between the type of a collection of
3324 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
3325 Occasionally this really doesn't work, in which case you can split the
3333 class CollE s => Coll s a where
3334 insert :: s -> a -> s
3341 <title>Background on functional dependencies</title>
3343 <para>The following description of the motivation and use of functional dependencies is taken
3344 from the Hugs user manual, reproduced here (with minor changes) by kind
3345 permission of Mark Jones.
3348 Consider the following class, intended as part of a
3349 library for collection types:
3351 class Collects e ce where
3353 insert :: e -> ce -> ce
3354 member :: e -> ce -> Bool
3356 The type variable e used here represents the element type, while ce is the type
3357 of the container itself. Within this framework, we might want to define
3358 instances of this class for lists or characteristic functions (both of which
3359 can be used to represent collections of any equality type), bit sets (which can
3360 be used to represent collections of characters), or hash tables (which can be
3361 used to represent any collection whose elements have a hash function). Omitting
3362 standard implementation details, this would lead to the following declarations:
3364 instance Eq e => Collects e [e] where ...
3365 instance Eq e => Collects e (e -> Bool) where ...
3366 instance Collects Char BitSet where ...
3367 instance (Hashable e, Collects a ce)
3368 => Collects e (Array Int ce) where ...
3370 All this looks quite promising; we have a class and a range of interesting
3371 implementations. Unfortunately, there are some serious problems with the class
3372 declaration. First, the empty function has an ambiguous type:
3374 empty :: Collects e ce => ce
3376 By "ambiguous" we mean that there is a type variable e that appears on the left
3377 of the <literal>=></literal> symbol, but not on the right. The problem with
3378 this is that, according to the theoretical foundations of Haskell overloading,
3379 we cannot guarantee a well-defined semantics for any term with an ambiguous
3383 We can sidestep this specific problem by removing the empty member from the
3384 class declaration. However, although the remaining members, insert and member,
3385 do not have ambiguous types, we still run into problems when we try to use
3386 them. For example, consider the following two functions:
3388 f x y = insert x . insert y
3391 for which GHC infers the following types:
3393 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3394 g :: (Collects Bool c, Collects Char c) => c -> c
3396 Notice that the type for f allows the two parameters x and y to be assigned
3397 different types, even though it attempts to insert each of the two values, one
3398 after the other, into the same collection. If we're trying to model collections
3399 that contain only one type of value, then this is clearly an inaccurate
3400 type. Worse still, the definition for g is accepted, without causing a type
3401 error. As a result, the error in this code will not be flagged at the point
3402 where it appears. Instead, it will show up only when we try to use g, which
3403 might even be in a different module.
3406 <sect4><title>An attempt to use constructor classes</title>
3409 Faced with the problems described above, some Haskell programmers might be
3410 tempted to use something like the following version of the class declaration:
3412 class Collects e c where
3414 insert :: e -> c e -> c e
3415 member :: e -> c e -> Bool
3417 The key difference here is that we abstract over the type constructor c that is
3418 used to form the collection type c e, and not over that collection type itself,
3419 represented by ce in the original class declaration. This avoids the immediate
3420 problems that we mentioned above: empty has type <literal>Collects e c => c
3421 e</literal>, which is not ambiguous.
3424 The function f from the previous section has a more accurate type:
3426 f :: (Collects e c) => e -> e -> c e -> c e
3428 The function g from the previous section is now rejected with a type error as
3429 we would hope because the type of f does not allow the two arguments to have
3431 This, then, is an example of a multiple parameter class that does actually work
3432 quite well in practice, without ambiguity problems.
3433 There is, however, a catch. This version of the Collects class is nowhere near
3434 as general as the original class seemed to be: only one of the four instances
3435 for <literal>Collects</literal>
3436 given above can be used with this version of Collects because only one of
3437 them---the instance for lists---has a collection type that can be written in
3438 the form c e, for some type constructor c, and element type e.
3442 <sect4><title>Adding functional dependencies</title>
3445 To get a more useful version of the Collects class, Hugs provides a mechanism
3446 that allows programmers to specify dependencies between the parameters of a
3447 multiple parameter class (For readers with an interest in theoretical
3448 foundations and previous work: The use of dependency information can be seen
3449 both as a generalization of the proposal for `parametric type classes' that was
3450 put forward by Chen, Hudak, and Odersky, or as a special case of Mark Jones's
3451 later framework for "improvement" of qualified types. The
3452 underlying ideas are also discussed in a more theoretical and abstract setting
3453 in a manuscript [implparam], where they are identified as one point in a
3454 general design space for systems of implicit parameterization.).
3456 To start with an abstract example, consider a declaration such as:
3458 class C a b where ...
3460 which tells us simply that C can be thought of as a binary relation on types
3461 (or type constructors, depending on the kinds of a and b). Extra clauses can be
3462 included in the definition of classes to add information about dependencies
3463 between parameters, as in the following examples:
3465 class D a b | a -> b where ...
3466 class E a b | a -> b, b -> a where ...
3468 The notation <literal>a -> b</literal> used here between the | and where
3469 symbols --- not to be
3470 confused with a function type --- indicates that the a parameter uniquely
3471 determines the b parameter, and might be read as "a determines b." Thus D is
3472 not just a relation, but actually a (partial) function. Similarly, from the two
3473 dependencies that are included in the definition of E, we can see that E
3474 represents a (partial) one-one mapping between types.
3477 More generally, dependencies take the form <literal>x1 ... xn -> y1 ... ym</literal>,
3478 where x1, ..., xn, and y1, ..., yn are type variables with n>0 and
3479 m>=0, meaning that the y parameters are uniquely determined by the x
3480 parameters. Spaces can be used as separators if more than one variable appears
3481 on any single side of a dependency, as in <literal>t -> a b</literal>. Note that a class may be
3482 annotated with multiple dependencies using commas as separators, as in the
3483 definition of E above. Some dependencies that we can write in this notation are
3484 redundant, and will be rejected because they don't serve any useful
3485 purpose, and may instead indicate an error in the program. Examples of
3486 dependencies like this include <literal>a -> a </literal>,
3487 <literal>a -> a a </literal>,
3488 <literal>a -> </literal>, etc. There can also be
3489 some redundancy if multiple dependencies are given, as in
3490 <literal>a->b</literal>,
3491 <literal>b->c </literal>, <literal>a->c </literal>, and
3492 in which some subset implies the remaining dependencies. Examples like this are
3493 not treated as errors. Note that dependencies appear only in class
3494 declarations, and not in any other part of the language. In particular, the
3495 syntax for instance declarations, class constraints, and types is completely
3499 By including dependencies in a class declaration, we provide a mechanism for
3500 the programmer to specify each multiple parameter class more precisely. The
3501 compiler, on the other hand, is responsible for ensuring that the set of
3502 instances that are in scope at any given point in the program is consistent
3503 with any declared dependencies. For example, the following pair of instance
3504 declarations cannot appear together in the same scope because they violate the
3505 dependency for D, even though either one on its own would be acceptable:
3507 instance D Bool Int where ...
3508 instance D Bool Char where ...
3510 Note also that the following declaration is not allowed, even by itself:
3512 instance D [a] b where ...
3514 The problem here is that this instance would allow one particular choice of [a]
3515 to be associated with more than one choice for b, which contradicts the
3516 dependency specified in the definition of D. More generally, this means that,
3517 in any instance of the form:
3519 instance D t s where ...
3521 for some particular types t and s, the only variables that can appear in s are
3522 the ones that appear in t, and hence, if the type t is known, then s will be
3523 uniquely determined.
3526 The benefit of including dependency information is that it allows us to define
3527 more general multiple parameter classes, without ambiguity problems, and with
3528 the benefit of more accurate types. To illustrate this, we return to the
3529 collection class example, and annotate the original definition of <literal>Collects</literal>
3530 with a simple dependency:
3532 class Collects e ce | ce -> e where
3534 insert :: e -> ce -> ce
3535 member :: e -> ce -> Bool
3537 The dependency <literal>ce -> e</literal> here specifies that the type e of elements is uniquely
3538 determined by the type of the collection ce. Note that both parameters of
3539 Collects are of kind *; there are no constructor classes here. Note too that
3540 all of the instances of Collects that we gave earlier can be used
3541 together with this new definition.
3544 What about the ambiguity problems that we encountered with the original
3545 definition? The empty function still has type Collects e ce => ce, but it is no
3546 longer necessary to regard that as an ambiguous type: Although the variable e
3547 does not appear on the right of the => symbol, the dependency for class
3548 Collects tells us that it is uniquely determined by ce, which does appear on
3549 the right of the => symbol. Hence the context in which empty is used can still
3550 give enough information to determine types for both ce and e, without
3551 ambiguity. More generally, we need only regard a type as ambiguous if it
3552 contains a variable on the left of the => that is not uniquely determined
3553 (either directly or indirectly) by the variables on the right.
3556 Dependencies also help to produce more accurate types for user defined
3557 functions, and hence to provide earlier detection of errors, and less cluttered
3558 types for programmers to work with. Recall the previous definition for a
3561 f x y = insert x y = insert x . insert y
3563 for which we originally obtained a type:
3565 f :: (Collects a c, Collects b c) => a -> b -> c -> c
3567 Given the dependency information that we have for Collects, however, we can
3568 deduce that a and b must be equal because they both appear as the second
3569 parameter in a Collects constraint with the same first parameter c. Hence we
3570 can infer a shorter and more accurate type for f:
3572 f :: (Collects a c) => a -> a -> c -> c
3574 In a similar way, the earlier definition of g will now be flagged as a type error.
3577 Although we have given only a few examples here, it should be clear that the
3578 addition of dependency information can help to make multiple parameter classes
3579 more useful in practice, avoiding ambiguity problems, and allowing more general
3580 sets of instance declarations.
3586 <sect2 id="instance-decls">
3587 <title>Instance declarations</title>
3589 <para>An instance declaration has the form
3591 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 ...
3593 The part before the "<literal>=></literal>" is the
3594 <emphasis>context</emphasis>, while the part after the
3595 "<literal>=></literal>" is the <emphasis>head</emphasis> of the instance declaration.
3598 <sect3 id="flexible-instance-head">
3599 <title>Relaxed rules for the instance head</title>
3602 In Haskell 98 the head of an instance declaration
3603 must be of the form <literal>C (T a1 ... an)</literal>, where
3604 <literal>C</literal> is the class, <literal>T</literal> is a data type constructor,
3605 and the <literal>a1 ... an</literal> are distinct type variables.
3606 GHC relaxes these rules in two ways.
3610 The <option>-XFlexibleInstances</option> flag allows the head of the instance
3611 declaration to mention arbitrary nested types.
3612 For example, this becomes a legal instance declaration
3614 instance C (Maybe Int) where ...
3616 See also the <link linkend="instance-overlap">rules on overlap</link>.
3619 With the <option>-XTypeSynonymInstances</option> flag, instance heads may use type
3620 synonyms. As always, using a type synonym is just shorthand for
3621 writing the RHS of the type synonym definition. For example:
3625 type Point = (Int,Int)
3626 instance C Point where ...
3627 instance C [Point] where ...
3631 is legal. However, if you added
3635 instance C (Int,Int) where ...
3639 as well, then the compiler will complain about the overlapping
3640 (actually, identical) instance declarations. As always, type synonyms
3641 must be fully applied. You cannot, for example, write:
3645 instance Monad P where ...
3653 <sect3 id="instance-rules">
3654 <title>Relaxed rules for instance contexts</title>
3656 <para>In Haskell 98, the assertions in the context of the instance declaration
3657 must be of the form <literal>C a</literal> where <literal>a</literal>
3658 is a type variable that occurs in the head.
3662 The <option>-XFlexibleContexts</option> flag relaxes this rule, as well
3663 as the corresponding rule for type signatures (see <xref linkend="flexible-contexts"/>).
3664 With this flag the context of the instance declaration can each consist of arbitrary
3665 (well-kinded) assertions <literal>(C t1 ... tn)</literal> subject only to the
3669 The Paterson Conditions: for each assertion in the context
3671 <listitem><para>No type variable has more occurrences in the assertion than in the head</para></listitem>
3672 <listitem><para>The assertion has fewer constructors and variables (taken together
3673 and counting repetitions) than the head</para></listitem>
3677 <listitem><para>The Coverage Condition. For each functional dependency,
3678 <replaceable>tvs</replaceable><subscript>left</subscript> <literal>-></literal>
3679 <replaceable>tvs</replaceable><subscript>right</subscript>, of the class,
3680 every type variable in
3681 S(<replaceable>tvs</replaceable><subscript>right</subscript>) must appear in
3682 S(<replaceable>tvs</replaceable><subscript>left</subscript>), where S is the
3683 substitution mapping each type variable in the class declaration to the
3684 corresponding type in the instance declaration.
3687 These restrictions ensure that context reduction terminates: each reduction
3688 step makes the problem smaller by at least one
3689 constructor. Both the Paterson Conditions and the Coverage Condition are lifted
3690 if you give the <option>-XUndecidableInstances</option>
3691 flag (<xref linkend="undecidable-instances"/>).
3692 You can find lots of background material about the reason for these
3693 restrictions in the paper <ulink
3694 url="http://research.microsoft.com/%7Esimonpj/papers/fd%2Dchr/">
3695 Understanding functional dependencies via Constraint Handling Rules</ulink>.
3698 For example, these are OK:
3700 instance C Int [a] -- Multiple parameters
3701 instance Eq (S [a]) -- Structured type in head
3703 -- Repeated type variable in head
3704 instance C4 a a => C4 [a] [a]
3705 instance Stateful (ST s) (MutVar s)
3707 -- Head can consist of type variables only
3709 instance (Eq a, Show b) => C2 a b
3711 -- Non-type variables in context
3712 instance Show (s a) => Show (Sized s a)
3713 instance C2 Int a => C3 Bool [a]
3714 instance C2 Int a => C3 [a] b
3718 -- Context assertion no smaller than head
3719 instance C a => C a where ...
3720 -- (C b b) has more more occurrences of b than the head
3721 instance C b b => Foo [b] where ...
3726 The same restrictions apply to instances generated by
3727 <literal>deriving</literal> clauses. Thus the following is accepted:
3729 data MinHeap h a = H a (h a)
3732 because the derived instance
3734 instance (Show a, Show (h a)) => Show (MinHeap h a)
3736 conforms to the above rules.
3740 A useful idiom permitted by the above rules is as follows.
3741 If one allows overlapping instance declarations then it's quite
3742 convenient to have a "default instance" declaration that applies if
3743 something more specific does not:
3751 <sect3 id="undecidable-instances">
3752 <title>Undecidable instances</title>
3755 Sometimes even the rules of <xref linkend="instance-rules"/> are too onerous.
3756 For example, sometimes you might want to use the following to get the
3757 effect of a "class synonym":
3759 class (C1 a, C2 a, C3 a) => C a where { }
3761 instance (C1 a, C2 a, C3 a) => C a where { }
3763 This allows you to write shorter signatures:
3769 f :: (C1 a, C2 a, C3 a) => ...
3771 The restrictions on functional dependencies (<xref
3772 linkend="functional-dependencies"/>) are particularly troublesome.
3773 It is tempting to introduce type variables in the context that do not appear in
3774 the head, something that is excluded by the normal rules. For example:
3776 class HasConverter a b | a -> b where
3779 data Foo a = MkFoo a
3781 instance (HasConverter a b,Show b) => Show (Foo a) where
3782 show (MkFoo value) = show (convert value)
3784 This is dangerous territory, however. Here, for example, is a program that would make the
3789 instance F [a] [[a]]
3790 instance (D c, F a c) => D [a] -- 'c' is not mentioned in the head
3792 Similarly, it can be tempting to lift the coverage condition:
3794 class Mul a b c | a b -> c where
3795 (.*.) :: a -> b -> c
3797 instance Mul Int Int Int where (.*.) = (*)
3798 instance Mul Int Float Float where x .*. y = fromIntegral x * y
3799 instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
3801 The third instance declaration does not obey the coverage condition;
3802 and indeed the (somewhat strange) definition:
3804 f = \ b x y -> if b then x .*. [y] else y
3806 makes instance inference go into a loop, because it requires the constraint
3807 <literal>(Mul a [b] b)</literal>.
3810 Nevertheless, GHC allows you to experiment with more liberal rules. If you use
3811 the experimental flag <option>-XUndecidableInstances</option>
3812 <indexterm><primary>-XUndecidableInstances</primary></indexterm>,
3813 both the Paterson Conditions and the Coverage Condition
3814 (described in <xref linkend="instance-rules"/>) are lifted. Termination is ensured by having a
3815 fixed-depth recursion stack. If you exceed the stack depth you get a
3816 sort of backtrace, and the opportunity to increase the stack depth
3817 with <option>-fcontext-stack=</option><emphasis>N</emphasis>.
3823 <sect3 id="instance-overlap">
3824 <title>Overlapping instances</title>
3826 In general, <emphasis>GHC requires that that it be unambiguous which instance
3828 should be used to resolve a type-class constraint</emphasis>. This behaviour
3829 can be modified by two flags: <option>-XOverlappingInstances</option>
3830 <indexterm><primary>-XOverlappingInstances
3831 </primary></indexterm>
3832 and <option>-XIncoherentInstances</option>
3833 <indexterm><primary>-XIncoherentInstances
3834 </primary></indexterm>, as this section discusses. Both these
3835 flags are dynamic flags, and can be set on a per-module basis, using
3836 an <literal>OPTIONS_GHC</literal> pragma if desired (<xref linkend="source-file-options"/>).</para>
3838 When GHC tries to resolve, say, the constraint <literal>C Int Bool</literal>,
3839 it tries to match every instance declaration against the
3841 by instantiating the head of the instance declaration. For example, consider
3844 instance context1 => C Int a where ... -- (A)
3845 instance context2 => C a Bool where ... -- (B)
3846 instance context3 => C Int [a] where ... -- (C)
3847 instance context4 => C Int [Int] where ... -- (D)
3849 The instances (A) and (B) match the constraint <literal>C Int Bool</literal>,
3850 but (C) and (D) do not. When matching, GHC takes
3851 no account of the context of the instance declaration
3852 (<literal>context1</literal> etc).
3853 GHC's default behaviour is that <emphasis>exactly one instance must match the
3854 constraint it is trying to resolve</emphasis>.
3855 It is fine for there to be a <emphasis>potential</emphasis> of overlap (by
3856 including both declarations (A) and (B), say); an error is only reported if a
3857 particular constraint matches more than one.
3861 The <option>-XOverlappingInstances</option> flag instructs GHC to allow
3862 more than one instance to match, provided there is a most specific one. For
3863 example, the constraint <literal>C Int [Int]</literal> matches instances (A),
3864 (C) and (D), but the last is more specific, and hence is chosen. If there is no
3865 most-specific match, the program is rejected.
3868 However, GHC is conservative about committing to an overlapping instance. For example:
3873 Suppose that from the RHS of <literal>f</literal> we get the constraint
3874 <literal>C Int [b]</literal>. But
3875 GHC does not commit to instance (C), because in a particular
3876 call of <literal>f</literal>, <literal>b</literal> might be instantiate
3877 to <literal>Int</literal>, in which case instance (D) would be more specific still.
3878 So GHC rejects the program.
3879 (If you add the flag <option>-XIncoherentInstances</option>,
3880 GHC will instead pick (C), without complaining about
3881 the problem of subsequent instantiations.)
3884 Notice that we gave a type signature to <literal>f</literal>, so GHC had to
3885 <emphasis>check</emphasis> that <literal>f</literal> has the specified type.
3886 Suppose instead we do not give a type signature, asking GHC to <emphasis>infer</emphasis>
3887 it instead. In this case, GHC will refrain from
3888 simplifying the constraint <literal>C Int [b]</literal> (for the same reason
3889 as before) but, rather than rejecting the program, it will infer the type
3891 f :: C Int [b] => [b] -> [b]
3893 That postpones the question of which instance to pick to the
3894 call site for <literal>f</literal>
3895 by which time more is known about the type <literal>b</literal>.
3896 You can write this type signature yourself if you use the
3897 <link linkend="flexible-contexts"><option>-XFlexibleContexts</option></link>
3901 Exactly the same situation can arise in instance declarations themselves. Suppose we have
3905 instance Foo [b] where
3908 and, as before, the constraint <literal>C Int [b]</literal> arises from <literal>f</literal>'s
3909 right hand side. GHC will reject the instance, complaining as before that it does not know how to resolve
3910 the constraint <literal>C Int [b]</literal>, because it matches more than one instance
3911 declaration. The solution is to postpone the choice by adding the constraint to the context
3912 of the instance declaration, thus:
3914 instance C Int [b] => Foo [b] where
3917 (You need <link linkend="instance-rules"><option>-XFlexibleInstances</option></link> to do this.)
3920 The willingness to be overlapped or incoherent is a property of
3921 the <emphasis>instance declaration</emphasis> itself, controlled by the
3922 presence or otherwise of the <option>-XOverlappingInstances</option>
3923 and <option>-XIncoherentInstances</option> flags when that module is
3924 being defined. Neither flag is required in a module that imports and uses the
3925 instance declaration. Specifically, during the lookup process:
3928 An instance declaration is ignored during the lookup process if (a) a more specific
3929 match is found, and (b) the instance declaration was compiled with
3930 <option>-XOverlappingInstances</option>. The flag setting for the
3931 more-specific instance does not matter.
3934 Suppose an instance declaration does not match the constraint being looked up, but
3935 does unify with it, so that it might match when the constraint is further
3936 instantiated. Usually GHC will regard this as a reason for not committing to
3937 some other constraint. But if the instance declaration was compiled with
3938 <option>-XIncoherentInstances</option>, GHC will skip the "does-it-unify?"
3939 check for that declaration.
3942 These rules make it possible for a library author to design a library that relies on
3943 overlapping instances without the library client having to know.
3946 If an instance declaration is compiled without
3947 <option>-XOverlappingInstances</option>,
3948 then that instance can never be overlapped. This could perhaps be
3949 inconvenient. Perhaps the rule should instead say that the
3950 <emphasis>overlapping</emphasis> instance declaration should be compiled in
3951 this way, rather than the <emphasis>overlapped</emphasis> one. Perhaps overlap
3952 at a usage site should be permitted regardless of how the instance declarations
3953 are compiled, if the <option>-XOverlappingInstances</option> flag is
3954 used at the usage site. (Mind you, the exact usage site can occasionally be
3955 hard to pin down.) We are interested to receive feedback on these points.
3957 <para>The <option>-XIncoherentInstances</option> flag implies the
3958 <option>-XOverlappingInstances</option> flag, but not vice versa.
3966 <sect2 id="overloaded-strings">
3967 <title>Overloaded string literals
3971 GHC supports <emphasis>overloaded string literals</emphasis>. Normally a
3972 string literal has type <literal>String</literal>, but with overloaded string
3973 literals enabled (with <literal>-XOverloadedStrings</literal>)
3974 a string literal has type <literal>(IsString a) => a</literal>.
3977 This means that the usual string syntax can be used, e.g., for packed strings
3978 and other variations of string like types. String literals behave very much
3979 like integer literals, i.e., they can be used in both expressions and patterns.
3980 If used in a pattern the literal with be replaced by an equality test, in the same
3981 way as an integer literal is.
3984 The class <literal>IsString</literal> is defined as:
3986 class IsString a where
3987 fromString :: String -> a
3989 The only predefined instance is the obvious one to make strings work as usual:
3991 instance IsString [Char] where
3994 The class <literal>IsString</literal> is not in scope by default. If you want to mention
3995 it explicitly (for example, to give an instance declaration for it), you can import it
3996 from module <literal>GHC.Exts</literal>.
3999 Haskell's defaulting mechanism is extended to cover string literals, when <option>-XOverloadedStrings</option> is specified.
4003 Each type in a default declaration must be an
4004 instance of <literal>Num</literal> <emphasis>or</emphasis> of <literal>IsString</literal>.
4008 The standard defaulting rule (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.3.4">Haskell Report, Section 4.3.4</ulink>)
4009 is extended thus: defaulting applies when all the unresolved constraints involve standard classes
4010 <emphasis>or</emphasis> <literal>IsString</literal>; and at least one is a numeric class
4011 <emphasis>or</emphasis> <literal>IsString</literal>.
4020 import GHC.Exts( IsString(..) )
4022 newtype MyString = MyString String deriving (Eq, Show)
4023 instance IsString MyString where
4024 fromString = MyString
4026 greet :: MyString -> MyString
4027 greet "hello" = "world"
4031 print $ greet "hello"
4032 print $ greet "fool"
4036 Note that deriving <literal>Eq</literal> is necessary for the pattern matching
4037 to work since it gets translated into an equality comparison.
4043 <sect1 id="type-families">
4044 <title>Type families</title>
4047 <firstterm>Indexed type families</firstterm> are a new GHC extension to
4048 facilitate type-level
4049 programming. Type families are a generalisation of <firstterm>associated
4050 data types</firstterm>
4051 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKPM05.html">Associated
4052 Types with Class</ulink>”, M. Chakravarty, G. Keller, S. Peyton Jones,
4053 and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLAN-SIGACT
4054 Symposium on Principles of Programming Languages (POPL'05)”, pages
4055 1-13, ACM Press, 2005) and <firstterm>associated type synonyms</firstterm>
4056 (“<ulink url="http://www.cse.unsw.edu.au/~chak/papers/CKP05.html">Type
4057 Associated Type Synonyms</ulink>”. M. Chakravarty, G. Keller, and
4059 In Proceedings of “The Tenth ACM SIGPLAN International Conference on
4060 Functional Programming”, ACM Press, pages 241-253, 2005). Type families
4061 themselves are described in the paper “<ulink
4062 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4063 Checking with Open Type Functions</ulink>”, T. Schrijvers,
4065 M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The
4066 13th ACM SIGPLAN International Conference on Functional
4067 Programming”, ACM Press, pages 51-62, 2008. Type families
4068 essentially provide type-indexed data types and named functions on types,
4069 which are useful for generic programming and highly parameterised library
4070 interfaces as well as interfaces with enhanced static information, much like
4071 dependent types. They might also be regarded as an alternative to functional
4072 dependencies, but provide a more functional style of type-level programming
4073 than the relational style of functional dependencies.
4076 Indexed type families, or type families for short, are type constructors that
4077 represent sets of types. Set members are denoted by supplying the type family
4078 constructor with type parameters, which are called <firstterm>type
4079 indices</firstterm>. The
4080 difference between vanilla parametrised type constructors and family
4081 constructors is much like between parametrically polymorphic functions and
4082 (ad-hoc polymorphic) methods of type classes. Parametric polymorphic functions
4083 behave the same at all type instances, whereas class methods can change their
4084 behaviour in dependence on the class type parameters. Similarly, vanilla type
4085 constructors imply the same data representation for all type instances, but
4086 family constructors can have varying representation types for varying type
4090 Indexed type families come in two flavours: <firstterm>data
4091 families</firstterm> and <firstterm>type synonym
4092 families</firstterm>. They are the indexed family variants of algebraic
4093 data types and type synonyms, respectively. The instances of data families
4094 can be data types and newtypes.
4097 Type families are enabled by the flag <option>-XTypeFamilies</option>.
4098 Additional information on the use of type families in GHC is available on
4099 <ulink url="http://www.haskell.org/haskellwiki/GHC/Indexed_types">the
4100 Haskell wiki page on type families</ulink>.
4103 <sect2 id="data-families">
4104 <title>Data families</title>
4107 Data families appear in two flavours: (1) they can be defined on the
4109 or (2) they can appear inside type classes (in which case they are known as
4110 associated types). The former is the more general variant, as it lacks the
4111 requirement for the type-indexes to coincide with the class
4112 parameters. However, the latter can lead to more clearly structured code and
4113 compiler warnings if some type instances were - possibly accidentally -
4114 omitted. In the following, we always discuss the general toplevel form first
4115 and then cover the additional constraints placed on associated types.
4118 <sect3 id="data-family-declarations">
4119 <title>Data family declarations</title>
4122 Indexed data families are introduced by a signature, such as
4124 data family GMap k :: * -> *
4126 The special <literal>family</literal> distinguishes family from standard
4127 data declarations. The result kind annotation is optional and, as
4128 usual, defaults to <literal>*</literal> if omitted. An example is
4132 Named arguments can also be given explicit kind signatures if needed.
4134 [http://www.haskell.org/ghc/docs/latest/html/users_guide/gadt.html GADT
4135 declarations] named arguments are entirely optional, so that we can
4136 declare <literal>Array</literal> alternatively with
4138 data family Array :: * -> *
4142 <sect4 id="assoc-data-family-decl">
4143 <title>Associated data family declarations</title>
4145 When a data family is declared as part of a type class, we drop
4146 the <literal>family</literal> special. The <literal>GMap</literal>
4147 declaration takes the following form
4149 class GMapKey k where
4150 data GMap k :: * -> *
4153 In contrast to toplevel declarations, named arguments must be used for
4154 all type parameters that are to be used as type-indexes. Moreover,
4155 the argument names must be class parameters. Each class parameter may
4156 only be used at most once per associated type, but some may be omitted
4157 and they may be in an order other than in the class head. Hence, the
4158 following contrived example is admissible:
4167 <sect3 id="data-instance-declarations">
4168 <title>Data instance declarations</title>
4171 Instance declarations of data and newtype families are very similar to
4172 standard data and newtype declarations. The only two differences are
4173 that the keyword <literal>data</literal> or <literal>newtype</literal>
4174 is followed by <literal>instance</literal> and that some or all of the
4175 type arguments can be non-variable types, but may not contain forall
4176 types or type synonym families. However, data families are generally
4177 allowed in type parameters, and type synonyms are allowed as long as
4178 they are fully applied and expand to a type that is itself admissible -
4179 exactly as this is required for occurrences of type synonyms in class
4180 instance parameters. For example, the <literal>Either</literal>
4181 instance for <literal>GMap</literal> is
4183 data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4185 In this example, the declaration has only one variant. In general, it
4189 Data and newtype instance declarations are only permitted when an
4190 appropriate family declaration is in scope - just as a class instance declaratoin
4191 requires the class declaration to be visible. Moreover, each instance
4192 declaration has to conform to the kind determined by its family
4193 declaration. This implies that the number of parameters of an instance
4194 declaration matches the arity determined by the kind of the family.
4197 A data family instance declaration can use the full exprssiveness of
4198 ordinary <literal>data</literal> or <literal>newtype</literal> declarations:
4200 <listitem><para> Although, a data family is <emphasis>introduced</emphasis> with
4201 the keyword "<literal>data</literal>", a data family <emphasis>instance</emphasis> can
4202 use either <literal>data</literal> or <literal>newtype</literal>. For example:
4205 data instance T Int = T1 Int | T2 Bool
4206 newtype instance T Char = TC Bool
4209 <listitem><para> A <literal>data instance</literal> can use GADT syntax for the data constructors,
4210 and indeed can define a GADT. For example:
4213 data instance G [a] b where
4214 G1 :: c -> G [Int] b
4218 <listitem><para> You can use a <literal>deriving</literal> clause on a
4219 <literal>data instance</literal> or <literal>newtype instance</literal>
4226 Even if type families are defined as toplevel declarations, functions
4227 that perform different computations for different family instances may still
4228 need to be defined as methods of type classes. In particular, the
4229 following is not possible:
4232 data instance T Int = A
4233 data instance T Char = B
4235 foo A = 1 -- WRONG: These two equations together...
4236 foo B = 2 -- ...will produce a type error.
4238 Instead, you would have to write <literal>foo</literal> as a class operation, thus:
4242 instance Foo Int where
4244 instance Foo Char where
4247 (Given the functionality provided by GADTs (Generalised Algebraic Data
4248 Types), it might seem as if a definition, such as the above, should be
4249 feasible. However, type families are - in contrast to GADTs - are
4250 <emphasis>open;</emphasis> i.e., new instances can always be added,
4252 modules. Supporting pattern matching across different data instances
4253 would require a form of extensible case construct.)
4256 <sect4 id="assoc-data-inst">
4257 <title>Associated data instances</title>
4259 When an associated data family instance is declared within a type
4260 class instance, we drop the <literal>instance</literal> keyword in the
4261 family instance. So, the <literal>Either</literal> instance
4262 for <literal>GMap</literal> becomes:
4264 instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
4265 data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
4268 The most important point about associated family instances is that the
4269 type indexes corresponding to class parameters must be identical to
4270 the type given in the instance head; here this is the first argument
4271 of <literal>GMap</literal>, namely <literal>Either a b</literal>,
4272 which coincides with the only class parameter. Any parameters to the
4273 family constructor that do not correspond to class parameters, need to
4274 be variables in every instance; here this is the
4275 variable <literal>v</literal>.
4278 Instances for an associated family can only appear as part of
4279 instances declarations of the class in which the family was declared -
4280 just as with the equations of the methods of a class. Also in
4281 correspondence to how methods are handled, declarations of associated
4282 types can be omitted in class instances. If an associated family
4283 instance is omitted, the corresponding instance type is not inhabited;
4284 i.e., only diverging expressions, such
4285 as <literal>undefined</literal>, can assume the type.
4289 <sect4 id="scoping-class-params">
4290 <title>Scoping of class parameters</title>
4292 In the case of multi-parameter type classes, the visibility of class
4293 parameters in the right-hand side of associated family instances
4294 depends <emphasis>solely</emphasis> on the parameters of the data
4295 family. As an example, consider the simple class declaration
4300 Only one of the two class parameters is a parameter to the data
4301 family. Hence, the following instance declaration is invalid:
4303 instance C [c] d where
4304 data T [c] = MkT (c, d) -- WRONG!! 'd' is not in scope
4306 Here, the right-hand side of the data instance mentions the type
4307 variable <literal>d</literal> that does not occur in its left-hand
4308 side. We cannot admit such data instances as they would compromise
4313 <sect4 id="family-class-inst">
4314 <title>Type class instances of family instances</title>
4316 Type class instances of instances of data families can be defined as
4317 usual, and in particular data instance declarations can
4318 have <literal>deriving</literal> clauses. For example, we can write
4320 data GMap () v = GMapUnit (Maybe v)
4323 which implicitly defines an instance of the form
4325 instance Show v => Show (GMap () v) where ...
4329 Note that class instances are always for
4330 particular <emphasis>instances</emphasis> of a data family and never
4331 for an entire family as a whole. This is for essentially the same
4332 reasons that we cannot define a toplevel function that performs
4333 pattern matching on the data constructors
4334 of <emphasis>different</emphasis> instances of a single type family.
4335 It would require a form of extensible case construct.
4339 <sect4 id="data-family-overlap">
4340 <title>Overlap of data instances</title>
4342 The instance declarations of a data family used in a single program
4343 may not overlap at all, independent of whether they are associated or
4344 not. In contrast to type class instances, this is not only a matter
4345 of consistency, but one of type safety.
4351 <sect3 id="data-family-import-export">
4352 <title>Import and export</title>
4355 The association of data constructors with type families is more dynamic
4356 than that is the case with standard data and newtype declarations. In
4357 the standard case, the notation <literal>T(..)</literal> in an import or
4358 export list denotes the type constructor and all the data constructors
4359 introduced in its declaration. However, a family declaration never
4360 introduces any data constructors; instead, data constructors are
4361 introduced by family instances. As a result, which data constructors
4362 are associated with a type family depends on the currently visible
4363 instance declarations for that family. Consequently, an import or
4364 export item of the form <literal>T(..)</literal> denotes the family
4365 constructor and all currently visible data constructors - in the case of
4366 an export item, these may be either imported or defined in the current
4367 module. The treatment of import and export items that explicitly list
4368 data constructors, such as <literal>GMap(GMapEither)</literal>, is
4372 <sect4 id="data-family-impexp-assoc">
4373 <title>Associated families</title>
4375 As expected, an import or export item of the
4376 form <literal>C(..)</literal> denotes all of the class' methods and
4377 associated types. However, when associated types are explicitly
4378 listed as subitems of a class, we need some new syntax, as uppercase
4379 identifiers as subitems are usually data constructors, not type
4380 constructors. To clarify that we denote types here, each associated
4381 type name needs to be prefixed by the keyword <literal>type</literal>.
4382 So for example, when explicitly listing the components of
4383 the <literal>GMapKey</literal> class, we write <literal>GMapKey(type
4384 GMap, empty, lookup, insert)</literal>.
4388 <sect4 id="data-family-impexp-examples">
4389 <title>Examples</title>
4391 Assuming our running <literal>GMapKey</literal> class example, let us
4392 look at some export lists and their meaning:
4395 <para><literal>module GMap (GMapKey) where...</literal>: Exports
4396 just the class name.</para>
4399 <para><literal>module GMap (GMapKey(..)) where...</literal>:
4400 Exports the class, the associated type <literal>GMap</literal>
4402 functions <literal>empty</literal>, <literal>lookup</literal>,
4403 and <literal>insert</literal>. None of the data constructors is
4407 <para><literal>module GMap (GMapKey(..), GMap(..))
4408 where...</literal>: As before, but also exports all the data
4409 constructors <literal>GMapInt</literal>,
4410 <literal>GMapChar</literal>,
4411 <literal>GMapUnit</literal>, <literal>GMapPair</literal>,
4412 and <literal>GMapUnit</literal>.</para>
4415 <para><literal>module GMap (GMapKey(empty, lookup, insert),
4416 GMap(..)) where...</literal>: As before.</para>
4419 <para><literal>module GMap (GMapKey, empty, lookup, insert, GMap(..))
4420 where...</literal>: As before.</para>
4425 Finally, you can write <literal>GMapKey(type GMap)</literal> to denote
4426 both the class <literal>GMapKey</literal> as well as its associated
4427 type <literal>GMap</literal>. However, you cannot
4428 write <literal>GMapKey(type GMap(..))</literal> — i.e.,
4429 sub-component specifications cannot be nested. To
4430 specify <literal>GMap</literal>'s data constructors, you have to list
4435 <sect4 id="data-family-impexp-instances">
4436 <title>Instances</title>
4438 Family instances are implicitly exported, just like class instances.
4439 However, this applies only to the heads of instances, not to the data
4440 constructors an instance defines.
4448 <sect2 id="synonym-families">
4449 <title>Synonym families</title>
4452 Type families appear in two flavours: (1) they can be defined on the
4453 toplevel or (2) they can appear inside type classes (in which case they
4454 are known as associated type synonyms). The former is the more general
4455 variant, as it lacks the requirement for the type-indexes to coincide with
4456 the class parameters. However, the latter can lead to more clearly
4457 structured code and compiler warnings if some type instances were -
4458 possibly accidentally - omitted. In the following, we always discuss the
4459 general toplevel form first and then cover the additional constraints
4460 placed on associated types.
4463 <sect3 id="type-family-declarations">
4464 <title>Type family declarations</title>
4467 Indexed type families are introduced by a signature, such as
4469 type family Elem c :: *
4471 The special <literal>family</literal> distinguishes family from standard
4472 type declarations. The result kind annotation is optional and, as
4473 usual, defaults to <literal>*</literal> if omitted. An example is
4477 Parameters can also be given explicit kind signatures if needed. We
4478 call the number of parameters in a type family declaration, the family's
4479 arity, and all applications of a type family must be fully saturated
4480 w.r.t. to that arity. This requirement is unlike ordinary type synonyms
4481 and it implies that the kind of a type family is not sufficient to
4482 determine a family's arity, and hence in general, also insufficient to
4483 determine whether a type family application is well formed. As an
4484 example, consider the following declaration:
4486 type family F a b :: * -> * -- F's arity is 2,
4487 -- although its overall kind is * -> * -> * -> *
4489 Given this declaration the following are examples of well-formed and
4492 F Char [Int] -- OK! Kind: * -> *
4493 F Char [Int] Bool -- OK! Kind: *
4494 F IO Bool -- WRONG: kind mismatch in the first argument
4495 F Bool -- WRONG: unsaturated application
4499 <sect4 id="assoc-type-family-decl">
4500 <title>Associated type family declarations</title>
4502 When a type family is declared as part of a type class, we drop
4503 the <literal>family</literal> special. The <literal>Elem</literal>
4504 declaration takes the following form
4506 class Collects ce where
4510 The argument names of the type family must be class parameters. Each
4511 class parameter may only be used at most once per associated type, but
4512 some may be omitted and they may be in an order other than in the
4513 class head. Hence, the following contrived example is admissible:
4518 These rules are exactly as for associated data families.
4523 <sect3 id="type-instance-declarations">
4524 <title>Type instance declarations</title>
4526 Instance declarations of type families are very similar to standard type
4527 synonym declarations. The only two differences are that the
4528 keyword <literal>type</literal> is followed
4529 by <literal>instance</literal> and that some or all of the type
4530 arguments can be non-variable types, but may not contain forall types or
4531 type synonym families. However, data families are generally allowed, and
4532 type synonyms are allowed as long as they are fully applied and expand
4533 to a type that is admissible - these are the exact same requirements as
4534 for data instances. For example, the <literal>[e]</literal> instance
4535 for <literal>Elem</literal> is
4537 type instance Elem [e] = e
4541 Type family instance declarations are only legitimate when an
4542 appropriate family declaration is in scope - just like class instances
4543 require the class declaration to be visible. Moreover, each instance
4544 declaration has to conform to the kind determined by its family
4545 declaration, and the number of type parameters in an instance
4546 declaration must match the number of type parameters in the family
4547 declaration. Finally, the right-hand side of a type instance must be a
4548 monotype (i.e., it may not include foralls) and after the expansion of
4549 all saturated vanilla type synonyms, no synonyms, except family synonyms
4550 may remain. Here are some examples of admissible and illegal type
4553 type family F a :: *
4554 type instance F [Int] = Int -- OK!
4555 type instance F String = Char -- OK!
4556 type instance F (F a) = a -- WRONG: type parameter mentions a type family
4557 type instance F (forall a. (a, b)) = b -- WRONG: a forall type appears in a type parameter
4558 type instance F Float = forall a.a -- WRONG: right-hand side may not be a forall type
4560 type family G a b :: * -> *
4561 type instance G Int = (,) -- WRONG: must be two type parameters
4562 type instance G Int Char Float = Double -- WRONG: must be two type parameters
4566 <sect4 id="assoc-type-instance">
4567 <title>Associated type instance declarations</title>
4569 When an associated family instance is declared within a type class
4570 instance, we drop the <literal>instance</literal> keyword in the family
4571 instance. So, the <literal>[e]</literal> instance
4572 for <literal>Elem</literal> becomes:
4574 instance (Eq (Elem [e])) => Collects ([e]) where
4578 The most important point about associated family instances is that the
4579 type indexes corresponding to class parameters must be identical to the
4580 type given in the instance head; here this is <literal>[e]</literal>,
4581 which coincides with the only class parameter.
4584 Instances for an associated family can only appear as part of instances
4585 declarations of the class in which the family was declared - just as
4586 with the equations of the methods of a class. Also in correspondence to
4587 how methods are handled, declarations of associated types can be omitted
4588 in class instances. If an associated family instance is omitted, the
4589 corresponding instance type is not inhabited; i.e., only diverging
4590 expressions, such as <literal>undefined</literal>, can assume the type.
4594 <sect4 id="type-family-overlap">
4595 <title>Overlap of type synonym instances</title>
4597 The instance declarations of a type family used in a single program
4598 may only overlap if the right-hand sides of the overlapping instances
4599 coincide for the overlapping types. More formally, two instance
4600 declarations overlap if there is a substitution that makes the
4601 left-hand sides of the instances syntactically the same. Whenever
4602 that is the case, the right-hand sides of the instances must also be
4603 syntactically equal under the same substitution. This condition is
4604 independent of whether the type family is associated or not, and it is
4605 not only a matter of consistency, but one of type safety.
4608 Here are two example to illustrate the condition under which overlap
4611 type instance F (a, Int) = [a]
4612 type instance F (Int, b) = [b] -- overlap permitted
4614 type instance G (a, Int) = [a]
4615 type instance G (Char, a) = [a] -- ILLEGAL overlap, as [Char] /= [Int]
4620 <sect4 id="type-family-decidability">
4621 <title>Decidability of type synonym instances</title>
4623 In order to guarantee that type inference in the presence of type
4624 families decidable, we need to place a number of additional
4625 restrictions on the formation of type instance declarations (c.f.,
4626 Definition 5 (Relaxed Conditions) of “<ulink
4627 url="http://www.cse.unsw.edu.au/~chak/papers/SPCS08.html">Type
4628 Checking with Open Type Functions</ulink>”). Instance
4629 declarations have the general form
4631 type instance F t1 .. tn = t
4633 where we require that for every type family application <literal>(G s1
4634 .. sm)</literal> in <literal>t</literal>,
4637 <para><literal>s1 .. sm</literal> do not contain any type family
4638 constructors,</para>
4641 <para>the total number of symbols (data type constructors and type
4642 variables) in <literal>s1 .. sm</literal> is strictly smaller than
4643 in <literal>t1 .. tn</literal>, and</para>
4646 <para>for every type
4647 variable <literal>a</literal>, <literal>a</literal> occurs
4648 in <literal>s1 .. sm</literal> at most as often as in <literal>t1
4649 .. tn</literal>.</para>
4652 These restrictions are easily verified and ensure termination of type
4653 inference. However, they are not sufficient to guarantee completeness
4654 of type inference in the presence of, so called, ''loopy equalities'',
4655 such as <literal>a ~ [F a]</literal>, where a recursive occurrence of
4656 a type variable is underneath a family application and data
4657 constructor application - see the above mentioned paper for details.
4660 If the option <option>-XUndecidableInstances</option> is passed to the
4661 compiler, the above restrictions are not enforced and it is on the
4662 programmer to ensure termination of the normalisation of type families
4663 during type inference.
4668 <sect3 id-="equality-constraints">
4669 <title>Equality constraints</title>
4671 Type context can include equality constraints of the form <literal>t1 ~
4672 t2</literal>, which denote that the types <literal>t1</literal>
4673 and <literal>t2</literal> need to be the same. In the presence of type
4674 families, whether two types are equal cannot generally be decided
4675 locally. Hence, the contexts of function signatures may include
4676 equality constraints, as in the following example:
4678 sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
4680 where we require that the element type of <literal>c1</literal>
4681 and <literal>c2</literal> are the same. In general, the
4682 types <literal>t1</literal> and <literal>t2</literal> of an equality
4683 constraint may be arbitrary monotypes; i.e., they may not contain any
4684 quantifiers, independent of whether higher-rank types are otherwise
4688 Equality constraints can also appear in class and instance contexts.
4689 The former enable a simple translation of programs using functional
4690 dependencies into programs using family synonyms instead. The general
4691 idea is to rewrite a class declaration of the form
4693 class C a b | a -> b
4697 class (F a ~ b) => C a b where
4700 That is, we represent every functional dependency (FD) <literal>a1 .. an
4701 -> b</literal> by an FD type family <literal>F a1 .. an</literal> and a
4702 superclass context equality <literal>F a1 .. an ~ b</literal>,
4703 essentially giving a name to the functional dependency. In class
4704 instances, we define the type instances of FD families in accordance
4705 with the class head. Method signatures are not affected by that
4709 NB: Equalities in superclass contexts are not fully implemented in
4714 <sect3 id-="ty-fams-in-instances">
4715 <title>Type families and instance declarations</title>
4716 <para>Type families require us to extend the rules for
4717 the form of instance heads, which are given
4718 in <xref linkend="flexible-instance-head"/>.
4721 <listitem><para>Data type families may appear in an instance head</para></listitem>
4722 <listitem><para>Type synonym families may not appear (at all) in an instance head</para></listitem>
4724 The reason for the latter restriction is that there is no way to check for. Consider
4727 type instance F Bool = Int
4734 Now a constraint <literal>(C (F Bool))</literal> would match both instances.
4735 The situation is especially bad because the type instance for <literal>F Bool</literal>
4736 might be in another module, or even in a module that is not yet written.
4743 <sect1 id="other-type-extensions">
4744 <title>Other type system extensions</title>
4746 <sect2 id="explicit-foralls"><title>Explicit universal quantification (forall)</title>
4748 Haskell type signatures are implicitly quantified. When the language option <option>-XExplicitForAll</option>
4749 is used, the keyword <literal>forall</literal>
4750 allows us to say exactly what this means. For example:
4758 g :: forall b. (b -> b)
4760 The two are treated identically.
4763 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
4764 a type variable any more!
4769 <sect2 id="flexible-contexts"><title>The context of a type signature</title>
4771 The <option>-XFlexibleContexts</option> flag lifts the Haskell 98 restriction
4772 that the type-class constraints in a type signature must have the
4773 form <emphasis>(class type-variable)</emphasis> or
4774 <emphasis>(class (type-variable type-variable ...))</emphasis>.
4775 With <option>-XFlexibleContexts</option>
4776 these type signatures are perfectly OK
4779 g :: Ord (T a ()) => ...
4781 The flag <option>-XFlexibleContexts</option> also lifts the corresponding
4782 restriction on class declarations (<xref linkend="superclass-rules"/>) and instance declarations
4783 (<xref linkend="instance-rules"/>).
4787 GHC imposes the following restrictions on the constraints in a type signature.
4791 forall tv1..tvn (c1, ...,cn) => type
4794 (Here, we write the "foralls" explicitly, although the Haskell source
4795 language omits them; in Haskell 98, all the free type variables of an
4796 explicit source-language type signature are universally quantified,
4797 except for the class type variables in a class declaration. However,
4798 in GHC, you can give the foralls if you want. See <xref linkend="explicit-foralls"/>).
4807 <emphasis>Each universally quantified type variable
4808 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
4810 A type variable <literal>a</literal> is "reachable" if it appears
4811 in the same constraint as either a type variable free in
4812 <literal>type</literal>, or another reachable type variable.
4813 A value with a type that does not obey
4814 this reachability restriction cannot be used without introducing
4815 ambiguity; that is why the type is rejected.
4816 Here, for example, is an illegal type:
4820 forall a. Eq a => Int
4824 When a value with this type was used, the constraint <literal>Eq tv</literal>
4825 would be introduced where <literal>tv</literal> is a fresh type variable, and
4826 (in the dictionary-translation implementation) the value would be
4827 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
4828 can never know which instance of <literal>Eq</literal> to use because we never
4829 get any more information about <literal>tv</literal>.
4833 that the reachability condition is weaker than saying that <literal>a</literal> is
4834 functionally dependent on a type variable free in
4835 <literal>type</literal> (see <xref
4836 linkend="functional-dependencies"/>). The reason for this is there
4837 might be a "hidden" dependency, in a superclass perhaps. So
4838 "reachable" is a conservative approximation to "functionally dependent".
4839 For example, consider:
4841 class C a b | a -> b where ...
4842 class C a b => D a b where ...
4843 f :: forall a b. D a b => a -> a
4845 This is fine, because in fact <literal>a</literal> does functionally determine <literal>b</literal>
4846 but that is not immediately apparent from <literal>f</literal>'s type.
4852 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
4853 universally quantified type variables <literal>tvi</literal></emphasis>.
4855 For example, this type is OK because <literal>C a b</literal> mentions the
4856 universally quantified type variable <literal>b</literal>:
4860 forall a. C a b => burble
4864 The next type is illegal because the constraint <literal>Eq b</literal> does not
4865 mention <literal>a</literal>:
4869 forall a. Eq b => burble
4873 The reason for this restriction is milder than the other one. The
4874 excluded types are never useful or necessary (because the offending
4875 context doesn't need to be witnessed at this point; it can be floated
4876 out). Furthermore, floating them out increases sharing. Lastly,
4877 excluding them is a conservative choice; it leaves a patch of
4878 territory free in case we need it later.
4889 <sect2 id="implicit-parameters">
4890 <title>Implicit parameters</title>
4892 <para> Implicit parameters are implemented as described in
4893 "Implicit parameters: dynamic scoping with static types",
4894 J Lewis, MB Shields, E Meijer, J Launchbury,
4895 27th ACM Symposium on Principles of Programming Languages (POPL'00),
4899 <para>(Most of the following, still rather incomplete, documentation is
4900 due to Jeff Lewis.)</para>
4902 <para>Implicit parameter support is enabled with the option
4903 <option>-XImplicitParams</option>.</para>
4906 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
4907 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
4908 context. In Haskell, all variables are statically bound. Dynamic
4909 binding of variables is a notion that goes back to Lisp, but was later
4910 discarded in more modern incarnations, such as Scheme. Dynamic binding
4911 can be very confusing in an untyped language, and unfortunately, typed
4912 languages, in particular Hindley-Milner typed languages like Haskell,
4913 only support static scoping of variables.
4916 However, by a simple extension to the type class system of Haskell, we
4917 can support dynamic binding. Basically, we express the use of a
4918 dynamically bound variable as a constraint on the type. These
4919 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
4920 function uses a dynamically-bound variable <literal>?x</literal>
4921 of type <literal>t'</literal>". For
4922 example, the following expresses the type of a sort function,
4923 implicitly parameterized by a comparison function named <literal>cmp</literal>.
4925 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4927 The dynamic binding constraints are just a new form of predicate in the type class system.
4930 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
4931 where <literal>x</literal> is
4932 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
4933 Use of this construct also introduces a new
4934 dynamic-binding constraint in the type of the expression.
4935 For example, the following definition
4936 shows how we can define an implicitly parameterized sort function in
4937 terms of an explicitly parameterized <literal>sortBy</literal> function:
4939 sortBy :: (a -> a -> Bool) -> [a] -> [a]
4941 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
4947 <title>Implicit-parameter type constraints</title>
4949 Dynamic binding constraints behave just like other type class
4950 constraints in that they are automatically propagated. Thus, when a
4951 function is used, its implicit parameters are inherited by the
4952 function that called it. For example, our <literal>sort</literal> function might be used
4953 to pick out the least value in a list:
4955 least :: (?cmp :: a -> a -> Bool) => [a] -> a
4956 least xs = head (sort xs)
4958 Without lifting a finger, the <literal>?cmp</literal> parameter is
4959 propagated to become a parameter of <literal>least</literal> as well. With explicit
4960 parameters, the default is that parameters must always be explicit
4961 propagated. With implicit parameters, the default is to always
4965 An implicit-parameter type constraint differs from other type class constraints in the
4966 following way: All uses of a particular implicit parameter must have
4967 the same type. This means that the type of <literal>(?x, ?x)</literal>
4968 is <literal>(?x::a) => (a,a)</literal>, and not
4969 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
4973 <para> You can't have an implicit parameter in the context of a class or instance
4974 declaration. For example, both these declarations are illegal:
4976 class (?x::Int) => C a where ...
4977 instance (?x::a) => Foo [a] where ...
4979 Reason: exactly which implicit parameter you pick up depends on exactly where
4980 you invoke a function. But the ``invocation'' of instance declarations is done
4981 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
4982 Easiest thing is to outlaw the offending types.</para>
4984 Implicit-parameter constraints do not cause ambiguity. For example, consider:
4986 f :: (?x :: [a]) => Int -> Int
4989 g :: (Read a, Show a) => String -> String
4992 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
4993 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
4994 quite unambiguous, and fixes the type <literal>a</literal>.
4999 <title>Implicit-parameter bindings</title>
5002 An implicit parameter is <emphasis>bound</emphasis> using the standard
5003 <literal>let</literal> or <literal>where</literal> binding forms.
5004 For example, we define the <literal>min</literal> function by binding
5005 <literal>cmp</literal>.
5008 min = let ?cmp = (<=) in least
5012 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
5013 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
5014 (including in a list comprehension, or do-notation, or pattern guards),
5015 or a <literal>where</literal> clause.
5016 Note the following points:
5019 An implicit-parameter binding group must be a
5020 collection of simple bindings to implicit-style variables (no
5021 function-style bindings, and no type signatures); these bindings are
5022 neither polymorphic or recursive.
5025 You may not mix implicit-parameter bindings with ordinary bindings in a
5026 single <literal>let</literal>
5027 expression; use two nested <literal>let</literal>s instead.
5028 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
5032 You may put multiple implicit-parameter bindings in a
5033 single binding group; but they are <emphasis>not</emphasis> treated
5034 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
5035 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
5036 parameter. The bindings are not nested, and may be re-ordered without changing
5037 the meaning of the program.
5038 For example, consider:
5040 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
5042 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
5043 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
5045 f :: (?x::Int) => Int -> Int
5053 <sect3><title>Implicit parameters and polymorphic recursion</title>
5056 Consider these two definitions:
5059 len1 xs = let ?acc = 0 in len_acc1 xs
5062 len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs
5067 len2 xs = let ?acc = 0 in len_acc2 xs
5069 len_acc2 :: (?acc :: Int) => [a] -> Int
5071 len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
5073 The only difference between the two groups is that in the second group
5074 <literal>len_acc</literal> is given a type signature.
5075 In the former case, <literal>len_acc1</literal> is monomorphic in its own
5076 right-hand side, so the implicit parameter <literal>?acc</literal> is not
5077 passed to the recursive call. In the latter case, because <literal>len_acc2</literal>
5078 has a type signature, the recursive call is made to the
5079 <emphasis>polymorphic</emphasis> version, which takes <literal>?acc</literal>
5080 as an implicit parameter. So we get the following results in GHCi:
5087 Adding a type signature dramatically changes the result! This is a rather
5088 counter-intuitive phenomenon, worth watching out for.
5092 <sect3><title>Implicit parameters and monomorphism</title>
5094 <para>GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the
5095 Haskell Report) to implicit parameters. For example, consider:
5103 Since the binding for <literal>y</literal> falls under the Monomorphism
5104 Restriction it is not generalised, so the type of <literal>y</literal> is
5105 simply <literal>Int</literal>, not <literal>(?x::Int) => Int</literal>.
5106 Hence, <literal>(f 9)</literal> returns result <literal>9</literal>.
5107 If you add a type signature for <literal>y</literal>, then <literal>y</literal>
5108 will get type <literal>(?x::Int) => Int</literal>, so the occurrence of
5109 <literal>y</literal> in the body of the <literal>let</literal> will see the
5110 inner binding of <literal>?x</literal>, so <literal>(f 9)</literal> will return
5111 <literal>14</literal>.
5116 <!-- ======================= COMMENTED OUT ========================
5118 We intend to remove linear implicit parameters, so I'm at least removing
5119 them from the 6.6 user manual
5121 <sect2 id="linear-implicit-parameters">
5122 <title>Linear implicit parameters</title>
5124 Linear implicit parameters are an idea developed by Koen Claessen,
5125 Mark Shields, and Simon PJ. They address the long-standing
5126 problem that monads seem over-kill for certain sorts of problem, notably:
5129 <listitem> <para> distributing a supply of unique names </para> </listitem>
5130 <listitem> <para> distributing a supply of random numbers </para> </listitem>
5131 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
5135 Linear implicit parameters are just like ordinary implicit parameters,
5136 except that they are "linear"; that is, they cannot be copied, and
5137 must be explicitly "split" instead. Linear implicit parameters are
5138 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
5139 (The '/' in the '%' suggests the split!)
5144 import GHC.Exts( Splittable )
5146 data NameSupply = ...
5148 splitNS :: NameSupply -> (NameSupply, NameSupply)
5149 newName :: NameSupply -> Name
5151 instance Splittable NameSupply where
5155 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5156 f env (Lam x e) = Lam x' (f env e)
5159 env' = extend env x x'
5160 ...more equations for f...
5162 Notice that the implicit parameter %ns is consumed
5164 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
5165 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
5169 So the translation done by the type checker makes
5170 the parameter explicit:
5172 f :: NameSupply -> Env -> Expr -> Expr
5173 f ns env (Lam x e) = Lam x' (f ns1 env e)
5175 (ns1,ns2) = splitNS ns
5177 env = extend env x x'
5179 Notice the call to 'split' introduced by the type checker.
5180 How did it know to use 'splitNS'? Because what it really did
5181 was to introduce a call to the overloaded function 'split',
5182 defined by the class <literal>Splittable</literal>:
5184 class Splittable a where
5187 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
5188 split for name supplies. But we can simply write
5194 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
5196 The <literal>Splittable</literal> class is built into GHC. It's exported by module
5197 <literal>GHC.Exts</literal>.
5202 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
5203 are entirely distinct implicit parameters: you
5204 can use them together and they won't interfere with each other. </para>
5207 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
5209 <listitem> <para>You cannot have implicit parameters (whether linear or not)
5210 in the context of a class or instance declaration. </para></listitem>
5214 <sect3><title>Warnings</title>
5217 The monomorphism restriction is even more important than usual.
5218 Consider the example above:
5220 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5221 f env (Lam x e) = Lam x' (f env e)
5224 env' = extend env x x'
5226 If we replaced the two occurrences of x' by (newName %ns), which is
5227 usually a harmless thing to do, we get:
5229 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
5230 f env (Lam x e) = Lam (newName %ns) (f env e)
5232 env' = extend env x (newName %ns)
5234 But now the name supply is consumed in <emphasis>three</emphasis> places
5235 (the two calls to newName,and the recursive call to f), so
5236 the result is utterly different. Urk! We don't even have
5240 Well, this is an experimental change. With implicit
5241 parameters we have already lost beta reduction anyway, and
5242 (as John Launchbury puts it) we can't sensibly reason about
5243 Haskell programs without knowing their typing.
5248 <sect3><title>Recursive functions</title>
5249 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
5252 foo :: %x::T => Int -> [Int]
5254 foo n = %x : foo (n-1)
5256 where T is some type in class Splittable.</para>
5258 Do you get a list of all the same T's or all different T's
5259 (assuming that split gives two distinct T's back)?
5261 If you supply the type signature, taking advantage of polymorphic
5262 recursion, you get what you'd probably expect. Here's the
5263 translated term, where the implicit param is made explicit:
5266 foo x n = let (x1,x2) = split x
5267 in x1 : foo x2 (n-1)
5269 But if you don't supply a type signature, GHC uses the Hindley
5270 Milner trick of using a single monomorphic instance of the function
5271 for the recursive calls. That is what makes Hindley Milner type inference
5272 work. So the translation becomes
5276 foom n = x : foom (n-1)
5280 Result: 'x' is not split, and you get a list of identical T's. So the
5281 semantics of the program depends on whether or not foo has a type signature.
5284 You may say that this is a good reason to dislike linear implicit parameters
5285 and you'd be right. That is why they are an experimental feature.
5291 ================ END OF Linear Implicit Parameters commented out -->
5293 <sect2 id="kinding">
5294 <title>Explicitly-kinded quantification</title>
5297 Haskell infers the kind of each type variable. Sometimes it is nice to be able
5298 to give the kind explicitly as (machine-checked) documentation,
5299 just as it is nice to give a type signature for a function. On some occasions,
5300 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
5301 John Hughes had to define the data type:
5303 data Set cxt a = Set [a]
5304 | Unused (cxt a -> ())
5306 The only use for the <literal>Unused</literal> constructor was to force the correct
5307 kind for the type variable <literal>cxt</literal>.
5310 GHC now instead allows you to specify the kind of a type variable directly, wherever
5311 a type variable is explicitly bound, with the flag <option>-XKindSignatures</option>.
5314 This flag enables kind signatures in the following places:
5316 <listitem><para><literal>data</literal> declarations:
5318 data Set (cxt :: * -> *) a = Set [a]
5319 </screen></para></listitem>
5320 <listitem><para><literal>type</literal> declarations:
5322 type T (f :: * -> *) = f Int
5323 </screen></para></listitem>
5324 <listitem><para><literal>class</literal> declarations:
5326 class (Eq a) => C (f :: * -> *) a where ...
5327 </screen></para></listitem>
5328 <listitem><para><literal>forall</literal>'s in type signatures:
5330 f :: forall (cxt :: * -> *). Set cxt Int
5331 </screen></para></listitem>
5336 The parentheses are required. Some of the spaces are required too, to
5337 separate the lexemes. If you write <literal>(f::*->*)</literal> you
5338 will get a parse error, because "<literal>::*->*</literal>" is a
5339 single lexeme in Haskell.
5343 As part of the same extension, you can put kind annotations in types
5346 f :: (Int :: *) -> Int
5347 g :: forall a. a -> (a :: *)
5351 atype ::= '(' ctype '::' kind ')
5353 The parentheses are required.
5358 <sect2 id="universal-quantification">
5359 <title>Arbitrary-rank polymorphism
5363 GHC's type system supports <emphasis>arbitrary-rank</emphasis>
5364 explicit universal quantification in
5366 For example, all the following types are legal:
5368 f1 :: forall a b. a -> b -> a
5369 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
5371 f2 :: (forall a. a->a) -> Int -> Int
5372 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
5374 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
5376 f4 :: Int -> (forall a. a -> a)
5378 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
5379 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
5380 The <literal>forall</literal> makes explicit the universal quantification that
5381 is implicitly added by Haskell.
5384 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
5385 the <literal>forall</literal> is on the left of a function arrow. As <literal>g2</literal>
5386 shows, the polymorphic type on the left of the function arrow can be overloaded.
5389 The function <literal>f3</literal> has a rank-3 type;
5390 it has rank-2 types on the left of a function arrow.
5393 GHC has three flags to control higher-rank types:
5396 <option>-XPolymorphicComponents</option>: data constructors (only) can have polymorphic argument types.
5399 <option>-XRank2Types</option>: any function (including data constructors) can have a rank-2 type.
5402 <option>-XRankNTypes</option>: any function (including data constructors) can have an arbitrary-rank type.
5403 That is, you can nest <literal>forall</literal>s
5404 arbitrarily deep in function arrows.
5405 In particular, a forall-type (also called a "type scheme"),
5406 including an operational type class context, is legal:
5408 <listitem> <para> On the left or right (see <literal>f4</literal>, for example)
5409 of a function arrow </para> </listitem>
5410 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
5411 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
5412 field type signatures.</para> </listitem>
5413 <listitem> <para> As the type of an implicit parameter </para> </listitem>
5414 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables"/>) </para> </listitem>
5426 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
5427 the types of the constructor arguments. Here are several examples:
5433 data T a = T1 (forall b. b -> b -> b) a
5435 data MonadT m = MkMonad { return :: forall a. a -> m a,
5436 bind :: forall a b. m a -> (a -> m b) -> m b
5439 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
5445 The constructors have rank-2 types:
5451 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
5452 MkMonad :: forall m. (forall a. a -> m a)
5453 -> (forall a b. m a -> (a -> m b) -> m b)
5455 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
5461 Notice that you don't need to use a <literal>forall</literal> if there's an
5462 explicit context. For example in the first argument of the
5463 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
5464 prefixed to the argument type. The implicit <literal>forall</literal>
5465 quantifies all type variables that are not already in scope, and are
5466 mentioned in the type quantified over.
5470 As for type signatures, implicit quantification happens for non-overloaded
5471 types too. So if you write this:
5474 data T a = MkT (Either a b) (b -> b)
5477 it's just as if you had written this:
5480 data T a = MkT (forall b. Either a b) (forall b. b -> b)
5483 That is, since the type variable <literal>b</literal> isn't in scope, it's
5484 implicitly universally quantified. (Arguably, it would be better
5485 to <emphasis>require</emphasis> explicit quantification on constructor arguments
5486 where that is what is wanted. Feedback welcomed.)
5490 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
5491 the constructor to suitable values, just as usual. For example,
5502 a3 = MkSwizzle reverse
5505 a4 = let r x = Just x
5512 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
5513 mkTs f x y = [T1 f x, T1 f y]
5519 The type of the argument can, as usual, be more general than the type
5520 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
5521 does not need the <literal>Ord</literal> constraint.)
5525 When you use pattern matching, the bound variables may now have
5526 polymorphic types. For example:
5532 f :: T a -> a -> (a, Char)
5533 f (T1 w k) x = (w k x, w 'c' 'd')
5535 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
5536 g (MkSwizzle s) xs f = s (map f (s xs))
5538 h :: MonadT m -> [m a] -> m [a]
5539 h m [] = return m []
5540 h m (x:xs) = bind m x $ \y ->
5541 bind m (h m xs) $ \ys ->
5548 In the function <function>h</function> we use the record selectors <literal>return</literal>
5549 and <literal>bind</literal> to extract the polymorphic bind and return functions
5550 from the <literal>MonadT</literal> data structure, rather than using pattern
5556 <title>Type inference</title>
5559 In general, type inference for arbitrary-rank types is undecidable.
5560 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
5561 to get a decidable algorithm by requiring some help from the programmer.
5562 We do not yet have a formal specification of "some help" but the rule is this:
5565 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
5566 provides an explicit polymorphic type for x, or GHC's type inference will assume
5567 that x's type has no foralls in it</emphasis>.
5570 What does it mean to "provide" an explicit type for x? You can do that by
5571 giving a type signature for x directly, using a pattern type signature
5572 (<xref linkend="scoped-type-variables"/>), thus:
5574 \ f :: (forall a. a->a) -> (f True, f 'c')
5576 Alternatively, you can give a type signature to the enclosing
5577 context, which GHC can "push down" to find the type for the variable:
5579 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
5581 Here the type signature on the expression can be pushed inwards
5582 to give a type signature for f. Similarly, and more commonly,
5583 one can give a type signature for the function itself:
5585 h :: (forall a. a->a) -> (Bool,Char)
5586 h f = (f True, f 'c')
5588 You don't need to give a type signature if the lambda bound variable
5589 is a constructor argument. Here is an example we saw earlier:
5591 f :: T a -> a -> (a, Char)
5592 f (T1 w k) x = (w k x, w 'c' 'd')
5594 Here we do not need to give a type signature to <literal>w</literal>, because
5595 it is an argument of constructor <literal>T1</literal> and that tells GHC all
5602 <sect3 id="implicit-quant">
5603 <title>Implicit quantification</title>
5606 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
5607 user-written types, if and only if there is no explicit <literal>forall</literal>,
5608 GHC finds all the type variables mentioned in the type that are not already
5609 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
5613 f :: forall a. a -> a
5620 h :: forall b. a -> b -> b
5626 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
5629 f :: (a -> a) -> Int
5631 f :: forall a. (a -> a) -> Int
5633 f :: (forall a. a -> a) -> Int
5636 g :: (Ord a => a -> a) -> Int
5637 -- MEANS the illegal type
5638 g :: forall a. (Ord a => a -> a) -> Int
5640 g :: (forall a. Ord a => a -> a) -> Int
5642 The latter produces an illegal type, which you might think is silly,
5643 but at least the rule is simple. If you want the latter type, you
5644 can write your for-alls explicitly. Indeed, doing so is strongly advised
5651 <sect2 id="impredicative-polymorphism">
5652 <title>Impredicative polymorphism
5654 <para>GHC supports <emphasis>impredicative polymorphism</emphasis>,
5655 enabled with <option>-XImpredicativeTypes</option>.
5657 that you can call a polymorphic function at a polymorphic type, and
5658 parameterise data structures over polymorphic types. For example:
5660 f :: Maybe (forall a. [a] -> [a]) -> Maybe ([Int], [Char])
5661 f (Just g) = Just (g [3], g "hello")
5664 Notice here that the <literal>Maybe</literal> type is parameterised by the
5665 <emphasis>polymorphic</emphasis> type <literal>(forall a. [a] ->
5668 <para>The technical details of this extension are described in the paper
5669 <ulink url="http://research.microsoft.com/%7Esimonpj/papers/boxy/">Boxy types:
5670 type inference for higher-rank types and impredicativity</ulink>,
5671 which appeared at ICFP 2006.
5675 <sect2 id="scoped-type-variables">
5676 <title>Lexically scoped type variables
5680 GHC supports <emphasis>lexically scoped type variables</emphasis>, without
5681 which some type signatures are simply impossible to write. For example:
5683 f :: forall a. [a] -> [a]
5689 The type signature for <literal>f</literal> brings the type variable <literal>a</literal> into scope,
5690 because of the explicit <literal>forall</literal> (<xref linkend="decl-type-sigs"/>).
5691 The type variables bound by a <literal>forall</literal> scope over
5692 the entire definition of the accompanying value declaration.
5693 In this example, the type variable <literal>a</literal> scopes over the whole
5694 definition of <literal>f</literal>, including over
5695 the type signature for <varname>ys</varname>.
5696 In Haskell 98 it is not possible to declare
5697 a type for <varname>ys</varname>; a major benefit of scoped type variables is that
5698 it becomes possible to do so.
5700 <para>Lexically-scoped type variables are enabled by
5701 <option>-XScopedTypeVariables</option>. This flag implies <option>-XRelaxedPolyRec</option>.
5703 <para>Note: GHC 6.6 contains substantial changes to the way that scoped type
5704 variables work, compared to earlier releases. Read this section
5708 <title>Overview</title>
5710 <para>The design follows the following principles
5712 <listitem><para>A scoped type variable stands for a type <emphasis>variable</emphasis>, and not for
5713 a <emphasis>type</emphasis>. (This is a change from GHC's earlier
5714 design.)</para></listitem>
5715 <listitem><para>Furthermore, distinct lexical type variables stand for distinct
5716 type variables. This means that every programmer-written type signature
5717 (including one that contains free scoped type variables) denotes a
5718 <emphasis>rigid</emphasis> type; that is, the type is fully known to the type
5719 checker, and no inference is involved.</para></listitem>
5720 <listitem><para>Lexical type variables may be alpha-renamed freely, without
5721 changing the program.</para></listitem>
5725 A <emphasis>lexically scoped type variable</emphasis> can be bound by:
5727 <listitem><para>A declaration type signature (<xref linkend="decl-type-sigs"/>)</para></listitem>
5728 <listitem><para>An expression type signature (<xref linkend="exp-type-sigs"/>)</para></listitem>
5729 <listitem><para>A pattern type signature (<xref linkend="pattern-type-sigs"/>)</para></listitem>
5730 <listitem><para>Class and instance declarations (<xref linkend="cls-inst-scoped-tyvars"/>)</para></listitem>
5734 In Haskell, a programmer-written type signature is implicitly quantified over
5735 its free type variables (<ulink
5736 url="http://www.haskell.org/onlinereport/decls.html#sect4.1.2">Section
5738 of the Haskell Report).
5739 Lexically scoped type variables affect this implicit quantification rules
5740 as follows: any type variable that is in scope is <emphasis>not</emphasis> universally
5741 quantified. For example, if type variable <literal>a</literal> is in scope,
5744 (e :: a -> a) means (e :: a -> a)
5745 (e :: b -> b) means (e :: forall b. b->b)
5746 (e :: a -> b) means (e :: forall b. a->b)
5754 <sect3 id="decl-type-sigs">
5755 <title>Declaration type signatures</title>
5756 <para>A declaration type signature that has <emphasis>explicit</emphasis>
5757 quantification (using <literal>forall</literal>) brings into scope the
5758 explicitly-quantified
5759 type variables, in the definition of the named function. For example:
5761 f :: forall a. [a] -> [a]
5762 f (x:xs) = xs ++ [ x :: a ]
5764 The "<literal>forall a</literal>" brings "<literal>a</literal>" into scope in
5765 the definition of "<literal>f</literal>".
5767 <para>This only happens if:
5769 <listitem><para> The quantification in <literal>f</literal>'s type
5770 signature is explicit. For example:
5773 g (x:xs) = xs ++ [ x :: a ]
5775 This program will be rejected, because "<literal>a</literal>" does not scope
5776 over the definition of "<literal>f</literal>", so "<literal>x::a</literal>"
5777 means "<literal>x::forall a. a</literal>" by Haskell's usual implicit
5778 quantification rules.
5780 <listitem><para> The signature gives a type for a function binding or a bare variable binding,
5781 not a pattern binding.
5784 f1 :: forall a. [a] -> [a]
5785 f1 (x:xs) = xs ++ [ x :: a ] -- OK
5787 f2 :: forall a. [a] -> [a]
5788 f2 = \(x:xs) -> xs ++ [ x :: a ] -- OK
5790 f3 :: forall a. [a] -> [a]
5791 Just f3 = Just (\(x:xs) -> xs ++ [ x :: a ]) -- Not OK!
5793 The binding for <literal>f3</literal> is a pattern binding, and so its type signature
5794 does not bring <literal>a</literal> into scope. However <literal>f1</literal> is a
5795 function binding, and <literal>f2</literal> binds a bare variable; in both cases
5796 the type signature brings <literal>a</literal> into scope.
5802 <sect3 id="exp-type-sigs">
5803 <title>Expression type signatures</title>
5805 <para>An expression type signature that has <emphasis>explicit</emphasis>
5806 quantification (using <literal>forall</literal>) brings into scope the
5807 explicitly-quantified
5808 type variables, in the annotated expression. For example:
5810 f = runST ( (op >>= \(x :: STRef s Int) -> g x) :: forall s. ST s Bool )
5812 Here, the type signature <literal>forall a. ST s Bool</literal> brings the
5813 type variable <literal>s</literal> into scope, in the annotated expression
5814 <literal>(op >>= \(x :: STRef s Int) -> g x)</literal>.
5819 <sect3 id="pattern-type-sigs">
5820 <title>Pattern type signatures</title>
5822 A type signature may occur in any pattern; this is a <emphasis>pattern type
5823 signature</emphasis>.
5826 -- f and g assume that 'a' is already in scope
5827 f = \(x::Int, y::a) -> x
5829 h ((x,y) :: (Int,Bool)) = (y,x)
5831 In the case where all the type variables in the pattern type signature are
5832 already in scope (i.e. bound by the enclosing context), matters are simple: the
5833 signature simply constrains the type of the pattern in the obvious way.
5836 Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised.
5837 The pattern in a <emphasis>pattern binding</emphasis> may only mention type variables
5838 that are already in scope. For example:
5840 f :: forall a. [a] -> (Int, [a])
5843 (ys::[a], n) = (reverse xs, length xs) -- OK
5844 zs::[a] = xs ++ ys -- OK
5846 Just (v::b) = ... -- Not OK; b is not in scope
5848 Here, the pattern signatures for <literal>ys</literal> and <literal>zs</literal>
5849 are fine, but the one for <literal>v</literal> is not because <literal>b</literal> is
5853 However, in all patterns <emphasis>other</emphasis> than pattern bindings, a pattern
5854 type signature may mention a type variable that is not in scope; in this case,
5855 <emphasis>the signature brings that type variable into scope</emphasis>.
5856 This is particularly important for existential data constructors. For example:
5858 data T = forall a. MkT [a]
5861 k (MkT [t::a]) = MkT t3
5865 Here, the pattern type signature <literal>(t::a)</literal> mentions a lexical type
5866 variable that is not already in scope. Indeed, it <emphasis>cannot</emphasis> already be in scope,
5867 because it is bound by the pattern match. GHC's rule is that in this situation
5868 (and only then), a pattern type signature can mention a type variable that is
5869 not already in scope; the effect is to bring it into scope, standing for the
5870 existentially-bound type variable.
5873 When a pattern type signature binds a type variable in this way, GHC insists that the
5874 type variable is bound to a <emphasis>rigid</emphasis>, or fully-known, type variable.
5875 This means that any user-written type signature always stands for a completely known type.
5878 If all this seems a little odd, we think so too. But we must have
5879 <emphasis>some</emphasis> way to bring such type variables into scope, else we
5880 could not name existentially-bound type variables in subsequent type signatures.
5883 This is (now) the <emphasis>only</emphasis> situation in which a pattern type
5884 signature is allowed to mention a lexical variable that is not already in
5886 For example, both <literal>f</literal> and <literal>g</literal> would be
5887 illegal if <literal>a</literal> was not already in scope.
5893 <!-- ==================== Commented out part about result type signatures
5895 <sect3 id="result-type-sigs">
5896 <title>Result type signatures</title>
5899 The result type of a function, lambda, or case expression alternative can be given a signature, thus:
5902 {- f assumes that 'a' is already in scope -}
5903 f x y :: [a] = [x,y,x]
5905 g = \ x :: [Int] -> [3,4]
5907 h :: forall a. [a] -> a
5911 The final <literal>:: [a]</literal> after the patterns of <literal>f</literal> gives the type of
5912 the result of the function. Similarly, the body of the lambda in the RHS of
5913 <literal>g</literal> is <literal>[Int]</literal>, and the RHS of the case
5914 alternative in <literal>h</literal> is <literal>a</literal>.
5916 <para> A result type signature never brings new type variables into scope.</para>
5918 There are a couple of syntactic wrinkles. First, notice that all three
5919 examples would parse quite differently with parentheses:
5921 {- f assumes that 'a' is already in scope -}
5922 f x (y :: [a]) = [x,y,x]
5924 g = \ (x :: [Int]) -> [3,4]
5926 h :: forall a. [a] -> a
5930 Now the signature is on the <emphasis>pattern</emphasis>; and
5931 <literal>h</literal> would certainly be ill-typed (since the pattern
5932 <literal>(y:ys)</literal> cannot have the type <literal>a</literal>.
5934 Second, to avoid ambiguity, the type after the “<literal>::</literal>” in a result
5935 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
5936 token or a parenthesised type of some sort). To see why,
5937 consider how one would parse this:
5946 <sect3 id="cls-inst-scoped-tyvars">
5947 <title>Class and instance declarations</title>
5950 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
5951 scope over the methods defined in the <literal>where</literal> part. For example:
5969 <sect2 id="typing-binds">
5970 <title>Generalised typing of mutually recursive bindings</title>
5973 The Haskell Report specifies that a group of bindings (at top level, or in a
5974 <literal>let</literal> or <literal>where</literal>) should be sorted into
5975 strongly-connected components, and then type-checked in dependency order
5976 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.1">Haskell
5977 Report, Section 4.5.1</ulink>).
5978 As each group is type-checked, any binders of the group that
5980 an explicit type signature are put in the type environment with the specified
5982 and all others are monomorphic until the group is generalised
5983 (<ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.2">Haskell Report, Section 4.5.2</ulink>).
5986 <para>Following a suggestion of Mark Jones, in his paper
5987 <ulink url="http://citeseer.ist.psu.edu/424440.html">Typing Haskell in
5989 GHC implements a more general scheme. If <option>-XRelaxedPolyRec</option> is
5991 <emphasis>the dependency analysis ignores references to variables that have an explicit
5992 type signature</emphasis>.
5993 As a result of this refined dependency analysis, the dependency groups are smaller, and more bindings will
5994 typecheck. For example, consider:
5996 f :: Eq a => a -> Bool
5997 f x = (x == x) || g True || g "Yes"
5999 g y = (y <= y) || f True
6001 This is rejected by Haskell 98, but under Jones's scheme the definition for
6002 <literal>g</literal> is typechecked first, separately from that for
6003 <literal>f</literal>,
6004 because the reference to <literal>f</literal> in <literal>g</literal>'s right
6005 hand side is ignored by the dependency analysis. Then <literal>g</literal>'s
6006 type is generalised, to get
6008 g :: Ord a => a -> Bool
6010 Now, the definition for <literal>f</literal> is typechecked, with this type for
6011 <literal>g</literal> in the type environment.
6015 The same refined dependency analysis also allows the type signatures of
6016 mutually-recursive functions to have different contexts, something that is illegal in
6017 Haskell 98 (Section 4.5.2, last sentence). With
6018 <option>-XRelaxedPolyRec</option>
6019 GHC only insists that the type signatures of a <emphasis>refined</emphasis> group have identical
6020 type signatures; in practice this means that only variables bound by the same
6021 pattern binding must have the same context. For example, this is fine:
6023 f :: Eq a => a -> Bool
6024 f x = (x == x) || g True
6026 g :: Ord a => a -> Bool
6027 g y = (y <= y) || f True
6032 <sect2 id="mono-local-binds">
6033 <title>Monomorphic local bindings</title>
6035 We are actively thinking of simplifying GHC's type system, by <emphasis>not generalising local bindings</emphasis>.
6036 The rationale is described in the paper
6037 <ulink url="http://research.microsoft.com/~simonpj/papers/constraints/index.htm">Let should not be generalised</ulink>.
6040 The experimental new behaviour is enabled by the flag <option>-XMonoLocalBinds</option>. The effect is
6041 that local (that is, non-top-level) bindings without a type signature are not generalised at all. You can
6042 think of it as an extreme (but much more predictable) version of the Monomorphism Restriction.
6043 If you supply a type signature, then the flag has no effect.
6048 <!-- ==================== End of type system extensions ================= -->
6050 <!-- ====================== TEMPLATE HASKELL ======================= -->
6052 <sect1 id="template-haskell">
6053 <title>Template Haskell</title>
6055 <para>Template Haskell allows you to do compile-time meta-programming in
6058 the main technical innovations is discussed in "<ulink
6059 url="http://research.microsoft.com/~simonpj/papers/meta-haskell/">
6060 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
6063 There is a Wiki page about
6064 Template Haskell at <ulink url="http://www.haskell.org/haskellwiki/Template_Haskell">
6065 http://www.haskell.org/haskellwiki/Template_Haskell</ulink>, and that is the best place to look for
6069 url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online
6070 Haskell library reference material</ulink>
6071 (look for module <literal>Language.Haskell.TH</literal>).
6072 Many changes to the original design are described in
6073 <ulink url="http://research.microsoft.com/~simonpj/papers/meta-haskell/notes2.ps">
6074 Notes on Template Haskell version 2</ulink>.
6075 Not all of these changes are in GHC, however.
6078 <para> The first example from that paper is set out below (<xref linkend="th-example"/>)
6079 as a worked example to help get you started.
6083 The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to
6084 understand Template Haskell; see the <ulink url="http://haskell.org/haskellwiki/Template_Haskell">
6089 <title>Syntax</title>
6091 <para> Template Haskell has the following new syntactic
6092 constructions. You need to use the flag
6093 <option>-XTemplateHaskell</option>
6094 <indexterm><primary><option>-XTemplateHaskell</option></primary>
6095 </indexterm>to switch these syntactic extensions on
6096 (<option>-XTemplateHaskell</option> is no longer implied by
6097 <option>-fglasgow-exts</option>).</para>
6101 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
6102 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
6103 There must be no space between the "$" and the identifier or parenthesis. This use
6104 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
6105 of "." as an infix operator. If you want the infix operator, put spaces around it.
6107 <para> A splice can occur in place of
6109 <listitem><para> an expression; the spliced expression must
6110 have type <literal>Q Exp</literal></para></listitem>
6111 <listitem><para> an type; the spliced expression must
6112 have type <literal>Q Typ</literal></para></listitem>
6113 <listitem><para> a list of top-level declarations; the spliced expression
6114 must have type <literal>Q [Dec]</literal></para></listitem>
6116 Inside a splice you can can only call functions defined in imported modules,
6117 not functions defined elsewhere in the same module.</para></listitem>
6120 A expression quotation is written in Oxford brackets, thus:
6122 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
6123 the quotation has type <literal>Q Exp</literal>.</para></listitem>
6124 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
6125 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
6126 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
6127 the quotation has type <literal>Q Typ</literal>.</para></listitem>
6128 </itemizedlist></para></listitem>
6131 A quasi-quotation can appear in either a pattern context or an
6132 expression context and is also written in Oxford brackets:
6134 <listitem><para> <literal>[$<replaceable>varid</replaceable>| ... |]</literal>,
6135 where the "..." is an arbitrary string; a full description of the
6136 quasi-quotation facility is given in <xref linkend="th-quasiquotation"/>.</para></listitem>
6137 </itemizedlist></para></listitem>
6140 A name can be quoted with either one or two prefix single quotes:
6142 <listitem><para> <literal>'f</literal> has type <literal>Name</literal>, and names the function <literal>f</literal>.
6143 Similarly <literal>'C</literal> has type <literal>Name</literal> and names the data constructor <literal>C</literal>.
6144 In general <literal>'</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in an expression context.
6146 <listitem><para> <literal>''T</literal> has type <literal>Name</literal>, and names the type constructor <literal>T</literal>.
6147 That is, <literal>''</literal><replaceable>thing</replaceable> interprets <replaceable>thing</replaceable> in a type context.
6150 These <literal>Names</literal> can be used to construct Template Haskell expressions, patterns, declarations etc. They
6151 may also be given as an argument to the <literal>reify</literal> function.
6155 <listitem><para> You may omit the <literal>$(...)</literal> in a top-level declaration splice.
6156 Simply writing an expression (rather than a declaration) implies a splice. For example, you can write
6163 $(deriveStuff 'f) -- Uses the $(...) notation
6167 deriveStuff 'g -- Omits the $(...)
6171 This abbreviation makes top-level declaration slices quieter and less intimidating.
6176 (Compared to the original paper, there are many differences of detail.
6177 The syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>".
6178 The type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>.
6179 Pattern splices and quotations are not implemented.)
6183 <sect2> <title> Using Template Haskell </title>
6187 The data types and monadic constructor functions for Template Haskell are in the library
6188 <literal>Language.Haskell.THSyntax</literal>.
6192 You can only run a function at compile time if it is imported from another module. That is,
6193 you can't define a function in a module, and call it from within a splice in the same module.
6194 (It would make sense to do so, but it's hard to implement.)
6198 You can only run a function at compile time if it is imported
6199 from another module <emphasis>that is not part of a mutually-recursive group of modules
6200 that includes the module currently being compiled</emphasis>. Furthermore, all of the modules of
6201 the mutually-recursive group must be reachable by non-SOURCE imports from the module where the
6202 splice is to be run.</para>
6204 For example, when compiling module A,
6205 you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly).
6206 The reason should be clear: to run B we must compile and run A, but we are currently type-checking A.
6210 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
6213 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
6214 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
6215 compiles and runs a program, and then looks at the result. So it's important that
6216 the program it compiles produces results whose representations are identical to
6217 those of the compiler itself.
6221 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
6222 or file-at-a-time). There used to be a restriction to the former two, but that restriction
6227 <sect2 id="th-example"> <title> A Template Haskell Worked Example </title>
6228 <para>To help you get over the confidence barrier, try out this skeletal worked example.
6229 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
6236 -- Import our template "pr"
6237 import Printf ( pr )
6239 -- The splice operator $ takes the Haskell source code
6240 -- generated at compile time by "pr" and splices it into
6241 -- the argument of "putStrLn".
6242 main = putStrLn ( $(pr "Hello") )
6248 -- Skeletal printf from the paper.
6249 -- It needs to be in a separate module to the one where
6250 -- you intend to use it.
6252 -- Import some Template Haskell syntax
6253 import Language.Haskell.TH
6255 -- Describe a format string
6256 data Format = D | S | L String
6258 -- Parse a format string. This is left largely to you
6259 -- as we are here interested in building our first ever
6260 -- Template Haskell program and not in building printf.
6261 parse :: String -> [Format]
6264 -- Generate Haskell source code from a parsed representation
6265 -- of the format string. This code will be spliced into
6266 -- the module which calls "pr", at compile time.
6267 gen :: [Format] -> Q Exp
6268 gen [D] = [| \n -> show n |]
6269 gen [S] = [| \s -> s |]
6270 gen [L s] = stringE s
6272 -- Here we generate the Haskell code for the splice
6273 -- from an input format string.
6274 pr :: String -> Q Exp
6275 pr s = gen (parse s)
6278 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
6281 $ ghc --make -XTemplateHaskell main.hs -o main.exe
6284 <para>Run "main.exe" and here is your output:</para>
6294 <title>Using Template Haskell with Profiling</title>
6295 <indexterm><primary>profiling</primary><secondary>with Template Haskell</secondary></indexterm>
6297 <para>Template Haskell relies on GHC's built-in bytecode compiler and
6298 interpreter to run the splice expressions. The bytecode interpreter
6299 runs the compiled expression on top of the same runtime on which GHC
6300 itself is running; this means that the compiled code referred to by
6301 the interpreted expression must be compatible with this runtime, and
6302 in particular this means that object code that is compiled for
6303 profiling <emphasis>cannot</emphasis> be loaded and used by a splice
6304 expression, because profiled object code is only compatible with the
6305 profiling version of the runtime.</para>
6307 <para>This causes difficulties if you have a multi-module program
6308 containing Template Haskell code and you need to compile it for
6309 profiling, because GHC cannot load the profiled object code and use it
6310 when executing the splices. Fortunately GHC provides a workaround.
6311 The basic idea is to compile the program twice:</para>
6315 <para>Compile the program or library first the normal way, without
6316 <option>-prof</option><indexterm><primary><option>-prof</option></primary></indexterm>.</para>
6319 <para>Then compile it again with <option>-prof</option>, and
6320 additionally use <option>-osuf
6321 p_o</option><indexterm><primary><option>-osuf</option></primary></indexterm>
6322 to name the object files differently (you can choose any suffix
6323 that isn't the normal object suffix here). GHC will automatically
6324 load the object files built in the first step when executing splice
6325 expressions. If you omit the <option>-osuf</option> flag when
6326 building with <option>-prof</option> and Template Haskell is used,
6327 GHC will emit an error message. </para>
6332 <sect2 id="th-quasiquotation"> <title> Template Haskell Quasi-quotation </title>
6333 <para>Quasi-quotation allows patterns and expressions to be written using
6334 programmer-defined concrete syntax; the motivation behind the extension and
6335 several examples are documented in
6336 "<ulink url="http://www.eecs.harvard.edu/~mainland/ghc-quasiquoting/">Why It's
6337 Nice to be Quoted: Quasiquoting for Haskell</ulink>" (Proc Haskell Workshop
6338 2007). The example below shows how to write a quasiquoter for a simple
6339 expression language.</para>
6342 In the example, the quasiquoter <literal>expr</literal> is bound to a value of
6343 type <literal>Language.Haskell.TH.Quote.QuasiQuoter</literal> which contains two
6344 functions for quoting expressions and patterns, respectively. The first argument
6345 to each quoter is the (arbitrary) string enclosed in the Oxford brackets. The
6346 context of the quasi-quotation statement determines which of the two parsers is
6347 called: if the quasi-quotation occurs in an expression context, the expression
6348 parser is called, and if it occurs in a pattern context, the pattern parser is
6352 Note that in the example we make use of an antiquoted
6353 variable <literal>n</literal>, indicated by the syntax <literal>'int:n</literal>
6354 (this syntax for anti-quotation was defined by the parser's
6355 author, <emphasis>not</emphasis> by GHC). This binds <literal>n</literal> to the
6356 integer value argument of the constructor <literal>IntExpr</literal> when
6357 pattern matching. Please see the referenced paper for further details regarding
6358 anti-quotation as well as the description of a technique that uses SYB to
6359 leverage a single parser of type <literal>String -> a</literal> to generate both
6360 an expression parser that returns a value of type <literal>Q Exp</literal> and a
6361 pattern parser that returns a value of type <literal>Q Pat</literal>.
6364 <para>In general, a quasi-quote has the form
6365 <literal>[$<replaceable>quoter</replaceable>| <replaceable>string</replaceable> |]</literal>.
6366 The <replaceable>quoter</replaceable> must be the name of an imported quoter; it
6367 cannot be an arbitrary expression. The quoted <replaceable>string</replaceable>
6368 can be arbitrary, and may contain newlines.
6371 Quasiquoters must obey the same stage restrictions as Template Haskell, e.g., in
6372 the example, <literal>expr</literal> cannot be defined
6373 in <literal>Main.hs</literal> where it is used, but must be imported.
6384 main = do { print $ eval [$expr|1 + 2|]
6386 { [$expr|'int:n|] -> print n
6395 import qualified Language.Haskell.TH as TH
6396 import Language.Haskell.TH.Quote
6398 data Expr = IntExpr Integer
6399 | AntiIntExpr String
6400 | BinopExpr BinOp Expr Expr
6402 deriving(Show, Typeable, Data)
6408 deriving(Show, Typeable, Data)
6410 eval :: Expr -> Integer
6411 eval (IntExpr n) = n
6412 eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
6419 expr = QuasiQuoter parseExprExp parseExprPat
6421 -- Parse an Expr, returning its representation as
6422 -- either a Q Exp or a Q Pat. See the referenced paper
6423 -- for how to use SYB to do this by writing a single
6424 -- parser of type String -> Expr instead of two
6425 -- separate parsers.
6427 parseExprExp :: String -> Q Exp
6430 parseExprPat :: String -> Q Pat
6434 <para>Now run the compiler:
6437 $ ghc --make -XQuasiQuotes Main.hs -o main
6440 <para>Run "main" and here is your output:</para>
6452 <!-- ===================== Arrow notation =================== -->
6454 <sect1 id="arrow-notation">
6455 <title>Arrow notation
6458 <para>Arrows are a generalization of monads introduced by John Hughes.
6459 For more details, see
6464 “Generalising Monads to Arrows”,
6465 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
6466 pp67–111, May 2000.
6467 The paper that introduced arrows: a friendly introduction, motivated with
6468 programming examples.
6474 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
6475 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
6476 Introduced the notation described here.
6482 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
6483 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
6490 “<ulink url="http://www.cs.chalmers.se/~rjmh/afp-arrows.pdf">Programming with Arrows</ulink>”,
6491 John Hughes, in <citetitle>5th International Summer School on
6492 Advanced Functional Programming</citetitle>,
6493 <citetitle>Lecture Notes in Computer Science</citetitle> vol. 3622,
6495 This paper includes another introduction to the notation,
6496 with practical examples.
6502 “<ulink url="http://www.haskell.org/ghc/docs/papers/arrow-rules.pdf">Type and Translation Rules for Arrow Notation in GHC</ulink>”,
6503 Ross Paterson and Simon Peyton Jones, September 16, 2004.
6504 A terse enumeration of the formal rules used
6505 (extracted from comments in the source code).
6511 The arrows web page at
6512 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
6517 With the <option>-XArrows</option> flag, GHC supports the arrow
6518 notation described in the second of these papers,
6519 translating it using combinators from the
6520 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6522 What follows is a brief introduction to the notation;
6523 it won't make much sense unless you've read Hughes's paper.
6526 <para>The extension adds a new kind of expression for defining arrows:
6528 <replaceable>exp</replaceable><superscript>10</superscript> ::= ...
6529 | proc <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6531 where <literal>proc</literal> is a new keyword.
6532 The variables of the pattern are bound in the body of the
6533 <literal>proc</literal>-expression,
6534 which is a new sort of thing called a <firstterm>command</firstterm>.
6535 The syntax of commands is as follows:
6537 <replaceable>cmd</replaceable> ::= <replaceable>exp</replaceable><superscript>10</superscript> -< <replaceable>exp</replaceable>
6538 | <replaceable>exp</replaceable><superscript>10</superscript> -<< <replaceable>exp</replaceable>
6539 | <replaceable>cmd</replaceable><superscript>0</superscript>
6541 with <replaceable>cmd</replaceable><superscript>0</superscript> up to
6542 <replaceable>cmd</replaceable><superscript>9</superscript> defined using
6543 infix operators as for expressions, and
6545 <replaceable>cmd</replaceable><superscript>10</superscript> ::= \ <replaceable>apat</replaceable> ... <replaceable>apat</replaceable> -> <replaceable>cmd</replaceable>
6546 | let <replaceable>decls</replaceable> in <replaceable>cmd</replaceable>
6547 | if <replaceable>exp</replaceable> then <replaceable>cmd</replaceable> else <replaceable>cmd</replaceable>
6548 | case <replaceable>exp</replaceable> of { <replaceable>calts</replaceable> }
6549 | do { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> ; <replaceable>cmd</replaceable> }
6550 | <replaceable>fcmd</replaceable>
6552 <replaceable>fcmd</replaceable> ::= <replaceable>fcmd</replaceable> <replaceable>aexp</replaceable>
6553 | ( <replaceable>cmd</replaceable> )
6554 | (| <replaceable>aexp</replaceable> <replaceable>cmd</replaceable> ... <replaceable>cmd</replaceable> |)
6556 <replaceable>cstmt</replaceable> ::= let <replaceable>decls</replaceable>
6557 | <replaceable>pat</replaceable> <- <replaceable>cmd</replaceable>
6558 | rec { <replaceable>cstmt</replaceable> ; ... <replaceable>cstmt</replaceable> [;] }
6559 | <replaceable>cmd</replaceable>
6561 where <replaceable>calts</replaceable> are like <replaceable>alts</replaceable>
6562 except that the bodies are commands instead of expressions.
6566 Commands produce values, but (like monadic computations)
6567 may yield more than one value,
6568 or none, and may do other things as well.
6569 For the most part, familiarity with monadic notation is a good guide to
6571 However the values of expressions, even monadic ones,
6572 are determined by the values of the variables they contain;
6573 this is not necessarily the case for commands.
6577 A simple example of the new notation is the expression
6579 proc x -> f -< x+1
6581 We call this a <firstterm>procedure</firstterm> or
6582 <firstterm>arrow abstraction</firstterm>.
6583 As with a lambda expression, the variable <literal>x</literal>
6584 is a new variable bound within the <literal>proc</literal>-expression.
6585 It refers to the input to the arrow.
6586 In the above example, <literal>-<</literal> is not an identifier but an
6587 new reserved symbol used for building commands from an expression of arrow
6588 type and an expression to be fed as input to that arrow.
6589 (The weird look will make more sense later.)
6590 It may be read as analogue of application for arrows.
6591 The above example is equivalent to the Haskell expression
6593 arr (\ x -> x+1) >>> f
6595 That would make no sense if the expression to the left of
6596 <literal>-<</literal> involves the bound variable <literal>x</literal>.
6597 More generally, the expression to the left of <literal>-<</literal>
6598 may not involve any <firstterm>local variable</firstterm>,
6599 i.e. a variable bound in the current arrow abstraction.
6600 For such a situation there is a variant <literal>-<<</literal>, as in
6602 proc x -> f x -<< x+1
6604 which is equivalent to
6606 arr (\ x -> (f x, x+1)) >>> app
6608 so in this case the arrow must belong to the <literal>ArrowApply</literal>
6610 Such an arrow is equivalent to a monad, so if you're using this form
6611 you may find a monadic formulation more convenient.
6615 <title>do-notation for commands</title>
6618 Another form of command is a form of <literal>do</literal>-notation.
6619 For example, you can write
6628 You can read this much like ordinary <literal>do</literal>-notation,
6629 but with commands in place of monadic expressions.
6630 The first line sends the value of <literal>x+1</literal> as an input to
6631 the arrow <literal>f</literal>, and matches its output against
6632 <literal>y</literal>.
6633 In the next line, the output is discarded.
6634 The arrow <function>returnA</function> is defined in the
6635 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6636 module as <literal>arr id</literal>.
6637 The above example is treated as an abbreviation for
6639 arr (\ x -> (x, x)) >>>
6640 first (arr (\ x -> x+1) >>> f) >>>
6641 arr (\ (y, x) -> (y, (x, y))) >>>
6642 first (arr (\ y -> 2*y) >>> g) >>>
6644 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
6645 first (arr (\ (x, z) -> x*z) >>> h) >>>
6646 arr (\ (t, z) -> t+z) >>>
6649 Note that variables not used later in the composition are projected out.
6650 After simplification using rewrite rules (see <xref linkend="rewrite-rules"/>)
6652 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>
6653 module, this reduces to
6655 arr (\ x -> (x+1, x)) >>>
6657 arr (\ (y, x) -> (2*y, (x, y))) >>>
6659 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
6661 arr (\ (t, z) -> t+z)
6663 which is what you might have written by hand.
6664 With arrow notation, GHC keeps track of all those tuples of variables for you.
6668 Note that although the above translation suggests that
6669 <literal>let</literal>-bound variables like <literal>z</literal> must be
6670 monomorphic, the actual translation produces Core,
6671 so polymorphic variables are allowed.
6675 It's also possible to have mutually recursive bindings,
6676 using the new <literal>rec</literal> keyword, as in the following example:
6678 counter :: ArrowCircuit a => a Bool Int
6679 counter = proc reset -> do
6680 rec output <- returnA -< if reset then 0 else next
6681 next <- delay 0 -< output+1
6682 returnA -< output
6684 The translation of such forms uses the <function>loop</function> combinator,
6685 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
6691 <title>Conditional commands</title>
6694 In the previous example, we used a conditional expression to construct the
6696 Sometimes we want to conditionally execute different commands, as in
6703 which is translated to
6705 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
6706 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
6708 Since the translation uses <function>|||</function>,
6709 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
6713 There are also <literal>case</literal> commands, like
6719 y <- h -< (x1, x2)
6723 The syntax is the same as for <literal>case</literal> expressions,
6724 except that the bodies of the alternatives are commands rather than expressions.
6725 The translation is similar to that of <literal>if</literal> commands.
6731 <title>Defining your own control structures</title>
6734 As we're seen, arrow notation provides constructs,
6735 modelled on those for expressions,
6736 for sequencing, value recursion and conditionals.
6737 But suitable combinators,
6738 which you can define in ordinary Haskell,
6739 may also be used to build new commands out of existing ones.
6740 The basic idea is that a command defines an arrow from environments to values.
6741 These environments assign values to the free local variables of the command.
6742 Thus combinators that produce arrows from arrows
6743 may also be used to build commands from commands.
6744 For example, the <literal>ArrowChoice</literal> class includes a combinator
6746 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
6748 so we can use it to build commands:
6750 expr' = proc x -> do
6753 symbol Plus -< ()
6754 y <- term -< ()
6757 symbol Minus -< ()
6758 y <- term -< ()
6761 (The <literal>do</literal> on the first line is needed to prevent the first
6762 <literal><+> ...</literal> from being interpreted as part of the
6763 expression on the previous line.)
6764 This is equivalent to
6766 expr' = (proc x -> returnA -< x)
6767 <+> (proc x -> do
6768 symbol Plus -< ()
6769 y <- term -< ()
6771 <+> (proc x -> do
6772 symbol Minus -< ()
6773 y <- term -< ()
6776 It is essential that this operator be polymorphic in <literal>e</literal>
6777 (representing the environment input to the command
6778 and thence to its subcommands)
6779 and satisfy the corresponding naturality property
6781 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
6783 at least for strict <literal>k</literal>.
6784 (This should be automatic if you're not using <function>seq</function>.)
6785 This ensures that environments seen by the subcommands are environments
6786 of the whole command,
6787 and also allows the translation to safely trim these environments.
6788 The operator must also not use any variable defined within the current
6793 We could define our own operator
6795 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
6796 untilA body cond = proc x ->
6797 b <- cond -< x
6798 if b then returnA -< ()
6801 untilA body cond -< x
6803 and use it in the same way.
6804 Of course this infix syntax only makes sense for binary operators;
6805 there is also a more general syntax involving special brackets:
6809 (|untilA (increment -< x+y) (within 0.5 -< x)|)
6816 <title>Primitive constructs</title>
6819 Some operators will need to pass additional inputs to their subcommands.
6820 For example, in an arrow type supporting exceptions,
6821 the operator that attaches an exception handler will wish to pass the
6822 exception that occurred to the handler.
6823 Such an operator might have a type
6825 handleA :: ... => a e c -> a (e,Ex) c -> a e c
6827 where <literal>Ex</literal> is the type of exceptions handled.
6828 You could then use this with arrow notation by writing a command
6830 body `handleA` \ ex -> handler
6832 so that if an exception is raised in the command <literal>body</literal>,
6833 the variable <literal>ex</literal> is bound to the value of the exception
6834 and the command <literal>handler</literal>,
6835 which typically refers to <literal>ex</literal>, is entered.
6836 Though the syntax here looks like a functional lambda,
6837 we are talking about commands, and something different is going on.
6838 The input to the arrow represented by a command consists of values for
6839 the free local variables in the command, plus a stack of anonymous values.
6840 In all the prior examples, this stack was empty.
6841 In the second argument to <function>handleA</function>,
6842 this stack consists of one value, the value of the exception.
6843 The command form of lambda merely gives this value a name.
6848 the values on the stack are paired to the right of the environment.
6849 So operators like <function>handleA</function> that pass
6850 extra inputs to their subcommands can be designed for use with the notation
6851 by pairing the values with the environment in this way.
6852 More precisely, the type of each argument of the operator (and its result)
6853 should have the form
6855 a (...(e,t1), ... tn) t
6857 where <replaceable>e</replaceable> is a polymorphic variable
6858 (representing the environment)
6859 and <replaceable>ti</replaceable> are the types of the values on the stack,
6860 with <replaceable>t1</replaceable> being the <quote>top</quote>.
6861 The polymorphic variable <replaceable>e</replaceable> must not occur in
6862 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
6863 <replaceable>t</replaceable>.
6864 However the arrows involved need not be the same.
6865 Here are some more examples of suitable operators:
6867 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
6868 runReader :: ... => a e c -> a' (e,State) c
6869 runState :: ... => a e c -> a' (e,State) (c,State)
6871 We can supply the extra input required by commands built with the last two
6872 by applying them to ordinary expressions, as in
6876 (|runReader (do { ... })|) s
6878 which adds <literal>s</literal> to the stack of inputs to the command
6879 built using <function>runReader</function>.
6883 The command versions of lambda abstraction and application are analogous to
6884 the expression versions.
6885 In particular, the beta and eta rules describe equivalences of commands.
6886 These three features (operators, lambda abstraction and application)
6887 are the core of the notation; everything else can be built using them,
6888 though the results would be somewhat clumsy.
6889 For example, we could simulate <literal>do</literal>-notation by defining
6891 bind :: Arrow a => a e b -> a (e,b) c -> a e c
6892 u `bind` f = returnA &&& u >>> f
6894 bind_ :: Arrow a => a e b -> a e c -> a e c
6895 u `bind_` f = u `bind` (arr fst >>> f)
6897 We could simulate <literal>if</literal> by defining
6899 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
6900 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
6907 <title>Differences with the paper</title>
6912 <para>Instead of a single form of arrow application (arrow tail) with two
6913 translations, the implementation provides two forms
6914 <quote><literal>-<</literal></quote> (first-order)
6915 and <quote><literal>-<<</literal></quote> (higher-order).
6920 <para>User-defined operators are flagged with banana brackets instead of
6921 a new <literal>form</literal> keyword.
6930 <title>Portability</title>
6933 Although only GHC implements arrow notation directly,
6934 there is also a preprocessor
6936 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
6937 that translates arrow notation into Haskell 98
6938 for use with other Haskell systems.
6939 You would still want to check arrow programs with GHC;
6940 tracing type errors in the preprocessor output is not easy.
6941 Modules intended for both GHC and the preprocessor must observe some
6942 additional restrictions:
6947 The module must import
6948 <ulink url="../libraries/base/Control-Arrow.html"><literal>Control.Arrow</literal></ulink>.
6954 The preprocessor cannot cope with other Haskell extensions.
6955 These would have to go in separate modules.
6961 Because the preprocessor targets Haskell (rather than Core),
6962 <literal>let</literal>-bound variables are monomorphic.
6973 <!-- ==================== BANG PATTERNS ================= -->
6975 <sect1 id="bang-patterns">
6976 <title>Bang patterns
6977 <indexterm><primary>Bang patterns</primary></indexterm>
6979 <para>GHC supports an extension of pattern matching called <emphasis>bang
6980 patterns</emphasis>, written <literal>!<replaceable>pat</replaceable></literal>.
6981 Bang patterns are under consideration for Haskell Prime.
6983 url="http://hackage.haskell.org/trac/haskell-prime/wiki/BangPatterns">Haskell
6984 prime feature description</ulink> contains more discussion and examples
6985 than the material below.
6988 The key change is the addition of a new rule to the
6989 <ulink url="http://haskell.org/onlinereport/exps.html#sect3.17.2">semantics of pattern matching in the Haskell 98 report</ulink>.
6990 Add new bullet 10, saying: Matching the pattern <literal>!</literal><replaceable>pat</replaceable>
6991 against a value <replaceable>v</replaceable> behaves as follows:
6993 <listitem><para>if <replaceable>v</replaceable> is bottom, the match diverges</para></listitem>
6994 <listitem><para>otherwise, <replaceable>pat</replaceable> is matched against <replaceable>v</replaceable> </para></listitem>
6998 Bang patterns are enabled by the flag <option>-XBangPatterns</option>.
7001 <sect2 id="bang-patterns-informal">
7002 <title>Informal description of bang patterns
7005 The main idea is to add a single new production to the syntax of patterns:
7009 Matching an expression <literal>e</literal> against a pattern <literal>!p</literal> is done by first
7010 evaluating <literal>e</literal> (to WHNF) and then matching the result against <literal>p</literal>.
7015 This definition makes <literal>f1</literal> is strict in <literal>x</literal>,
7016 whereas without the bang it would be lazy.
7017 Bang patterns can be nested of course:
7021 Here, <literal>f2</literal> is strict in <literal>x</literal> but not in
7022 <literal>y</literal>.
7023 A bang only really has an effect if it precedes a variable or wild-card pattern:
7028 Here, <literal>f3</literal> and <literal>f4</literal> are identical;
7029 putting a bang before a pattern that
7030 forces evaluation anyway does nothing.
7033 There is one (apparent) exception to this general rule that a bang only
7034 makes a difference when it precedes a variable or wild-card: a bang at the
7035 top level of a <literal>let</literal> or <literal>where</literal>
7036 binding makes the binding strict, regardless of the pattern. For example:
7040 is a strict binding: operationally, it evaluates <literal>e</literal>, matches
7041 it against the pattern <literal>[x,y]</literal>, and then evaluates <literal>b</literal>.
7042 (We say "apparent" exception because the Right Way to think of it is that the bang
7043 at the top of a binding is not part of the <emphasis>pattern</emphasis>; rather it
7044 is part of the syntax of the <emphasis>binding</emphasis>.)
7045 Nested bangs in a pattern binding behave uniformly with all other forms of
7046 pattern matching. For example
7048 let (!x,[y]) = e in b
7050 is equivalent to this:
7052 let { t = case e of (x,[y]) -> x `seq` (x,y)
7057 The binding is lazy, but when either <literal>x</literal> or <literal>y</literal> is
7058 evaluated by <literal>b</literal> the entire pattern is matched, including forcing the
7059 evaluation of <literal>x</literal>.
7062 Bang patterns work in <literal>case</literal> expressions too, of course:
7064 g5 x = let y = f x in body
7065 g6 x = case f x of { y -> body }
7066 g7 x = case f x of { !y -> body }
7068 The functions <literal>g5</literal> and <literal>g6</literal> mean exactly the same thing.
7069 But <literal>g7</literal> evaluates <literal>(f x)</literal>, binds <literal>y</literal> to the
7070 result, and then evaluates <literal>body</literal>.
7075 <sect2 id="bang-patterns-sem">
7076 <title>Syntax and semantics
7080 We add a single new production to the syntax of patterns:
7084 There is one problem with syntactic ambiguity. Consider:
7088 Is this a definition of the infix function "<literal>(!)</literal>",
7089 or of the "<literal>f</literal>" with a bang pattern? GHC resolves this
7090 ambiguity in favour of the latter. If you want to define
7091 <literal>(!)</literal> with bang-patterns enabled, you have to do so using
7096 The semantics of Haskell pattern matching is described in <ulink
7097 url="http://www.haskell.org/onlinereport/exps.html#sect3.17.2">
7098 Section 3.17.2</ulink> of the Haskell Report. To this description add
7099 one extra item 10, saying:
7100 <itemizedlist><listitem><para>Matching
7101 the pattern <literal>!pat</literal> against a value <literal>v</literal> behaves as follows:
7102 <itemizedlist><listitem><para>if <literal>v</literal> is bottom, the match diverges</para></listitem>
7103 <listitem><para>otherwise, <literal>pat</literal> is matched against
7104 <literal>v</literal></para></listitem>
7106 </para></listitem></itemizedlist>
7107 Similarly, in Figure 4 of <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.17.3">
7108 Section 3.17.3</ulink>, add a new case (t):
7110 case v of { !pat -> e; _ -> e' }
7111 = v `seq` case v of { pat -> e; _ -> e' }
7114 That leaves let expressions, whose translation is given in
7115 <ulink url="http://www.haskell.org/onlinereport/exps.html#sect3.12">Section
7117 of the Haskell Report.
7118 In the translation box, first apply
7119 the following transformation: for each pattern <literal>pi</literal> that is of
7120 form <literal>!qi = ei</literal>, transform it to <literal>(xi,!qi) = ((),ei)</literal>, and and replace <literal>e0</literal>
7121 by <literal>(xi `seq` e0)</literal>. Then, when none of the left-hand-side patterns
7122 have a bang at the top, apply the rules in the existing box.
7124 <para>The effect of the let rule is to force complete matching of the pattern
7125 <literal>qi</literal> before evaluation of the body is begun. The bang is
7126 retained in the translated form in case <literal>qi</literal> is a variable,
7134 The let-binding can be recursive. However, it is much more common for
7135 the let-binding to be non-recursive, in which case the following law holds:
7136 <literal>(let !p = rhs in body)</literal>
7138 <literal>(case rhs of !p -> body)</literal>
7141 A pattern with a bang at the outermost level is not allowed at the top level of
7147 <!-- ==================== ASSERTIONS ================= -->
7149 <sect1 id="assertions">
7151 <indexterm><primary>Assertions</primary></indexterm>
7155 If you want to make use of assertions in your standard Haskell code, you
7156 could define a function like the following:
7162 assert :: Bool -> a -> a
7163 assert False x = error "assertion failed!"
7170 which works, but gives you back a less than useful error message --
7171 an assertion failed, but which and where?
7175 One way out is to define an extended <function>assert</function> function which also
7176 takes a descriptive string to include in the error message and
7177 perhaps combine this with the use of a pre-processor which inserts
7178 the source location where <function>assert</function> was used.
7182 Ghc offers a helping hand here, doing all of this for you. For every
7183 use of <function>assert</function> in the user's source:
7189 kelvinToC :: Double -> Double
7190 kelvinToC k = assert (k >= 0.0) (k+273.15)
7196 Ghc will rewrite this to also include the source location where the
7203 assert pred val ==> assertError "Main.hs|15" pred val
7209 The rewrite is only performed by the compiler when it spots
7210 applications of <function>Control.Exception.assert</function>, so you
7211 can still define and use your own versions of
7212 <function>assert</function>, should you so wish. If not, import
7213 <literal>Control.Exception</literal> to make use
7214 <function>assert</function> in your code.
7218 GHC ignores assertions when optimisation is turned on with the
7219 <option>-O</option><indexterm><primary><option>-O</option></primary></indexterm> flag. That is, expressions of the form
7220 <literal>assert pred e</literal> will be rewritten to
7221 <literal>e</literal>. You can also disable assertions using the
7222 <option>-fignore-asserts</option>
7223 option<indexterm><primary><option>-fignore-asserts</option></primary>
7224 </indexterm>.</para>
7227 Assertion failures can be caught, see the documentation for the
7228 <literal>Control.Exception</literal> library for the details.
7234 <!-- =============================== PRAGMAS =========================== -->
7236 <sect1 id="pragmas">
7237 <title>Pragmas</title>
7239 <indexterm><primary>pragma</primary></indexterm>
7241 <para>GHC supports several pragmas, or instructions to the
7242 compiler placed in the source code. Pragmas don't normally affect
7243 the meaning of the program, but they might affect the efficiency
7244 of the generated code.</para>
7246 <para>Pragmas all take the form
7248 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
7250 where <replaceable>word</replaceable> indicates the type of
7251 pragma, and is followed optionally by information specific to that
7252 type of pragma. Case is ignored in
7253 <replaceable>word</replaceable>. The various values for
7254 <replaceable>word</replaceable> that GHC understands are described
7255 in the following sections; any pragma encountered with an
7256 unrecognised <replaceable>word</replaceable> is
7257 ignored. The layout rule applies in pragmas, so the closing <literal>#-}</literal>
7258 should start in a column to the right of the opening <literal>{-#</literal>. </para>
7260 <para>Certain pragmas are <emphasis>file-header pragmas</emphasis>:
7264 pragma must precede the <literal>module</literal> keyword in the file.
7267 There can be as many file-header pragmas as you please, and they can be
7268 preceded or followed by comments.
7271 File-header pragmas are read once only, before
7272 pre-processing the file (e.g. with cpp).
7275 The file-header pragmas are: <literal>{-# LANGUAGE #-}</literal>,
7276 <literal>{-# OPTIONS_GHC #-}</literal>, and
7277 <literal>{-# INCLUDE #-}</literal>.
7282 <sect2 id="language-pragma">
7283 <title>LANGUAGE pragma</title>
7285 <indexterm><primary>LANGUAGE</primary><secondary>pragma</secondary></indexterm>
7286 <indexterm><primary>pragma</primary><secondary>LANGUAGE</secondary></indexterm>
7288 <para>The <literal>LANGUAGE</literal> pragma allows language extensions to be enabled
7290 It is the intention that all Haskell compilers support the
7291 <literal>LANGUAGE</literal> pragma with the same syntax, although not
7292 all extensions are supported by all compilers, of
7293 course. The <literal>LANGUAGE</literal> pragma should be used instead
7294 of <literal>OPTIONS_GHC</literal>, if possible.</para>
7296 <para>For example, to enable the FFI and preprocessing with CPP:</para>
7298 <programlisting>{-# LANGUAGE ForeignFunctionInterface, CPP #-}</programlisting>
7300 <para><literal>LANGUAGE</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7302 <para>Every language extension can also be turned into a command-line flag
7303 by prefixing it with "<literal>-X</literal>"; for example <option>-XForeignFunctionInterface</option>.
7304 (Similarly, all "<literal>-X</literal>" flags can be written as <literal>LANGUAGE</literal> pragmas.
7307 <para>A list of all supported language extensions can be obtained by invoking
7308 <literal>ghc --supported-languages</literal> (see <xref linkend="modes"/>).</para>
7310 <para>Any extension from the <literal>Extension</literal> type defined in
7312 url="../libraries/Cabal/Language-Haskell-Extension.html"><literal>Language.Haskell.Extension</literal></ulink>
7313 may be used. GHC will report an error if any of the requested extensions are not supported.</para>
7317 <sect2 id="options-pragma">
7318 <title>OPTIONS_GHC pragma</title>
7319 <indexterm><primary>OPTIONS_GHC</primary>
7321 <indexterm><primary>pragma</primary><secondary>OPTIONS_GHC</secondary>
7324 <para>The <literal>OPTIONS_GHC</literal> pragma is used to specify
7325 additional options that are given to the compiler when compiling
7326 this source file. See <xref linkend="source-file-options"/> for
7329 <para>Previous versions of GHC accepted <literal>OPTIONS</literal> rather
7330 than <literal>OPTIONS_GHC</literal>, but that is now deprecated.</para>
7333 <para><literal>OPTIONS_GHC</literal> is a file-header pragma (see <xref linkend="pragmas"/>).</para>
7335 <sect2 id="include-pragma">
7336 <title>INCLUDE pragma</title>
7338 <para>The <literal>INCLUDE</literal> used to be necessary for
7339 specifying header files to be included when using the FFI and
7340 compiling via C. It is no longer required for GHC, but is
7341 accepted (and ignored) for compatibility with other
7345 <sect2 id="warning-deprecated-pragma">
7346 <title>WARNING and DEPRECATED pragmas</title>
7347 <indexterm><primary>WARNING</primary></indexterm>
7348 <indexterm><primary>DEPRECATED</primary></indexterm>
7350 <para>The WARNING pragma allows you to attach an arbitrary warning
7351 to a particular function, class, or type.
7352 A DEPRECATED pragma lets you specify that
7353 a particular function, class, or type is deprecated.
7354 There are two ways of using these pragmas.
7358 <para>You can work on an entire module thus:</para>
7360 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
7365 module Wibble {-# WARNING "This is an unstable interface." #-} where
7368 <para>When you compile any module that import
7369 <literal>Wibble</literal>, GHC will print the specified
7374 <para>You can attach a warning to a function, class, type, or data constructor, with the
7375 following top-level declarations:</para>
7377 {-# DEPRECATED f, C, T "Don't use these" #-}
7378 {-# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #-}
7380 <para>When you compile any module that imports and uses any
7381 of the specified entities, GHC will print the specified
7383 <para> You can only attach to entities declared at top level in the module
7384 being compiled, and you can only use unqualified names in the list of
7385 entities. A capitalised name, such as <literal>T</literal>
7386 refers to <emphasis>either</emphasis> the type constructor <literal>T</literal>
7387 <emphasis>or</emphasis> the data constructor <literal>T</literal>, or both if
7388 both are in scope. If both are in scope, there is currently no way to
7389 specify one without the other (c.f. fixities
7390 <xref linkend="infix-tycons"/>).</para>
7393 Warnings and deprecations are not reported for
7394 (a) uses within the defining module, and
7395 (b) uses in an export list.
7396 The latter reduces spurious complaints within a library
7397 in which one module gathers together and re-exports
7398 the exports of several others.
7400 <para>You can suppress the warnings with the flag
7401 <option>-fno-warn-warnings-deprecations</option>.</para>
7404 <sect2 id="inline-noinline-pragma">
7405 <title>INLINE and NOINLINE pragmas</title>
7407 <para>These pragmas control the inlining of function
7410 <sect3 id="inline-pragma">
7411 <title>INLINE pragma</title>
7412 <indexterm><primary>INLINE</primary></indexterm>
7414 <para>GHC (with <option>-O</option>, as always) tries to
7415 inline (or “unfold”) functions/values that are
7416 “small enough,” thus avoiding the call overhead
7417 and possibly exposing other more-wonderful optimisations.
7418 Normally, if GHC decides a function is “too
7419 expensive” to inline, it will not do so, nor will it
7420 export that unfolding for other modules to use.</para>
7422 <para>The sledgehammer you can bring to bear is the
7423 <literal>INLINE</literal><indexterm><primary>INLINE
7424 pragma</primary></indexterm> pragma, used thusly:</para>
7427 key_function :: Int -> String -> (Bool, Double)
7428 {-# INLINE key_function #-}
7431 <para>The major effect of an <literal>INLINE</literal> pragma
7432 is to declare a function's “cost” to be very low.
7433 The normal unfolding machinery will then be very keen to
7434 inline it. However, an <literal>INLINE</literal> pragma for a
7435 function "<literal>f</literal>" has a number of other effects:
7438 No functions are inlined into <literal>f</literal>. Otherwise
7439 GHC might inline a big function into <literal>f</literal>'s right hand side,
7440 making <literal>f</literal> big; and then inline <literal>f</literal> blindly.
7443 The float-in, float-out, and common-sub-expression transformations are not
7444 applied to the body of <literal>f</literal>.
7447 An INLINE function is not worker/wrappered by strictness analysis.
7448 It's going to be inlined wholesale instead.
7451 All of these effects are aimed at ensuring that what gets inlined is
7452 exactly what you asked for, no more and no less.
7454 <para>GHC ensures that inlining cannot go on forever: every mutually-recursive
7455 group is cut by one or more <emphasis>loop breakers</emphasis> that is never inlined
7456 (see <ulink url="http://research.microsoft.com/%7Esimonpj/Papers/inlining/index.htm">
7457 Secrets of the GHC inliner, JFP 12(4) July 2002</ulink>).
7458 GHC tries not to select a function with an INLINE pragma as a loop breaker, but
7459 when there is no choice even an INLINE function can be selected, in which case
7460 the INLINE pragma is ignored.
7461 For example, for a self-recursive function, the loop breaker can only be the function
7462 itself, so an INLINE pragma is always ignored.</para>
7464 <para>Syntactically, an <literal>INLINE</literal> pragma for a
7465 function can be put anywhere its type signature could be
7468 <para><literal>INLINE</literal> pragmas are a particularly
7470 <literal>then</literal>/<literal>return</literal> (or
7471 <literal>bind</literal>/<literal>unit</literal>) functions in
7472 a monad. For example, in GHC's own
7473 <literal>UniqueSupply</literal> monad code, we have:</para>
7476 {-# INLINE thenUs #-}
7477 {-# INLINE returnUs #-}
7480 <para>See also the <literal>NOINLINE</literal> pragma (<xref
7481 linkend="noinline-pragma"/>).</para>
7483 <para>Note: the HBC compiler doesn't like <literal>INLINE</literal> pragmas,
7484 so if you want your code to be HBC-compatible you'll have to surround
7485 the pragma with C pre-processor directives
7486 <literal>#ifdef __GLASGOW_HASKELL__</literal>...<literal>#endif</literal>.</para>
7490 <sect3 id="noinline-pragma">
7491 <title>NOINLINE pragma</title>
7493 <indexterm><primary>NOINLINE</primary></indexterm>
7494 <indexterm><primary>NOTINLINE</primary></indexterm>
7496 <para>The <literal>NOINLINE</literal> pragma does exactly what
7497 you'd expect: it stops the named function from being inlined
7498 by the compiler. You shouldn't ever need to do this, unless
7499 you're very cautious about code size.</para>
7501 <para><literal>NOTINLINE</literal> is a synonym for
7502 <literal>NOINLINE</literal> (<literal>NOINLINE</literal> is
7503 specified by Haskell 98 as the standard way to disable
7504 inlining, so it should be used if you want your code to be
7508 <sect3 id="phase-control">
7509 <title>Phase control</title>
7511 <para> Sometimes you want to control exactly when in GHC's
7512 pipeline the INLINE pragma is switched on. Inlining happens
7513 only during runs of the <emphasis>simplifier</emphasis>. Each
7514 run of the simplifier has a different <emphasis>phase
7515 number</emphasis>; the phase number decreases towards zero.
7516 If you use <option>-dverbose-core2core</option> you'll see the
7517 sequence of phase numbers for successive runs of the
7518 simplifier. In an INLINE pragma you can optionally specify a
7522 <para>"<literal>INLINE[k] f</literal>" means: do not inline
7523 <literal>f</literal>
7524 until phase <literal>k</literal>, but from phase
7525 <literal>k</literal> onwards be very keen to inline it.
7528 <para>"<literal>INLINE[~k] f</literal>" means: be very keen to inline
7529 <literal>f</literal>
7530 until phase <literal>k</literal>, but from phase
7531 <literal>k</literal> onwards do not inline it.
7534 <para>"<literal>NOINLINE[k] f</literal>" means: do not inline
7535 <literal>f</literal>
7536 until phase <literal>k</literal>, but from phase
7537 <literal>k</literal> onwards be willing to inline it (as if
7538 there was no pragma).
7541 <para>"<literal>NOINLINE[~k] f</literal>" means: be willing to inline
7542 <literal>f</literal>
7543 until phase <literal>k</literal>, but from phase
7544 <literal>k</literal> onwards do not inline it.
7547 The same information is summarised here:
7549 -- Before phase 2 Phase 2 and later
7550 {-# INLINE [2] f #-} -- No Yes
7551 {-# INLINE [~2] f #-} -- Yes No
7552 {-# NOINLINE [2] f #-} -- No Maybe
7553 {-# NOINLINE [~2] f #-} -- Maybe No
7555 {-# INLINE f #-} -- Yes Yes
7556 {-# NOINLINE f #-} -- No No
7558 By "Maybe" we mean that the usual heuristic inlining rules apply (if the
7559 function body is small, or it is applied to interesting-looking arguments etc).
7560 Another way to understand the semantics is this:
7562 <listitem><para>For both INLINE and NOINLINE, the phase number says
7563 when inlining is allowed at all.</para></listitem>
7564 <listitem><para>The INLINE pragma has the additional effect of making the
7565 function body look small, so that when inlining is allowed it is very likely to
7570 <para>The same phase-numbering control is available for RULES
7571 (<xref linkend="rewrite-rules"/>).</para>
7575 <sect2 id="annotation-pragmas">
7576 <title>ANN pragmas</title>
7578 <para>GHC offers the ability to annotate various code constructs with additional
7579 data by using three pragmas. This data can then be inspected at a later date by
7580 using GHC-as-a-library.</para>
7582 <sect3 id="ann-pragma">
7583 <title>Annotating values</title>
7585 <indexterm><primary>ANN</primary></indexterm>
7587 <para>Any expression that has both <literal>Typeable</literal> and <literal>Data</literal> instances may be attached to a top-level value
7588 binding using an <literal>ANN</literal> pragma. In particular, this means you can use <literal>ANN</literal>
7589 to annotate data constructors (e.g. <literal>Just</literal>) as well as normal values (e.g. <literal>take</literal>).
7590 By way of example, to annotate the function <literal>foo</literal> with the annotation <literal>Just "Hello"</literal>
7591 you would do this:</para>
7594 {-# ANN foo (Just "Hello") #-}
7599 A number of restrictions apply to use of annotations:
7601 <listitem><para>The binder being annotated must be at the top level (i.e. no nested binders)</para></listitem>
7602 <listitem><para>The binder being annotated must be declared in the current module</para></listitem>
7603 <listitem><para>The expression you are annotating with must have a type with <literal>Typeable</literal> and <literal>Data</literal> instances</para></listitem>
7604 <listitem><para>The <ulink linkend="using-template-haskell">Template Haskell staging restrictions</ulink> apply to the
7605 expression being annotated with, so for example you cannot run a function from the module being compiled.</para>
7607 <para>To be precise, the annotation <literal>{-# ANN x e #-}</literal> is well staged if and only if <literal>$(e)</literal> would be
7608 (disregarding the usual type restrictions of the splice syntax, and the usual restriction on splicing inside a splice - <literal>$([|1|])</literal> is fine as an annotation, albeit redundant).</para></listitem>
7611 If you feel strongly that any of these restrictions are too onerous, <ulink url="http://hackage.haskell.org/trac/ghc/wiki/MailingListsAndIRC">
7612 please give the GHC team a shout</ulink>.
7615 <para>However, apart from these restrictions, many things are allowed, including expressions which are not fully evaluated!
7616 Annotation expressions will be evaluated by the compiler just like Template Haskell splices are. So, this annotation is fine:</para>
7619 {-# ANN f SillyAnnotation { foo = (id 10) + $([| 20 |]), bar = 'f } #-}
7624 <sect3 id="typeann-pragma">
7625 <title>Annotating types</title>
7627 <indexterm><primary>ANN type</primary></indexterm>
7628 <indexterm><primary>ANN</primary></indexterm>
7630 <para>You can annotate types with the <literal>ANN</literal> pragma by using the <literal>type</literal> keyword. For example:</para>
7633 {-# ANN type Foo (Just "A `Maybe String' annotation") #-}
7638 <sect3 id="modann-pragma">
7639 <title>Annotating modules</title>
7641 <indexterm><primary>ANN module</primary></indexterm>
7642 <indexterm><primary>ANN</primary></indexterm>
7644 <para>You can annotate modules with the <literal>ANN</literal> pragma by using the <literal>module</literal> keyword. For example:</para>
7647 {-# ANN module (Just "A `Maybe String' annotation") #-}
7652 <sect2 id="line-pragma">
7653 <title>LINE pragma</title>
7655 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
7656 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
7657 <para>This pragma is similar to C's <literal>#line</literal>
7658 pragma, and is mainly for use in automatically generated Haskell
7659 code. It lets you specify the line number and filename of the
7660 original code; for example</para>
7662 <programlisting>{-# LINE 42 "Foo.vhs" #-}</programlisting>
7664 <para>if you'd generated the current file from something called
7665 <filename>Foo.vhs</filename> and this line corresponds to line
7666 42 in the original. GHC will adjust its error messages to refer
7667 to the line/file named in the <literal>LINE</literal>
7672 <title>RULES pragma</title>
7674 <para>The RULES pragma lets you specify rewrite rules. It is
7675 described in <xref linkend="rewrite-rules"/>.</para>
7678 <sect2 id="specialize-pragma">
7679 <title>SPECIALIZE pragma</title>
7681 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7682 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
7683 <indexterm><primary>overloading, death to</primary></indexterm>
7685 <para>(UK spelling also accepted.) For key overloaded
7686 functions, you can create extra versions (NB: more code space)
7687 specialised to particular types. Thus, if you have an
7688 overloaded function:</para>
7691 hammeredLookup :: Ord key => [(key, value)] -> key -> value
7694 <para>If it is heavily used on lists with
7695 <literal>Widget</literal> keys, you could specialise it as
7699 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
7702 <para>A <literal>SPECIALIZE</literal> pragma for a function can
7703 be put anywhere its type signature could be put.</para>
7705 <para>A <literal>SPECIALIZE</literal> has the effect of generating
7706 (a) a specialised version of the function and (b) a rewrite rule
7707 (see <xref linkend="rewrite-rules"/>) that rewrites a call to the
7708 un-specialised function into a call to the specialised one.</para>
7710 <para>The type in a SPECIALIZE pragma can be any type that is less
7711 polymorphic than the type of the original function. In concrete terms,
7712 if the original function is <literal>f</literal> then the pragma
7714 {-# SPECIALIZE f :: <type> #-}
7716 is valid if and only if the definition
7718 f_spec :: <type>
7721 is valid. Here are some examples (where we only give the type signature
7722 for the original function, not its code):
7724 f :: Eq a => a -> b -> b
7725 {-# SPECIALISE f :: Int -> b -> b #-}
7727 g :: (Eq a, Ix b) => a -> b -> b
7728 {-# SPECIALISE g :: (Eq a) => a -> Int -> Int #-}
7730 h :: Eq a => a -> a -> a
7731 {-# SPECIALISE h :: (Eq a) => [a] -> [a] -> [a] #-}
7733 The last of these examples will generate a
7734 RULE with a somewhat-complex left-hand side (try it yourself), so it might not fire very
7735 well. If you use this kind of specialisation, let us know how well it works.
7738 <para>A <literal>SPECIALIZE</literal> pragma can optionally be followed with a
7739 <literal>INLINE</literal> or <literal>NOINLINE</literal> pragma, optionally
7740 followed by a phase, as described in <xref linkend="inline-noinline-pragma"/>.
7741 The <literal>INLINE</literal> pragma affects the specialised version of the
7742 function (only), and applies even if the function is recursive. The motivating
7745 -- A GADT for arrays with type-indexed representation
7747 ArrInt :: !Int -> ByteArray# -> Arr Int
7748 ArrPair :: !Int -> Arr e1 -> Arr e2 -> Arr (e1, e2)
7750 (!:) :: Arr e -> Int -> e
7751 {-# SPECIALISE INLINE (!:) :: Arr Int -> Int -> Int #-}
7752 {-# SPECIALISE INLINE (!:) :: Arr (a, b) -> Int -> (a, b) #-}
7753 (ArrInt _ ba) !: (I# i) = I# (indexIntArray# ba i)
7754 (ArrPair _ a1 a2) !: i = (a1 !: i, a2 !: i)
7756 Here, <literal>(!:)</literal> is a recursive function that indexes arrays
7757 of type <literal>Arr e</literal>. Consider a call to <literal>(!:)</literal>
7758 at type <literal>(Int,Int)</literal>. The second specialisation will fire, and
7759 the specialised function will be inlined. It has two calls to
7760 <literal>(!:)</literal>,
7761 both at type <literal>Int</literal>. Both these calls fire the first
7762 specialisation, whose body is also inlined. The result is a type-based
7763 unrolling of the indexing function.</para>
7764 <para>Warning: you can make GHC diverge by using <literal>SPECIALISE INLINE</literal>
7765 on an ordinarily-recursive function.</para>
7767 <para>Note: In earlier versions of GHC, it was possible to provide your own
7768 specialised function for a given type:
7771 {-# SPECIALIZE hammeredLookup :: [(Int, value)] -> Int -> value = intLookup #-}
7774 This feature has been removed, as it is now subsumed by the
7775 <literal>RULES</literal> pragma (see <xref linkend="rule-spec"/>).</para>
7779 <sect2 id="specialize-instance-pragma">
7780 <title>SPECIALIZE instance pragma
7784 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
7785 <indexterm><primary>overloading, death to</primary></indexterm>
7786 Same idea, except for instance declarations. For example:
7789 instance (Eq a) => Eq (Foo a) where {
7790 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
7794 The pragma must occur inside the <literal>where</literal> part
7795 of the instance declaration.
7798 Compatible with HBC, by the way, except perhaps in the placement
7804 <sect2 id="unpack-pragma">
7805 <title>UNPACK pragma</title>
7807 <indexterm><primary>UNPACK</primary></indexterm>
7809 <para>The <literal>UNPACK</literal> indicates to the compiler
7810 that it should unpack the contents of a constructor field into
7811 the constructor itself, removing a level of indirection. For
7815 data T = T {-# UNPACK #-} !Float
7816 {-# UNPACK #-} !Float
7819 <para>will create a constructor <literal>T</literal> containing
7820 two unboxed floats. This may not always be an optimisation: if
7821 the <function>T</function> constructor is scrutinised and the
7822 floats passed to a non-strict function for example, they will
7823 have to be reboxed (this is done automatically by the
7826 <para>Unpacking constructor fields should only be used in
7827 conjunction with <option>-O</option>, in order to expose
7828 unfoldings to the compiler so the reboxing can be removed as
7829 often as possible. For example:</para>
7833 f (T f1 f2) = f1 + f2
7836 <para>The compiler will avoid reboxing <function>f1</function>
7837 and <function>f2</function> by inlining <function>+</function>
7838 on floats, but only when <option>-O</option> is on.</para>
7840 <para>Any single-constructor data is eligible for unpacking; for
7844 data T = T {-# UNPACK #-} !(Int,Int)
7847 <para>will store the two <literal>Int</literal>s directly in the
7848 <function>T</function> constructor, by flattening the pair.
7849 Multi-level unpacking is also supported:
7852 data T = T {-# UNPACK #-} !S
7853 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
7856 will store two unboxed <literal>Int#</literal>s
7857 directly in the <function>T</function> constructor. The
7858 unpacker can see through newtypes, too.</para>
7860 <para>If a field cannot be unpacked, you will not get a warning,
7861 so it might be an idea to check the generated code with
7862 <option>-ddump-simpl</option>.</para>
7864 <para>See also the <option>-funbox-strict-fields</option> flag,
7865 which essentially has the effect of adding
7866 <literal>{-# UNPACK #-}</literal> to every strict
7867 constructor field.</para>
7870 <sect2 id="source-pragma">
7871 <title>SOURCE pragma</title>
7873 <indexterm><primary>SOURCE</primary></indexterm>
7874 <para>The <literal>{-# SOURCE #-}</literal> pragma is used only in <literal>import</literal> declarations,
7875 to break a module loop. It is described in detail in <xref linkend="mutual-recursion"/>.
7881 <!-- ======================= REWRITE RULES ======================== -->
7883 <sect1 id="rewrite-rules">
7884 <title>Rewrite rules
7886 <indexterm><primary>RULES pragma</primary></indexterm>
7887 <indexterm><primary>pragma, RULES</primary></indexterm>
7888 <indexterm><primary>rewrite rules</primary></indexterm></title>
7891 The programmer can specify rewrite rules as part of the source program
7897 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7902 Use the debug flag <option>-ddump-simpl-stats</option> to see what rules fired.
7903 If you need more information, then <option>-ddump-rule-firings</option> shows you
7904 each individual rule firing in detail.
7908 <title>Syntax</title>
7911 From a syntactic point of view:
7917 There may be zero or more rules in a <literal>RULES</literal> pragma, separated by semicolons (which
7918 may be generated by the layout rule).
7924 The layout rule applies in a pragma.
7925 Currently no new indentation level
7926 is set, so if you put several rules in single RULES pragma and wish to use layout to separate them,
7927 you must lay out the starting in the same column as the enclosing definitions.
7930 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
7931 "map/append" forall f xs ys. map f (xs ++ ys) = map f xs ++ map f ys
7934 Furthermore, the closing <literal>#-}</literal>
7935 should start in a column to the right of the opening <literal>{-#</literal>.
7941 Each rule has a name, enclosed in double quotes. The name itself has
7942 no significance at all. It is only used when reporting how many times the rule fired.
7948 A rule may optionally have a phase-control number (see <xref linkend="phase-control"/>),
7949 immediately after the name of the rule. Thus:
7952 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
7955 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
7956 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
7965 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
7966 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
7967 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
7968 by spaces, just like in a type <literal>forall</literal>.
7974 A pattern variable may optionally have a type signature.
7975 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
7976 For example, here is the <literal>foldr/build</literal> rule:
7979 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
7980 foldr k z (build g) = g k z
7983 Since <function>g</function> has a polymorphic type, it must have a type signature.
7990 The left hand side of a rule must consist of a top-level variable applied
7991 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
7994 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
7995 "wrong2" forall f. f True = True
7998 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
8005 A rule does not need to be in the same module as (any of) the
8006 variables it mentions, though of course they need to be in scope.
8012 All rules are implicitly exported from the module, and are therefore
8013 in force in any module that imports the module that defined the rule, directly
8014 or indirectly. (That is, if A imports B, which imports C, then C's rules are
8015 in force when compiling A.) The situation is very similar to that for instance
8023 Inside a RULE "<literal>forall</literal>" is treated as a keyword, regardless of
8024 any other flag settings. Furthermore, inside a RULE, the language extension
8025 <option>-XScopedTypeVariables</option> is automatically enabled; see
8026 <xref linkend="scoped-type-variables"/>.
8032 Like other pragmas, RULE pragmas are always checked for scope errors, and
8033 are typechecked. Typechecking means that the LHS and RHS of a rule are typechecked,
8034 and must have the same type. However, rules are only <emphasis>enabled</emphasis>
8035 if the <option>-fenable-rewrite-rules</option> flag is
8036 on (see <xref linkend="rule-semantics"/>).
8045 <sect2 id="rule-semantics">
8046 <title>Semantics</title>
8049 From a semantic point of view:
8054 Rules are enabled (that is, used during optimisation)
8055 by the <option>-fenable-rewrite-rules</option> flag.
8056 This flag is implied by <option>-O</option>, and may be switched
8057 off (as usual) by <option>-fno-enable-rewrite-rules</option>.
8058 (NB: enabling <option>-fenable-rewrite-rules</option> without <option>-O</option>
8059 may not do what you expect, though, because without <option>-O</option> GHC
8060 ignores all optimisation information in interface files;
8061 see <option>-fignore-interface-pragmas</option>, <xref linkend="options-f"/>.)
8062 Note that <option>-fenable-rewrite-rules</option> is an <emphasis>optimisation</emphasis> flag, and
8063 has no effect on parsing or typechecking.
8069 Rules are regarded as left-to-right rewrite rules.
8070 When GHC finds an expression that is a substitution instance of the LHS
8071 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
8072 By "a substitution instance" we mean that the LHS can be made equal to the
8073 expression by substituting for the pattern variables.
8080 GHC makes absolutely no attempt to verify that the LHS and RHS
8081 of a rule have the same meaning. That is undecidable in general, and
8082 infeasible in most interesting cases. The responsibility is entirely the programmer's!
8089 GHC makes no attempt to make sure that the rules are confluent or
8090 terminating. For example:
8093 "loop" forall x y. f x y = f y x
8096 This rule will cause the compiler to go into an infinite loop.
8103 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
8109 GHC currently uses a very simple, syntactic, matching algorithm
8110 for matching a rule LHS with an expression. It seeks a substitution
8111 which makes the LHS and expression syntactically equal modulo alpha
8112 conversion. The pattern (rule), but not the expression, is eta-expanded if
8113 necessary. (Eta-expanding the expression can lead to laziness bugs.)
8114 But not beta conversion (that's called higher-order matching).
8118 Matching is carried out on GHC's intermediate language, which includes
8119 type abstractions and applications. So a rule only matches if the
8120 types match too. See <xref linkend="rule-spec"/> below.
8126 GHC keeps trying to apply the rules as it optimises the program.
8127 For example, consider:
8136 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
8137 will substitute for <varname>s</varname> and <varname>t</varname>, giving an expression which does match.
8138 If <varname>s</varname> or <varname>t</varname> was (a) used more than once, and (b) large or a redex, then it would
8139 not be substituted, and the rule would not fire.
8146 Ordinary inlining happens at the same time as rule rewriting, which may lead to unexpected
8147 results. Consider this (artificial) example
8150 {-# RULES "f" f True = False #-}
8156 Since <literal>f</literal>'s right-hand side is small, it is inlined into <literal>g</literal>,
8161 Now <literal>g</literal> is inlined into <literal>h</literal>, but <literal>f</literal>'s RULE has
8163 If instead GHC had first inlined <literal>g</literal> into <literal>h</literal> then there
8164 would have been a better chance that <literal>f</literal>'s RULE might fire.
8167 The way to get predictable behaviour is to use a NOINLINE
8168 pragma on <literal>f</literal>, to ensure
8169 that it is not inlined until its RULEs have had a chance to fire.
8179 <title>List fusion</title>
8182 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
8183 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
8184 intermediate list should be eliminated entirely.
8188 The following are good producers:
8200 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
8206 Explicit lists (e.g. <literal>[True, False]</literal>)
8212 The cons constructor (e.g <literal>3:4:[]</literal>)
8218 <function>++</function>
8224 <function>map</function>
8230 <function>take</function>, <function>filter</function>
8236 <function>iterate</function>, <function>repeat</function>
8242 <function>zip</function>, <function>zipWith</function>
8251 The following are good consumers:
8263 <function>array</function> (on its second argument)
8269 <function>++</function> (on its first argument)
8275 <function>foldr</function>
8281 <function>map</function>
8287 <function>take</function>, <function>filter</function>
8293 <function>concat</function>
8299 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
8305 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
8306 will fuse with one but not the other)
8312 <function>partition</function>
8318 <function>head</function>
8324 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
8330 <function>sequence_</function>
8336 <function>msum</function>
8342 <function>sortBy</function>
8351 So, for example, the following should generate no intermediate lists:
8354 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
8360 This list could readily be extended; if there are Prelude functions that you use
8361 a lot which are not included, please tell us.
8365 If you want to write your own good consumers or producers, look at the
8366 Prelude definitions of the above functions to see how to do so.
8371 <sect2 id="rule-spec">
8372 <title>Specialisation
8376 Rewrite rules can be used to get the same effect as a feature
8377 present in earlier versions of GHC.
8378 For example, suppose that:
8381 genericLookup :: Ord a => Table a b -> a -> b
8382 intLookup :: Table Int b -> Int -> b
8385 where <function>intLookup</function> is an implementation of
8386 <function>genericLookup</function> that works very fast for
8387 keys of type <literal>Int</literal>. You might wish
8388 to tell GHC to use <function>intLookup</function> instead of
8389 <function>genericLookup</function> whenever the latter was called with
8390 type <literal>Table Int b -> Int -> b</literal>.
8391 It used to be possible to write
8394 {-# SPECIALIZE genericLookup :: Table Int b -> Int -> b = intLookup #-}
8397 This feature is no longer in GHC, but rewrite rules let you do the same thing:
8400 {-# RULES "genericLookup/Int" genericLookup = intLookup #-}
8403 This slightly odd-looking rule instructs GHC to replace
8404 <function>genericLookup</function> by <function>intLookup</function>
8405 <emphasis>whenever the types match</emphasis>.
8406 What is more, this rule does not need to be in the same
8407 file as <function>genericLookup</function>, unlike the
8408 <literal>SPECIALIZE</literal> pragmas which currently do (so that they
8409 have an original definition available to specialise).
8412 <para>It is <emphasis>Your Responsibility</emphasis> to make sure that
8413 <function>intLookup</function> really behaves as a specialised version
8414 of <function>genericLookup</function>!!!</para>
8416 <para>An example in which using <literal>RULES</literal> for
8417 specialisation will Win Big:
8420 toDouble :: Real a => a -> Double
8421 toDouble = fromRational . toRational
8423 {-# RULES "toDouble/Int" toDouble = i2d #-}
8424 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
8427 The <function>i2d</function> function is virtually one machine
8428 instruction; the default conversion—via an intermediate
8429 <literal>Rational</literal>—is obscenely expensive by
8436 <title>Controlling what's going on</title>
8444 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
8450 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
8451 If you add <option>-dppr-debug</option> you get a more detailed listing.
8457 The definition of (say) <function>build</function> in <filename>GHC/Base.lhs</filename> looks like this:
8460 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
8461 {-# INLINE build #-}
8465 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
8466 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
8467 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
8468 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
8475 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
8476 see how to write rules that will do fusion and yet give an efficient
8477 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
8487 <sect2 id="core-pragma">
8488 <title>CORE pragma</title>
8490 <indexterm><primary>CORE pragma</primary></indexterm>
8491 <indexterm><primary>pragma, CORE</primary></indexterm>
8492 <indexterm><primary>core, annotation</primary></indexterm>
8495 The external core format supports <quote>Note</quote> annotations;
8496 the <literal>CORE</literal> pragma gives a way to specify what these
8497 should be in your Haskell source code. Syntactically, core
8498 annotations are attached to expressions and take a Haskell string
8499 literal as an argument. The following function definition shows an
8503 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
8506 Semantically, this is equivalent to:
8514 However, when external core is generated (via
8515 <option>-fext-core</option>), there will be Notes attached to the
8516 expressions <function>show</function> and <varname>x</varname>.
8517 The core function declaration for <function>f</function> is:
8521 f :: %forall a . GHCziShow.ZCTShow a ->
8522 a -> GHCziBase.ZMZN GHCziBase.Char =
8523 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
8525 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
8527 (tpl1::GHCziBase.Int ->
8529 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8531 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
8532 (tpl3::GHCziBase.ZMZN a ->
8533 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
8541 Here, we can see that the function <function>show</function> (which
8542 has been expanded out to a case expression over the Show dictionary)
8543 has a <literal>%note</literal> attached to it, as does the
8544 expression <varname>eta</varname> (which used to be called
8545 <varname>x</varname>).
8552 <sect1 id="special-ids">
8553 <title>Special built-in functions</title>
8554 <para>GHC has a few built-in functions with special behaviour. These
8555 are now described in the module <ulink
8556 url="../libraries/ghc-prim/GHC-Prim.html"><literal>GHC.Prim</literal></ulink>
8557 in the library documentation.</para>
8561 <sect1 id="generic-classes">
8562 <title>Generic classes</title>
8565 The ideas behind this extension are described in detail in "Derivable type classes",
8566 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
8567 An example will give the idea:
8575 fromBin :: [Int] -> (a, [Int])
8577 toBin {| Unit |} Unit = []
8578 toBin {| a :+: b |} (Inl x) = 0 : toBin x
8579 toBin {| a :+: b |} (Inr y) = 1 : toBin y
8580 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
8582 fromBin {| Unit |} bs = (Unit, bs)
8583 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
8584 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
8585 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
8586 (y,bs'') = fromBin bs'
8589 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
8590 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
8591 which are defined thus in the library module <literal>Generics</literal>:
8595 data a :+: b = Inl a | Inr b
8596 data a :*: b = a :*: b
8599 Now you can make a data type into an instance of Bin like this:
8601 instance (Bin a, Bin b) => Bin (a,b)
8602 instance Bin a => Bin [a]
8604 That is, just leave off the "where" clause. Of course, you can put in the
8605 where clause and over-ride whichever methods you please.
8609 <title> Using generics </title>
8610 <para>To use generics you need to</para>
8613 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
8614 <option>-XGenerics</option> (to generate extra per-data-type code),
8615 and <option>-package lang</option> (to make the <literal>Generics</literal> library
8619 <para>Import the module <literal>Generics</literal> from the
8620 <literal>lang</literal> package. This import brings into
8621 scope the data types <literal>Unit</literal>,
8622 <literal>:*:</literal>, and <literal>:+:</literal>. (You
8623 don't need this import if you don't mention these types
8624 explicitly; for example, if you are simply giving instance
8625 declarations.)</para>
8630 <sect2> <title> Changes wrt the paper </title>
8632 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
8633 can be written infix (indeed, you can now use
8634 any operator starting in a colon as an infix type constructor). Also note that
8635 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
8636 Finally, note that the syntax of the type patterns in the class declaration
8637 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
8638 alone would ambiguous when they appear on right hand sides (an extension we
8639 anticipate wanting).
8643 <sect2> <title>Terminology and restrictions</title>
8645 Terminology. A "generic default method" in a class declaration
8646 is one that is defined using type patterns as above.
8647 A "polymorphic default method" is a default method defined as in Haskell 98.
8648 A "generic class declaration" is a class declaration with at least one
8649 generic default method.
8657 Alas, we do not yet implement the stuff about constructor names and
8664 A generic class can have only one parameter; you can't have a generic
8665 multi-parameter class.
8671 A default method must be defined entirely using type patterns, or entirely
8672 without. So this is illegal:
8675 op :: a -> (a, Bool)
8676 op {| Unit |} Unit = (Unit, True)
8679 However it is perfectly OK for some methods of a generic class to have
8680 generic default methods and others to have polymorphic default methods.
8686 The type variable(s) in the type pattern for a generic method declaration
8687 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:
8691 op {| p :*: q |} (x :*: y) = op (x :: p)
8699 The type patterns in a generic default method must take one of the forms:
8705 where "a" and "b" are type variables. Furthermore, all the type patterns for
8706 a single type constructor (<literal>:*:</literal>, say) must be identical; they
8707 must use the same type variables. So this is illegal:
8711 op {| a :+: b |} (Inl x) = True
8712 op {| p :+: q |} (Inr y) = False
8714 The type patterns must be identical, even in equations for different methods of the class.
8715 So this too is illegal:
8719 op1 {| a :*: b |} (x :*: y) = True
8722 op2 {| p :*: q |} (x :*: y) = False
8724 (The reason for this restriction is that we gather all the equations for a particular type constructor
8725 into a single generic instance declaration.)
8731 A generic method declaration must give a case for each of the three type constructors.
8737 The type for a generic method can be built only from:
8739 <listitem> <para> Function arrows </para> </listitem>
8740 <listitem> <para> Type variables </para> </listitem>
8741 <listitem> <para> Tuples </para> </listitem>
8742 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
8744 Here are some example type signatures for generic methods:
8747 op2 :: Bool -> (a,Bool)
8748 op3 :: [Int] -> a -> a
8751 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
8755 This restriction is an implementation restriction: we just haven't got around to
8756 implementing the necessary bidirectional maps over arbitrary type constructors.
8757 It would be relatively easy to add specific type constructors, such as Maybe and list,
8758 to the ones that are allowed.</para>
8763 In an instance declaration for a generic class, the idea is that the compiler
8764 will fill in the methods for you, based on the generic templates. However it can only
8769 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
8774 No constructor of the instance type has unboxed fields.
8778 (Of course, these things can only arise if you are already using GHC extensions.)
8779 However, you can still give an instance declarations for types which break these rules,
8780 provided you give explicit code to override any generic default methods.
8788 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
8789 what the compiler does with generic declarations.
8794 <sect2> <title> Another example </title>
8796 Just to finish with, here's another example I rather like:
8800 nCons {| Unit |} _ = 1
8801 nCons {| a :*: b |} _ = 1
8802 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
8805 tag {| Unit |} _ = 1
8806 tag {| a :*: b |} _ = 1
8807 tag {| a :+: b |} (Inl x) = tag x
8808 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
8814 <sect1 id="monomorphism">
8815 <title>Control over monomorphism</title>
8817 <para>GHC supports two flags that control the way in which generalisation is
8818 carried out at let and where bindings.
8822 <title>Switching off the dreaded Monomorphism Restriction</title>
8823 <indexterm><primary><option>-XNoMonomorphismRestriction</option></primary></indexterm>
8825 <para>Haskell's monomorphism restriction (see
8826 <ulink url="http://www.haskell.org/onlinereport/decls.html#sect4.5.5">Section
8828 of the Haskell Report)
8829 can be completely switched off by
8830 <option>-XNoMonomorphismRestriction</option>.
8835 <title>Monomorphic pattern bindings</title>
8836 <indexterm><primary><option>-XNoMonoPatBinds</option></primary></indexterm>
8837 <indexterm><primary><option>-XMonoPatBinds</option></primary></indexterm>
8839 <para> As an experimental change, we are exploring the possibility of
8840 making pattern bindings monomorphic; that is, not generalised at all.
8841 A pattern binding is a binding whose LHS has no function arguments,
8842 and is not a simple variable. For example:
8844 f x = x -- Not a pattern binding
8845 f = \x -> x -- Not a pattern binding
8846 f :: Int -> Int = \x -> x -- Not a pattern binding
8848 (g,h) = e -- A pattern binding
8849 (f) = e -- A pattern binding
8850 [x] = e -- A pattern binding
8852 Experimentally, GHC now makes pattern bindings monomorphic <emphasis>by
8853 default</emphasis>. Use <option>-XNoMonoPatBinds</option> to recover the
8862 ;;; Local Variables: ***
8864 ;;; sgml-parent-document: ("users_guide.xml" "book" "chapter" "sect1") ***
8865 ;;; ispell-local-dictionary: "british" ***
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