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="infix-tycons">
222 <title>Infix type constructors</title>
225 GHC allows type constructors to be operators, and to be written infix, very much
226 like expressions. More specifically:
229 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
230 The lexical syntax is the same as that for data constructors.
233 Types can be written infix. For example <literal>Int :*: Bool</literal>.
237 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
238 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
241 Fixities may be declared for type constructors just as for data constructors. However,
242 one cannot distinguish between the two in a fixity declaration; a fixity declaration
243 sets the fixity for a data constructor and the corresponding type constructor. For example:
247 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
248 and similarly for <literal>:*:</literal>.
249 <literal>Int `a` Bool</literal>.
252 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
255 Data type and type-synonym declarations can be written infix. E.g.
257 data a :*: b = Foo a b
258 type a :+: b = Either a b
262 The only thing that differs between operators in types and operators in expressions is that
263 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
264 are not allowed in types. Reason: the uniform thing to do would be to make them type
265 variables, but that's not very useful. A less uniform but more useful thing would be to
266 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
267 lists. So for now we just exclude them.
274 <sect2 id="class-method-types">
275 <title>Class method types
278 Haskell 98 prohibits class method types to mention constraints on the
279 class type variable, thus:
282 fromList :: [a] -> s a
283 elem :: Eq a => a -> s a -> Bool
285 The type of <literal>elem</literal> is illegal in Haskell 98, because it
286 contains the constraint <literal>Eq a</literal>, constrains only the
287 class type variable (in this case <literal>a</literal>).
290 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
295 <sect2 id="multi-param-type-classes">
296 <title>Multi-parameter type classes
300 This section documents GHC's implementation of multi-parameter type
301 classes. There's lots of background in the paper <ULink
302 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
303 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
308 I'd like to thank people who reported shorcomings in the GHC 3.02
309 implementation. Our default decisions were all conservative ones, and
310 the experience of these heroic pioneers has given useful concrete
311 examples to support several generalisations. (These appear below as
312 design choices not implemented in 3.02.)
316 I've discussed these notes with Mark Jones, and I believe that Hugs
317 will migrate towards the same design choices as I outline here.
318 Thanks to him, and to many others who have offered very useful
326 There are the following restrictions on the form of a qualified
333 forall tv1..tvn (c1, ...,cn) => type
339 (Here, I write the "foralls" explicitly, although the Haskell source
340 language omits them; in Haskell 1.4, all the free type variables of an
341 explicit source-language type signature are universally quantified,
342 except for the class type variables in a class declaration. However,
343 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
352 <emphasis>Each universally quantified type variable
353 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
355 The reason for this is that a value with a type that does not obey
356 this restriction could not be used without introducing
357 ambiguity. Here, for example, is an illegal type:
361 forall a. Eq a => Int
365 When a value with this type was used, the constraint <literal>Eq tv</literal>
366 would be introduced where <literal>tv</literal> is a fresh type variable, and
367 (in the dictionary-translation implementation) the value would be
368 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
369 can never know which instance of <literal>Eq</literal> to use because we never
370 get any more information about <literal>tv</literal>.
377 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
378 universally quantified type variables <literal>tvi</literal></emphasis>.
380 For example, this type is OK because <literal>C a b</literal> mentions the
381 universally quantified type variable <literal>b</literal>:
385 forall a. C a b => burble
389 The next type is illegal because the constraint <literal>Eq b</literal> does not
390 mention <literal>a</literal>:
394 forall a. Eq b => burble
398 The reason for this restriction is milder than the other one. The
399 excluded types are never useful or necessary (because the offending
400 context doesn't need to be witnessed at this point; it can be floated
401 out). Furthermore, floating them out increases sharing. Lastly,
402 excluding them is a conservative choice; it leaves a patch of
403 territory free in case we need it later.
413 These restrictions apply to all types, whether declared in a type signature
418 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
419 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
426 f :: Eq (m a) => [m a] -> [m a]
433 This choice recovers principal types, a property that Haskell 1.4 does not have.
439 <title>Class declarations</title>
447 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
451 class Collection c a where
452 union :: c a -> c a -> c a
463 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
464 of "acyclic" involves only the superclass relationships. For example,
470 op :: D b => a -> b -> b
473 class C a => D a where { ... }
477 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
478 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
479 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
486 <emphasis>There are no restrictions on the context in a class declaration
487 (which introduces superclasses), except that the class hierarchy must
488 be acyclic</emphasis>. So these class declarations are OK:
492 class Functor (m k) => FiniteMap m k where
495 class (Monad m, Monad (t m)) => Transform t m where
496 lift :: m a -> (t m) a
505 <emphasis>In the signature of a class operation, every constraint
506 must mention at least one type variable that is not a class type
513 class Collection c a where
514 mapC :: Collection c b => (a->b) -> c a -> c b
518 is OK because the constraint <literal>(Collection a b)</literal> mentions
519 <literal>b</literal>, even though it also mentions the class variable
520 <literal>a</literal>. On the other hand:
525 op :: Eq a => (a,b) -> (a,b)
529 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
530 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
531 example is easily fixed by moving the offending context up to the
536 class Eq a => C a where
541 A yet more relaxed rule would allow the context of a class-op signature
542 to mention only class type variables. However, that conflicts with
543 Rule 1(b) for types above.
550 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
551 the class type variables</emphasis>. For example:
557 insert :: s -> a -> s
561 is not OK, because the type of <literal>empty</literal> doesn't mention
562 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
563 types, and has the same motivation.
565 Sometimes, offending class declarations exhibit misunderstandings. For
566 example, <literal>Coll</literal> might be rewritten
572 insert :: s a -> a -> s a
576 which makes the connection between the type of a collection of
577 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
578 Occasionally this really doesn't work, in which case you can split the
586 class CollE s => Coll s a where
587 insert :: s -> a -> s
600 <sect3 id="instance-decls">
601 <title>Instance declarations</title>
609 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
614 instance context1 => C type1 where ...
615 instance context2 => C type2 where ...
619 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
621 However, if you give the command line option
622 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
623 option</primary></indexterm> then overlapping instance declarations are permitted.
624 However, GHC arranges never to commit to using an instance declaration
625 if another instance declaration also applies, either now or later.
631 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
637 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
638 (but not identical to <literal>type1</literal>), or vice versa.
642 Notice that these rules
647 make it clear which instance decl to use
648 (pick the most specific one that matches)
655 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
656 Reason: you can pick which instance decl
657 "matches" based on the type.
662 However the rules are over-conservative. Two instance declarations can overlap,
663 but it can still be clear in particular situations which to use. For example:
665 instance C (Int,a) where ...
666 instance C (a,Bool) where ...
668 These are rejected by GHC's rules, but it is clear what to do when trying
669 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
670 cannot apply. Yell if this restriction bites you.
673 GHC is also conservative about committing to an overlapping instance. For example:
675 class C a where { op :: a -> a }
676 instance C [Int] where ...
677 instance C a => C [a] where ...
679 f :: C b => [b] -> [b]
682 From the RHS of f we get the constraint <literal>C [b]</literal>. But
683 GHC does not commit to the second instance declaration, because in a paricular
684 call of f, b might be instantiate to Int, so the first instance declaration
685 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
686 GHC will instead silently pick the second instance, without complaining about
687 the problem of subsequent instantiations.
690 Regrettably, GHC doesn't guarantee to detect overlapping instance
691 declarations if they appear in different modules. GHC can "see" the
692 instance declarations in the transitive closure of all the modules
693 imported by the one being compiled, so it can "see" all instance decls
694 when it is compiling <literal>Main</literal>. However, it currently chooses not
695 to look at ones that can't possibly be of use in the module currently
696 being compiled, in the interests of efficiency. (Perhaps we should
697 change that decision, at least for <literal>Main</literal>.)
704 <emphasis>There are no restrictions on the type in an instance
705 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
706 The instance "head" is the bit after the "=>" in an instance decl. For
707 example, these are OK:
711 instance C Int a where ...
713 instance D (Int, Int) where ...
715 instance E [[a]] where ...
719 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
720 For example, this is OK:
724 instance Stateful (ST s) (MutVar s) where ...
728 The "at least one not a type variable" restriction is to ensure that
729 context reduction terminates: each reduction step removes one type
730 constructor. For example, the following would make the type checker
731 loop if it wasn't excluded:
735 instance C a => C a where ...
739 There are two situations in which the rule is a bit of a pain. First,
740 if one allows overlapping instance declarations then it's quite
741 convenient to have a "default instance" declaration that applies if
742 something more specific does not:
751 Second, sometimes you might want to use the following to get the
752 effect of a "class synonym":
756 class (C1 a, C2 a, C3 a) => C a where { }
758 instance (C1 a, C2 a, C3 a) => C a where { }
762 This allows you to write shorter signatures:
774 f :: (C1 a, C2 a, C3 a) => ...
778 I'm on the lookout for a simple rule that preserves decidability while
779 allowing these idioms. The experimental flag
780 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
781 option</primary></indexterm> lifts this restriction, allowing all the types in an
782 instance head to be type variables.
789 <emphasis>Unlike Haskell 1.4, instance heads may use type
790 synonyms</emphasis>. As always, using a type synonym is just shorthand for
791 writing the RHS of the type synonym definition. For example:
795 type Point = (Int,Int)
796 instance C Point where ...
797 instance C [Point] where ...
801 is legal. However, if you added
805 instance C (Int,Int) where ...
809 as well, then the compiler will complain about the overlapping
810 (actually, identical) instance declarations. As always, type synonyms
811 must be fully applied. You cannot, for example, write:
816 instance Monad P where ...
820 This design decision is independent of all the others, and easily
821 reversed, but it makes sense to me.
828 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
829 be type variables</emphasis>. Thus
833 instance C a b => Eq (a,b) where ...
841 instance C Int b => Foo b where ...
845 is not OK. Again, the intent here is to make sure that context
846 reduction terminates.
848 Voluminous correspondence on the Haskell mailing list has convinced me
849 that it's worth experimenting with a more liberal rule. If you use
850 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
851 types in an instance context. Termination is ensured by having a
852 fixed-depth recursion stack. If you exceed the stack depth you get a
853 sort of backtrace, and the opportunity to increase the stack depth
854 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
867 <sect2 id="implicit-parameters">
868 <title>Implicit parameters
871 <para> Implicit paramters are implemented as described in
872 "Implicit parameters: dynamic scoping with static types",
873 J Lewis, MB Shields, E Meijer, J Launchbury,
874 27th ACM Symposium on Principles of Programming Languages (POPL'00),
877 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
879 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
880 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
881 context. In Haskell, all variables are statically bound. Dynamic
882 binding of variables is a notion that goes back to Lisp, but was later
883 discarded in more modern incarnations, such as Scheme. Dynamic binding
884 can be very confusing in an untyped language, and unfortunately, typed
885 languages, in particular Hindley-Milner typed languages like Haskell,
886 only support static scoping of variables.
889 However, by a simple extension to the type class system of Haskell, we
890 can support dynamic binding. Basically, we express the use of a
891 dynamically bound variable as a constraint on the type. These
892 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
893 function uses a dynamically-bound variable <literal>?x</literal>
894 of type <literal>t'</literal>". For
895 example, the following expresses the type of a sort function,
896 implicitly parameterized by a comparison function named <literal>cmp</literal>.
898 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
900 The dynamic binding constraints are just a new form of predicate in the type class system.
903 An implicit parameter is introduced by the special form <literal>?x</literal>,
904 where <literal>x</literal> is
905 any valid identifier. Use if this construct also introduces new
906 dynamic binding constraints. For example, the following definition
907 shows how we can define an implicitly parameterized sort function in
908 terms of an explicitly parameterized <literal>sortBy</literal> function:
910 sortBy :: (a -> a -> Bool) -> [a] -> [a]
912 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
915 Dynamic binding constraints behave just like other type class
916 constraints in that they are automatically propagated. Thus, when a
917 function is used, its implicit parameters are inherited by the
918 function that called it. For example, our <literal>sort</literal> function might be used
919 to pick out the least value in a list:
921 least :: (?cmp :: a -> a -> Bool) => [a] -> a
922 least xs = fst (sort xs)
924 Without lifting a finger, the <literal>?cmp</literal> parameter is
925 propagated to become a parameter of <literal>least</literal> as well. With explicit
926 parameters, the default is that parameters must always be explicit
927 propagated. With implicit parameters, the default is to always
931 An implicit parameter differs from other type class constraints in the
932 following way: All uses of a particular implicit parameter must have
933 the same type. This means that the type of <literal>(?x, ?x)</literal>
934 is <literal>(?x::a) => (a,a)</literal>, and not
935 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
939 An implicit parameter is bound using an expression of the form
940 <emphasis>expr</emphasis> <literal>with</literal> <emphasis>binds</emphasis>,
941 where <literal>with</literal> is a new keyword. This form binds the implicit
942 parameters arising in the body, not the free variables as a <literal>let</literal> or
943 <literal>where</literal> would do. For example, we define the <literal>min</literal> function by binding
944 <literal>cmp</literal>.
947 min = least with ?cmp = (<=)
949 Syntactically, the <emphasis>binds</emphasis> part of a <literal>with</literal> construct must be a
950 collection of simple bindings to variables (no function-style
951 bindings, and no type signatures); these bindings are neither
952 polymorphic or recursive.
955 Note the following additional constraints:
958 <para> You can't have an implicit parameter in the context of a class or instance
959 declaration. For example, both these declarations are illegal:
961 class (?x::Int) => C a where ...
962 instance (?x::a) => Foo [a] where ...
964 Reason: exactly which implicit parameter you pick up depends on exactly where
965 you invoke a function. But the ``invocation'' of instance declarations is done
966 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
967 Easiest thing is to outlaw the offending types.</para>
974 <sect2 id="linear-implicit-parameters">
975 <title>Linear implicit parameters
978 Linear implicit parameters are an idea developed by Koen Claessen,
979 Mark Shields, and Simon PJ. They address the long-standing
980 problem that monads seem over-kill for certain sorts of problem, notably:
983 <listitem> <para> distributing a supply of unique names </para> </listitem>
984 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
985 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
989 Linear implicit parameters are just like ordinary implicit parameters,
990 except that they are "linear" -- that is, they cannot be copied, and
991 must be explicitly "split" instead. Linear implicit parameters are
992 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
993 (The '/' in the '%' suggests the split!)
998 import GHC.Exts( Splittable )
1000 data NameSupply = ...
1002 splitNS :: NameSupply -> (NameSupply, NameSupply)
1003 newName :: NameSupply -> Name
1005 instance Splittable NameSupply where
1009 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1010 f env (Lam x e) = Lam x' (f env e)
1013 env' = extend env x x'
1014 ...more equations for f...
1016 Notice that the implicit parameter %ns is consumed
1018 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1019 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1023 So the translation done by the type checker makes
1024 the parameter explicit:
1026 f :: NameSupply -> Env -> Expr -> Expr
1027 f ns env (Lam x e) = Lam x' (f ns1 env e)
1029 (ns1,ns2) = splitNS ns
1031 env = extend env x x'
1033 Notice the call to 'split' introduced by the type checker.
1034 How did it know to use 'splitNS'? Because what it really did
1035 was to introduce a call to the overloaded function 'split',
1036 defined by the class <literal>Splittable</literal>:
1038 class Splittable a where
1041 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1042 split for name supplies. But we can simply write
1048 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1050 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1051 <literal>GHC.Exts</literal>.
1056 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1057 are entirely distinct implicit parameters: you
1058 can use them together and they won't intefere with each other. </para>
1061 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1063 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1064 in the context of a class or instance declaration. </para></listitem>
1068 <sect3><title>Warnings</title>
1071 The monomorphism restriction is even more important than usual.
1072 Consider the example above:
1074 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1075 f env (Lam x e) = Lam x' (f env e)
1078 env' = extend env x x'
1080 If we replaced the two occurrences of x' by (newName %ns), which is
1081 usually a harmless thing to do, we get:
1083 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1084 f env (Lam x e) = Lam (newName %ns) (f env e)
1086 env' = extend env x (newName %ns)
1088 But now the name supply is consumed in <emphasis>three</emphasis> places
1089 (the two calls to newName,and the recursive call to f), so
1090 the result is utterly different. Urk! We don't even have
1094 Well, this is an experimental change. With implicit
1095 parameters we have already lost beta reduction anyway, and
1096 (as John Launchbury puts it) we can't sensibly reason about
1097 Haskell programs without knowing their typing.
1104 <sect2 id="functional-dependencies">
1105 <title>Functional dependencies
1108 <para> Functional dependencies are implemented as described by Mark Jones
1109 in "Type Classes with Functional Dependencies", Mark P. Jones,
1110 In Proceedings of the 9th European Symposium on Programming,
1111 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1115 There should be more documentation, but there isn't (yet). Yell if you need it.
1120 <sect2 id="universal-quantification">
1121 <title>Arbitrary-rank polymorphism
1125 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1126 allows us to say exactly what this means. For example:
1134 g :: forall b. (b -> b)
1136 The two are treated identically.
1140 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1141 explicit universal quantification in
1143 For example, all the following types are legal:
1145 f1 :: forall a b. a -> b -> a
1146 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1148 f2 :: (forall a. a->a) -> Int -> Int
1149 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1151 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1153 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1154 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1155 The <literal>forall</literal> makes explicit the universal quantification that
1156 is implicitly added by Haskell.
1159 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1160 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1161 shows, the polymorphic type on the left of the function arrow can be overloaded.
1164 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1165 they have rank-2 types on the left of a function arrow.
1168 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1169 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1170 that restriction has now been lifted.)
1171 In particular, a forall-type (also called a "type scheme"),
1172 including an operational type class context, is legal:
1174 <listitem> <para> On the left of a function arrow </para> </listitem>
1175 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1176 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1177 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1178 field type signatures.</para> </listitem>
1179 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1180 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1182 There is one place you cannot put a <literal>forall</literal>:
1183 you cannot instantiate a type variable with a forall-type. So you cannot
1184 make a forall-type the argument of a type constructor. So these types are illegal:
1186 x1 :: [forall a. a->a]
1187 x2 :: (forall a. a->a, Int)
1188 x3 :: Maybe (forall a. a->a)
1190 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1191 a type variable any more!
1200 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1201 the types of the constructor arguments. Here are several examples:
1207 data T a = T1 (forall b. b -> b -> b) a
1209 data MonadT m = MkMonad { return :: forall a. a -> m a,
1210 bind :: forall a b. m a -> (a -> m b) -> m b
1213 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1219 The constructors have rank-2 types:
1225 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1226 MkMonad :: forall m. (forall a. a -> m a)
1227 -> (forall a b. m a -> (a -> m b) -> m b)
1229 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1235 Notice that you don't need to use a <literal>forall</literal> if there's an
1236 explicit context. For example in the first argument of the
1237 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1238 prefixed to the argument type. The implicit <literal>forall</literal>
1239 quantifies all type variables that are not already in scope, and are
1240 mentioned in the type quantified over.
1244 As for type signatures, implicit quantification happens for non-overloaded
1245 types too. So if you write this:
1248 data T a = MkT (Either a b) (b -> b)
1251 it's just as if you had written this:
1254 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1257 That is, since the type variable <literal>b</literal> isn't in scope, it's
1258 implicitly universally quantified. (Arguably, it would be better
1259 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1260 where that is what is wanted. Feedback welcomed.)
1264 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1265 the constructor to suitable values, just as usual. For example,
1276 a3 = MkSwizzle reverse
1279 a4 = let r x = Just x
1286 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1287 mkTs f x y = [T1 f x, T1 f y]
1293 The type of the argument can, as usual, be more general than the type
1294 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1295 does not need the <literal>Ord</literal> constraint.)
1299 When you use pattern matching, the bound variables may now have
1300 polymorphic types. For example:
1306 f :: T a -> a -> (a, Char)
1307 f (T1 w k) x = (w k x, w 'c' 'd')
1309 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1310 g (MkSwizzle s) xs f = s (map f (s xs))
1312 h :: MonadT m -> [m a] -> m [a]
1313 h m [] = return m []
1314 h m (x:xs) = bind m x $ \y ->
1315 bind m (h m xs) $ \ys ->
1322 In the function <function>h</function> we use the record selectors <literal>return</literal>
1323 and <literal>bind</literal> to extract the polymorphic bind and return functions
1324 from the <literal>MonadT</literal> data structure, rather than using pattern
1330 <title>Type inference</title>
1333 In general, type inference for arbitrary-rank types is undecideable.
1334 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1335 to get a decidable algorithm by requiring some help from the programmer.
1336 We do not yet have a formal specification of "some help" but the rule is this:
1339 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1340 provides an explicit polymorphic type for x, or GHC's type inference will assume
1341 that x's type has no foralls in it</emphasis>.
1344 What does it mean to "provide" an explicit type for x? You can do that by
1345 giving a type signature for x directly, using a pattern type signature
1346 (<xref linkend="scoped-type-variables">), thus:
1348 \ f :: (forall a. a->a) -> (f True, f 'c')
1350 Alternatively, you can give a type signature to the enclosing
1351 context, which GHC can "push down" to find the type for the variable:
1353 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1355 Here the type signature on the expression can be pushed inwards
1356 to give a type signature for f. Similarly, and more commonly,
1357 one can give a type signature for the function itself:
1359 h :: (forall a. a->a) -> (Bool,Char)
1360 h f = (f True, f 'c')
1362 You don't need to give a type signature if the lambda bound variable
1363 is a constructor argument. Here is an example we saw earlier:
1365 f :: T a -> a -> (a, Char)
1366 f (T1 w k) x = (w k x, w 'c' 'd')
1368 Here we do not need to give a type signature to <literal>w</literal>, because
1369 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1376 <sect3 id="implicit-quant">
1377 <title>Implicit quantification</title>
1380 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1381 user-written types, if and only if there is no explicit <literal>forall</literal>,
1382 GHC finds all the type variables mentioned in the type that are not already
1383 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1387 f :: forall a. a -> a
1394 h :: forall b. a -> b -> b
1400 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1403 f :: (a -> a) -> Int
1405 f :: forall a. (a -> a) -> Int
1407 f :: (forall a. a -> a) -> Int
1410 g :: (Ord a => a -> a) -> Int
1411 -- MEANS the illegal type
1412 g :: forall a. (Ord a => a -> a) -> Int
1414 g :: (forall a. Ord a => a -> a) -> Int
1416 The latter produces an illegal type, which you might think is silly,
1417 but at least the rule is simple. If you want the latter type, you
1418 can write your for-alls explicitly. Indeed, doing so is strongly advised
1425 <title>Liberalised type synonyms
1429 Type synonmys are like macros at the type level, and
1430 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1431 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1433 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1434 in a type synonym, thus:
1436 type Discard a = forall b. Show b => a -> b -> (a, String)
1441 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1448 You can write an unboxed tuple in a type synonym:
1450 type Pr = (# Int, Int #)
1458 You can apply a type synonym to a forall type:
1460 type Foo a = a -> a -> Bool
1462 f :: Foo (forall b. b->b)
1464 After epxanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1466 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1471 You can apply a type synonym to a partially applied type synonym:
1473 type Generic i o = forall x. i x -> o x
1476 foo :: Generic Id []
1478 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1480 foo :: forall x. x -> [x]
1488 GHC currently does kind checking before expanding synonyms (though even that
1492 After expanding type synonyms, GHC does validity checking on types, looking for
1493 the following mal-formedness which isn't detected simply by kind checking:
1496 Type constructor applied to a type involving for-alls.
1499 Unboxed tuple on left of an arrow.
1502 Partially-applied type synonym.
1506 this will be rejected:
1508 type Pr = (# Int, Int #)
1513 because GHC does not allow unboxed tuples on the left of a function arrow.
1518 <title>For-all hoisting</title>
1520 It is often convenient to use generalised type synonyms at the right hand
1521 end of an arrow, thus:
1523 type Discard a = forall b. a -> b -> a
1525 g :: Int -> Discard Int
1528 Simply expanding the type synonym would give
1530 g :: Int -> (forall b. Int -> b -> Int)
1532 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1534 g :: forall b. Int -> Int -> b -> Int
1536 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1537 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1538 performs the transformation:</emphasis>
1540 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1542 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1544 (In fact, GHC tries to retain as much synonym information as possible for use in
1545 error messages, but that is a usability issue.) This rule applies, of course, whether
1546 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1547 valid way to write <literal>g</literal>'s type signature:
1549 g :: Int -> Int -> forall b. b -> Int
1555 <sect2 id="existential-quantification">
1556 <title>Existentially quantified data constructors
1560 The idea of using existential quantification in data type declarations
1561 was suggested by Laufer (I believe, thought doubtless someone will
1562 correct me), and implemented in Hope+. It's been in Lennart
1563 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1564 proved very useful. Here's the idea. Consider the declaration:
1570 data Foo = forall a. MkFoo a (a -> Bool)
1577 The data type <literal>Foo</literal> has two constructors with types:
1583 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1590 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1591 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1592 For example, the following expression is fine:
1598 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1604 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1605 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1606 isUpper</function> packages a character with a compatible function. These
1607 two things are each of type <literal>Foo</literal> and can be put in a list.
1611 What can we do with a value of type <literal>Foo</literal>?. In particular,
1612 what happens when we pattern-match on <function>MkFoo</function>?
1618 f (MkFoo val fn) = ???
1624 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1625 are compatible, the only (useful) thing we can do with them is to
1626 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1633 f (MkFoo val fn) = fn val
1639 What this allows us to do is to package heterogenous values
1640 together with a bunch of functions that manipulate them, and then treat
1641 that collection of packages in a uniform manner. You can express
1642 quite a bit of object-oriented-like programming this way.
1645 <sect3 id="existential">
1646 <title>Why existential?
1650 What has this to do with <emphasis>existential</emphasis> quantification?
1651 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1657 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1663 But Haskell programmers can safely think of the ordinary
1664 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1665 adding a new existential quantification construct.
1671 <title>Type classes</title>
1674 An easy extension (implemented in <Command>hbc</Command>) is to allow
1675 arbitrary contexts before the constructor. For example:
1681 data Baz = forall a. Eq a => Baz1 a a
1682 | forall b. Show b => Baz2 b (b -> b)
1688 The two constructors have the types you'd expect:
1694 Baz1 :: forall a. Eq a => a -> a -> Baz
1695 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1701 But when pattern matching on <function>Baz1</function> the matched values can be compared
1702 for equality, and when pattern matching on <function>Baz2</function> the first matched
1703 value can be converted to a string (as well as applying the function to it).
1704 So this program is legal:
1711 f (Baz1 p q) | p == q = "Yes"
1713 f (Baz2 v fn) = show (fn v)
1719 Operationally, in a dictionary-passing implementation, the
1720 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1721 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1722 extract it on pattern matching.
1726 Notice the way that the syntax fits smoothly with that used for
1727 universal quantification earlier.
1733 <title>Restrictions</title>
1736 There are several restrictions on the ways in which existentially-quantified
1737 constructors can be use.
1746 When pattern matching, each pattern match introduces a new,
1747 distinct, type for each existential type variable. These types cannot
1748 be unified with any other type, nor can they escape from the scope of
1749 the pattern match. For example, these fragments are incorrect:
1757 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1758 is the result of <function>f1</function>. One way to see why this is wrong is to
1759 ask what type <function>f1</function> has:
1763 f1 :: Foo -> a -- Weird!
1767 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1772 f1 :: forall a. Foo -> a -- Wrong!
1776 The original program is just plain wrong. Here's another sort of error
1780 f2 (Baz1 a b) (Baz1 p q) = a==q
1784 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1785 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1786 from the two <function>Baz1</function> constructors.
1794 You can't pattern-match on an existentially quantified
1795 constructor in a <literal>let</literal> or <literal>where</literal> group of
1796 bindings. So this is illegal:
1800 f3 x = a==b where { Baz1 a b = x }
1804 You can only pattern-match
1805 on an existentially-quantified constructor in a <literal>case</literal> expression or
1806 in the patterns of a function definition.
1808 The reason for this restriction is really an implementation one.
1809 Type-checking binding groups is already a nightmare without
1810 existentials complicating the picture. Also an existential pattern
1811 binding at the top level of a module doesn't make sense, because it's
1812 not clear how to prevent the existentially-quantified type "escaping".
1813 So for now, there's a simple-to-state restriction. We'll see how
1821 You can't use existential quantification for <literal>newtype</literal>
1822 declarations. So this is illegal:
1826 newtype T = forall a. Ord a => MkT a
1830 Reason: a value of type <literal>T</literal> must be represented as a pair
1831 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1832 That contradicts the idea that <literal>newtype</literal> should have no
1833 concrete representation. You can get just the same efficiency and effect
1834 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1835 overloading involved, then there is more of a case for allowing
1836 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1837 because the <literal>data</literal> version does carry an implementation cost,
1838 but single-field existentially quantified constructors aren't much
1839 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1840 stands, unless there are convincing reasons to change it.
1848 You can't use <literal>deriving</literal> to define instances of a
1849 data type with existentially quantified data constructors.
1851 Reason: in most cases it would not make sense. For example:#
1854 data T = forall a. MkT [a] deriving( Eq )
1857 To derive <literal>Eq</literal> in the standard way we would need to have equality
1858 between the single component of two <function>MkT</function> constructors:
1862 (MkT a) == (MkT b) = ???
1865 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1866 It's just about possible to imagine examples in which the derived instance
1867 would make sense, but it seems altogether simpler simply to prohibit such
1868 declarations. Define your own instances!
1880 <sect2 id="scoped-type-variables">
1881 <title>Scoped type variables
1885 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1886 variable</emphasis>. For example
1892 f (xs::[a]) = ys ++ ys
1901 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1902 This brings the type variable <literal>a</literal> into scope; it scopes over
1903 all the patterns and right hand sides for this equation for <function>f</function>.
1904 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1908 Pattern type signatures are completely orthogonal to ordinary, separate
1909 type signatures. The two can be used independently or together.
1910 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1911 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1912 implicitly universally quantified. (If there are no type variables in
1913 scope, all type variables mentioned in the signature are universally
1914 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1915 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1916 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1917 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1918 it becomes possible to do so.
1922 Scoped type variables are implemented in both GHC and Hugs. Where the
1923 implementations differ from the specification below, those differences
1928 So much for the basic idea. Here are the details.
1932 <title>What a pattern type signature means</title>
1934 A type variable brought into scope by a pattern type signature is simply
1935 the name for a type. The restriction they express is that all occurrences
1936 of the same name mean the same type. For example:
1938 f :: [Int] -> Int -> Int
1939 f (xs::[a]) (y::a) = (head xs + y) :: a
1941 The pattern type signatures on the left hand side of
1942 <literal>f</literal> express the fact that <literal>xs</literal>
1943 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1944 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1945 specifies that this expression must have the same type <literal>a</literal>.
1946 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1947 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1948 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1949 rules, which specified that a pattern-bound type variable should be universally quantified.)
1950 For example, all of these are legal:</para>
1953 t (x::a) (y::a) = x+y*2
1955 f (x::a) (y::b) = [x,y] -- a unifies with b
1957 g (x::a) = x + 1::Int -- a unifies with Int
1959 h x = let k (y::a) = [x,y] -- a is free in the
1960 in k x -- environment
1962 k (x::a) True = ... -- a unifies with Int
1963 k (x::Int) False = ...
1966 w (x::a) = x -- a unifies with [b]
1972 <title>Scope and implicit quantification</title>
1980 All the type variables mentioned in a pattern,
1981 that are not already in scope,
1982 are brought into scope by the pattern. We describe this set as
1983 the <emphasis>type variables bound by the pattern</emphasis>.
1986 f (x::a) = let g (y::(a,b)) = fst y
1990 The pattern <literal>(x::a)</literal> brings the type variable
1991 <literal>a</literal> into scope, as well as the term
1992 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
1993 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
1994 and brings into scope the type variable <literal>b</literal>.
2000 The type variable(s) bound by the pattern have the same scope
2001 as the term variable(s) bound by the pattern. For example:
2004 f (x::a) = <...rhs of f...>
2005 (p::b, q::b) = (1,2)
2006 in <...body of let...>
2008 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2009 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2010 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2011 just like <literal>p</literal> and <literal>q</literal> do.
2012 Indeed, the newly bound type variables also scope over any ordinary, separate
2013 type signatures in the <literal>let</literal> group.
2020 The type variables bound by the pattern may be
2021 mentioned in ordinary type signatures or pattern
2022 type signatures anywhere within their scope.
2029 In ordinary type signatures, any type variable mentioned in the
2030 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2038 Ordinary type signatures do not bring any new type variables
2039 into scope (except in the type signature itself!). So this is illegal:
2046 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2047 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2048 and that is an incorrect typing.
2055 The pattern type signature is a monotype:
2060 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2064 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2065 not to type schemes.
2069 There is no implicit universal quantification on pattern type signatures (in contrast to
2070 ordinary type signatures).
2080 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2081 scope over the methods defined in the <literal>where</literal> part. For example:
2095 (Not implemented in Hugs yet, Dec 98).
2106 <title>Result type signatures</title>
2114 The result type of a function can be given a signature,
2119 f (x::a) :: [a] = [x,x,x]
2123 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2124 result type. Sometimes this is the only way of naming the type variable
2129 f :: Int -> [a] -> [a]
2130 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2131 in \xs -> map g (reverse xs `zip` xs)
2143 Result type signatures are not yet implemented in Hugs.
2149 <title>Where a pattern type signature can occur</title>
2152 A pattern type signature can occur in any pattern. For example:
2157 A pattern type signature can be on an arbitrary sub-pattern, not
2162 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2171 Pattern type signatures, including the result part, can be used
2172 in lambda abstractions:
2175 (\ (x::a, y) :: a -> x)
2182 Pattern type signatures, including the result part, can be used
2183 in <literal>case</literal> expressions:
2187 case e of { (x::a, y) :: a -> x }
2195 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2196 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2197 token or a parenthesised type of some sort). To see why,
2198 consider how one would parse this:
2212 Pattern type signatures can bind existential type variables.
2217 data T = forall a. MkT [a]
2220 f (MkT [t::a]) = MkT t3
2233 Pattern type signatures
2234 can be used in pattern bindings:
2237 f x = let (y, z::a) = x in ...
2238 f1 x = let (y, z::Int) = x in ...
2239 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2240 f3 :: (b->b) = \x -> x
2243 In all such cases, the binding is not generalised over the pattern-bound
2244 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2245 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2246 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2247 In contrast, the binding
2252 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2253 in <literal>f4</literal>'s scope.
2263 <sect2 id="sec-kinding">
2264 <title>Explicitly-kinded quantification</title>
2267 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2268 to give the kind explicitly as (machine-checked) documentation,
2269 just as it is nice to give a type signature for a function. On some occasions,
2270 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2271 John Hughes had to define the data type:
2273 data Set cxt a = Set [a]
2274 | Unused (cxt a -> ())
2276 The only use for the <literal>Unused</literal> constructor was to force the correct
2277 kind for the type variable <literal>cxt</literal>.
2280 GHC now instead allows you to specify the kind of a type variable directly, wherever
2281 a type variable is explicitly bound. Namely:
2283 <listitem><para><literal>data</literal> declarations:
2285 data Set (cxt :: * -> *) a = Set [a]
2286 </Screen></para></listitem>
2287 <listitem><para><literal>type</literal> declarations:
2289 type T (f :: * -> *) = f Int
2290 </Screen></para></listitem>
2291 <listitem><para><literal>class</literal> declarations:
2293 class (Eq a) => C (f :: * -> *) a where ...
2294 </Screen></para></listitem>
2295 <listitem><para><literal>forall</literal>'s in type signatures:
2297 f :: forall (cxt :: * -> *). Set cxt Int
2298 </Screen></para></listitem>
2303 The parentheses are required. Some of the spaces are required too, to
2304 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2305 will get a parse error, because "<literal>::*->*</literal>" is a
2306 single lexeme in Haskell.
2310 As part of the same extension, you can put kind annotations in types
2313 f :: (Int :: *) -> Int
2314 g :: forall a. a -> (a :: *)
2318 atype ::= '(' ctype '::' kind ')
2320 The parentheses are required.
2325 <!-- ==================== End of type system extensions ================= -->
2328 <!-- ==================== ASSERTIONS ================= -->
2330 <sect1 id="sec-assertions">
2332 <indexterm><primary>Assertions</primary></indexterm>
2336 If you want to make use of assertions in your standard Haskell code, you
2337 could define a function like the following:
2343 assert :: Bool -> a -> a
2344 assert False x = error "assertion failed!"
2351 which works, but gives you back a less than useful error message --
2352 an assertion failed, but which and where?
2356 One way out is to define an extended <function>assert</function> function which also
2357 takes a descriptive string to include in the error message and
2358 perhaps combine this with the use of a pre-processor which inserts
2359 the source location where <function>assert</function> was used.
2363 Ghc offers a helping hand here, doing all of this for you. For every
2364 use of <function>assert</function> in the user's source:
2370 kelvinToC :: Double -> Double
2371 kelvinToC k = assert (k >= 0.0) (k+273.15)
2377 Ghc will rewrite this to also include the source location where the
2384 assert pred val ==> assertError "Main.hs|15" pred val
2390 The rewrite is only performed by the compiler when it spots
2391 applications of <function>Exception.assert</function>, so you can still define and
2392 use your own versions of <function>assert</function>, should you so wish. If not,
2393 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2397 To have the compiler ignore uses of assert, use the compiler option
2398 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2399 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2403 Assertion failures can be caught, see the documentation for the
2404 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2410 <!-- ====================== PATTERN GUARDS ======================= -->
2412 <sect1 id="pattern-guards">
2413 <title>Pattern guards</title>
2416 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2417 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.)
2421 Suppose we have an abstract data type of finite maps, with a
2425 lookup :: FiniteMap -> Int -> Maybe Int
2428 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2429 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2433 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2434 | otherwise = var1 + var2
2436 m1 = lookup env var1
2437 m2 = lookup env var2
2438 ok1 = maybeToBool m1
2439 ok2 = maybeToBool m2
2440 val1 = expectJust m1
2441 val2 = expectJust m2
2445 The auxiliary functions are
2449 maybeToBool :: Maybe a -> Bool
2450 maybeToBool (Just x) = True
2451 maybeToBool Nothing = False
2453 expectJust :: Maybe a -> a
2454 expectJust (Just x) = x
2455 expectJust Nothing = error "Unexpected Nothing"
2459 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2460 ok2</literal> checks that both lookups succeed, using
2461 <function>maybeToBool</function> to convert the <function>Maybe</function>
2462 types to booleans. The (lazily evaluated) <function>expectJust</function>
2463 calls extract the values from the results of the lookups, and binds the
2464 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2465 respectively. If either lookup fails, then clunky takes the
2466 <literal>otherwise</literal> case and returns the sum of its arguments.
2470 This is certainly legal Haskell, but it is a tremendously verbose and
2471 un-obvious way to achieve the desired effect. Arguably, a more direct way
2472 to write clunky would be to use case expressions:
2476 clunky env var1 var1 = case lookup env var1 of
2478 Just val1 -> case lookup env var2 of
2480 Just val2 -> val1 + val2
2486 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2487 of pattern-matching, guarded equations as case expressions; that is
2488 precisely what the compiler does when compiling equations! The reason that
2489 Haskell provides guarded equations is because they allow us to write down
2490 the cases we want to consider, one at a time, independently of each other.
2491 This structure is hidden in the case version. Two of the right-hand sides
2492 are really the same (<function>fail</function>), and the whole expression
2493 tends to become more and more indented.
2497 Here is how I would write clunky:
2501 clunky env var1 var1
2502 | Just val1 <- lookup env var1
2503 , Just val2 <- lookup env var2
2505 ...other equations for clunky...
2509 The semantics should be clear enough. The qualifers are matched in order.
2510 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2511 right hand side is evaluated and matched against the pattern on the left.
2512 If the match fails then the whole guard fails and the next equation is
2513 tried. If it succeeds, then the appropriate binding takes place, and the
2514 next qualifier is matched, in the augmented environment. Unlike list
2515 comprehensions, however, the type of the expression to the right of the
2516 <literal><-</literal> is the same as the type of the pattern to its
2517 left. The bindings introduced by pattern guards scope over all the
2518 remaining guard qualifiers, and over the right hand side of the equation.
2522 Just as with list comprehensions, boolean expressions can be freely mixed
2523 with among the pattern guards. For example:
2534 Haskell's current guards therefore emerge as a special case, in which the
2535 qualifier list has just one element, a boolean expression.
2539 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2541 <sect1 id="parallel-list-comprehensions">
2542 <title>Parallel List Comprehensions</title>
2543 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2545 <indexterm><primary>parallel list comprehensions</primary>
2548 <para>Parallel list comprehensions are a natural extension to list
2549 comprehensions. List comprehensions can be thought of as a nice
2550 syntax for writing maps and filters. Parallel comprehensions
2551 extend this to include the zipWith family.</para>
2553 <para>A parallel list comprehension has multiple independent
2554 branches of qualifier lists, each separated by a `|' symbol. For
2555 example, the following zips together two lists:</para>
2558 [ (x, y) | x <- xs | y <- ys ]
2561 <para>The behavior of parallel list comprehensions follows that of
2562 zip, in that the resulting list will have the same length as the
2563 shortest branch.</para>
2565 <para>We can define parallel list comprehensions by translation to
2566 regular comprehensions. Here's the basic idea:</para>
2568 <para>Given a parallel comprehension of the form: </para>
2571 [ e | p1 <- e11, p2 <- e12, ...
2572 | q1 <- e21, q2 <- e22, ...
2577 <para>This will be translated to: </para>
2580 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2581 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2586 <para>where `zipN' is the appropriate zip for the given number of
2591 <!-- =============================== PRAGMAS =========================== -->
2593 <sect1 id="pragmas">
2594 <title>Pragmas</title>
2596 <indexterm><primary>pragma</primary></indexterm>
2598 <para>GHC supports several pragmas, or instructions to the
2599 compiler placed in the source code. Pragmas don't normally affect
2600 the meaning of the program, but they might affect the efficiency
2601 of the generated code.</para>
2603 <para>Pragmas all take the form
2605 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2607 where <replaceable>word</replaceable> indicates the type of
2608 pragma, and is followed optionally by information specific to that
2609 type of pragma. Case is ignored in
2610 <replaceable>word</replaceable>. The various values for
2611 <replaceable>word</replaceable> that GHC understands are described
2612 in the following sections; any pragma encountered with an
2613 unrecognised <replaceable>word</replaceable> is (silently)
2616 <sect2 id="inline-pragma">
2617 <title>INLINE pragma
2619 <indexterm><primary>INLINE pragma</primary></indexterm>
2620 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2623 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2624 functions/values that are “small enough,” thus avoiding the call
2625 overhead and possibly exposing other more-wonderful optimisations.
2629 You will probably see these unfoldings (in Core syntax) in your
2634 Normally, if GHC decides a function is “too expensive” to inline, it
2635 will not do so, nor will it export that unfolding for other modules to
2640 The sledgehammer you can bring to bear is the
2641 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2644 key_function :: Int -> String -> (Bool, Double)
2646 #ifdef __GLASGOW_HASKELL__
2647 {-# INLINE key_function #-}
2651 (You don't need to do the C pre-processor carry-on unless you're going
2652 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2656 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2657 “cost” to be very low. The normal unfolding machinery will then be
2658 very keen to inline it.
2662 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2663 signature could be put.
2667 <literal>INLINE</literal> pragmas are a particularly good idea for the
2668 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2669 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2672 #ifdef __GLASGOW_HASKELL__
2673 {-# INLINE thenUs #-}
2674 {-# INLINE returnUs #-}
2682 <sect2 id="noinline-pragma">
2683 <title>NOINLINE pragma
2686 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2687 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2688 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2689 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2692 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2693 it stops the named function from being inlined by the compiler. You
2694 shouldn't ever need to do this, unless you're very cautious about code
2698 <para><literal>NOTINLINE</literal> is a synonym for
2699 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2700 by Haskell 98 as the standard way to disable inlining, so it should be
2701 used if you want your code to be portable).</para>
2705 <sect2 id="specialize-pragma">
2706 <title>SPECIALIZE pragma</title>
2708 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2709 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2710 <indexterm><primary>overloading, death to</primary></indexterm>
2712 <para>(UK spelling also accepted.) For key overloaded
2713 functions, you can create extra versions (NB: more code space)
2714 specialised to particular types. Thus, if you have an
2715 overloaded function:</para>
2718 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2721 <para>If it is heavily used on lists with
2722 <literal>Widget</literal> keys, you could specialise it as
2726 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2729 <para>To get very fancy, you can also specify a named function
2730 to use for the specialised value, as in:</para>
2733 {-# RULES hammeredLookup = blah #-}
2736 <para>where <literal>blah</literal> is an implementation of
2737 <literal>hammerdLookup</literal> written specialy for
2738 <literal>Widget</literal> lookups. It's <emphasis>Your
2739 Responsibility</emphasis> to make sure that
2740 <function>blah</function> really behaves as a specialised
2741 version of <function>hammeredLookup</function>!!!</para>
2743 <para>Note we use the <literal>RULE</literal> pragma here to
2744 indicate that <literal>hammeredLookup</literal> applied at a
2745 certain type should be replaced by <literal>blah</literal>. See
2746 <xref linkend="rules"> for more information on
2747 <literal>RULES</literal>.</para>
2749 <para>An example in which using <literal>RULES</literal> for
2750 specialisation will Win Big:
2753 toDouble :: Real a => a -> Double
2754 toDouble = fromRational . toRational
2756 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2757 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2760 The <function>i2d</function> function is virtually one machine
2761 instruction; the default conversion—via an intermediate
2762 <literal>Rational</literal>—is obscenely expensive by
2765 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2766 be put anywhere its type signature could be put.</para>
2770 <sect2 id="specialize-instance-pragma">
2771 <title>SPECIALIZE instance pragma
2775 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2776 <indexterm><primary>overloading, death to</primary></indexterm>
2777 Same idea, except for instance declarations. For example:
2780 instance (Eq a) => Eq (Foo a) where {
2781 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2785 The pragma must occur inside the <literal>where</literal> part
2786 of the instance declaration.
2789 Compatible with HBC, by the way, except perhaps in the placement
2795 <sect2 id="line-pragma">
2800 <indexterm><primary>LINE pragma</primary></indexterm>
2801 <indexterm><primary>pragma, LINE</primary></indexterm>
2805 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2806 automatically generated Haskell code. It lets you specify the line
2807 number and filename of the original code; for example
2813 {-# LINE 42 "Foo.vhs" #-}
2819 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2820 and this line corresponds to line 42 in the original. GHC will adjust
2821 its error messages to refer to the line/file named in the <literal>LINE</literal>
2828 <title>RULES pragma</title>
2831 The RULES pragma lets you specify rewrite rules. It is described in
2832 <xref LinkEnd="rewrite-rules">.
2837 <sect2 id="deprecated-pragma">
2838 <title>DEPRECATED pragma</title>
2841 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2842 There are two forms.
2846 You can deprecate an entire module thus:</para>
2848 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2852 When you compile any module that import <literal>Wibble</literal>, GHC will print
2853 the specified message.</para>
2858 You can deprecate a function, class, or type, with the following top-level declaration:
2861 {-# DEPRECATED f, C, T "Don't use these" #-}
2864 When you compile any module that imports and uses any of the specifed entities,
2865 GHC will print the specified message.
2869 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2875 <!-- ======================= REWRITE RULES ======================== -->
2877 <sect1 id="rewrite-rules">
2878 <title>Rewrite rules
2880 <indexterm><primary>RULES pagma</primary></indexterm>
2881 <indexterm><primary>pragma, RULES</primary></indexterm>
2882 <indexterm><primary>rewrite rules</primary></indexterm></title>
2885 The programmer can specify rewrite rules as part of the source program
2886 (in a pragma). GHC applies these rewrite rules wherever it can.
2894 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2901 <title>Syntax</title>
2904 From a syntactic point of view:
2910 Each rule has a name, enclosed in double quotes. The name itself has
2911 no significance at all. It is only used when reporting how many times the rule fired.
2917 There may be zero or more rules in a <literal>RULES</literal> pragma.
2923 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2924 is set, so you must lay out your rules starting in the same column as the
2925 enclosing definitions.
2931 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2932 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2933 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2934 by spaces, just like in a type <literal>forall</literal>.
2940 A pattern variable may optionally have a type signature.
2941 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2942 For example, here is the <literal>foldr/build</literal> rule:
2945 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2946 foldr k z (build g) = g k z
2949 Since <function>g</function> has a polymorphic type, it must have a type signature.
2956 The left hand side of a rule must consist of a top-level variable applied
2957 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2960 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2961 "wrong2" forall f. f True = True
2964 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2971 A rule does not need to be in the same module as (any of) the
2972 variables it mentions, though of course they need to be in scope.
2978 Rules are automatically exported from a module, just as instance declarations are.
2989 <title>Semantics</title>
2992 From a semantic point of view:
2998 Rules are only applied if you use the <option>-O</option> flag.
3004 Rules are regarded as left-to-right rewrite rules.
3005 When GHC finds an expression that is a substitution instance of the LHS
3006 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3007 By "a substitution instance" we mean that the LHS can be made equal to the
3008 expression by substituting for the pattern variables.
3015 The LHS and RHS of a rule are typechecked, and must have the
3023 GHC makes absolutely no attempt to verify that the LHS and RHS
3024 of a rule have the same meaning. That is undecideable in general, and
3025 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3032 GHC makes no attempt to make sure that the rules are confluent or
3033 terminating. For example:
3036 "loop" forall x,y. f x y = f y x
3039 This rule will cause the compiler to go into an infinite loop.
3046 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3052 GHC currently uses a very simple, syntactic, matching algorithm
3053 for matching a rule LHS with an expression. It seeks a substitution
3054 which makes the LHS and expression syntactically equal modulo alpha
3055 conversion. The pattern (rule), but not the expression, is eta-expanded if
3056 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3057 But not beta conversion (that's called higher-order matching).
3061 Matching is carried out on GHC's intermediate language, which includes
3062 type abstractions and applications. So a rule only matches if the
3063 types match too. See <xref LinkEnd="rule-spec"> below.
3069 GHC keeps trying to apply the rules as it optimises the program.
3070 For example, consider:
3079 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3080 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3081 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3082 not be substituted, and the rule would not fire.
3089 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3090 that appears on the LHS of a rule</emphasis>, because once you have substituted
3091 for something you can't match against it (given the simple minded
3092 matching). So if you write the rule
3095 "map/map" forall f,g. map f . map g = map (f.g)
3098 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3099 It will only match something written with explicit use of ".".
3100 Well, not quite. It <emphasis>will</emphasis> match the expression
3106 where <function>wibble</function> is defined:
3109 wibble f g = map f . map g
3112 because <function>wibble</function> will be inlined (it's small).
3114 Later on in compilation, GHC starts inlining even things on the
3115 LHS of rules, but still leaves the rules enabled. This inlining
3116 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3123 All rules are implicitly exported from the module, and are therefore
3124 in force in any module that imports the module that defined the rule, directly
3125 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3126 in force when compiling A.) The situation is very similar to that for instance
3138 <title>List fusion</title>
3141 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3142 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3143 intermediate list should be eliminated entirely.
3147 The following are good producers:
3159 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3165 Explicit lists (e.g. <literal>[True, False]</literal>)
3171 The cons constructor (e.g <literal>3:4:[]</literal>)
3177 <function>++</function>
3183 <function>map</function>
3189 <function>filter</function>
3195 <function>iterate</function>, <function>repeat</function>
3201 <function>zip</function>, <function>zipWith</function>
3210 The following are good consumers:
3222 <function>array</function> (on its second argument)
3228 <function>length</function>
3234 <function>++</function> (on its first argument)
3240 <function>foldr</function>
3246 <function>map</function>
3252 <function>filter</function>
3258 <function>concat</function>
3264 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3270 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3271 will fuse with one but not the other)
3277 <function>partition</function>
3283 <function>head</function>
3289 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3295 <function>sequence_</function>
3301 <function>msum</function>
3307 <function>sortBy</function>
3316 So, for example, the following should generate no intermediate lists:
3319 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3325 This list could readily be extended; if there are Prelude functions that you use
3326 a lot which are not included, please tell us.
3330 If you want to write your own good consumers or producers, look at the
3331 Prelude definitions of the above functions to see how to do so.
3336 <sect2 id="rule-spec">
3337 <title>Specialisation
3341 Rewrite rules can be used to get the same effect as a feature
3342 present in earlier version of GHC:
3345 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3348 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3349 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3350 specialising the original definition of <function>fromIntegral</function> the programmer is
3351 promising that it is safe to use <function>int8ToInt16</function> instead.
3355 This feature is no longer in GHC. But rewrite rules let you do the
3360 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3364 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3365 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3366 GHC adds the type and dictionary applications to get the typed rule
3369 forall (d1::Integral Int8) (d2::Num Int16) .
3370 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3374 this rule does not need to be in the same file as fromIntegral,
3375 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3376 have an original definition available to specialise).
3382 <title>Controlling what's going on</title>
3390 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3396 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3397 If you add <option>-dppr-debug</option> you get a more detailed listing.
3403 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3406 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3407 {-# INLINE build #-}
3411 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3412 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3413 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3414 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3421 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3422 see how to write rules that will do fusion and yet give an efficient
3423 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3435 <sect1 id="generic-classes">
3436 <title>Generic classes</title>
3438 <para>(Note: support for generic classes is currently broken in
3442 The ideas behind this extension are described in detail in "Derivable type classes",
3443 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3444 An example will give the idea:
3452 fromBin :: [Int] -> (a, [Int])
3454 toBin {| Unit |} Unit = []
3455 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3456 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3457 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3459 fromBin {| Unit |} bs = (Unit, bs)
3460 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3461 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3462 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3463 (y,bs'') = fromBin bs'
3466 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3467 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3468 which are defined thus in the library module <literal>Generics</literal>:
3472 data a :+: b = Inl a | Inr b
3473 data a :*: b = a :*: b
3476 Now you can make a data type into an instance of Bin like this:
3478 instance (Bin a, Bin b) => Bin (a,b)
3479 instance Bin a => Bin [a]
3481 That is, just leave off the "where" clasuse. Of course, you can put in the
3482 where clause and over-ride whichever methods you please.
3486 <title> Using generics </title>
3487 <para>To use generics you need to</para>
3490 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3491 <option>-fgenerics</option> (to generate extra per-data-type code),
3492 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3496 <para>Import the module <literal>Generics</literal> from the
3497 <literal>lang</literal> package. This import brings into
3498 scope the data types <literal>Unit</literal>,
3499 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3500 don't need this import if you don't mention these types
3501 explicitly; for example, if you are simply giving instance
3502 declarations.)</para>
3507 <sect2> <title> Changes wrt the paper </title>
3509 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3510 can be written infix (indeed, you can now use
3511 any operator starting in a colon as an infix type constructor). Also note that
3512 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3513 Finally, note that the syntax of the type patterns in the class declaration
3514 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3515 alone would ambiguous when they appear on right hand sides (an extension we
3516 anticipate wanting).
3520 <sect2> <title>Terminology and restrictions</title>
3522 Terminology. A "generic default method" in a class declaration
3523 is one that is defined using type patterns as above.
3524 A "polymorphic default method" is a default method defined as in Haskell 98.
3525 A "generic class declaration" is a class declaration with at least one
3526 generic default method.
3534 Alas, we do not yet implement the stuff about constructor names and
3541 A generic class can have only one parameter; you can't have a generic
3542 multi-parameter class.
3548 A default method must be defined entirely using type patterns, or entirely
3549 without. So this is illegal:
3552 op :: a -> (a, Bool)
3553 op {| Unit |} Unit = (Unit, True)
3556 However it is perfectly OK for some methods of a generic class to have
3557 generic default methods and others to have polymorphic default methods.
3563 The type variable(s) in the type pattern for a generic method declaration
3564 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:
3568 op {| p :*: q |} (x :*: y) = op (x :: p)
3576 The type patterns in a generic default method must take one of the forms:
3582 where "a" and "b" are type variables. Furthermore, all the type patterns for
3583 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3584 must use the same type variables. So this is illegal:
3588 op {| a :+: b |} (Inl x) = True
3589 op {| p :+: q |} (Inr y) = False
3591 The type patterns must be identical, even in equations for different methods of the class.
3592 So this too is illegal:
3596 op1 {| a :*: b |} (x :*: y) = True
3599 op2 {| p :*: q |} (x :*: y) = False
3601 (The reason for this restriction is that we gather all the equations for a particular type consructor
3602 into a single generic instance declaration.)
3608 A generic method declaration must give a case for each of the three type constructors.
3614 The type for a generic method can be built only from:
3616 <listitem> <para> Function arrows </para> </listitem>
3617 <listitem> <para> Type variables </para> </listitem>
3618 <listitem> <para> Tuples </para> </listitem>
3619 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3621 Here are some example type signatures for generic methods:
3624 op2 :: Bool -> (a,Bool)
3625 op3 :: [Int] -> a -> a
3628 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3632 This restriction is an implementation restriction: we just havn't got around to
3633 implementing the necessary bidirectional maps over arbitrary type constructors.
3634 It would be relatively easy to add specific type constructors, such as Maybe and list,
3635 to the ones that are allowed.</para>
3640 In an instance declaration for a generic class, the idea is that the compiler
3641 will fill in the methods for you, based on the generic templates. However it can only
3646 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3651 No constructor of the instance type has unboxed fields.
3655 (Of course, these things can only arise if you are already using GHC extensions.)
3656 However, you can still give an instance declarations for types which break these rules,
3657 provided you give explicit code to override any generic default methods.
3665 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3666 what the compiler does with generic declarations.
3671 <sect2> <title> Another example </title>
3673 Just to finish with, here's another example I rather like:
3677 nCons {| Unit |} _ = 1
3678 nCons {| a :*: b |} _ = 1
3679 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3682 tag {| Unit |} _ = 1
3683 tag {| a :*: b |} _ = 1
3684 tag {| a :+: b |} (Inl x) = tag x
3685 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3691 <sect1 id="newtype-deriving">
3692 <title>Generalised derived instances for newtypes</title>
3695 When you define an abstract type using <literal>newtype</literal>, you may want
3696 the new type to inherit some instances from its representation. In
3697 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3698 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3699 other classes you have to write an explicit instance declaration. For
3700 example, if you define
3703 newtype Dollars = Dollars Int
3706 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3707 explicitly define an instance of <literal>Num</literal>:
3710 instance Num Dollars where
3711 Dollars a + Dollars b = Dollars (a+b)
3714 All the instance does is apply and remove the <literal>newtype</literal>
3715 constructor. It is particularly galling that, since the constructor
3716 doesn't appear at run-time, this instance declaration defines a
3717 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3718 dictionary, only slower!
3721 <sect2> <title> Generalising the deriving clause </title>
3723 GHC now permits such instances to be derived instead, so one can write
3725 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3728 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3729 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3730 derives an instance declaration of the form
3733 instance Num Int => Num Dollars
3736 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3740 We can also derive instances of constructor classes in a similar
3741 way. For example, suppose we have implemented state and failure monad
3742 transformers, such that
3745 instance Monad m => Monad (State s m)
3746 instance Monad m => Monad (Failure m)
3748 In Haskell 98, we can define a parsing monad by
3750 type Parser tok m a = State [tok] (Failure m) a
3753 which is automatically a monad thanks to the instance declarations
3754 above. With the extension, we can make the parser type abstract,
3755 without needing to write an instance of class <literal>Monad</literal>, via
3758 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3761 In this case the derived instance declaration is of the form
3763 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3766 Notice that, since <literal>Monad</literal> is a constructor class, the
3767 instance is a <emphasis>partial application</emphasis> of the new type, not the
3768 entire left hand side. We can imagine that the type declaration is
3769 ``eta-converted'' to generate the context of the instance
3774 We can even derive instances of multi-parameter classes, provided the
3775 newtype is the last class parameter. In this case, a ``partial
3776 application'' of the class appears in the <literal>deriving</literal>
3777 clause. For example, given the class
3780 class StateMonad s m | m -> s where ...
3781 instance Monad m => StateMonad s (State s m) where ...
3783 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3785 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3786 deriving (Monad, StateMonad [tok])
3789 The derived instance is obtained by completing the application of the
3790 class to the new type:
3793 instance StateMonad [tok] (State [tok] (Failure m)) =>
3794 StateMonad [tok] (Parser tok m)
3799 As a result of this extension, all derived instances in newtype
3800 declarations are treated uniformly (and implemented just by reusing
3801 the dictionary for the representation type), <emphasis>except</emphasis>
3802 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3803 the newtype and its representation.
3807 <sect2> <title> A more precise specification </title>
3809 Derived instance declarations are constructed as follows. Consider the
3810 declaration (after expansion of any type synonyms)
3813 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3816 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3818 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3819 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3820 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3821 declarations are, for each <literal>ci</literal>,
3824 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3826 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3827 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3831 As an example which does <emphasis>not</emphasis> work, consider
3833 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3835 Here we cannot derive the instance
3837 instance Monad (State s m) => Monad (NonMonad m)
3840 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3841 and so cannot be "eta-converted" away. It is a good thing that this
3842 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3843 not, in fact, a monad --- for the same reason. Try defining
3844 <literal>>>=</literal> with the correct type: you won't be able to.
3848 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3849 important, since we can only derive instances for the last one. If the
3850 <literal>StateMonad</literal> class above were instead defined as
3853 class StateMonad m s | m -> s where ...
3856 then we would not have been able to derive an instance for the
3857 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3858 classes usually have one "main" parameter for which deriving new
3859 instances is most interesting.
3867 ;;; Local Variables: ***
3869 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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