2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
6 <indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. See
23 <xref linkend="book-hslibs">.
26 <!-- LANGUAGE OPTIONS -->
27 <sect1 id="options-language">
28 <title>Language options</title>
30 <indexterm><primary>language</primary><secondary>option</secondary>
32 <indexterm><primary>options</primary><secondary>language</secondary>
34 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
37 <para> These flags control what variation of the language are
38 permitted. Leaving out all of them gives you standard Haskell
44 <term><option>-fglasgow-exts</option>:</term>
45 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
47 <para>This simultaneously enables all of the extensions to
48 Haskell 98 described in <xref
49 linkend="ghc-language-features">, except where otherwise
55 <term><option>-ffi</option> and <option>-fffi</option>:</term>
56 <indexterm><primary><option>-ffi</option></primary></indexterm>
57 <indexterm><primary><option>-fffi</option></primary></indexterm>
59 <para>This option enables the language extension defined in the
60 Haskell 98 Foreign Function Interface Addendum plus deprecated
61 syntax of previous versions of the FFI for backwards
67 <term><option>-fwith</option>:</term>
68 <indexterm><primary><option>-fwith</option></primary></indexterm>
70 <para>This option enables the deprecated <literal>with</literal>
71 keyword for implicit parameters; it is merely provided for backwards
73 It is independent of the <option>-fglasgow-exts</option>
79 <term><option>-fno-monomorphism-restriction</option>:</term>
80 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
82 <para> Switch off the Haskell 98 monomorphism restriction.
83 Independent of the <option>-fglasgow-exts</option>
89 <term><option>-fallow-overlapping-instances</option></term>
90 <term><option>-fallow-undecidable-instances</option></term>
91 <term><option>-fallow-incoherent-instances</option></term>
92 <term><option>-fcontext-stack</option></term>
93 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
94 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
97 <para> See <xref LinkEnd="instance-decls">. Only relevant
98 if you also use <option>-fglasgow-exts</option>.</para>
103 <term><option>-finline-phase</option></term>
104 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
106 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
107 you also use <option>-fglasgow-exts</option>.</para>
112 <term><option>-fgenerics</option></term>
113 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
115 <para>See <xref LinkEnd="generic-classes">. Independent of
116 <option>-fglasgow-exts</option>.</para>
121 <term><option>-fno-implicit-prelude</option></term>
123 <para><indexterm><primary>-fno-implicit-prelude
124 option</primary></indexterm> GHC normally imports
125 <filename>Prelude.hi</filename> files for you. If you'd
126 rather it didn't, then give it a
127 <option>-fno-implicit-prelude</option> option. The idea
128 is that you can then import a Prelude of your own. (But
129 don't call it <literal>Prelude</literal>; the Haskell
130 module namespace is flat, and you must not conflict with
131 any Prelude module.)</para>
133 <para>Even though you have not imported the Prelude, most of
134 the built-in syntax still refers to the built-in Haskell
135 Prelude types and values, as specified by the Haskell
136 Report. For example, the type <literal>[Int]</literal>
137 still means <literal>Prelude.[] Int</literal>; tuples
138 continue to refer to the standard Prelude tuples; the
139 translation for list comprehensions continues to use
140 <literal>Prelude.map</literal> etc.</para>
142 <para>However, <option>-fno-implicit-prelude</option> does
143 change the handling of certain built-in syntax: see
144 <xref LinkEnd="rebindable-syntax">.</para>
152 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
153 <!-- included from primitives.sgml -->
157 <!-- TYPE SYSTEM EXTENSIONS -->
158 <sect1 id="type-extensions">
159 <title>Type system extensions</title>
161 <sect2 id="nullary-types">
162 <title>Data types with no constructors</title>
164 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
165 a data type with no constructors. For example:</para>
168 data T a -- T :: * -> *
170 <para>Syntactically, the declaration lacks the "= constrs" part. The
171 type can be parameterised, but only over ordinary types, of kind *; since
172 Haskell does not have kind signatures, you cannot parameterise over higher-kinded
175 <para>Such data types have only one value, namely bottom.
176 Nevertheless, they can be useful when defining "phantom types".</para>
179 <sect2 id="infix-tycons">
180 <title>Infix type constructors</title>
183 GHC allows type constructors to be operators, and to be written infix, very much
184 like expressions. More specifically:
187 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
188 The lexical syntax is the same as that for data constructors.
191 Types can be written infix. For example <literal>Int :*: Bool</literal>.
195 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
196 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
199 Fixities may be declared for type constructors just as for data constructors. However,
200 one cannot distinguish between the two in a fixity declaration; a fixity declaration
201 sets the fixity for a data constructor and the corresponding type constructor. For example:
205 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
206 and similarly for <literal>:*:</literal>.
207 <literal>Int `a` Bool</literal>.
210 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
213 Data type and type-synonym declarations can be written infix. E.g.
215 data a :*: b = Foo a b
216 type a :+: b = Either a b
220 The only thing that differs between operators in types and operators in expressions is that
221 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
222 are not allowed in types. Reason: the uniform thing to do would be to make them type
223 variables, but that's not very useful. A less uniform but more useful thing would be to
224 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
225 lists. So for now we just exclude them.
232 <sect2 id="class-method-types">
233 <title>Class method types
236 Haskell 98 prohibits class method types to mention constraints on the
237 class type variable, thus:
240 fromList :: [a] -> s a
241 elem :: Eq a => a -> s a -> Bool
243 The type of <literal>elem</literal> is illegal in Haskell 98, because it
244 contains the constraint <literal>Eq a</literal>, constrains only the
245 class type variable (in this case <literal>a</literal>).
248 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
253 <sect2 id="multi-param-type-classes">
254 <title>Multi-parameter type classes
258 This section documents GHC's implementation of multi-parameter type
259 classes. There's lots of background in the paper <ULink
260 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
261 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
266 I'd like to thank people who reported shorcomings in the GHC 3.02
267 implementation. Our default decisions were all conservative ones, and
268 the experience of these heroic pioneers has given useful concrete
269 examples to support several generalisations. (These appear below as
270 design choices not implemented in 3.02.)
274 I've discussed these notes with Mark Jones, and I believe that Hugs
275 will migrate towards the same design choices as I outline here.
276 Thanks to him, and to many others who have offered very useful
284 There are the following restrictions on the form of a qualified
291 forall tv1..tvn (c1, ...,cn) => type
297 (Here, I write the "foralls" explicitly, although the Haskell source
298 language omits them; in Haskell 1.4, all the free type variables of an
299 explicit source-language type signature are universally quantified,
300 except for the class type variables in a class declaration. However,
301 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
310 <emphasis>Each universally quantified type variable
311 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
313 The reason for this is that a value with a type that does not obey
314 this restriction could not be used without introducing
315 ambiguity. Here, for example, is an illegal type:
319 forall a. Eq a => Int
323 When a value with this type was used, the constraint <literal>Eq tv</literal>
324 would be introduced where <literal>tv</literal> is a fresh type variable, and
325 (in the dictionary-translation implementation) the value would be
326 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
327 can never know which instance of <literal>Eq</literal> to use because we never
328 get any more information about <literal>tv</literal>.
335 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
336 universally quantified type variables <literal>tvi</literal></emphasis>.
338 For example, this type is OK because <literal>C a b</literal> mentions the
339 universally quantified type variable <literal>b</literal>:
343 forall a. C a b => burble
347 The next type is illegal because the constraint <literal>Eq b</literal> does not
348 mention <literal>a</literal>:
352 forall a. Eq b => burble
356 The reason for this restriction is milder than the other one. The
357 excluded types are never useful or necessary (because the offending
358 context doesn't need to be witnessed at this point; it can be floated
359 out). Furthermore, floating them out increases sharing. Lastly,
360 excluding them is a conservative choice; it leaves a patch of
361 territory free in case we need it later.
371 These restrictions apply to all types, whether declared in a type signature
376 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
377 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
384 f :: Eq (m a) => [m a] -> [m a]
391 This choice recovers principal types, a property that Haskell 1.4 does not have.
397 <title>Class declarations</title>
405 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
409 class Collection c a where
410 union :: c a -> c a -> c a
421 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
422 of "acyclic" involves only the superclass relationships. For example,
428 op :: D b => a -> b -> b
431 class C a => D a where { ... }
435 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
436 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
437 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
444 <emphasis>There are no restrictions on the context in a class declaration
445 (which introduces superclasses), except that the class hierarchy must
446 be acyclic</emphasis>. So these class declarations are OK:
450 class Functor (m k) => FiniteMap m k where
453 class (Monad m, Monad (t m)) => Transform t m where
454 lift :: m a -> (t m) a
463 <emphasis>In the signature of a class operation, every constraint
464 must mention at least one type variable that is not a class type
471 class Collection c a where
472 mapC :: Collection c b => (a->b) -> c a -> c b
476 is OK because the constraint <literal>(Collection a b)</literal> mentions
477 <literal>b</literal>, even though it also mentions the class variable
478 <literal>a</literal>. On the other hand:
483 op :: Eq a => (a,b) -> (a,b)
487 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
488 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
489 example is easily fixed by moving the offending context up to the
494 class Eq a => C a where
499 A yet more relaxed rule would allow the context of a class-op signature
500 to mention only class type variables. However, that conflicts with
501 Rule 1(b) for types above.
508 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
509 the class type variables</emphasis>. For example:
515 insert :: s -> a -> s
519 is not OK, because the type of <literal>empty</literal> doesn't mention
520 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
521 types, and has the same motivation.
523 Sometimes, offending class declarations exhibit misunderstandings. For
524 example, <literal>Coll</literal> might be rewritten
530 insert :: s a -> a -> s a
534 which makes the connection between the type of a collection of
535 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
536 Occasionally this really doesn't work, in which case you can split the
544 class CollE s => Coll s a where
545 insert :: s -> a -> s
558 <sect3 id="instance-decls">
559 <title>Instance declarations</title>
567 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
572 instance context1 => C type1 where ...
573 instance context2 => C type2 where ...
577 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
579 However, if you give the command line option
580 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
581 option</primary></indexterm> then overlapping instance declarations are permitted.
582 However, GHC arranges never to commit to using an instance declaration
583 if another instance declaration also applies, either now or later.
589 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
595 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
596 (but not identical to <literal>type1</literal>), or vice versa.
600 Notice that these rules
605 make it clear which instance decl to use
606 (pick the most specific one that matches)
613 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
614 Reason: you can pick which instance decl
615 "matches" based on the type.
620 However the rules are over-conservative. Two instance declarations can overlap,
621 but it can still be clear in particular situations which to use. For example:
623 instance C (Int,a) where ...
624 instance C (a,Bool) where ...
626 These are rejected by GHC's rules, but it is clear what to do when trying
627 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
628 cannot apply. Yell if this restriction bites you.
631 GHC is also conservative about committing to an overlapping instance. For example:
633 class C a where { op :: a -> a }
634 instance C [Int] where ...
635 instance C a => C [a] where ...
637 f :: C b => [b] -> [b]
640 From the RHS of f we get the constraint <literal>C [b]</literal>. But
641 GHC does not commit to the second instance declaration, because in a paricular
642 call of f, b might be instantiate to Int, so the first instance declaration
643 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
644 GHC will instead silently pick the second instance, without complaining about
645 the problem of subsequent instantiations.
648 Regrettably, GHC doesn't guarantee to detect overlapping instance
649 declarations if they appear in different modules. GHC can "see" the
650 instance declarations in the transitive closure of all the modules
651 imported by the one being compiled, so it can "see" all instance decls
652 when it is compiling <literal>Main</literal>. However, it currently chooses not
653 to look at ones that can't possibly be of use in the module currently
654 being compiled, in the interests of efficiency. (Perhaps we should
655 change that decision, at least for <literal>Main</literal>.)
662 <emphasis>There are no restrictions on the type in an instance
663 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
664 The instance "head" is the bit after the "=>" in an instance decl. For
665 example, these are OK:
669 instance C Int a where ...
671 instance D (Int, Int) where ...
673 instance E [[a]] where ...
677 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
678 For example, this is OK:
682 instance Stateful (ST s) (MutVar s) where ...
686 The "at least one not a type variable" restriction is to ensure that
687 context reduction terminates: each reduction step removes one type
688 constructor. For example, the following would make the type checker
689 loop if it wasn't excluded:
693 instance C a => C a where ...
697 There are two situations in which the rule is a bit of a pain. First,
698 if one allows overlapping instance declarations then it's quite
699 convenient to have a "default instance" declaration that applies if
700 something more specific does not:
709 Second, sometimes you might want to use the following to get the
710 effect of a "class synonym":
714 class (C1 a, C2 a, C3 a) => C a where { }
716 instance (C1 a, C2 a, C3 a) => C a where { }
720 This allows you to write shorter signatures:
732 f :: (C1 a, C2 a, C3 a) => ...
736 I'm on the lookout for a simple rule that preserves decidability while
737 allowing these idioms. The experimental flag
738 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
739 option</primary></indexterm> lifts this restriction, allowing all the types in an
740 instance head to be type variables.
747 <emphasis>Unlike Haskell 1.4, instance heads may use type
748 synonyms</emphasis>. As always, using a type synonym is just shorthand for
749 writing the RHS of the type synonym definition. For example:
753 type Point = (Int,Int)
754 instance C Point where ...
755 instance C [Point] where ...
759 is legal. However, if you added
763 instance C (Int,Int) where ...
767 as well, then the compiler will complain about the overlapping
768 (actually, identical) instance declarations. As always, type synonyms
769 must be fully applied. You cannot, for example, write:
774 instance Monad P where ...
778 This design decision is independent of all the others, and easily
779 reversed, but it makes sense to me.
786 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
787 be type variables</emphasis>. Thus
791 instance C a b => Eq (a,b) where ...
799 instance C Int b => Foo b where ...
803 is not OK. Again, the intent here is to make sure that context
804 reduction terminates.
806 Voluminous correspondence on the Haskell mailing list has convinced me
807 that it's worth experimenting with a more liberal rule. If you use
808 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
809 types in an instance context. Termination is ensured by having a
810 fixed-depth recursion stack. If you exceed the stack depth you get a
811 sort of backtrace, and the opportunity to increase the stack depth
812 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
825 <sect2 id="implicit-parameters">
826 <title>Implicit parameters
829 <para> Implicit paramters are implemented as described in
830 "Implicit parameters: dynamic scoping with static types",
831 J Lewis, MB Shields, E Meijer, J Launchbury,
832 27th ACM Symposium on Principles of Programming Languages (POPL'00),
835 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
837 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
838 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
839 context. In Haskell, all variables are statically bound. Dynamic
840 binding of variables is a notion that goes back to Lisp, but was later
841 discarded in more modern incarnations, such as Scheme. Dynamic binding
842 can be very confusing in an untyped language, and unfortunately, typed
843 languages, in particular Hindley-Milner typed languages like Haskell,
844 only support static scoping of variables.
847 However, by a simple extension to the type class system of Haskell, we
848 can support dynamic binding. Basically, we express the use of a
849 dynamically bound variable as a constraint on the type. These
850 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
851 function uses a dynamically-bound variable <literal>?x</literal>
852 of type <literal>t'</literal>". For
853 example, the following expresses the type of a sort function,
854 implicitly parameterized by a comparison function named <literal>cmp</literal>.
856 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
858 The dynamic binding constraints are just a new form of predicate in the type class system.
861 An implicit parameter is introduced by the special form <literal>?x</literal>,
862 where <literal>x</literal> is
863 any valid identifier. Use if this construct also introduces new
864 dynamic binding constraints. For example, the following definition
865 shows how we can define an implicitly parameterized sort function in
866 terms of an explicitly parameterized <literal>sortBy</literal> function:
868 sortBy :: (a -> a -> Bool) -> [a] -> [a]
870 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
873 Dynamic binding constraints behave just like other type class
874 constraints in that they are automatically propagated. Thus, when a
875 function is used, its implicit parameters are inherited by the
876 function that called it. For example, our <literal>sort</literal> function might be used
877 to pick out the least value in a list:
879 least :: (?cmp :: a -> a -> Bool) => [a] -> a
880 least xs = fst (sort xs)
882 Without lifting a finger, the <literal>?cmp</literal> parameter is
883 propagated to become a parameter of <literal>least</literal> as well. With explicit
884 parameters, the default is that parameters must always be explicit
885 propagated. With implicit parameters, the default is to always
889 An implicit parameter differs from other type class constraints in the
890 following way: All uses of a particular implicit parameter must have
891 the same type. This means that the type of <literal>(?x, ?x)</literal>
892 is <literal>(?x::a) => (a,a)</literal>, and not
893 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
897 An implicit parameter is bound using an expression of the form
898 <emphasis>expr</emphasis> <literal>with</literal> <emphasis>binds</emphasis>,
899 where <literal>with</literal> is a new keyword. This form binds the implicit
900 parameters arising in the body, not the free variables as a <literal>let</literal> or
901 <literal>where</literal> would do. For example, we define the <literal>min</literal> function by binding
902 <literal>cmp</literal>.
905 min = least with ?cmp = (<=)
907 Syntactically, the <emphasis>binds</emphasis> part of a <literal>with</literal> construct must be a
908 collection of simple bindings to variables (no function-style
909 bindings, and no type signatures); these bindings are neither
910 polymorphic or recursive.
913 Note the following additional constraints:
916 <para> You can't have an implicit parameter in the context of a class or instance
917 declaration. For example, both these declarations are illegal:
919 class (?x::Int) => C a where ...
920 instance (?x::a) => Foo [a] where ...
922 Reason: exactly which implicit parameter you pick up depends on exactly where
923 you invoke a function. But the ``invocation'' of instance declarations is done
924 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
925 Easiest thing is to outlaw the offending types.</para>
932 <sect2 id="linear-implicit-parameters">
933 <title>Linear implicit parameters
936 Linear implicit parameters are an idea developed by Koen Claessen,
937 Mark Shields, and Simon PJ. They address the long-standing
938 problem that monads seem over-kill for certain sorts of problem, notably:
941 <listitem> <para> distributing a supply of unique names </para> </listitem>
942 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
943 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
947 Linear implicit parameters are just like ordinary implicit parameters,
948 except that they are "linear" -- that is, they cannot be copied, and
949 must be explicitly "split" instead. Linear implicit parameters are
950 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
951 (The '/' in the '%' suggests the split!)
956 import GHC.Exts( Splittable )
958 data NameSupply = ...
960 splitNS :: NameSupply -> (NameSupply, NameSupply)
961 newName :: NameSupply -> Name
963 instance Splittable NameSupply where
967 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
968 f env (Lam x e) = Lam x' (f env e)
971 env' = extend env x x'
972 ...more equations for f...
974 Notice that the implicit parameter %ns is consumed
976 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
977 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
981 So the translation done by the type checker makes
982 the parameter explicit:
984 f :: NameSupply -> Env -> Expr -> Expr
985 f ns env (Lam x e) = Lam x' (f ns1 env e)
987 (ns1,ns2) = splitNS ns
989 env = extend env x x'
991 Notice the call to 'split' introduced by the type checker.
992 How did it know to use 'splitNS'? Because what it really did
993 was to introduce a call to the overloaded function 'split',
994 defined by the class <literal>Splittable</literal>:
996 class Splittable a where
999 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1000 split for name supplies. But we can simply write
1006 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1008 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1009 <literal>GHC.Exts</literal>.
1014 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1015 are entirely distinct implicit parameters: you
1016 can use them together and they won't intefere with each other. </para>
1019 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1021 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1022 in the context of a class or instance declaration. </para></listitem>
1026 <sect3><title>Warnings</title>
1029 The monomorphism restriction is even more important than usual.
1030 Consider the example above:
1032 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1033 f env (Lam x e) = Lam x' (f env e)
1036 env' = extend env x x'
1038 If we replaced the two occurrences of x' by (newName %ns), which is
1039 usually a harmless thing to do, we get:
1041 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1042 f env (Lam x e) = Lam (newName %ns) (f env e)
1044 env' = extend env x (newName %ns)
1046 But now the name supply is consumed in <emphasis>three</emphasis> places
1047 (the two calls to newName,and the recursive call to f), so
1048 the result is utterly different. Urk! We don't even have
1052 Well, this is an experimental change. With implicit
1053 parameters we have already lost beta reduction anyway, and
1054 (as John Launchbury puts it) we can't sensibly reason about
1055 Haskell programs without knowing their typing.
1062 <sect2 id="functional-dependencies">
1063 <title>Functional dependencies
1066 <para> Functional dependencies are implemented as described by Mark Jones
1067 in "Type Classes with Functional Dependencies", Mark P. Jones,
1068 In Proceedings of the 9th European Symposium on Programming,
1069 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1073 There should be more documentation, but there isn't (yet). Yell if you need it.
1078 <sect2 id="universal-quantification">
1079 <title>Arbitrary-rank polymorphism
1083 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1084 allows us to say exactly what this means. For example:
1092 g :: forall b. (b -> b)
1094 The two are treated identically.
1098 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1099 explicit universal quantification in
1101 For example, all the following types are legal:
1103 f1 :: forall a b. a -> b -> a
1104 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1106 f2 :: (forall a. a->a) -> Int -> Int
1107 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1109 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1111 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1112 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1113 The <literal>forall</literal> makes explicit the universal quantification that
1114 is implicitly added by Haskell.
1117 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1118 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1119 shows, the polymorphic type on the left of the function arrow can be overloaded.
1122 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1123 they have rank-2 types on the left of a function arrow.
1126 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1127 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1128 that restriction has now been lifted.)
1129 In particular, a forall-type (also called a "type scheme"),
1130 including an operational type class context, is legal:
1132 <listitem> <para> On the left of a function arrow </para> </listitem>
1133 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1134 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1135 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1136 field type signatures.</para> </listitem>
1137 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1138 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1140 There is one place you cannot put a <literal>forall</literal>:
1141 you cannot instantiate a type variable with a forall-type. So you cannot
1142 make a forall-type the argument of a type constructor. So these types are illegal:
1144 x1 :: [forall a. a->a]
1145 x2 :: (forall a. a->a, Int)
1146 x3 :: Maybe (forall a. a->a)
1148 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1149 a type variable any more!
1158 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1159 the types of the constructor arguments. Here are several examples:
1165 data T a = T1 (forall b. b -> b -> b) a
1167 data MonadT m = MkMonad { return :: forall a. a -> m a,
1168 bind :: forall a b. m a -> (a -> m b) -> m b
1171 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1177 The constructors have rank-2 types:
1183 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1184 MkMonad :: forall m. (forall a. a -> m a)
1185 -> (forall a b. m a -> (a -> m b) -> m b)
1187 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1193 Notice that you don't need to use a <literal>forall</literal> if there's an
1194 explicit context. For example in the first argument of the
1195 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1196 prefixed to the argument type. The implicit <literal>forall</literal>
1197 quantifies all type variables that are not already in scope, and are
1198 mentioned in the type quantified over.
1202 As for type signatures, implicit quantification happens for non-overloaded
1203 types too. So if you write this:
1206 data T a = MkT (Either a b) (b -> b)
1209 it's just as if you had written this:
1212 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1215 That is, since the type variable <literal>b</literal> isn't in scope, it's
1216 implicitly universally quantified. (Arguably, it would be better
1217 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1218 where that is what is wanted. Feedback welcomed.)
1222 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1223 the constructor to suitable values, just as usual. For example,
1234 a3 = MkSwizzle reverse
1237 a4 = let r x = Just x
1244 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1245 mkTs f x y = [T1 f x, T1 f y]
1251 The type of the argument can, as usual, be more general than the type
1252 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1253 does not need the <literal>Ord</literal> constraint.)
1257 When you use pattern matching, the bound variables may now have
1258 polymorphic types. For example:
1264 f :: T a -> a -> (a, Char)
1265 f (T1 w k) x = (w k x, w 'c' 'd')
1267 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1268 g (MkSwizzle s) xs f = s (map f (s xs))
1270 h :: MonadT m -> [m a] -> m [a]
1271 h m [] = return m []
1272 h m (x:xs) = bind m x $ \y ->
1273 bind m (h m xs) $ \ys ->
1280 In the function <function>h</function> we use the record selectors <literal>return</literal>
1281 and <literal>bind</literal> to extract the polymorphic bind and return functions
1282 from the <literal>MonadT</literal> data structure, rather than using pattern
1288 <title>Type inference</title>
1291 In general, type inference for arbitrary-rank types is undecideable.
1292 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1293 to get a decidable algorithm by requiring some help from the programmer.
1294 We do not yet have a formal specification of "some help" but the rule is this:
1297 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1298 provides an explicit polymorphic type for x, or GHC's type inference will assume
1299 that x's type has no foralls in it</emphasis>.
1302 What does it mean to "provide" an explicit type for x? You can do that by
1303 giving a type signature for x directly, using a pattern type signature
1304 (<xref linkend="scoped-type-variables">), thus:
1306 \ f :: (forall a. a->a) -> (f True, f 'c')
1308 Alternatively, you can give a type signature to the enclosing
1309 context, which GHC can "push down" to find the type for the variable:
1311 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1313 Here the type signature on the expression can be pushed inwards
1314 to give a type signature for f. Similarly, and more commonly,
1315 one can give a type signature for the function itself:
1317 h :: (forall a. a->a) -> (Bool,Char)
1318 h f = (f True, f 'c')
1320 You don't need to give a type signature if the lambda bound variable
1321 is a constructor argument. Here is an example we saw earlier:
1323 f :: T a -> a -> (a, Char)
1324 f (T1 w k) x = (w k x, w 'c' 'd')
1326 Here we do not need to give a type signature to <literal>w</literal>, because
1327 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1334 <sect3 id="implicit-quant">
1335 <title>Implicit quantification</title>
1338 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1339 user-written types, if and only if there is no explicit <literal>forall</literal>,
1340 GHC finds all the type variables mentioned in the type that are not already
1341 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1345 f :: forall a. a -> a
1352 h :: forall b. a -> b -> b
1358 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1361 f :: (a -> a) -> Int
1363 f :: forall a. (a -> a) -> Int
1365 f :: (forall a. a -> a) -> Int
1368 g :: (Ord a => a -> a) -> Int
1369 -- MEANS the illegal type
1370 g :: forall a. (Ord a => a -> a) -> Int
1372 g :: (forall a. Ord a => a -> a) -> Int
1374 The latter produces an illegal type, which you might think is silly,
1375 but at least the rule is simple. If you want the latter type, you
1376 can write your for-alls explicitly. Indeed, doing so is strongly advised
1383 <title>Liberalised type synonyms
1387 Type synonmys are like macros at the type level, and
1388 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1389 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1391 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1392 in a type synonym, thus:
1394 type Discard a = forall b. Show b => a -> b -> (a, String)
1399 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1406 You can write an unboxed tuple in a type synonym:
1408 type Pr = (# Int, Int #)
1416 You can apply a type synonym to a forall type:
1418 type Foo a = a -> a -> Bool
1420 f :: Foo (forall b. b->b)
1422 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1424 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1429 You can apply a type synonym to a partially applied type synonym:
1431 type Generic i o = forall x. i x -> o x
1434 foo :: Generic Id []
1436 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1438 foo :: forall x. x -> [x]
1446 GHC currently does kind checking before expanding synonyms (though even that
1450 After expanding type synonyms, GHC does validity checking on types, looking for
1451 the following mal-formedness which isn't detected simply by kind checking:
1454 Type constructor applied to a type involving for-alls.
1457 Unboxed tuple on left of an arrow.
1460 Partially-applied type synonym.
1464 this will be rejected:
1466 type Pr = (# Int, Int #)
1471 because GHC does not allow unboxed tuples on the left of a function arrow.
1476 <title>For-all hoisting</title>
1478 It is often convenient to use generalised type synonyms at the right hand
1479 end of an arrow, thus:
1481 type Discard a = forall b. a -> b -> a
1483 g :: Int -> Discard Int
1486 Simply expanding the type synonym would give
1488 g :: Int -> (forall b. Int -> b -> Int)
1490 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1492 g :: forall b. Int -> Int -> b -> Int
1494 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1495 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1496 performs the transformation:</emphasis>
1498 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1500 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1502 (In fact, GHC tries to retain as much synonym information as possible for use in
1503 error messages, but that is a usability issue.) This rule applies, of course, whether
1504 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1505 valid way to write <literal>g</literal>'s type signature:
1507 g :: Int -> Int -> forall b. b -> Int
1513 <sect2 id="existential-quantification">
1514 <title>Existentially quantified data constructors
1518 The idea of using existential quantification in data type declarations
1519 was suggested by Laufer (I believe, thought doubtless someone will
1520 correct me), and implemented in Hope+. It's been in Lennart
1521 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1522 proved very useful. Here's the idea. Consider the declaration:
1528 data Foo = forall a. MkFoo a (a -> Bool)
1535 The data type <literal>Foo</literal> has two constructors with types:
1541 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1548 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1549 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1550 For example, the following expression is fine:
1556 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1562 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1563 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1564 isUpper</function> packages a character with a compatible function. These
1565 two things are each of type <literal>Foo</literal> and can be put in a list.
1569 What can we do with a value of type <literal>Foo</literal>?. In particular,
1570 what happens when we pattern-match on <function>MkFoo</function>?
1576 f (MkFoo val fn) = ???
1582 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1583 are compatible, the only (useful) thing we can do with them is to
1584 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1591 f (MkFoo val fn) = fn val
1597 What this allows us to do is to package heterogenous values
1598 together with a bunch of functions that manipulate them, and then treat
1599 that collection of packages in a uniform manner. You can express
1600 quite a bit of object-oriented-like programming this way.
1603 <sect3 id="existential">
1604 <title>Why existential?
1608 What has this to do with <emphasis>existential</emphasis> quantification?
1609 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1615 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1621 But Haskell programmers can safely think of the ordinary
1622 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1623 adding a new existential quantification construct.
1629 <title>Type classes</title>
1632 An easy extension (implemented in <Command>hbc</Command>) is to allow
1633 arbitrary contexts before the constructor. For example:
1639 data Baz = forall a. Eq a => Baz1 a a
1640 | forall b. Show b => Baz2 b (b -> b)
1646 The two constructors have the types you'd expect:
1652 Baz1 :: forall a. Eq a => a -> a -> Baz
1653 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1659 But when pattern matching on <function>Baz1</function> the matched values can be compared
1660 for equality, and when pattern matching on <function>Baz2</function> the first matched
1661 value can be converted to a string (as well as applying the function to it).
1662 So this program is legal:
1669 f (Baz1 p q) | p == q = "Yes"
1671 f (Baz2 v fn) = show (fn v)
1677 Operationally, in a dictionary-passing implementation, the
1678 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1679 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1680 extract it on pattern matching.
1684 Notice the way that the syntax fits smoothly with that used for
1685 universal quantification earlier.
1691 <title>Restrictions</title>
1694 There are several restrictions on the ways in which existentially-quantified
1695 constructors can be use.
1704 When pattern matching, each pattern match introduces a new,
1705 distinct, type for each existential type variable. These types cannot
1706 be unified with any other type, nor can they escape from the scope of
1707 the pattern match. For example, these fragments are incorrect:
1715 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1716 is the result of <function>f1</function>. One way to see why this is wrong is to
1717 ask what type <function>f1</function> has:
1721 f1 :: Foo -> a -- Weird!
1725 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1730 f1 :: forall a. Foo -> a -- Wrong!
1734 The original program is just plain wrong. Here's another sort of error
1738 f2 (Baz1 a b) (Baz1 p q) = a==q
1742 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1743 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1744 from the two <function>Baz1</function> constructors.
1752 You can't pattern-match on an existentially quantified
1753 constructor in a <literal>let</literal> or <literal>where</literal> group of
1754 bindings. So this is illegal:
1758 f3 x = a==b where { Baz1 a b = x }
1762 You can only pattern-match
1763 on an existentially-quantified constructor in a <literal>case</literal> expression or
1764 in the patterns of a function definition.
1766 The reason for this restriction is really an implementation one.
1767 Type-checking binding groups is already a nightmare without
1768 existentials complicating the picture. Also an existential pattern
1769 binding at the top level of a module doesn't make sense, because it's
1770 not clear how to prevent the existentially-quantified type "escaping".
1771 So for now, there's a simple-to-state restriction. We'll see how
1779 You can't use existential quantification for <literal>newtype</literal>
1780 declarations. So this is illegal:
1784 newtype T = forall a. Ord a => MkT a
1788 Reason: a value of type <literal>T</literal> must be represented as a pair
1789 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1790 That contradicts the idea that <literal>newtype</literal> should have no
1791 concrete representation. You can get just the same efficiency and effect
1792 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1793 overloading involved, then there is more of a case for allowing
1794 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1795 because the <literal>data</literal> version does carry an implementation cost,
1796 but single-field existentially quantified constructors aren't much
1797 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1798 stands, unless there are convincing reasons to change it.
1806 You can't use <literal>deriving</literal> to define instances of a
1807 data type with existentially quantified data constructors.
1809 Reason: in most cases it would not make sense. For example:#
1812 data T = forall a. MkT [a] deriving( Eq )
1815 To derive <literal>Eq</literal> in the standard way we would need to have equality
1816 between the single component of two <function>MkT</function> constructors:
1820 (MkT a) == (MkT b) = ???
1823 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1824 It's just about possible to imagine examples in which the derived instance
1825 would make sense, but it seems altogether simpler simply to prohibit such
1826 declarations. Define your own instances!
1838 <sect2 id="scoped-type-variables">
1839 <title>Scoped type variables
1843 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1844 variable</emphasis>. For example
1850 f (xs::[a]) = ys ++ ys
1859 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1860 This brings the type variable <literal>a</literal> into scope; it scopes over
1861 all the patterns and right hand sides for this equation for <function>f</function>.
1862 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1866 Pattern type signatures are completely orthogonal to ordinary, separate
1867 type signatures. The two can be used independently or together.
1868 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1869 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1870 implicitly universally quantified. (If there are no type variables in
1871 scope, all type variables mentioned in the signature are universally
1872 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1873 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1874 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1875 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1876 it becomes possible to do so.
1880 Scoped type variables are implemented in both GHC and Hugs. Where the
1881 implementations differ from the specification below, those differences
1886 So much for the basic idea. Here are the details.
1890 <title>What a pattern type signature means</title>
1892 A type variable brought into scope by a pattern type signature is simply
1893 the name for a type. The restriction they express is that all occurrences
1894 of the same name mean the same type. For example:
1896 f :: [Int] -> Int -> Int
1897 f (xs::[a]) (y::a) = (head xs + y) :: a
1899 The pattern type signatures on the left hand side of
1900 <literal>f</literal> express the fact that <literal>xs</literal>
1901 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1902 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1903 specifies that this expression must have the same type <literal>a</literal>.
1904 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1905 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1906 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1907 rules, which specified that a pattern-bound type variable should be universally quantified.)
1908 For example, all of these are legal:</para>
1911 t (x::a) (y::a) = x+y*2
1913 f (x::a) (y::b) = [x,y] -- a unifies with b
1915 g (x::a) = x + 1::Int -- a unifies with Int
1917 h x = let k (y::a) = [x,y] -- a is free in the
1918 in k x -- environment
1920 k (x::a) True = ... -- a unifies with Int
1921 k (x::Int) False = ...
1924 w (x::a) = x -- a unifies with [b]
1930 <title>Scope and implicit quantification</title>
1938 All the type variables mentioned in a pattern,
1939 that are not already in scope,
1940 are brought into scope by the pattern. We describe this set as
1941 the <emphasis>type variables bound by the pattern</emphasis>.
1944 f (x::a) = let g (y::(a,b)) = fst y
1948 The pattern <literal>(x::a)</literal> brings the type variable
1949 <literal>a</literal> into scope, as well as the term
1950 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
1951 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
1952 and brings into scope the type variable <literal>b</literal>.
1958 The type variable(s) bound by the pattern have the same scope
1959 as the term variable(s) bound by the pattern. For example:
1962 f (x::a) = <...rhs of f...>
1963 (p::b, q::b) = (1,2)
1964 in <...body of let...>
1966 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
1967 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
1968 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
1969 just like <literal>p</literal> and <literal>q</literal> do.
1970 Indeed, the newly bound type variables also scope over any ordinary, separate
1971 type signatures in the <literal>let</literal> group.
1978 The type variables bound by the pattern may be
1979 mentioned in ordinary type signatures or pattern
1980 type signatures anywhere within their scope.
1987 In ordinary type signatures, any type variable mentioned in the
1988 signature that is in scope is <emphasis>not</emphasis> universally quantified.
1996 Ordinary type signatures do not bring any new type variables
1997 into scope (except in the type signature itself!). So this is illegal:
2004 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2005 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2006 and that is an incorrect typing.
2013 The pattern type signature is a monotype:
2018 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2022 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2023 not to type schemes.
2027 There is no implicit universal quantification on pattern type signatures (in contrast to
2028 ordinary type signatures).
2038 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2039 scope over the methods defined in the <literal>where</literal> part. For example:
2053 (Not implemented in Hugs yet, Dec 98).
2064 <title>Result type signatures</title>
2072 The result type of a function can be given a signature,
2077 f (x::a) :: [a] = [x,x,x]
2081 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2082 result type. Sometimes this is the only way of naming the type variable
2087 f :: Int -> [a] -> [a]
2088 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2089 in \xs -> map g (reverse xs `zip` xs)
2101 Result type signatures are not yet implemented in Hugs.
2107 <title>Where a pattern type signature can occur</title>
2110 A pattern type signature can occur in any pattern. For example:
2115 A pattern type signature can be on an arbitrary sub-pattern, not
2120 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2129 Pattern type signatures, including the result part, can be used
2130 in lambda abstractions:
2133 (\ (x::a, y) :: a -> x)
2140 Pattern type signatures, including the result part, can be used
2141 in <literal>case</literal> expressions:
2145 case e of { (x::a, y) :: a -> x }
2153 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2154 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2155 token or a parenthesised type of some sort). To see why,
2156 consider how one would parse this:
2170 Pattern type signatures can bind existential type variables.
2175 data T = forall a. MkT [a]
2178 f (MkT [t::a]) = MkT t3
2191 Pattern type signatures
2192 can be used in pattern bindings:
2195 f x = let (y, z::a) = x in ...
2196 f1 x = let (y, z::Int) = x in ...
2197 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2198 f3 :: (b->b) = \x -> x
2201 In all such cases, the binding is not generalised over the pattern-bound
2202 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2203 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2204 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2205 In contrast, the binding
2210 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2211 in <literal>f4</literal>'s scope.
2221 <sect2 id="sec-kinding">
2222 <title>Explicitly-kinded quantification</title>
2225 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2226 to give the kind explicitly as (machine-checked) documentation,
2227 just as it is nice to give a type signature for a function. On some occasions,
2228 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2229 John Hughes had to define the data type:
2231 data Set cxt a = Set [a]
2232 | Unused (cxt a -> ())
2234 The only use for the <literal>Unused</literal> constructor was to force the correct
2235 kind for the type variable <literal>cxt</literal>.
2238 GHC now instead allows you to specify the kind of a type variable directly, wherever
2239 a type variable is explicitly bound. Namely:
2241 <listitem><para><literal>data</literal> declarations:
2243 data Set (cxt :: * -> *) a = Set [a]
2244 </Screen></para></listitem>
2245 <listitem><para><literal>type</literal> declarations:
2247 type T (f :: * -> *) = f Int
2248 </Screen></para></listitem>
2249 <listitem><para><literal>class</literal> declarations:
2251 class (Eq a) => C (f :: * -> *) a where ...
2252 </Screen></para></listitem>
2253 <listitem><para><literal>forall</literal>'s in type signatures:
2255 f :: forall (cxt :: * -> *). Set cxt Int
2256 </Screen></para></listitem>
2261 The parentheses are required. Some of the spaces are required too, to
2262 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2263 will get a parse error, because "<literal>::*->*</literal>" is a
2264 single lexeme in Haskell.
2268 As part of the same extension, you can put kind annotations in types
2271 f :: (Int :: *) -> Int
2272 g :: forall a. a -> (a :: *)
2276 atype ::= '(' ctype '::' kind ')
2278 The parentheses are required.
2283 <!-- ==================== End of type system extensions ================= -->
2286 <!-- ==================== ASSERTIONS ================= -->
2288 <sect1 id="sec-assertions">
2290 <indexterm><primary>Assertions</primary></indexterm>
2294 If you want to make use of assertions in your standard Haskell code, you
2295 could define a function like the following:
2301 assert :: Bool -> a -> a
2302 assert False x = error "assertion failed!"
2309 which works, but gives you back a less than useful error message --
2310 an assertion failed, but which and where?
2314 One way out is to define an extended <function>assert</function> function which also
2315 takes a descriptive string to include in the error message and
2316 perhaps combine this with the use of a pre-processor which inserts
2317 the source location where <function>assert</function> was used.
2321 Ghc offers a helping hand here, doing all of this for you. For every
2322 use of <function>assert</function> in the user's source:
2328 kelvinToC :: Double -> Double
2329 kelvinToC k = assert (k >= 0.0) (k+273.15)
2335 Ghc will rewrite this to also include the source location where the
2342 assert pred val ==> assertError "Main.hs|15" pred val
2348 The rewrite is only performed by the compiler when it spots
2349 applications of <function>Exception.assert</function>, so you can still define and
2350 use your own versions of <function>assert</function>, should you so wish. If not,
2351 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2355 To have the compiler ignore uses of assert, use the compiler option
2356 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2357 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2361 Assertion failures can be caught, see the documentation for the
2362 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2369 <sect1 id="syntax-extns">
2370 <title>Syntactic extensions</title>
2372 <!-- ====================== PATTERN GUARDS ======================= -->
2374 <sect2 id="pattern-guards">
2375 <title>Pattern guards</title>
2378 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2379 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.)
2383 Suppose we have an abstract data type of finite maps, with a
2387 lookup :: FiniteMap -> Int -> Maybe Int
2390 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2391 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2395 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2396 | otherwise = var1 + var2
2398 m1 = lookup env var1
2399 m2 = lookup env var2
2400 ok1 = maybeToBool m1
2401 ok2 = maybeToBool m2
2402 val1 = expectJust m1
2403 val2 = expectJust m2
2407 The auxiliary functions are
2411 maybeToBool :: Maybe a -> Bool
2412 maybeToBool (Just x) = True
2413 maybeToBool Nothing = False
2415 expectJust :: Maybe a -> a
2416 expectJust (Just x) = x
2417 expectJust Nothing = error "Unexpected Nothing"
2421 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2422 ok2</literal> checks that both lookups succeed, using
2423 <function>maybeToBool</function> to convert the <function>Maybe</function>
2424 types to booleans. The (lazily evaluated) <function>expectJust</function>
2425 calls extract the values from the results of the lookups, and binds the
2426 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2427 respectively. If either lookup fails, then clunky takes the
2428 <literal>otherwise</literal> case and returns the sum of its arguments.
2432 This is certainly legal Haskell, but it is a tremendously verbose and
2433 un-obvious way to achieve the desired effect. Arguably, a more direct way
2434 to write clunky would be to use case expressions:
2438 clunky env var1 var1 = case lookup env var1 of
2440 Just val1 -> case lookup env var2 of
2442 Just val2 -> val1 + val2
2448 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2449 of pattern-matching, guarded equations as case expressions; that is
2450 precisely what the compiler does when compiling equations! The reason that
2451 Haskell provides guarded equations is because they allow us to write down
2452 the cases we want to consider, one at a time, independently of each other.
2453 This structure is hidden in the case version. Two of the right-hand sides
2454 are really the same (<function>fail</function>), and the whole expression
2455 tends to become more and more indented.
2459 Here is how I would write clunky:
2463 clunky env var1 var1
2464 | Just val1 <- lookup env var1
2465 , Just val2 <- lookup env var2
2467 ...other equations for clunky...
2471 The semantics should be clear enough. The qualifers are matched in order.
2472 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2473 right hand side is evaluated and matched against the pattern on the left.
2474 If the match fails then the whole guard fails and the next equation is
2475 tried. If it succeeds, then the appropriate binding takes place, and the
2476 next qualifier is matched, in the augmented environment. Unlike list
2477 comprehensions, however, the type of the expression to the right of the
2478 <literal><-</literal> is the same as the type of the pattern to its
2479 left. The bindings introduced by pattern guards scope over all the
2480 remaining guard qualifiers, and over the right hand side of the equation.
2484 Just as with list comprehensions, boolean expressions can be freely mixed
2485 with among the pattern guards. For example:
2496 Haskell's current guards therefore emerge as a special case, in which the
2497 qualifier list has just one element, a boolean expression.
2501 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2503 <sect2 id="parallel-list-comprehensions">
2504 <title>Parallel List Comprehensions</title>
2505 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2507 <indexterm><primary>parallel list comprehensions</primary>
2510 <para>Parallel list comprehensions are a natural extension to list
2511 comprehensions. List comprehensions can be thought of as a nice
2512 syntax for writing maps and filters. Parallel comprehensions
2513 extend this to include the zipWith family.</para>
2515 <para>A parallel list comprehension has multiple independent
2516 branches of qualifier lists, each separated by a `|' symbol. For
2517 example, the following zips together two lists:</para>
2520 [ (x, y) | x <- xs | y <- ys ]
2523 <para>The behavior of parallel list comprehensions follows that of
2524 zip, in that the resulting list will have the same length as the
2525 shortest branch.</para>
2527 <para>We can define parallel list comprehensions by translation to
2528 regular comprehensions. Here's the basic idea:</para>
2530 <para>Given a parallel comprehension of the form: </para>
2533 [ e | p1 <- e11, p2 <- e12, ...
2534 | q1 <- e21, q2 <- e22, ...
2539 <para>This will be translated to: </para>
2542 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2543 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2548 <para>where `zipN' is the appropriate zip for the given number of
2553 <sect2 id="rebindable-syntax">
2554 <title>Rebindable syntax</title>
2557 <para> Your may want to
2558 define your own numeric class hierarchy. It completely
2559 defeats that purpose if the literal "1" means
2560 "<literal>Prelude.fromInteger 1</literal>", which is what
2561 the Haskell Report specifies. So the
2562 <option>-fno-implicit-prelude</option> flag causes the
2563 following pieces of built-in syntax to refer to <emphasis>whatever
2564 is in scope</emphasis>, not the Prelude versions:</para>
2568 <para>Integer and fractional literals mean
2569 "<literal>fromInteger 1</literal>" and
2570 "<literal>fromRational 3.2</literal>", not the
2571 Prelude-qualified versions; both in expressions and in
2576 <para>Negation (e.g. "<literal>- (f x)</literal>")
2577 means "<literal>negate (f x)</literal>" (not
2578 <literal>Prelude.negate</literal>).</para>
2582 <para>In an n+k pattern, the standard Prelude
2583 <literal>Ord</literal> class is still used for comparison,
2584 but the necessary subtraction uses whatever
2585 "<literal>(-)</literal>" is in scope (not
2586 "<literal>Prelude.(-)</literal>").</para>
2590 <para>"Do" notation is translated using whatever functions
2591 <literal>(>>=)</literal>, <literal>(>>)</literal>, <literal>fail</literal>,
2592 and <literal>return</literal>, are in scope (not the Prelude versions).
2593 List comprehensions, and parallel array comprehensions, are unaffected.
2597 <para>Be warned: this is an experimental facility, with fewer checks than
2598 usual. In particular, it is essential that the functions GHC finds in scope
2599 must have the appropriate types, namely:
2601 fromInteger :: forall a. (...) => Integer -> a
2602 fromRational :: forall a. (...) => Rational -> a
2603 negate :: forall a. (...) => a -> a
2604 (-) :: forall a. (...) => a -> a -> a
2605 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
2606 (>>) :: forall m a. (...) => m a -> m b -> m b
2607 return :: forall m a. (...) => a -> m a
2608 fail :: forall m a. (...) => String -> m a
2610 (The (...) part can be any context including the empty context; that part
2612 If the functions don't have the right type, very peculiar things may
2613 happen. Use <literal>-dcore-lint</literal> to
2614 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
2619 <!-- =============================== PRAGMAS =========================== -->
2621 <sect1 id="pragmas">
2622 <title>Pragmas</title>
2624 <indexterm><primary>pragma</primary></indexterm>
2626 <para>GHC supports several pragmas, or instructions to the
2627 compiler placed in the source code. Pragmas don't normally affect
2628 the meaning of the program, but they might affect the efficiency
2629 of the generated code.</para>
2631 <para>Pragmas all take the form
2633 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2635 where <replaceable>word</replaceable> indicates the type of
2636 pragma, and is followed optionally by information specific to that
2637 type of pragma. Case is ignored in
2638 <replaceable>word</replaceable>. The various values for
2639 <replaceable>word</replaceable> that GHC understands are described
2640 in the following sections; any pragma encountered with an
2641 unrecognised <replaceable>word</replaceable> is (silently)
2644 <sect2 id="inline-pragma">
2645 <title>INLINE pragma
2647 <indexterm><primary>INLINE pragma</primary></indexterm>
2648 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2651 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2652 functions/values that are “small enough,” thus avoiding the call
2653 overhead and possibly exposing other more-wonderful optimisations.
2657 You will probably see these unfoldings (in Core syntax) in your
2662 Normally, if GHC decides a function is “too expensive” to inline, it
2663 will not do so, nor will it export that unfolding for other modules to
2668 The sledgehammer you can bring to bear is the
2669 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2672 key_function :: Int -> String -> (Bool, Double)
2674 #ifdef __GLASGOW_HASKELL__
2675 {-# INLINE key_function #-}
2679 (You don't need to do the C pre-processor carry-on unless you're going
2680 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2684 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2685 “cost” to be very low. The normal unfolding machinery will then be
2686 very keen to inline it.
2690 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2691 signature could be put.
2695 <literal>INLINE</literal> pragmas are a particularly good idea for the
2696 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2697 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2700 #ifdef __GLASGOW_HASKELL__
2701 {-# INLINE thenUs #-}
2702 {-# INLINE returnUs #-}
2710 <sect2 id="noinline-pragma">
2711 <title>NOINLINE pragma
2714 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2715 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2716 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2717 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2720 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2721 it stops the named function from being inlined by the compiler. You
2722 shouldn't ever need to do this, unless you're very cautious about code
2726 <para><literal>NOTINLINE</literal> is a synonym for
2727 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2728 by Haskell 98 as the standard way to disable inlining, so it should be
2729 used if you want your code to be portable).</para>
2733 <sect2 id="specialize-pragma">
2734 <title>SPECIALIZE pragma</title>
2736 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2737 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2738 <indexterm><primary>overloading, death to</primary></indexterm>
2740 <para>(UK spelling also accepted.) For key overloaded
2741 functions, you can create extra versions (NB: more code space)
2742 specialised to particular types. Thus, if you have an
2743 overloaded function:</para>
2746 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2749 <para>If it is heavily used on lists with
2750 <literal>Widget</literal> keys, you could specialise it as
2754 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2757 <para>To get very fancy, you can also specify a named function
2758 to use for the specialised value, as in:</para>
2761 {-# RULES hammeredLookup = blah #-}
2764 <para>where <literal>blah</literal> is an implementation of
2765 <literal>hammerdLookup</literal> written specialy for
2766 <literal>Widget</literal> lookups. It's <emphasis>Your
2767 Responsibility</emphasis> to make sure that
2768 <function>blah</function> really behaves as a specialised
2769 version of <function>hammeredLookup</function>!!!</para>
2771 <para>Note we use the <literal>RULE</literal> pragma here to
2772 indicate that <literal>hammeredLookup</literal> applied at a
2773 certain type should be replaced by <literal>blah</literal>. See
2774 <xref linkend="rules"> for more information on
2775 <literal>RULES</literal>.</para>
2777 <para>An example in which using <literal>RULES</literal> for
2778 specialisation will Win Big:
2781 toDouble :: Real a => a -> Double
2782 toDouble = fromRational . toRational
2784 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2785 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2788 The <function>i2d</function> function is virtually one machine
2789 instruction; the default conversion—via an intermediate
2790 <literal>Rational</literal>—is obscenely expensive by
2793 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2794 be put anywhere its type signature could be put.</para>
2798 <sect2 id="specialize-instance-pragma">
2799 <title>SPECIALIZE instance pragma
2803 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2804 <indexterm><primary>overloading, death to</primary></indexterm>
2805 Same idea, except for instance declarations. For example:
2808 instance (Eq a) => Eq (Foo a) where {
2809 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2813 The pragma must occur inside the <literal>where</literal> part
2814 of the instance declaration.
2817 Compatible with HBC, by the way, except perhaps in the placement
2823 <sect2 id="line-pragma">
2828 <indexterm><primary>LINE pragma</primary></indexterm>
2829 <indexterm><primary>pragma, LINE</primary></indexterm>
2833 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2834 automatically generated Haskell code. It lets you specify the line
2835 number and filename of the original code; for example
2841 {-# LINE 42 "Foo.vhs" #-}
2847 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2848 and this line corresponds to line 42 in the original. GHC will adjust
2849 its error messages to refer to the line/file named in the <literal>LINE</literal>
2856 <title>RULES pragma</title>
2859 The RULES pragma lets you specify rewrite rules. It is described in
2860 <xref LinkEnd="rewrite-rules">.
2865 <sect2 id="deprecated-pragma">
2866 <title>DEPRECATED pragma</title>
2869 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2870 There are two forms.
2874 You can deprecate an entire module thus:</para>
2876 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2880 When you compile any module that import <literal>Wibble</literal>, GHC will print
2881 the specified message.</para>
2886 You can deprecate a function, class, or type, with the following top-level declaration:
2889 {-# DEPRECATED f, C, T "Don't use these" #-}
2892 When you compile any module that imports and uses any of the specifed entities,
2893 GHC will print the specified message.
2897 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2903 <!-- ======================= REWRITE RULES ======================== -->
2905 <sect1 id="rewrite-rules">
2906 <title>Rewrite rules
2908 <indexterm><primary>RULES pagma</primary></indexterm>
2909 <indexterm><primary>pragma, RULES</primary></indexterm>
2910 <indexterm><primary>rewrite rules</primary></indexterm></title>
2913 The programmer can specify rewrite rules as part of the source program
2914 (in a pragma). GHC applies these rewrite rules wherever it can.
2922 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2929 <title>Syntax</title>
2932 From a syntactic point of view:
2938 Each rule has a name, enclosed in double quotes. The name itself has
2939 no significance at all. It is only used when reporting how many times the rule fired.
2945 There may be zero or more rules in a <literal>RULES</literal> pragma.
2951 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2952 is set, so you must lay out your rules starting in the same column as the
2953 enclosing definitions.
2959 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2960 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2961 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2962 by spaces, just like in a type <literal>forall</literal>.
2968 A pattern variable may optionally have a type signature.
2969 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2970 For example, here is the <literal>foldr/build</literal> rule:
2973 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2974 foldr k z (build g) = g k z
2977 Since <function>g</function> has a polymorphic type, it must have a type signature.
2984 The left hand side of a rule must consist of a top-level variable applied
2985 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2988 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2989 "wrong2" forall f. f True = True
2992 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2999 A rule does not need to be in the same module as (any of) the
3000 variables it mentions, though of course they need to be in scope.
3006 Rules are automatically exported from a module, just as instance declarations are.
3017 <title>Semantics</title>
3020 From a semantic point of view:
3026 Rules are only applied if you use the <option>-O</option> flag.
3032 Rules are regarded as left-to-right rewrite rules.
3033 When GHC finds an expression that is a substitution instance of the LHS
3034 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3035 By "a substitution instance" we mean that the LHS can be made equal to the
3036 expression by substituting for the pattern variables.
3043 The LHS and RHS of a rule are typechecked, and must have the
3051 GHC makes absolutely no attempt to verify that the LHS and RHS
3052 of a rule have the same meaning. That is undecideable in general, and
3053 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3060 GHC makes no attempt to make sure that the rules are confluent or
3061 terminating. For example:
3064 "loop" forall x,y. f x y = f y x
3067 This rule will cause the compiler to go into an infinite loop.
3074 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3080 GHC currently uses a very simple, syntactic, matching algorithm
3081 for matching a rule LHS with an expression. It seeks a substitution
3082 which makes the LHS and expression syntactically equal modulo alpha
3083 conversion. The pattern (rule), but not the expression, is eta-expanded if
3084 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3085 But not beta conversion (that's called higher-order matching).
3089 Matching is carried out on GHC's intermediate language, which includes
3090 type abstractions and applications. So a rule only matches if the
3091 types match too. See <xref LinkEnd="rule-spec"> below.
3097 GHC keeps trying to apply the rules as it optimises the program.
3098 For example, consider:
3107 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3108 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3109 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3110 not be substituted, and the rule would not fire.
3117 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3118 that appears on the LHS of a rule</emphasis>, because once you have substituted
3119 for something you can't match against it (given the simple minded
3120 matching). So if you write the rule
3123 "map/map" forall f,g. map f . map g = map (f.g)
3126 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3127 It will only match something written with explicit use of ".".
3128 Well, not quite. It <emphasis>will</emphasis> match the expression
3134 where <function>wibble</function> is defined:
3137 wibble f g = map f . map g
3140 because <function>wibble</function> will be inlined (it's small).
3142 Later on in compilation, GHC starts inlining even things on the
3143 LHS of rules, but still leaves the rules enabled. This inlining
3144 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3151 All rules are implicitly exported from the module, and are therefore
3152 in force in any module that imports the module that defined the rule, directly
3153 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3154 in force when compiling A.) The situation is very similar to that for instance
3166 <title>List fusion</title>
3169 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3170 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3171 intermediate list should be eliminated entirely.
3175 The following are good producers:
3187 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3193 Explicit lists (e.g. <literal>[True, False]</literal>)
3199 The cons constructor (e.g <literal>3:4:[]</literal>)
3205 <function>++</function>
3211 <function>map</function>
3217 <function>filter</function>
3223 <function>iterate</function>, <function>repeat</function>
3229 <function>zip</function>, <function>zipWith</function>
3238 The following are good consumers:
3250 <function>array</function> (on its second argument)
3256 <function>length</function>
3262 <function>++</function> (on its first argument)
3268 <function>foldr</function>
3274 <function>map</function>
3280 <function>filter</function>
3286 <function>concat</function>
3292 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3298 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3299 will fuse with one but not the other)
3305 <function>partition</function>
3311 <function>head</function>
3317 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3323 <function>sequence_</function>
3329 <function>msum</function>
3335 <function>sortBy</function>
3344 So, for example, the following should generate no intermediate lists:
3347 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3353 This list could readily be extended; if there are Prelude functions that you use
3354 a lot which are not included, please tell us.
3358 If you want to write your own good consumers or producers, look at the
3359 Prelude definitions of the above functions to see how to do so.
3364 <sect2 id="rule-spec">
3365 <title>Specialisation
3369 Rewrite rules can be used to get the same effect as a feature
3370 present in earlier version of GHC:
3373 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3376 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3377 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3378 specialising the original definition of <function>fromIntegral</function> the programmer is
3379 promising that it is safe to use <function>int8ToInt16</function> instead.
3383 This feature is no longer in GHC. But rewrite rules let you do the
3388 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3392 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3393 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3394 GHC adds the type and dictionary applications to get the typed rule
3397 forall (d1::Integral Int8) (d2::Num Int16) .
3398 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3402 this rule does not need to be in the same file as fromIntegral,
3403 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3404 have an original definition available to specialise).
3410 <title>Controlling what's going on</title>
3418 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3424 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3425 If you add <option>-dppr-debug</option> you get a more detailed listing.
3431 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3434 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3435 {-# INLINE build #-}
3439 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3440 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3441 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3442 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3449 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3450 see how to write rules that will do fusion and yet give an efficient
3451 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3463 <sect1 id="generic-classes">
3464 <title>Generic classes</title>
3466 <para>(Note: support for generic classes is currently broken in
3470 The ideas behind this extension are described in detail in "Derivable type classes",
3471 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3472 An example will give the idea:
3480 fromBin :: [Int] -> (a, [Int])
3482 toBin {| Unit |} Unit = []
3483 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3484 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3485 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3487 fromBin {| Unit |} bs = (Unit, bs)
3488 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3489 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3490 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3491 (y,bs'') = fromBin bs'
3494 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3495 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3496 which are defined thus in the library module <literal>Generics</literal>:
3500 data a :+: b = Inl a | Inr b
3501 data a :*: b = a :*: b
3504 Now you can make a data type into an instance of Bin like this:
3506 instance (Bin a, Bin b) => Bin (a,b)
3507 instance Bin a => Bin [a]
3509 That is, just leave off the "where" clasuse. Of course, you can put in the
3510 where clause and over-ride whichever methods you please.
3514 <title> Using generics </title>
3515 <para>To use generics you need to</para>
3518 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3519 <option>-fgenerics</option> (to generate extra per-data-type code),
3520 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3524 <para>Import the module <literal>Generics</literal> from the
3525 <literal>lang</literal> package. This import brings into
3526 scope the data types <literal>Unit</literal>,
3527 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3528 don't need this import if you don't mention these types
3529 explicitly; for example, if you are simply giving instance
3530 declarations.)</para>
3535 <sect2> <title> Changes wrt the paper </title>
3537 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3538 can be written infix (indeed, you can now use
3539 any operator starting in a colon as an infix type constructor). Also note that
3540 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3541 Finally, note that the syntax of the type patterns in the class declaration
3542 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3543 alone would ambiguous when they appear on right hand sides (an extension we
3544 anticipate wanting).
3548 <sect2> <title>Terminology and restrictions</title>
3550 Terminology. A "generic default method" in a class declaration
3551 is one that is defined using type patterns as above.
3552 A "polymorphic default method" is a default method defined as in Haskell 98.
3553 A "generic class declaration" is a class declaration with at least one
3554 generic default method.
3562 Alas, we do not yet implement the stuff about constructor names and
3569 A generic class can have only one parameter; you can't have a generic
3570 multi-parameter class.
3576 A default method must be defined entirely using type patterns, or entirely
3577 without. So this is illegal:
3580 op :: a -> (a, Bool)
3581 op {| Unit |} Unit = (Unit, True)
3584 However it is perfectly OK for some methods of a generic class to have
3585 generic default methods and others to have polymorphic default methods.
3591 The type variable(s) in the type pattern for a generic method declaration
3592 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:
3596 op {| p :*: q |} (x :*: y) = op (x :: p)
3604 The type patterns in a generic default method must take one of the forms:
3610 where "a" and "b" are type variables. Furthermore, all the type patterns for
3611 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3612 must use the same type variables. So this is illegal:
3616 op {| a :+: b |} (Inl x) = True
3617 op {| p :+: q |} (Inr y) = False
3619 The type patterns must be identical, even in equations for different methods of the class.
3620 So this too is illegal:
3624 op1 {| a :*: b |} (x :*: y) = True
3627 op2 {| p :*: q |} (x :*: y) = False
3629 (The reason for this restriction is that we gather all the equations for a particular type consructor
3630 into a single generic instance declaration.)
3636 A generic method declaration must give a case for each of the three type constructors.
3642 The type for a generic method can be built only from:
3644 <listitem> <para> Function arrows </para> </listitem>
3645 <listitem> <para> Type variables </para> </listitem>
3646 <listitem> <para> Tuples </para> </listitem>
3647 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3649 Here are some example type signatures for generic methods:
3652 op2 :: Bool -> (a,Bool)
3653 op3 :: [Int] -> a -> a
3656 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3660 This restriction is an implementation restriction: we just havn't got around to
3661 implementing the necessary bidirectional maps over arbitrary type constructors.
3662 It would be relatively easy to add specific type constructors, such as Maybe and list,
3663 to the ones that are allowed.</para>
3668 In an instance declaration for a generic class, the idea is that the compiler
3669 will fill in the methods for you, based on the generic templates. However it can only
3674 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3679 No constructor of the instance type has unboxed fields.
3683 (Of course, these things can only arise if you are already using GHC extensions.)
3684 However, you can still give an instance declarations for types which break these rules,
3685 provided you give explicit code to override any generic default methods.
3693 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3694 what the compiler does with generic declarations.
3699 <sect2> <title> Another example </title>
3701 Just to finish with, here's another example I rather like:
3705 nCons {| Unit |} _ = 1
3706 nCons {| a :*: b |} _ = 1
3707 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3710 tag {| Unit |} _ = 1
3711 tag {| a :*: b |} _ = 1
3712 tag {| a :+: b |} (Inl x) = tag x
3713 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3719 <sect1 id="newtype-deriving">
3720 <title>Generalised derived instances for newtypes</title>
3723 When you define an abstract type using <literal>newtype</literal>, you may want
3724 the new type to inherit some instances from its representation. In
3725 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3726 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3727 other classes you have to write an explicit instance declaration. For
3728 example, if you define
3731 newtype Dollars = Dollars Int
3734 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3735 explicitly define an instance of <literal>Num</literal>:
3738 instance Num Dollars where
3739 Dollars a + Dollars b = Dollars (a+b)
3742 All the instance does is apply and remove the <literal>newtype</literal>
3743 constructor. It is particularly galling that, since the constructor
3744 doesn't appear at run-time, this instance declaration defines a
3745 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3746 dictionary, only slower!
3749 <sect2> <title> Generalising the deriving clause </title>
3751 GHC now permits such instances to be derived instead, so one can write
3753 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3756 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3757 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3758 derives an instance declaration of the form
3761 instance Num Int => Num Dollars
3764 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3768 We can also derive instances of constructor classes in a similar
3769 way. For example, suppose we have implemented state and failure monad
3770 transformers, such that
3773 instance Monad m => Monad (State s m)
3774 instance Monad m => Monad (Failure m)
3776 In Haskell 98, we can define a parsing monad by
3778 type Parser tok m a = State [tok] (Failure m) a
3781 which is automatically a monad thanks to the instance declarations
3782 above. With the extension, we can make the parser type abstract,
3783 without needing to write an instance of class <literal>Monad</literal>, via
3786 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3789 In this case the derived instance declaration is of the form
3791 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3794 Notice that, since <literal>Monad</literal> is a constructor class, the
3795 instance is a <emphasis>partial application</emphasis> of the new type, not the
3796 entire left hand side. We can imagine that the type declaration is
3797 ``eta-converted'' to generate the context of the instance
3802 We can even derive instances of multi-parameter classes, provided the
3803 newtype is the last class parameter. In this case, a ``partial
3804 application'' of the class appears in the <literal>deriving</literal>
3805 clause. For example, given the class
3808 class StateMonad s m | m -> s where ...
3809 instance Monad m => StateMonad s (State s m) where ...
3811 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3813 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3814 deriving (Monad, StateMonad [tok])
3817 The derived instance is obtained by completing the application of the
3818 class to the new type:
3821 instance StateMonad [tok] (State [tok] (Failure m)) =>
3822 StateMonad [tok] (Parser tok m)
3827 As a result of this extension, all derived instances in newtype
3828 declarations are treated uniformly (and implemented just by reusing
3829 the dictionary for the representation type), <emphasis>except</emphasis>
3830 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3831 the newtype and its representation.
3835 <sect2> <title> A more precise specification </title>
3837 Derived instance declarations are constructed as follows. Consider the
3838 declaration (after expansion of any type synonyms)
3841 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3844 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3846 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3847 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3848 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3849 declarations are, for each <literal>ci</literal>,
3852 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3854 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3855 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3859 As an example which does <emphasis>not</emphasis> work, consider
3861 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3863 Here we cannot derive the instance
3865 instance Monad (State s m) => Monad (NonMonad m)
3868 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3869 and so cannot be "eta-converted" away. It is a good thing that this
3870 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3871 not, in fact, a monad --- for the same reason. Try defining
3872 <literal>>>=</literal> with the correct type: you won't be able to.
3876 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3877 important, since we can only derive instances for the last one. If the
3878 <literal>StateMonad</literal> class above were instead defined as
3881 class StateMonad m s | m -> s where ...
3884 then we would not have been able to derive an instance for the
3885 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3886 classes usually have one "main" parameter for which deriving new
3887 instances is most interesting.
3895 ;;; Local Variables: ***
3897 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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