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, all
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> With one group of exceptions! You may want to
143 define your own numeric class hierarchy. It completely
144 defeats that purpose if the literal "1" means
145 "<literal>Prelude.fromInteger 1</literal>", which is what
146 the Haskell Report specifies. So the
147 <option>-fno-implicit-prelude</option> flag causes the
148 following pieces of built-in syntax to refer to <emphasis>whatever
149 is in scope</emphasis>, not the Prelude versions:</para>
153 <para>Integer and fractional literals mean
154 "<literal>fromInteger 1</literal>" and
155 "<literal>fromRational 3.2</literal>", not the
156 Prelude-qualified versions; both in expressions and in
161 <para>Negation (e.g. "<literal>- (f x)</literal>")
162 means "<literal>negate (f x)</literal>" (not
163 <literal>Prelude.negate</literal>).</para>
167 <para>In an n+k pattern, the standard Prelude
168 <literal>Ord</literal> class is still used for comparison,
169 but the necessary subtraction uses whatever
170 "<literal>(-)</literal>" is in scope (not
171 "<literal>Prelude.(-)</literal>").</para>
175 <para>Note: Negative literals, such as <literal>-3</literal>, are
176 specified by (a careful reading of) the Haskell Report as
177 meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
178 However, GHC deviates from this slightly, and treats them as meaning
179 <literal>fromInteger (-3)</literal>. One particular effect of this
180 slightly-non-standard reading is that there is no difficulty with
181 the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
182 it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
183 would be <literal>negate (fromInteger 2147483648)</literal>,
184 and the call to <literal>fromInteger</literal> would overflow
185 (at type <literal>Int</literal>, remember).
194 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
195 <!-- included from primitives.sgml -->
199 <!-- TYPE SYSTEM EXTENSIONS -->
200 <sect1 id="type-extensions">
201 <title>Type system extensions</title>
203 <sect2 id="nullary-types">
204 <title>Data types with no constructors</title>
206 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
207 a data type with no constructors. For example:</para>
210 data T a -- T :: * -> *
212 <para>Syntactically, the declaration lacks the "= constrs" part. The
213 type can be parameterised, but only over ordinary types, of kind *; since
214 Haskell does not have kind signatures, you cannot parameterise over higher-kinded
217 <para>Such data types have only one value, namely bottom.
218 Nevertheless, they can be useful when defining "phantom types".</para>
221 <sect2 id="class-method-types">
222 <title>Class method types
225 Haskell 98 prohibits class method types to mention constraints on the
226 class type variable, thus:
229 fromList :: [a] -> s a
230 elem :: Eq a => a -> s a -> Bool
232 The type of <literal>elem</literal> is illegal in Haskell 98, because it
233 contains the constraint <literal>Eq a</literal>, constrains only the
234 class type variable (in this case <literal>a</literal>).
237 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
242 <sect2 id="multi-param-type-classes">
243 <title>Multi-parameter type classes
247 This section documents GHC's implementation of multi-parameter type
248 classes. There's lots of background in the paper <ULink
249 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
250 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
255 I'd like to thank people who reported shorcomings in the GHC 3.02
256 implementation. Our default decisions were all conservative ones, and
257 the experience of these heroic pioneers has given useful concrete
258 examples to support several generalisations. (These appear below as
259 design choices not implemented in 3.02.)
263 I've discussed these notes with Mark Jones, and I believe that Hugs
264 will migrate towards the same design choices as I outline here.
265 Thanks to him, and to many others who have offered very useful
273 There are the following restrictions on the form of a qualified
280 forall tv1..tvn (c1, ...,cn) => type
286 (Here, I write the "foralls" explicitly, although the Haskell source
287 language omits them; in Haskell 1.4, all the free type variables of an
288 explicit source-language type signature are universally quantified,
289 except for the class type variables in a class declaration. However,
290 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
299 <emphasis>Each universally quantified type variable
300 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
302 The reason for this is that a value with a type that does not obey
303 this restriction could not be used without introducing
304 ambiguity. Here, for example, is an illegal type:
308 forall a. Eq a => Int
312 When a value with this type was used, the constraint <literal>Eq tv</literal>
313 would be introduced where <literal>tv</literal> is a fresh type variable, and
314 (in the dictionary-translation implementation) the value would be
315 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
316 can never know which instance of <literal>Eq</literal> to use because we never
317 get any more information about <literal>tv</literal>.
324 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
325 universally quantified type variables <literal>tvi</literal></emphasis>.
327 For example, this type is OK because <literal>C a b</literal> mentions the
328 universally quantified type variable <literal>b</literal>:
332 forall a. C a b => burble
336 The next type is illegal because the constraint <literal>Eq b</literal> does not
337 mention <literal>a</literal>:
341 forall a. Eq b => burble
345 The reason for this restriction is milder than the other one. The
346 excluded types are never useful or necessary (because the offending
347 context doesn't need to be witnessed at this point; it can be floated
348 out). Furthermore, floating them out increases sharing. Lastly,
349 excluding them is a conservative choice; it leaves a patch of
350 territory free in case we need it later.
360 These restrictions apply to all types, whether declared in a type signature
365 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
366 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
373 f :: Eq (m a) => [m a] -> [m a]
380 This choice recovers principal types, a property that Haskell 1.4 does not have.
386 <title>Class declarations</title>
394 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
398 class Collection c a where
399 union :: c a -> c a -> c a
410 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
411 of "acyclic" involves only the superclass relationships. For example,
417 op :: D b => a -> b -> b
420 class C a => D a where { ... }
424 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
425 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
426 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
433 <emphasis>There are no restrictions on the context in a class declaration
434 (which introduces superclasses), except that the class hierarchy must
435 be acyclic</emphasis>. So these class declarations are OK:
439 class Functor (m k) => FiniteMap m k where
442 class (Monad m, Monad (t m)) => Transform t m where
443 lift :: m a -> (t m) a
452 <emphasis>In the signature of a class operation, every constraint
453 must mention at least one type variable that is not a class type
460 class Collection c a where
461 mapC :: Collection c b => (a->b) -> c a -> c b
465 is OK because the constraint <literal>(Collection a b)</literal> mentions
466 <literal>b</literal>, even though it also mentions the class variable
467 <literal>a</literal>. On the other hand:
472 op :: Eq a => (a,b) -> (a,b)
476 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
477 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
478 example is easily fixed by moving the offending context up to the
483 class Eq a => C a where
488 A yet more relaxed rule would allow the context of a class-op signature
489 to mention only class type variables. However, that conflicts with
490 Rule 1(b) for types above.
497 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
498 the class type variables</emphasis>. For example:
504 insert :: s -> a -> s
508 is not OK, because the type of <literal>empty</literal> doesn't mention
509 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
510 types, and has the same motivation.
512 Sometimes, offending class declarations exhibit misunderstandings. For
513 example, <literal>Coll</literal> might be rewritten
519 insert :: s a -> a -> s a
523 which makes the connection between the type of a collection of
524 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
525 Occasionally this really doesn't work, in which case you can split the
533 class CollE s => Coll s a where
534 insert :: s -> a -> s
547 <sect3 id="instance-decls">
548 <title>Instance declarations</title>
556 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
561 instance context1 => C type1 where ...
562 instance context2 => C type2 where ...
566 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
568 However, if you give the command line option
569 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
570 option</primary></indexterm> then overlapping instance declarations are permitted.
571 However, GHC arranges never to commit to using an instance declaration
572 if another instance declaration also applies, either now or later.
578 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
584 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
585 (but not identical to <literal>type1</literal>), or vice versa.
589 Notice that these rules
594 make it clear which instance decl to use
595 (pick the most specific one that matches)
602 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
603 Reason: you can pick which instance decl
604 "matches" based on the type.
609 However the rules are over-conservative. Two instance declarations can overlap,
610 but it can still be clear in particular situations which to use. For example:
612 instance C (Int,a) where ...
613 instance C (a,Bool) where ...
615 These are rejected by GHC's rules, but it is clear what to do when trying
616 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
617 cannot apply. Yell if this restriction bites you.
620 GHC is also conservative about committing to an overlapping instance. For example:
622 class C a where { op :: a -> a }
623 instance C [Int] where ...
624 instance C a => C [a] where ...
626 f :: C b => [b] -> [b]
629 From the RHS of f we get the constraint <literal>C [b]</literal>. But
630 GHC does not commit to the second instance declaration, because in a paricular
631 call of f, b might be instantiate to Int, so the first instance declaration
632 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
633 GHC will instead silently pick the second instance, without complaining about
634 the problem of subsequent instantiations.
637 Regrettably, GHC doesn't guarantee to detect overlapping instance
638 declarations if they appear in different modules. GHC can "see" the
639 instance declarations in the transitive closure of all the modules
640 imported by the one being compiled, so it can "see" all instance decls
641 when it is compiling <literal>Main</literal>. However, it currently chooses not
642 to look at ones that can't possibly be of use in the module currently
643 being compiled, in the interests of efficiency. (Perhaps we should
644 change that decision, at least for <literal>Main</literal>.)
651 <emphasis>There are no restrictions on the type in an instance
652 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
653 The instance "head" is the bit after the "=>" in an instance decl. For
654 example, these are OK:
658 instance C Int a where ...
660 instance D (Int, Int) where ...
662 instance E [[a]] where ...
666 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
667 For example, this is OK:
671 instance Stateful (ST s) (MutVar s) where ...
675 The "at least one not a type variable" restriction is to ensure that
676 context reduction terminates: each reduction step removes one type
677 constructor. For example, the following would make the type checker
678 loop if it wasn't excluded:
682 instance C a => C a where ...
686 There are two situations in which the rule is a bit of a pain. First,
687 if one allows overlapping instance declarations then it's quite
688 convenient to have a "default instance" declaration that applies if
689 something more specific does not:
698 Second, sometimes you might want to use the following to get the
699 effect of a "class synonym":
703 class (C1 a, C2 a, C3 a) => C a where { }
705 instance (C1 a, C2 a, C3 a) => C a where { }
709 This allows you to write shorter signatures:
721 f :: (C1 a, C2 a, C3 a) => ...
725 I'm on the lookout for a simple rule that preserves decidability while
726 allowing these idioms. The experimental flag
727 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
728 option</primary></indexterm> lifts this restriction, allowing all the types in an
729 instance head to be type variables.
736 <emphasis>Unlike Haskell 1.4, instance heads may use type
737 synonyms</emphasis>. As always, using a type synonym is just shorthand for
738 writing the RHS of the type synonym definition. For example:
742 type Point = (Int,Int)
743 instance C Point where ...
744 instance C [Point] where ...
748 is legal. However, if you added
752 instance C (Int,Int) where ...
756 as well, then the compiler will complain about the overlapping
757 (actually, identical) instance declarations. As always, type synonyms
758 must be fully applied. You cannot, for example, write:
763 instance Monad P where ...
767 This design decision is independent of all the others, and easily
768 reversed, but it makes sense to me.
775 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
776 be type variables</emphasis>. Thus
780 instance C a b => Eq (a,b) where ...
788 instance C Int b => Foo b where ...
792 is not OK. Again, the intent here is to make sure that context
793 reduction terminates.
795 Voluminous correspondence on the Haskell mailing list has convinced me
796 that it's worth experimenting with a more liberal rule. If you use
797 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
798 types in an instance context. Termination is ensured by having a
799 fixed-depth recursion stack. If you exceed the stack depth you get a
800 sort of backtrace, and the opportunity to increase the stack depth
801 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
814 <sect2 id="implicit-parameters">
815 <title>Implicit parameters
818 <para> Implicit paramters are implemented as described in
819 "Implicit parameters: dynamic scoping with static types",
820 J Lewis, MB Shields, E Meijer, J Launchbury,
821 27th ACM Symposium on Principles of Programming Languages (POPL'00),
824 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
826 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
827 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
828 context. In Haskell, all variables are statically bound. Dynamic
829 binding of variables is a notion that goes back to Lisp, but was later
830 discarded in more modern incarnations, such as Scheme. Dynamic binding
831 can be very confusing in an untyped language, and unfortunately, typed
832 languages, in particular Hindley-Milner typed languages like Haskell,
833 only support static scoping of variables.
836 However, by a simple extension to the type class system of Haskell, we
837 can support dynamic binding. Basically, we express the use of a
838 dynamically bound variable as a constraint on the type. These
839 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
840 function uses a dynamically-bound variable <literal>?x</literal>
841 of type <literal>t'</literal>". For
842 example, the following expresses the type of a sort function,
843 implicitly parameterized by a comparison function named <literal>cmp</literal>.
845 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
847 The dynamic binding constraints are just a new form of predicate in the type class system.
850 An implicit parameter is introduced by the special form <literal>?x</literal>,
851 where <literal>x</literal> is
852 any valid identifier. Use if this construct also introduces new
853 dynamic binding constraints. For example, the following definition
854 shows how we can define an implicitly parameterized sort function in
855 terms of an explicitly parameterized <literal>sortBy</literal> function:
857 sortBy :: (a -> a -> Bool) -> [a] -> [a]
859 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
862 Dynamic binding constraints behave just like other type class
863 constraints in that they are automatically propagated. Thus, when a
864 function is used, its implicit parameters are inherited by the
865 function that called it. For example, our <literal>sort</literal> function might be used
866 to pick out the least value in a list:
868 least :: (?cmp :: a -> a -> Bool) => [a] -> a
869 least xs = fst (sort xs)
871 Without lifting a finger, the <literal>?cmp</literal> parameter is
872 propagated to become a parameter of <literal>least</literal> as well. With explicit
873 parameters, the default is that parameters must always be explicit
874 propagated. With implicit parameters, the default is to always
878 An implicit parameter differs from other type class constraints in the
879 following way: All uses of a particular implicit parameter must have
880 the same type. This means that the type of <literal>(?x, ?x)</literal>
881 is <literal>(?x::a) => (a,a)</literal>, and not
882 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
886 An implicit parameter is bound using an expression of the form
887 <emphasis>expr</emphasis> <literal>with</literal> <emphasis>binds</emphasis>,
888 where <literal>with</literal> is a new keyword. This form binds the implicit
889 parameters arising in the body, not the free variables as a <literal>let</literal> or
890 <literal>where</literal> would do. For example, we define the <literal>min</literal> function by binding
891 <literal>cmp</literal>.
894 min = least with ?cmp = (<=)
896 Syntactically, the <emphasis>binds</emphasis> part of a <literal>with</literal> construct must be a
897 collection of simple bindings to variables (no function-style
898 bindings, and no type signatures); these bindings are neither
899 polymorphic or recursive.
902 Note the following additional constraints:
905 <para> You can't have an implicit parameter in the context of a class or instance
906 declaration. For example, both these declarations are illegal:
908 class (?x::Int) => C a where ...
909 instance (?x::a) => Foo [a] where ...
911 Reason: exactly which implicit parameter you pick up depends on exactly where
912 you invoke a function. But the ``invocation'' of instance declarations is done
913 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
914 Easiest thing is to outlaw the offending types.</para>
921 <sect2 id="linear-implicit-parameters">
922 <title>Linear implicit parameters
925 Linear implicit parameters are an idea developed by Koen Claessen,
926 Mark Shields, and Simon PJ. They address the long-standing
927 problem that monads seem over-kill for certain sorts of problem, notably:
930 <listitem> <para> distributing a supply of unique names </para> </listitem>
931 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
932 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
936 Linear implicit parameters are just like ordinary implicit parameters,
937 except that they are "linear" -- that is, they cannot be copied, and
938 must be explicitly "split" instead. Linear implicit parameters are
939 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
940 (The '/' in the '%' suggests the split!)
945 import GHC.Exts( Splittable )
947 data NameSupply = ...
949 splitNS :: NameSupply -> (NameSupply, NameSupply)
950 newName :: NameSupply -> Name
952 instance Splittable NameSupply where
956 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
957 f env (Lam x e) = Lam x' (f env e)
960 env' = extend env x x'
961 ...more equations for f...
963 Notice that the implicit parameter %ns is consumed
965 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
966 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
970 So the translation done by the type checker makes
971 the parameter explicit:
973 f :: NameSupply -> Env -> Expr -> Expr
974 f ns env (Lam x e) = Lam x' (f ns1 env e)
976 (ns1,ns2) = splitNS ns
978 env = extend env x x'
980 Notice the call to 'split' introduced by the type checker.
981 How did it know to use 'splitNS'? Because what it really did
982 was to introduce a call to the overloaded function 'split',
983 defined by the class <literal>Splittable</literal>:
985 class Splittable a where
988 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
989 split for name supplies. But we can simply write
995 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
997 The <literal>Splittable</literal> class is built into GHC. It's exported by module
998 <literal>GHC.Exts</literal>.
1003 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1004 are entirely distinct implicit parameters: you
1005 can use them together and they won't intefere with each other. </para>
1008 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1010 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1011 in the context of a class or instance declaration. </para></listitem>
1015 <sect3><title>Warnings</title>
1018 The monomorphism restriction is even more important than usual.
1019 Consider the example above:
1021 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1022 f env (Lam x e) = Lam x' (f env e)
1025 env' = extend env x x'
1027 If we replaced the two occurrences of x' by (newName %ns), which is
1028 usually a harmless thing to do, we get:
1030 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1031 f env (Lam x e) = Lam (newName %ns) (f env e)
1033 env' = extend env x (newName %ns)
1035 But now the name supply is consumed in <emphasis>three</emphasis> places
1036 (the two calls to newName,and the recursive call to f), so
1037 the result is utterly different. Urk! We don't even have
1041 Well, this is an experimental change. With implicit
1042 parameters we have already lost beta reduction anyway, and
1043 (as John Launchbury puts it) we can't sensibly reason about
1044 Haskell programs without knowing their typing.
1051 <sect2 id="functional-dependencies">
1052 <title>Functional dependencies
1055 <para> Functional dependencies are implemented as described by Mark Jones
1056 in "Type Classes with Functional Dependencies", Mark P. Jones,
1057 In Proceedings of the 9th European Symposium on Programming,
1058 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1062 There should be more documentation, but there isn't (yet). Yell if you need it.
1067 <sect2 id="universal-quantification">
1068 <title>Arbitrary-rank polymorphism
1072 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1073 allows us to say exactly what this means. For example:
1081 g :: forall b. (b -> b)
1083 The two are treated identically.
1087 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1088 explicit universal quantification in
1090 For example, all the following types are legal:
1092 f1 :: forall a b. a -> b -> a
1093 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1095 f2 :: (forall a. a->a) -> Int -> Int
1096 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1098 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1100 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1101 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1102 The <literal>forall</literal> makes explicit the universal quantification that
1103 is implicitly added by Haskell.
1106 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1107 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1108 shows, the polymorphic type on the left of the function arrow can be overloaded.
1111 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1112 they have rank-2 types on the left of a function arrow.
1115 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1116 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1117 that restriction has now been lifted.)
1118 In particular, a forall-type (also called a "type scheme"),
1119 including an operational type class context, is legal:
1121 <listitem> <para> On the left of a function arrow </para> </listitem>
1122 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1123 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1124 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1125 field type signatures.</para> </listitem>
1126 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1127 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1129 There is one place you cannot put a <literal>forall</literal>:
1130 you cannot instantiate a type variable with a forall-type. So you cannot
1131 make a forall-type the argument of a type constructor. So these types are illegal:
1133 x1 :: [forall a. a->a]
1134 x2 :: (forall a. a->a, Int)
1135 x3 :: Maybe (forall a. a->a)
1137 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1138 a type variable any more!
1147 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1148 the types of the constructor arguments. Here are several examples:
1154 data T a = T1 (forall b. b -> b -> b) a
1156 data MonadT m = MkMonad { return :: forall a. a -> m a,
1157 bind :: forall a b. m a -> (a -> m b) -> m b
1160 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1166 The constructors have rank-2 types:
1172 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1173 MkMonad :: forall m. (forall a. a -> m a)
1174 -> (forall a b. m a -> (a -> m b) -> m b)
1176 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1182 Notice that you don't need to use a <literal>forall</literal> if there's an
1183 explicit context. For example in the first argument of the
1184 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1185 prefixed to the argument type. The implicit <literal>forall</literal>
1186 quantifies all type variables that are not already in scope, and are
1187 mentioned in the type quantified over.
1191 As for type signatures, implicit quantification happens for non-overloaded
1192 types too. So if you write this:
1195 data T a = MkT (Either a b) (b -> b)
1198 it's just as if you had written this:
1201 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1204 That is, since the type variable <literal>b</literal> isn't in scope, it's
1205 implicitly universally quantified. (Arguably, it would be better
1206 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1207 where that is what is wanted. Feedback welcomed.)
1211 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1212 the constructor to suitable values, just as usual. For example,
1223 a3 = MkSwizzle reverse
1226 a4 = let r x = Just x
1233 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1234 mkTs f x y = [T1 f x, T1 f y]
1240 The type of the argument can, as usual, be more general than the type
1241 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1242 does not need the <literal>Ord</literal> constraint.)
1246 When you use pattern matching, the bound variables may now have
1247 polymorphic types. For example:
1253 f :: T a -> a -> (a, Char)
1254 f (T1 w k) x = (w k x, w 'c' 'd')
1256 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1257 g (MkSwizzle s) xs f = s (map f (s xs))
1259 h :: MonadT m -> [m a] -> m [a]
1260 h m [] = return m []
1261 h m (x:xs) = bind m x $ \y ->
1262 bind m (h m xs) $ \ys ->
1269 In the function <function>h</function> we use the record selectors <literal>return</literal>
1270 and <literal>bind</literal> to extract the polymorphic bind and return functions
1271 from the <literal>MonadT</literal> data structure, rather than using pattern
1277 <title>Type inference</title>
1280 In general, type inference for arbitrary-rank types is undecideable.
1281 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1282 to get a decidable algorithm by requiring some help from the programmer.
1283 We do not yet have a formal specification of "some help" but the rule is this:
1286 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1287 provides an explicit polymorphic type for x, or GHC's type inference will assume
1288 that x's type has no foralls in it</emphasis>.
1291 What does it mean to "provide" an explicit type for x? You can do that by
1292 giving a type signature for x directly, using a pattern type signature
1293 (<xref linkend="scoped-type-variables">), thus:
1295 \ f :: (forall a. a->a) -> (f True, f 'c')
1297 Alternatively, you can give a type signature to the enclosing
1298 context, which GHC can "push down" to find the type for the variable:
1300 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1302 Here the type signature on the expression can be pushed inwards
1303 to give a type signature for f. Similarly, and more commonly,
1304 one can give a type signature for the function itself:
1306 h :: (forall a. a->a) -> (Bool,Char)
1307 h f = (f True, f 'c')
1309 You don't need to give a type signature if the lambda bound variable
1310 is a constructor argument. Here is an example we saw earlier:
1312 f :: T a -> a -> (a, Char)
1313 f (T1 w k) x = (w k x, w 'c' 'd')
1315 Here we do not need to give a type signature to <literal>w</literal>, because
1316 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1323 <sect3 id="implicit-quant">
1324 <title>Implicit quantification</title>
1327 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1328 user-written types, if and only if there is no explicit <literal>forall</literal>,
1329 GHC finds all the type variables mentioned in the type that are not already
1330 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1334 f :: forall a. a -> a
1341 h :: forall b. a -> b -> b
1347 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1350 f :: (a -> a) -> Int
1352 f :: forall a. (a -> a) -> Int
1354 f :: (forall a. a -> a) -> Int
1357 g :: (Ord a => a -> a) -> Int
1358 -- MEANS the illegal type
1359 g :: forall a. (Ord a => a -> a) -> Int
1361 g :: (forall a. Ord a => a -> a) -> Int
1363 The latter produces an illegal type, which you might think is silly,
1364 but at least the rule is simple. If you want the latter type, you
1365 can write your for-alls explicitly. Indeed, doing so is strongly advised
1372 <title>Liberalised type synonyms
1376 Type synonmys are like macros at the type level, and
1377 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1378 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1380 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1381 in a type synonym, thus:
1383 type Discard a = forall b. Show b => a -> b -> (a, String)
1388 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1395 You can write an unboxed tuple in a type synonym:
1397 type Pr = (# Int, Int #)
1405 You can apply a type synonym to a forall type:
1407 type Foo a = a -> a -> Bool
1409 f :: Foo (forall b. b->b)
1411 After epxanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1413 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1418 You can apply a type synonym to a partially applied type synonym:
1420 type Generic i o = forall x. i x -> o x
1423 foo :: Generic Id []
1425 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1427 foo :: forall x. x -> [x]
1435 GHC currently does kind checking before expanding synonyms (though even that
1439 After expanding type synonyms, GHC does validity checking on types, looking for
1440 the following mal-formedness which isn't detected simply by kind checking:
1443 Type constructor applied to a type involving for-alls.
1446 Unboxed tuple on left of an arrow.
1449 Partially-applied type synonym.
1453 this will be rejected:
1455 type Pr = (# Int, Int #)
1460 because GHC does not allow unboxed tuples on the left of a function arrow.
1465 <title>For-all hoisting</title>
1467 It is often convenient to use generalised type synonyms at the right hand
1468 end of an arrow, thus:
1470 type Discard a = forall b. a -> b -> a
1472 g :: Int -> Discard Int
1475 Simply expanding the type synonym would give
1477 g :: Int -> (forall b. Int -> b -> Int)
1479 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1481 g :: forall b. Int -> Int -> b -> Int
1483 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1484 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1485 performs the transformation:</emphasis>
1487 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1489 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1491 (In fact, GHC tries to retain as much synonym information as possible for use in
1492 error messages, but that is a usability issue.) This rule applies, of course, whether
1493 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1494 valid way to write <literal>g</literal>'s type signature:
1496 g :: Int -> Int -> forall b. b -> Int
1502 <sect2 id="existential-quantification">
1503 <title>Existentially quantified data constructors
1507 The idea of using existential quantification in data type declarations
1508 was suggested by Laufer (I believe, thought doubtless someone will
1509 correct me), and implemented in Hope+. It's been in Lennart
1510 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1511 proved very useful. Here's the idea. Consider the declaration:
1517 data Foo = forall a. MkFoo a (a -> Bool)
1524 The data type <literal>Foo</literal> has two constructors with types:
1530 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1537 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1538 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1539 For example, the following expression is fine:
1545 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1551 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1552 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1553 isUpper</function> packages a character with a compatible function. These
1554 two things are each of type <literal>Foo</literal> and can be put in a list.
1558 What can we do with a value of type <literal>Foo</literal>?. In particular,
1559 what happens when we pattern-match on <function>MkFoo</function>?
1565 f (MkFoo val fn) = ???
1571 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1572 are compatible, the only (useful) thing we can do with them is to
1573 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1580 f (MkFoo val fn) = fn val
1586 What this allows us to do is to package heterogenous values
1587 together with a bunch of functions that manipulate them, and then treat
1588 that collection of packages in a uniform manner. You can express
1589 quite a bit of object-oriented-like programming this way.
1592 <sect3 id="existential">
1593 <title>Why existential?
1597 What has this to do with <emphasis>existential</emphasis> quantification?
1598 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1604 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1610 But Haskell programmers can safely think of the ordinary
1611 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1612 adding a new existential quantification construct.
1618 <title>Type classes</title>
1621 An easy extension (implemented in <Command>hbc</Command>) is to allow
1622 arbitrary contexts before the constructor. For example:
1628 data Baz = forall a. Eq a => Baz1 a a
1629 | forall b. Show b => Baz2 b (b -> b)
1635 The two constructors have the types you'd expect:
1641 Baz1 :: forall a. Eq a => a -> a -> Baz
1642 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1648 But when pattern matching on <function>Baz1</function> the matched values can be compared
1649 for equality, and when pattern matching on <function>Baz2</function> the first matched
1650 value can be converted to a string (as well as applying the function to it).
1651 So this program is legal:
1658 f (Baz1 p q) | p == q = "Yes"
1660 f (Baz2 v fn) = show (fn v)
1666 Operationally, in a dictionary-passing implementation, the
1667 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1668 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1669 extract it on pattern matching.
1673 Notice the way that the syntax fits smoothly with that used for
1674 universal quantification earlier.
1680 <title>Restrictions</title>
1683 There are several restrictions on the ways in which existentially-quantified
1684 constructors can be use.
1693 When pattern matching, each pattern match introduces a new,
1694 distinct, type for each existential type variable. These types cannot
1695 be unified with any other type, nor can they escape from the scope of
1696 the pattern match. For example, these fragments are incorrect:
1704 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1705 is the result of <function>f1</function>. One way to see why this is wrong is to
1706 ask what type <function>f1</function> has:
1710 f1 :: Foo -> a -- Weird!
1714 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1719 f1 :: forall a. Foo -> a -- Wrong!
1723 The original program is just plain wrong. Here's another sort of error
1727 f2 (Baz1 a b) (Baz1 p q) = a==q
1731 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1732 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1733 from the two <function>Baz1</function> constructors.
1741 You can't pattern-match on an existentially quantified
1742 constructor in a <literal>let</literal> or <literal>where</literal> group of
1743 bindings. So this is illegal:
1747 f3 x = a==b where { Baz1 a b = x }
1751 You can only pattern-match
1752 on an existentially-quantified constructor in a <literal>case</literal> expression or
1753 in the patterns of a function definition.
1755 The reason for this restriction is really an implementation one.
1756 Type-checking binding groups is already a nightmare without
1757 existentials complicating the picture. Also an existential pattern
1758 binding at the top level of a module doesn't make sense, because it's
1759 not clear how to prevent the existentially-quantified type "escaping".
1760 So for now, there's a simple-to-state restriction. We'll see how
1768 You can't use existential quantification for <literal>newtype</literal>
1769 declarations. So this is illegal:
1773 newtype T = forall a. Ord a => MkT a
1777 Reason: a value of type <literal>T</literal> must be represented as a pair
1778 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1779 That contradicts the idea that <literal>newtype</literal> should have no
1780 concrete representation. You can get just the same efficiency and effect
1781 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1782 overloading involved, then there is more of a case for allowing
1783 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1784 because the <literal>data</literal> version does carry an implementation cost,
1785 but single-field existentially quantified constructors aren't much
1786 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1787 stands, unless there are convincing reasons to change it.
1795 You can't use <literal>deriving</literal> to define instances of a
1796 data type with existentially quantified data constructors.
1798 Reason: in most cases it would not make sense. For example:#
1801 data T = forall a. MkT [a] deriving( Eq )
1804 To derive <literal>Eq</literal> in the standard way we would need to have equality
1805 between the single component of two <function>MkT</function> constructors:
1809 (MkT a) == (MkT b) = ???
1812 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1813 It's just about possible to imagine examples in which the derived instance
1814 would make sense, but it seems altogether simpler simply to prohibit such
1815 declarations. Define your own instances!
1827 <sect2 id="scoped-type-variables">
1828 <title>Scoped Type Variables
1832 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1833 variable</emphasis>. For example
1839 f (xs::[a]) = ys ++ ys
1848 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1849 This brings the type variable <literal>a</literal> into scope; it scopes over
1850 all the patterns and right hand sides for this equation for <function>f</function>.
1851 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1855 Pattern type signatures are completely orthogonal to ordinary, separate
1856 type signatures. The two can be used independently or together.
1857 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1858 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1859 implicitly universally quantified. (If there are no type variables in
1860 scope, all type variables mentioned in the signature are universally
1861 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1862 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1863 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1864 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1865 it becomes possible to do so.
1869 Scoped type variables are implemented in both GHC and Hugs. Where the
1870 implementations differ from the specification below, those differences
1875 So much for the basic idea. Here are the details.
1879 <title>What a pattern type signature means</title>
1881 A type variable brought into scope by a pattern type signature is simply
1882 the name for a type. The restriction they express is that all occurrences
1883 of the same name mean the same type. For example:
1885 f :: [Int] -> Int -> Int
1886 f (xs::[a]) (y::a) = (head xs + y) :: a
1888 The pattern type signatures on the left hand side of
1889 <literal>f</literal> express the fact that <literal>xs</literal>
1890 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1891 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1892 specifies that this expression must have the same type <literal>a</literal>.
1893 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1894 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1895 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1896 rules, which specified that a pattern-bound type variable should be universally quantified.)
1897 For example, all of these are legal:</para>
1900 t (x::a) (y::a) = x+y*2
1902 f (x::a) (y::b) = [x,y] -- a unifies with b
1904 g (x::a) = x + 1::Int -- a unifies with Int
1906 h x = let k (y::a) = [x,y] -- a is free in the
1907 in k x -- environment
1909 k (x::a) True = ... -- a unifies with Int
1910 k (x::Int) False = ...
1913 w (x::a) = x -- a unifies with [b]
1919 <title>Scope and implicit quantification</title>
1927 All the type variables mentioned in a pattern,
1928 that are not already in scope,
1929 are brought into scope by the pattern. We describe this set as
1930 the <emphasis>type variables bound by the pattern</emphasis>.
1933 f (x::a) = let g (y::(a,b)) = fst y
1937 The pattern <literal>(x::a)</literal> brings the type variable
1938 <literal>a</literal> into scope, as well as the term
1939 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
1940 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
1941 and brings into scope the type variable <literal>b</literal>.
1947 The type variable(s) bound by the pattern have the same scope
1948 as the term variable(s) bound by the pattern. For example:
1951 f (x::a) = <...rhs of f...>
1952 (p::b, q::b) = (1,2)
1953 in <...body of let...>
1955 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
1956 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
1957 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
1958 just like <literal>p</literal> and <literal>q</literal> do.
1959 Indeed, the newly bound type variables also scope over any ordinary, separate
1960 type signatures in the <literal>let</literal> group.
1967 The type variables bound by the pattern may be
1968 mentioned in ordinary type signatures or pattern
1969 type signatures anywhere within their scope.
1976 In ordinary type signatures, any type variable mentioned in the
1977 signature that is in scope is <emphasis>not</emphasis> universally quantified.
1985 Ordinary type signatures do not bring any new type variables
1986 into scope (except in the type signature itself!). So this is illegal:
1993 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
1994 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
1995 and that is an incorrect typing.
2002 The pattern type signature is a monotype:
2007 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2011 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2012 not to type schemes.
2016 There is no implicit universal quantification on pattern type signatures (in contrast to
2017 ordinary type signatures).
2027 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2028 scope over the methods defined in the <literal>where</literal> part. For example:
2042 (Not implemented in Hugs yet, Dec 98).
2053 <title>Result type signatures</title>
2061 The result type of a function can be given a signature,
2066 f (x::a) :: [a] = [x,x,x]
2070 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2071 result type. Sometimes this is the only way of naming the type variable
2076 f :: Int -> [a] -> [a]
2077 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2078 in \xs -> map g (reverse xs `zip` xs)
2090 Result type signatures are not yet implemented in Hugs.
2096 <title>Where a pattern type signature can occur</title>
2099 A pattern type signature can occur in any pattern. For example:
2104 A pattern type signature can be on an arbitrary sub-pattern, not
2109 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2118 Pattern type signatures, including the result part, can be used
2119 in lambda abstractions:
2122 (\ (x::a, y) :: a -> x)
2129 Pattern type signatures, including the result part, can be used
2130 in <literal>case</literal> expressions:
2134 case e of { (x::a, y) :: a -> x }
2142 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2143 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2144 token or a parenthesised type of some sort). To see why,
2145 consider how one would parse this:
2159 Pattern type signatures can bind existential type variables.
2164 data T = forall a. MkT [a]
2167 f (MkT [t::a]) = MkT t3
2180 Pattern type signatures
2181 can be used in pattern bindings:
2184 f x = let (y, z::a) = x in ...
2185 f1 x = let (y, z::Int) = x in ...
2186 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2187 f3 :: (b->b) = \x -> x
2190 In all such cases, the binding is not generalised over the pattern-bound
2191 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2192 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2193 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2194 In contrast, the binding
2199 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2200 in <literal>f4</literal>'s scope.
2210 <sect2 id="sec-kinding">
2211 <title>Explicitly-kinded quantification</title>
2214 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2215 to give the kind explicitly as (machine-checked) documentation,
2216 just as it is nice to give a type signature for a function. On some occasions,
2217 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2218 John Hughes had to define the data type:
2220 data Set cxt a = Set [a]
2221 | Unused (cxt a -> ())
2223 The only use for the <literal>Unused</literal> constructor was to force the correct
2224 kind for the type variable <literal>cxt</literal>.
2227 GHC now instead allows you to specify the kind of a type variable directly, wherever
2228 a type variable is explicitly bound. Namely:
2230 <listitem><para><literal>data</literal> declarations:
2232 data Set (cxt :: * -> *) a = Set [a]
2233 </Screen></para></listitem>
2234 <listitem><para><literal>type</literal> declarations:
2236 type T (f :: * -> *) = f Int
2237 </Screen></para></listitem>
2238 <listitem><para><literal>class</literal> declarations:
2240 class (Eq a) => C (f :: * -> *) a where ...
2241 </Screen></para></listitem>
2242 <listitem><para><literal>forall</literal>'s in type signatures:
2244 f :: forall (cxt :: * -> *). Set cxt Int
2245 </Screen></para></listitem>
2250 The parentheses are required. Some of the spaces are required too, to
2251 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2252 will get a parse error, because "<literal>::*->*</literal>" is a
2253 single lexeme in Haskell.
2257 As part of the same extension, you can put kind annotations in types
2260 f :: (Int :: *) -> Int
2261 g :: forall a. a -> (a :: *)
2265 atype ::= '(' ctype '::' kind ')
2267 The parentheses are required.
2272 <!-- ==================== End of type system extensions ================= -->
2275 <!-- ==================== ASSERTIONS ================= -->
2277 <sect1 id="sec-assertions">
2279 <indexterm><primary>Assertions</primary></indexterm>
2283 If you want to make use of assertions in your standard Haskell code, you
2284 could define a function like the following:
2290 assert :: Bool -> a -> a
2291 assert False x = error "assertion failed!"
2298 which works, but gives you back a less than useful error message --
2299 an assertion failed, but which and where?
2303 One way out is to define an extended <function>assert</function> function which also
2304 takes a descriptive string to include in the error message and
2305 perhaps combine this with the use of a pre-processor which inserts
2306 the source location where <function>assert</function> was used.
2310 Ghc offers a helping hand here, doing all of this for you. For every
2311 use of <function>assert</function> in the user's source:
2317 kelvinToC :: Double -> Double
2318 kelvinToC k = assert (k >= 0.0) (k+273.15)
2324 Ghc will rewrite this to also include the source location where the
2331 assert pred val ==> assertError "Main.hs|15" pred val
2337 The rewrite is only performed by the compiler when it spots
2338 applications of <function>Exception.assert</function>, so you can still define and
2339 use your own versions of <function>assert</function>, should you so wish. If not,
2340 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2344 To have the compiler ignore uses of assert, use the compiler option
2345 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2346 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2350 Assertion failures can be caught, see the documentation for the
2351 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2357 <!-- ====================== PATTERN GUARDS ======================= -->
2359 <sect1 id="pattern-guards">
2360 <title>Pattern guards</title>
2363 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2364 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.)
2368 Suppose we have an abstract data type of finite maps, with a
2372 lookup :: FiniteMap -> Int -> Maybe Int
2375 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2376 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2380 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2381 | otherwise = var1 + var2
2383 m1 = lookup env var1
2384 m2 = lookup env var2
2385 ok1 = maybeToBool m1
2386 ok2 = maybeToBool m2
2387 val1 = expectJust m1
2388 val2 = expectJust m2
2392 The auxiliary functions are
2396 maybeToBool :: Maybe a -> Bool
2397 maybeToBool (Just x) = True
2398 maybeToBool Nothing = False
2400 expectJust :: Maybe a -> a
2401 expectJust (Just x) = x
2402 expectJust Nothing = error "Unexpected Nothing"
2406 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2407 ok2</literal> checks that both lookups succeed, using
2408 <function>maybeToBool</function> to convert the <function>Maybe</function>
2409 types to booleans. The (lazily evaluated) <function>expectJust</function>
2410 calls extract the values from the results of the lookups, and binds the
2411 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2412 respectively. If either lookup fails, then clunky takes the
2413 <literal>otherwise</literal> case and returns the sum of its arguments.
2417 This is certainly legal Haskell, but it is a tremendously verbose and
2418 un-obvious way to achieve the desired effect. Arguably, a more direct way
2419 to write clunky would be to use case expressions:
2423 clunky env var1 var1 = case lookup env var1 of
2425 Just val1 -> case lookup env var2 of
2427 Just val2 -> val1 + val2
2433 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2434 of pattern-matching, guarded equations as case expressions; that is
2435 precisely what the compiler does when compiling equations! The reason that
2436 Haskell provides guarded equations is because they allow us to write down
2437 the cases we want to consider, one at a time, independently of each other.
2438 This structure is hidden in the case version. Two of the right-hand sides
2439 are really the same (<function>fail</function>), and the whole expression
2440 tends to become more and more indented.
2444 Here is how I would write clunky:
2448 clunky env var1 var1
2449 | Just val1 <- lookup env var1
2450 , Just val2 <- lookup env var2
2452 ...other equations for clunky...
2456 The semantics should be clear enough. The qualifers are matched in order.
2457 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2458 right hand side is evaluated and matched against the pattern on the left.
2459 If the match fails then the whole guard fails and the next equation is
2460 tried. If it succeeds, then the appropriate binding takes place, and the
2461 next qualifier is matched, in the augmented environment. Unlike list
2462 comprehensions, however, the type of the expression to the right of the
2463 <literal><-</literal> is the same as the type of the pattern to its
2464 left. The bindings introduced by pattern guards scope over all the
2465 remaining guard qualifiers, and over the right hand side of the equation.
2469 Just as with list comprehensions, boolean expressions can be freely mixed
2470 with among the pattern guards. For example:
2481 Haskell's current guards therefore emerge as a special case, in which the
2482 qualifier list has just one element, a boolean expression.
2486 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2488 <sect1 id="parallel-list-comprehensions">
2489 <title>Parallel List Comprehensions</title>
2490 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2492 <indexterm><primary>parallel list comprehensions</primary>
2495 <para>Parallel list comprehensions are a natural extension to list
2496 comprehensions. List comprehensions can be thought of as a nice
2497 syntax for writing maps and filters. Parallel comprehensions
2498 extend this to include the zipWith family.</para>
2500 <para>A parallel list comprehension has multiple independent
2501 branches of qualifier lists, each separated by a `|' symbol. For
2502 example, the following zips together two lists:</para>
2505 [ (x, y) | x <- xs | y <- ys ]
2508 <para>The behavior of parallel list comprehensions follows that of
2509 zip, in that the resulting list will have the same length as the
2510 shortest branch.</para>
2512 <para>We can define parallel list comprehensions by translation to
2513 regular comprehensions. Here's the basic idea:</para>
2515 <para>Given a parallel comprehension of the form: </para>
2518 [ e | p1 <- e11, p2 <- e12, ...
2519 | q1 <- e21, q2 <- e22, ...
2524 <para>This will be translated to: </para>
2527 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2528 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2533 <para>where `zipN' is the appropriate zip for the given number of
2538 <!-- =============================== PRAGMAS =========================== -->
2540 <sect1 id="pragmas">
2541 <title>Pragmas</title>
2543 <indexterm><primary>pragma</primary></indexterm>
2545 <para>GHC supports several pragmas, or instructions to the
2546 compiler placed in the source code. Pragmas don't normally affect
2547 the meaning of the program, but they might affect the efficiency
2548 of the generated code.</para>
2550 <para>Pragmas all take the form
2552 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2554 where <replaceable>word</replaceable> indicates the type of
2555 pragma, and is followed optionally by information specific to that
2556 type of pragma. Case is ignored in
2557 <replaceable>word</replaceable>. The various values for
2558 <replaceable>word</replaceable> that GHC understands are described
2559 in the following sections; any pragma encountered with an
2560 unrecognised <replaceable>word</replaceable> is (silently)
2563 <sect2 id="inline-pragma">
2564 <title>INLINE pragma
2566 <indexterm><primary>INLINE pragma</primary></indexterm>
2567 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2570 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2571 functions/values that are “small enough,” thus avoiding the call
2572 overhead and possibly exposing other more-wonderful optimisations.
2576 You will probably see these unfoldings (in Core syntax) in your
2581 Normally, if GHC decides a function is “too expensive” to inline, it
2582 will not do so, nor will it export that unfolding for other modules to
2587 The sledgehammer you can bring to bear is the
2588 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2591 key_function :: Int -> String -> (Bool, Double)
2593 #ifdef __GLASGOW_HASKELL__
2594 {-# INLINE key_function #-}
2598 (You don't need to do the C pre-processor carry-on unless you're going
2599 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2603 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2604 “cost” to be very low. The normal unfolding machinery will then be
2605 very keen to inline it.
2609 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2610 signature could be put.
2614 <literal>INLINE</literal> pragmas are a particularly good idea for the
2615 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2616 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2619 #ifdef __GLASGOW_HASKELL__
2620 {-# INLINE thenUs #-}
2621 {-# INLINE returnUs #-}
2629 <sect2 id="noinline-pragma">
2630 <title>NOINLINE pragma
2633 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2634 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2635 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2636 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2639 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2640 it stops the named function from being inlined by the compiler. You
2641 shouldn't ever need to do this, unless you're very cautious about code
2645 <para><literal>NOTINLINE</literal> is a synonym for
2646 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2647 by Haskell 98 as the standard way to disable inlining, so it should be
2648 used if you want your code to be portable).</para>
2652 <sect2 id="specialize-pragma">
2653 <title>SPECIALIZE pragma</title>
2655 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2656 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2657 <indexterm><primary>overloading, death to</primary></indexterm>
2659 <para>(UK spelling also accepted.) For key overloaded
2660 functions, you can create extra versions (NB: more code space)
2661 specialised to particular types. Thus, if you have an
2662 overloaded function:</para>
2665 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2668 <para>If it is heavily used on lists with
2669 <literal>Widget</literal> keys, you could specialise it as
2673 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2676 <para>To get very fancy, you can also specify a named function
2677 to use for the specialised value, as in:</para>
2680 {-# RULES hammeredLookup = blah #-}
2683 <para>where <literal>blah</literal> is an implementation of
2684 <literal>hammerdLookup</literal> written specialy for
2685 <literal>Widget</literal> lookups. It's <emphasis>Your
2686 Responsibility</emphasis> to make sure that
2687 <function>blah</function> really behaves as a specialised
2688 version of <function>hammeredLookup</function>!!!</para>
2690 <para>Note we use the <literal>RULE</literal> pragma here to
2691 indicate that <literal>hammeredLookup</literal> applied at a
2692 certain type should be replaced by <literal>blah</literal>. See
2693 <xref linkend="rules"> for more information on
2694 <literal>RULES</literal>.</para>
2696 <para>An example in which using <literal>RULES</literal> for
2697 specialisation will Win Big:
2700 toDouble :: Real a => a -> Double
2701 toDouble = fromRational . toRational
2703 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2704 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2707 The <function>i2d</function> function is virtually one machine
2708 instruction; the default conversion—via an intermediate
2709 <literal>Rational</literal>—is obscenely expensive by
2712 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2713 be put anywhere its type signature could be put.</para>
2717 <sect2 id="specialize-instance-pragma">
2718 <title>SPECIALIZE instance pragma
2722 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2723 <indexterm><primary>overloading, death to</primary></indexterm>
2724 Same idea, except for instance declarations. For example:
2727 instance (Eq a) => Eq (Foo a) where {
2728 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2732 The pragma must occur inside the <literal>where</literal> part
2733 of the instance declaration.
2736 Compatible with HBC, by the way, except perhaps in the placement
2742 <sect2 id="line-pragma">
2747 <indexterm><primary>LINE pragma</primary></indexterm>
2748 <indexterm><primary>pragma, LINE</primary></indexterm>
2752 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2753 automatically generated Haskell code. It lets you specify the line
2754 number and filename of the original code; for example
2760 {-# LINE 42 "Foo.vhs" #-}
2766 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2767 and this line corresponds to line 42 in the original. GHC will adjust
2768 its error messages to refer to the line/file named in the <literal>LINE</literal>
2775 <title>RULES pragma</title>
2778 The RULES pragma lets you specify rewrite rules. It is described in
2779 <xref LinkEnd="rewrite-rules">.
2784 <sect2 id="deprecated-pragma">
2785 <title>DEPRECATED pragma</title>
2788 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2789 There are two forms.
2793 You can deprecate an entire module thus:</para>
2795 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2799 When you compile any module that import <literal>Wibble</literal>, GHC will print
2800 the specified message.</para>
2805 You can deprecate a function, class, or type, with the following top-level declaration:
2808 {-# DEPRECATED f, C, T "Don't use these" #-}
2811 When you compile any module that imports and uses any of the specifed entities,
2812 GHC will print the specified message.
2816 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2822 <!-- ======================= REWRITE RULES ======================== -->
2824 <sect1 id="rewrite-rules">
2825 <title>Rewrite rules
2827 <indexterm><primary>RULES pagma</primary></indexterm>
2828 <indexterm><primary>pragma, RULES</primary></indexterm>
2829 <indexterm><primary>rewrite rules</primary></indexterm></title>
2832 The programmer can specify rewrite rules as part of the source program
2833 (in a pragma). GHC applies these rewrite rules wherever it can.
2841 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2848 <title>Syntax</title>
2851 From a syntactic point of view:
2857 Each rule has a name, enclosed in double quotes. The name itself has
2858 no significance at all. It is only used when reporting how many times the rule fired.
2864 There may be zero or more rules in a <literal>RULES</literal> pragma.
2870 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2871 is set, so you must lay out your rules starting in the same column as the
2872 enclosing definitions.
2878 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2879 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2880 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2881 by spaces, just like in a type <literal>forall</literal>.
2887 A pattern variable may optionally have a type signature.
2888 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2889 For example, here is the <literal>foldr/build</literal> rule:
2892 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2893 foldr k z (build g) = g k z
2896 Since <function>g</function> has a polymorphic type, it must have a type signature.
2903 The left hand side of a rule must consist of a top-level variable applied
2904 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2907 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2908 "wrong2" forall f. f True = True
2911 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2918 A rule does not need to be in the same module as (any of) the
2919 variables it mentions, though of course they need to be in scope.
2925 Rules are automatically exported from a module, just as instance declarations are.
2936 <title>Semantics</title>
2939 From a semantic point of view:
2945 Rules are only applied if you use the <option>-O</option> flag.
2951 Rules are regarded as left-to-right rewrite rules.
2952 When GHC finds an expression that is a substitution instance of the LHS
2953 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
2954 By "a substitution instance" we mean that the LHS can be made equal to the
2955 expression by substituting for the pattern variables.
2962 The LHS and RHS of a rule are typechecked, and must have the
2970 GHC makes absolutely no attempt to verify that the LHS and RHS
2971 of a rule have the same meaning. That is undecideable in general, and
2972 infeasible in most interesting cases. The responsibility is entirely the programmer's!
2979 GHC makes no attempt to make sure that the rules are confluent or
2980 terminating. For example:
2983 "loop" forall x,y. f x y = f y x
2986 This rule will cause the compiler to go into an infinite loop.
2993 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
2999 GHC currently uses a very simple, syntactic, matching algorithm
3000 for matching a rule LHS with an expression. It seeks a substitution
3001 which makes the LHS and expression syntactically equal modulo alpha
3002 conversion. The pattern (rule), but not the expression, is eta-expanded if
3003 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3004 But not beta conversion (that's called higher-order matching).
3008 Matching is carried out on GHC's intermediate language, which includes
3009 type abstractions and applications. So a rule only matches if the
3010 types match too. See <xref LinkEnd="rule-spec"> below.
3016 GHC keeps trying to apply the rules as it optimises the program.
3017 For example, consider:
3026 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3027 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3028 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3029 not be substituted, and the rule would not fire.
3036 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3037 that appears on the LHS of a rule</emphasis>, because once you have substituted
3038 for something you can't match against it (given the simple minded
3039 matching). So if you write the rule
3042 "map/map" forall f,g. map f . map g = map (f.g)
3045 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3046 It will only match something written with explicit use of ".".
3047 Well, not quite. It <emphasis>will</emphasis> match the expression
3053 where <function>wibble</function> is defined:
3056 wibble f g = map f . map g
3059 because <function>wibble</function> will be inlined (it's small).
3061 Later on in compilation, GHC starts inlining even things on the
3062 LHS of rules, but still leaves the rules enabled. This inlining
3063 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3070 All rules are implicitly exported from the module, and are therefore
3071 in force in any module that imports the module that defined the rule, directly
3072 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3073 in force when compiling A.) The situation is very similar to that for instance
3085 <title>List fusion</title>
3088 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3089 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3090 intermediate list should be eliminated entirely.
3094 The following are good producers:
3106 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3112 Explicit lists (e.g. <literal>[True, False]</literal>)
3118 The cons constructor (e.g <literal>3:4:[]</literal>)
3124 <function>++</function>
3130 <function>map</function>
3136 <function>filter</function>
3142 <function>iterate</function>, <function>repeat</function>
3148 <function>zip</function>, <function>zipWith</function>
3157 The following are good consumers:
3169 <function>array</function> (on its second argument)
3175 <function>length</function>
3181 <function>++</function> (on its first argument)
3187 <function>foldr</function>
3193 <function>map</function>
3199 <function>filter</function>
3205 <function>concat</function>
3211 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3217 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3218 will fuse with one but not the other)
3224 <function>partition</function>
3230 <function>head</function>
3236 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3242 <function>sequence_</function>
3248 <function>msum</function>
3254 <function>sortBy</function>
3263 So, for example, the following should generate no intermediate lists:
3266 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3272 This list could readily be extended; if there are Prelude functions that you use
3273 a lot which are not included, please tell us.
3277 If you want to write your own good consumers or producers, look at the
3278 Prelude definitions of the above functions to see how to do so.
3283 <sect2 id="rule-spec">
3284 <title>Specialisation
3288 Rewrite rules can be used to get the same effect as a feature
3289 present in earlier version of GHC:
3292 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3295 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3296 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3297 specialising the original definition of <function>fromIntegral</function> the programmer is
3298 promising that it is safe to use <function>int8ToInt16</function> instead.
3302 This feature is no longer in GHC. But rewrite rules let you do the
3307 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3311 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3312 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3313 GHC adds the type and dictionary applications to get the typed rule
3316 forall (d1::Integral Int8) (d2::Num Int16) .
3317 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3321 this rule does not need to be in the same file as fromIntegral,
3322 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3323 have an original definition available to specialise).
3329 <title>Controlling what's going on</title>
3337 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3343 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3344 If you add <option>-dppr-debug</option> you get a more detailed listing.
3350 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3353 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3354 {-# INLINE build #-}
3358 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3359 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3360 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3361 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3368 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3369 see how to write rules that will do fusion and yet give an efficient
3370 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3382 <sect1 id="generic-classes">
3383 <title>Generic classes</title>
3385 <para>(Note: support for generic classes is currently broken in
3389 The ideas behind this extension are described in detail in "Derivable type classes",
3390 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3391 An example will give the idea:
3399 fromBin :: [Int] -> (a, [Int])
3401 toBin {| Unit |} Unit = []
3402 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3403 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3404 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3406 fromBin {| Unit |} bs = (Unit, bs)
3407 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3408 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3409 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3410 (y,bs'') = fromBin bs'
3413 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3414 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3415 which are defined thus in the library module <literal>Generics</literal>:
3419 data a :+: b = Inl a | Inr b
3420 data a :*: b = a :*: b
3423 Now you can make a data type into an instance of Bin like this:
3425 instance (Bin a, Bin b) => Bin (a,b)
3426 instance Bin a => Bin [a]
3428 That is, just leave off the "where" clasuse. Of course, you can put in the
3429 where clause and over-ride whichever methods you please.
3433 <title> Using generics </title>
3434 <para>To use generics you need to</para>
3437 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3438 <option>-fgenerics</option> (to generate extra per-data-type code),
3439 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3443 <para>Import the module <literal>Generics</literal> from the
3444 <literal>lang</literal> package. This import brings into
3445 scope the data types <literal>Unit</literal>,
3446 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3447 don't need this import if you don't mention these types
3448 explicitly; for example, if you are simply giving instance
3449 declarations.)</para>
3454 <sect2> <title> Changes wrt the paper </title>
3456 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3457 can be written infix (indeed, you can now use
3458 any operator starting in a colon as an infix type constructor). Also note that
3459 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3460 Finally, note that the syntax of the type patterns in the class declaration
3461 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3462 alone would ambiguous when they appear on right hand sides (an extension we
3463 anticipate wanting).
3467 <sect2> <title>Terminology and restrictions</title>
3469 Terminology. A "generic default method" in a class declaration
3470 is one that is defined using type patterns as above.
3471 A "polymorphic default method" is a default method defined as in Haskell 98.
3472 A "generic class declaration" is a class declaration with at least one
3473 generic default method.
3481 Alas, we do not yet implement the stuff about constructor names and
3488 A generic class can have only one parameter; you can't have a generic
3489 multi-parameter class.
3495 A default method must be defined entirely using type patterns, or entirely
3496 without. So this is illegal:
3499 op :: a -> (a, Bool)
3500 op {| Unit |} Unit = (Unit, True)
3503 However it is perfectly OK for some methods of a generic class to have
3504 generic default methods and others to have polymorphic default methods.
3510 The type variable(s) in the type pattern for a generic method declaration
3511 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:
3515 op {| p :*: q |} (x :*: y) = op (x :: p)
3523 The type patterns in a generic default method must take one of the forms:
3529 where "a" and "b" are type variables. Furthermore, all the type patterns for
3530 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3531 must use the same type variables. So this is illegal:
3535 op {| a :+: b |} (Inl x) = True
3536 op {| p :+: q |} (Inr y) = False
3538 The type patterns must be identical, even in equations for different methods of the class.
3539 So this too is illegal:
3543 op1 {| a :*: b |} (x :*: y) = True
3546 op2 {| p :*: q |} (x :*: y) = False
3548 (The reason for this restriction is that we gather all the equations for a particular type consructor
3549 into a single generic instance declaration.)
3555 A generic method declaration must give a case for each of the three type constructors.
3561 The type for a generic method can be built only from:
3563 <listitem> <para> Function arrows </para> </listitem>
3564 <listitem> <para> Type variables </para> </listitem>
3565 <listitem> <para> Tuples </para> </listitem>
3566 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3568 Here are some example type signatures for generic methods:
3571 op2 :: Bool -> (a,Bool)
3572 op3 :: [Int] -> a -> a
3575 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3579 This restriction is an implementation restriction: we just havn't got around to
3580 implementing the necessary bidirectional maps over arbitrary type constructors.
3581 It would be relatively easy to add specific type constructors, such as Maybe and list,
3582 to the ones that are allowed.</para>
3587 In an instance declaration for a generic class, the idea is that the compiler
3588 will fill in the methods for you, based on the generic templates. However it can only
3593 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3598 No constructor of the instance type has unboxed fields.
3602 (Of course, these things can only arise if you are already using GHC extensions.)
3603 However, you can still give an instance declarations for types which break these rules,
3604 provided you give explicit code to override any generic default methods.
3612 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3613 what the compiler does with generic declarations.
3618 <sect2> <title> Another example </title>
3620 Just to finish with, here's another example I rather like:
3624 nCons {| Unit |} _ = 1
3625 nCons {| a :*: b |} _ = 1
3626 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3629 tag {| Unit |} _ = 1
3630 tag {| a :*: b |} _ = 1
3631 tag {| a :+: b |} (Inl x) = tag x
3632 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3638 <sect1 id="newtype-deriving">
3639 <title>Generalised derived instances for newtypes</title>
3642 When you define an abstract type using <literal>newtype</literal>, you may want
3643 the new type to inherit some instances from its representation. In
3644 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3645 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3646 other classes you have to write an explicit instance declaration. For
3647 example, if you define
3650 newtype Dollars = Dollars Int
3653 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3654 explicitly define an instance of <literal>Num</literal>:
3657 instance Num Dollars where
3658 Dollars a + Dollars b = Dollars (a+b)
3661 All the instance does is apply and remove the <literal>newtype</literal>
3662 constructor. It is particularly galling that, since the constructor
3663 doesn't appear at run-time, this instance declaration defines a
3664 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3665 dictionary, only slower!
3668 <sect2> <title> Generalising the deriving clause </title>
3670 GHC now permits such instances to be derived instead, so one can write
3672 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3675 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3676 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3677 derives an instance declaration of the form
3680 instance Num Int => Num Dollars
3683 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3687 We can also derive instances of constructor classes in a similar
3688 way. For example, suppose we have implemented state and failure monad
3689 transformers, such that
3692 instance Monad m => Monad (State s m)
3693 instance Monad m => Monad (Failure m)
3695 In Haskell 98, we can define a parsing monad by
3697 type Parser tok m a = State [tok] (Failure m) a
3700 which is automatically a monad thanks to the instance declarations
3701 above. With the extension, we can make the parser type abstract,
3702 without needing to write an instance of class <literal>Monad</literal>, via
3705 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3708 In this case the derived instance declaration is of the form
3710 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3713 Notice that, since <literal>Monad</literal> is a constructor class, the
3714 instance is a <emphasis>partial application</emphasis> of the new type, not the
3715 entire left hand side. We can imagine that the type declaration is
3716 ``eta-converted'' to generate the context of the instance
3721 We can even derive instances of multi-parameter classes, provided the
3722 newtype is the last class parameter. In this case, a ``partial
3723 application'' of the class appears in the <literal>deriving</literal>
3724 clause. For example, given the class
3727 class StateMonad s m | m -> s where ...
3728 instance Monad m => StateMonad s (State s m) where ...
3730 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3732 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3733 deriving (Monad, StateMonad [tok])
3736 The derived instance is obtained by completing the application of the
3737 class to the new type:
3740 instance StateMonad [tok] (State [tok] (Failure m)) =>
3741 StateMonad [tok] (Parser tok m)
3746 As a result of this extension, all derived instances in newtype
3747 declarations are treated uniformly (and implemented just by reusing
3748 the dictionary for the representation type), <emphasis>except</emphasis>
3749 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3750 the newtype and its representation.
3754 <sect2> <title> A more precise specification </title>
3756 Derived instance declarations are constructed as follows. Consider the
3757 declaration (after expansion of any type synonyms)
3760 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3763 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3765 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3766 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3767 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3768 declarations are, for each <literal>ci</literal>,
3771 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3773 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3774 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3778 As an example which does <emphasis>not</emphasis> work, consider
3780 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3782 Here we cannot derive the instance
3784 instance Monad (State s m) => Monad (NonMonad m)
3787 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3788 and so cannot be "eta-converted" away. It is a good thing that this
3789 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3790 not, in fact, a monad --- for the same reason. Try defining
3791 <literal>>>=</literal> with the correct type: you won't be able to.
3795 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3796 important, since we can only derive instances for the last one. If the
3797 <literal>StateMonad</literal> class above were instead defined as
3800 class StateMonad m s | m -> s where ...
3803 then we would not have been able to derive an instance for the
3804 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3805 classes usually have one "main" parameter for which deriving new
3806 instances is most interesting.
3814 ;;; Local Variables: ***
3816 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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