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>-fno-monomorphism-restriction</option>:</term>
56 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
58 <para> Switch off the Haskell 98 monomorphism restriction.
59 Independent of the <option>-fglasgow-exts</option>
65 <term><option>-fallow-overlapping-instances</option></term>
66 <term><option>-fallow-undecidable-instances</option></term>
67 <term><option>-fallow-incoherent-instances</option></term>
68 <term><option>-fcontext-stack</option></term>
69 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
70 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
71 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
73 <para> See <xref LinkEnd="instance-decls">. Only relevant
74 if you also use <option>-fglasgow-exts</option>.</para>
79 <term><option>-finline-phase</option></term>
80 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
82 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
83 you also use <option>-fglasgow-exts</option>.</para>
88 <term><option>-fgenerics</option></term>
89 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
91 <para>See <xref LinkEnd="generic-classes">. Independent of
92 <option>-fglasgow-exts</option>.</para>
97 <term><option>-fno-implicit-prelude</option></term>
99 <para><indexterm><primary>-fno-implicit-prelude
100 option</primary></indexterm> GHC normally imports
101 <filename>Prelude.hi</filename> files for you. If you'd
102 rather it didn't, then give it a
103 <option>-fno-implicit-prelude</option> option. The idea
104 is that you can then import a Prelude of your own. (But
105 don't call it <literal>Prelude</literal>; the Haskell
106 module namespace is flat, and you must not conflict with
107 any Prelude module.)</para>
109 <para>Even though you have not imported the Prelude, all
110 the built-in syntax still refers to the built-in Haskell
111 Prelude types and values, as specified by the Haskell
112 Report. For example, the type <literal>[Int]</literal>
113 still means <literal>Prelude.[] Int</literal>; tuples
114 continue to refer to the standard Prelude tuples; the
115 translation for list comprehensions continues to use
116 <literal>Prelude.map</literal> etc.</para>
118 <para> With one group of exceptions! You may want to
119 define your own numeric class hierarchy. It completely
120 defeats that purpose if the literal "1" means
121 "<literal>Prelude.fromInteger 1</literal>", which is what
122 the Haskell Report specifies. So the
123 <option>-fno-implicit-prelude</option> flag causes the
124 following pieces of built-in syntax to refer to <emphasis>whatever
125 is in scope</emphasis>, not the Prelude versions:</para>
129 <para>Integer and fractional literals mean
130 "<literal>fromInteger 1</literal>" and
131 "<literal>fromRational 3.2</literal>", not the
132 Prelude-qualified versions; both in expressions and in
137 <para>Negation (e.g. "<literal>- (f x)</literal>")
138 means "<literal>negate (f x)</literal>" (not
139 <literal>Prelude.negate</literal>).</para>
143 <para>In an n+k pattern, the standard Prelude
144 <literal>Ord</literal> class is still used for comparison,
145 but the necessary subtraction uses whatever
146 "<literal>(-)</literal>" is in scope (not
147 "<literal>Prelude.(-)</literal>").</para>
151 <para>Note: Negative literals, such as <literal>-3</literal>, are
152 specified by (a careful reading of) the Haskell Report as
153 meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
154 However, GHC deviates from this slightly, and treats them as meaning
155 <literal>fromInteger (-3)</literal>. One particular effect of this
156 slightly-non-standard reading is that there is no difficulty with
157 the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
158 it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
159 would be <literal>negate (fromInteger 2147483648)</literal>,
160 and the call to <literal>fromInteger</literal> would overflow
161 (at type <literal>Int</literal>, remember).
170 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
171 <!-- included from primitives.sgml -->
175 <!-- TYPE SYSTEM EXTENSIONS -->
176 <sect1 id="type-extensions">
177 <title>Type system extensions</title>
179 <sect2 id="nullary-types">
180 <title>Data types with no constructors</title>
182 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
183 a data type with no constructors. For example:</para>
186 data T a -- T :: * -> *
188 <para>Syntactically, the declaration lacks the "= constrs" part. The
189 type can be parameterised, but only over ordinary types, of kind *; since
190 Haskell does not have kind signatures, you cannot parameterise over higher-kinded
193 <para>Such data types have only one value, namely bottom.
194 Nevertheless, they can be useful when defining "phantom types".</para>
197 <sect2 id="class-method-types">
198 <title>Class method types
201 Haskell 98 prohibits class method types to mention constraints on the
202 class type variable, thus:
205 fromList :: [a] -> s a
206 elem :: Eq a => a -> s a -> Bool
208 The type of <literal>elem</literal> is illegal in Haskell 98, because it
209 contains the constraint <literal>Eq a</literal>, constrains only the
210 class type variable (in this case <literal>a</literal>).
213 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
218 <sect2 id="multi-param-type-classes">
219 <title>Multi-parameter type classes
223 This section documents GHC's implementation of multi-parameter type
224 classes. There's lots of background in the paper <ULink
225 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
226 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
231 I'd like to thank people who reported shorcomings in the GHC 3.02
232 implementation. Our default decisions were all conservative ones, and
233 the experience of these heroic pioneers has given useful concrete
234 examples to support several generalisations. (These appear below as
235 design choices not implemented in 3.02.)
239 I've discussed these notes with Mark Jones, and I believe that Hugs
240 will migrate towards the same design choices as I outline here.
241 Thanks to him, and to many others who have offered very useful
249 There are the following restrictions on the form of a qualified
256 forall tv1..tvn (c1, ...,cn) => type
262 (Here, I write the "foralls" explicitly, although the Haskell source
263 language omits them; in Haskell 1.4, all the free type variables of an
264 explicit source-language type signature are universally quantified,
265 except for the class type variables in a class declaration. However,
266 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
275 <emphasis>Each universally quantified type variable
276 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
278 The reason for this is that a value with a type that does not obey
279 this restriction could not be used without introducing
280 ambiguity. Here, for example, is an illegal type:
284 forall a. Eq a => Int
288 When a value with this type was used, the constraint <literal>Eq tv</literal>
289 would be introduced where <literal>tv</literal> is a fresh type variable, and
290 (in the dictionary-translation implementation) the value would be
291 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
292 can never know which instance of <literal>Eq</literal> to use because we never
293 get any more information about <literal>tv</literal>.
300 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
301 universally quantified type variables <literal>tvi</literal></emphasis>.
303 For example, this type is OK because <literal>C a b</literal> mentions the
304 universally quantified type variable <literal>b</literal>:
308 forall a. C a b => burble
312 The next type is illegal because the constraint <literal>Eq b</literal> does not
313 mention <literal>a</literal>:
317 forall a. Eq b => burble
321 The reason for this restriction is milder than the other one. The
322 excluded types are never useful or necessary (because the offending
323 context doesn't need to be witnessed at this point; it can be floated
324 out). Furthermore, floating them out increases sharing. Lastly,
325 excluding them is a conservative choice; it leaves a patch of
326 territory free in case we need it later.
336 These restrictions apply to all types, whether declared in a type signature
341 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
342 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
349 f :: Eq (m a) => [m a] -> [m a]
356 This choice recovers principal types, a property that Haskell 1.4 does not have.
362 <title>Class declarations</title>
370 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
374 class Collection c a where
375 union :: c a -> c a -> c a
386 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
387 of "acyclic" involves only the superclass relationships. For example,
393 op :: D b => a -> b -> b
396 class C a => D a where { ... }
400 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
401 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
402 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
409 <emphasis>There are no restrictions on the context in a class declaration
410 (which introduces superclasses), except that the class hierarchy must
411 be acyclic</emphasis>. So these class declarations are OK:
415 class Functor (m k) => FiniteMap m k where
418 class (Monad m, Monad (t m)) => Transform t m where
419 lift :: m a -> (t m) a
428 <emphasis>In the signature of a class operation, every constraint
429 must mention at least one type variable that is not a class type
436 class Collection c a where
437 mapC :: Collection c b => (a->b) -> c a -> c b
441 is OK because the constraint <literal>(Collection a b)</literal> mentions
442 <literal>b</literal>, even though it also mentions the class variable
443 <literal>a</literal>. On the other hand:
448 op :: Eq a => (a,b) -> (a,b)
452 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
453 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
454 example is easily fixed by moving the offending context up to the
459 class Eq a => C a where
464 A yet more relaxed rule would allow the context of a class-op signature
465 to mention only class type variables. However, that conflicts with
466 Rule 1(b) for types above.
473 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
474 the class type variables</emphasis>. For example:
480 insert :: s -> a -> s
484 is not OK, because the type of <literal>empty</literal> doesn't mention
485 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
486 types, and has the same motivation.
488 Sometimes, offending class declarations exhibit misunderstandings. For
489 example, <literal>Coll</literal> might be rewritten
495 insert :: s a -> a -> s a
499 which makes the connection between the type of a collection of
500 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
501 Occasionally this really doesn't work, in which case you can split the
509 class CollE s => Coll s a where
510 insert :: s -> a -> s
523 <sect3 id="instance-decls">
524 <title>Instance declarations</title>
532 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
537 instance context1 => C type1 where ...
538 instance context2 => C type2 where ...
542 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
544 However, if you give the command line option
545 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
546 option</primary></indexterm> then overlapping instance declarations are permitted.
547 However, GHC arranges never to commit to using an instance declaration
548 if another instance declaration also applies, either now or later.
554 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
560 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
561 (but not identical to <literal>type1</literal>), or vice versa.
565 Notice that these rules
570 make it clear which instance decl to use
571 (pick the most specific one that matches)
578 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
579 Reason: you can pick which instance decl
580 "matches" based on the type.
585 However the rules are over-conservative. Two instance declarations can overlap,
586 but it can still be clear in particular situations which to use. For example:
588 instance C (Int,a) where ...
589 instance C (a,Bool) where ...
591 These are rejected by GHC's rules, but it is clear what to do when trying
592 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
593 cannot apply. Yell if this restriction bites you.
596 GHC is also conservative about committing to an overlapping instance. For example:
598 class C a where { op :: a -> a }
599 instance C [Int] where ...
600 instance C a => C [a] where ...
602 f :: C b => [b] -> [b]
605 From the RHS of f we get the constraint <literal>C [b]</literal>. But
606 GHC does not commit to the second instance declaration, because in a paricular
607 call of f, b might be instantiate to Int, so the first instance declaration
608 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
609 GHC will instead silently pick the second instance, without complaining about
610 the problem of subsequent instantiations.
613 Regrettably, GHC doesn't guarantee to detect overlapping instance
614 declarations if they appear in different modules. GHC can "see" the
615 instance declarations in the transitive closure of all the modules
616 imported by the one being compiled, so it can "see" all instance decls
617 when it is compiling <literal>Main</literal>. However, it currently chooses not
618 to look at ones that can't possibly be of use in the module currently
619 being compiled, in the interests of efficiency. (Perhaps we should
620 change that decision, at least for <literal>Main</literal>.)
627 <emphasis>There are no restrictions on the type in an instance
628 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
629 The instance "head" is the bit after the "=>" in an instance decl. For
630 example, these are OK:
634 instance C Int a where ...
636 instance D (Int, Int) where ...
638 instance E [[a]] where ...
642 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
643 For example, this is OK:
647 instance Stateful (ST s) (MutVar s) where ...
651 The "at least one not a type variable" restriction is to ensure that
652 context reduction terminates: each reduction step removes one type
653 constructor. For example, the following would make the type checker
654 loop if it wasn't excluded:
658 instance C a => C a where ...
662 There are two situations in which the rule is a bit of a pain. First,
663 if one allows overlapping instance declarations then it's quite
664 convenient to have a "default instance" declaration that applies if
665 something more specific does not:
674 Second, sometimes you might want to use the following to get the
675 effect of a "class synonym":
679 class (C1 a, C2 a, C3 a) => C a where { }
681 instance (C1 a, C2 a, C3 a) => C a where { }
685 This allows you to write shorter signatures:
697 f :: (C1 a, C2 a, C3 a) => ...
701 I'm on the lookout for a simple rule that preserves decidability while
702 allowing these idioms. The experimental flag
703 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
704 option</primary></indexterm> lifts this restriction, allowing all the types in an
705 instance head to be type variables.
712 <emphasis>Unlike Haskell 1.4, instance heads may use type
713 synonyms</emphasis>. As always, using a type synonym is just shorthand for
714 writing the RHS of the type synonym definition. For example:
718 type Point = (Int,Int)
719 instance C Point where ...
720 instance C [Point] where ...
724 is legal. However, if you added
728 instance C (Int,Int) where ...
732 as well, then the compiler will complain about the overlapping
733 (actually, identical) instance declarations. As always, type synonyms
734 must be fully applied. You cannot, for example, write:
739 instance Monad P where ...
743 This design decision is independent of all the others, and easily
744 reversed, but it makes sense to me.
751 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
752 be type variables</emphasis>. Thus
756 instance C a b => Eq (a,b) where ...
764 instance C Int b => Foo b where ...
768 is not OK. Again, the intent here is to make sure that context
769 reduction terminates.
771 Voluminous correspondence on the Haskell mailing list has convinced me
772 that it's worth experimenting with a more liberal rule. If you use
773 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
774 types in an instance context. Termination is ensured by having a
775 fixed-depth recursion stack. If you exceed the stack depth you get a
776 sort of backtrace, and the opportunity to increase the stack depth
777 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
790 <sect2 id="implicit-parameters">
791 <title>Implicit parameters
794 <para> Implicit paramters are implemented as described in
795 "Implicit parameters: dynamic scoping with static types",
796 J Lewis, MB Shields, E Meijer, J Launchbury,
797 27th ACM Symposium on Principles of Programming Languages (POPL'00),
800 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
802 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
803 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
804 context. In Haskell, all variables are statically bound. Dynamic
805 binding of variables is a notion that goes back to Lisp, but was later
806 discarded in more modern incarnations, such as Scheme. Dynamic binding
807 can be very confusing in an untyped language, and unfortunately, typed
808 languages, in particular Hindley-Milner typed languages like Haskell,
809 only support static scoping of variables.
812 However, by a simple extension to the type class system of Haskell, we
813 can support dynamic binding. Basically, we express the use of a
814 dynamically bound variable as a constraint on the type. These
815 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
816 function uses a dynamically-bound variable <literal>?x</literal>
817 of type <literal>t'</literal>". For
818 example, the following expresses the type of a sort function,
819 implicitly parameterized by a comparison function named <literal>cmp</literal>.
821 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
823 The dynamic binding constraints are just a new form of predicate in the type class system.
826 An implicit parameter is introduced by the special form <literal>?x</literal>,
827 where <literal>x</literal> is
828 any valid identifier. Use if this construct also introduces new
829 dynamic binding constraints. For example, the following definition
830 shows how we can define an implicitly parameterized sort function in
831 terms of an explicitly parameterized <literal>sortBy</literal> function:
833 sortBy :: (a -> a -> Bool) -> [a] -> [a]
835 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
838 Dynamic binding constraints behave just like other type class
839 constraints in that they are automatically propagated. Thus, when a
840 function is used, its implicit parameters are inherited by the
841 function that called it. For example, our <literal>sort</literal> function might be used
842 to pick out the least value in a list:
844 least :: (?cmp :: a -> a -> Bool) => [a] -> a
845 least xs = fst (sort xs)
847 Without lifting a finger, the <literal>?cmp</literal> parameter is
848 propagated to become a parameter of <literal>least</literal> as well. With explicit
849 parameters, the default is that parameters must always be explicit
850 propagated. With implicit parameters, the default is to always
854 An implicit parameter differs from other type class constraints in the
855 following way: All uses of a particular implicit parameter must have
856 the same type. This means that the type of <literal>(?x, ?x)</literal>
857 is <literal>(?x::a) => (a,a)</literal>, and not
858 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
862 An implicit parameter is bound using an expression of the form
863 <emphasis>expr</emphasis> <literal>with</literal> <emphasis>binds</emphasis>,
864 where <literal>with</literal> is a new keyword. This form binds the implicit
865 parameters arising in the body, not the free variables as a <literal>let</literal> or
866 <literal>where</literal> would do. For example, we define the <literal>min</literal> function by binding
867 <literal>cmp</literal>.
870 min = least with ?cmp = (<=)
872 Syntactically, the <emphasis>binds</emphasis> part of a <literal>with</literal> construct must be a
873 collection of simple bindings to variables (no function-style
874 bindings, and no type signatures); these bindings are neither
875 polymorphic or recursive.
878 Note the following additional constraints:
881 <para> You can't have an implicit parameter in the context of a class or instance
882 declaration. For example, both these declarations are illegal:
884 class (?x::Int) => C a where ...
885 instance (?x::a) => Foo [a] where ...
887 Reason: exactly which implicit parameter you pick up depends on exactly where
888 you invoke a function. But the ``invocation'' of instance declarations is done
889 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
890 Easiest thing is to outlaw the offending types.</para>
897 <sect2 id="linear-implicit-parameters">
898 <title>Linear implicit parameters
901 Linear implicit parameters are an idea developed by Koen Claessen,
902 Mark Shields, and Simon PJ. They address the long-standing
903 problem that monads seem over-kill for certain sorts of problem, notably:
906 <listitem> <para> distributing a supply of unique names </para> </listitem>
907 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
908 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
912 Linear implicit parameters are just like ordinary implicit parameters,
913 except that they are "linear" -- that is, they cannot be copied, and
914 must be explicitly "split" instead. Linear implicit parameters are
915 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
916 (The '/' in the '%' suggests the split!)
921 data NameSupply = ...
923 splitNS :: NameSupply -> (NameSupply, NameSupply)
924 newName :: NameSupply -> Name
926 instance PrelSplit.Splittable NameSupply where
930 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
931 f env (Lam x e) = Lam x' (f env e)
934 env' = extend env x x'
935 ...more equations for f...
937 Notice that the implicit parameter %ns is consumed
939 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
940 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
944 So the translation done by the type checker makes
945 the parameter explicit:
947 f :: NameSupply -> Env -> Expr -> Expr
948 f ns env (Lam x e) = Lam x' (f ns1 env e)
950 (ns1,ns2) = splitNS ns
952 env = extend env x x'
954 Notice the call to 'split' introduced by the type checker.
955 How did it know to use 'splitNS'? Because what it really did
956 was to introduce a call to the overloaded function 'split',
959 class Splittable a where
962 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
963 split for name supplies. But we can simply write
969 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
971 The <literal>Splittable</literal> class is built into GHC. It's defined in <literal>PrelSplit</literal>,
972 and exported by <literal>GlaExts</literal>.
977 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
978 are entirely distinct implicit parameters: you
979 can use them together and they won't intefere with each other. </para>
982 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
984 <listitem> <para>You cannot have implicit parameters (whether linear or not)
985 in the context of a class or instance declaration. </para></listitem>
989 <sect3><title>Warnings</title>
992 The monomorphism restriction is even more important than usual.
993 Consider the example above:
995 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
996 f env (Lam x e) = Lam x' (f env e)
999 env' = extend env x x'
1001 If we replaced the two occurrences of x' by (newName %ns), which is
1002 usually a harmless thing to do, we get:
1004 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1005 f env (Lam x e) = Lam (newName %ns) (f env e)
1007 env' = extend env x (newName %ns)
1009 But now the name supply is consumed in <emphasis>three</emphasis> places
1010 (the two calls to newName,and the recursive call to f), so
1011 the result is utterly different. Urk! We don't even have
1015 Well, this is an experimental change. With implicit
1016 parameters we have already lost beta reduction anyway, and
1017 (as John Launchbury puts it) we can't sensibly reason about
1018 Haskell programs without knowing their typing.
1025 <sect2 id="functional-dependencies">
1026 <title>Functional dependencies
1029 <para> Functional dependencies are implemented as described by Mark Jones
1030 in "Type Classes with Functional Dependencies", Mark P. Jones,
1031 In Proceedings of the 9th European Symposium on Programming,
1032 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1036 There should be more documentation, but there isn't (yet). Yell if you need it.
1041 <sect2 id="universal-quantification">
1042 <title>Arbitrary-rank polymorphism
1046 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1047 allows us to say exactly what this means. For example:
1055 g :: forall b. (b -> b)
1057 The two are treated identically.
1061 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1062 explicit universal quantification in
1064 For example, all the following types are legal:
1066 f1 :: forall a b. a -> b -> a
1067 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1069 f2 :: (forall a. a->a) -> Int -> Int
1070 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1072 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1074 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1075 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1076 The <literal>forall</literal> makes explicit the universal quantification that
1077 is implicitly added by Haskell.
1080 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1081 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1082 shows, the polymorphic type on the left of the function arrow can be overloaded.
1085 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1086 they have rank-2 types on the left of a function arrow.
1089 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1090 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1091 that restriction has now been lifted.)
1092 In particular, a forall-type (also called a "type scheme"),
1093 including an operational type class context, is legal:
1095 <listitem> <para> On the left of a function arrow </para> </listitem>
1096 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1097 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1098 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1099 field type signatures.</para> </listitem>
1100 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1101 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1103 There is one place you cannot put a <literal>forall</literal>:
1104 you cannot instantiate a type variable with a forall-type. So you cannot
1105 make a forall-type the argument of a type constructor. So these types are illegal:
1107 x1 :: [forall a. a->a]
1108 x2 :: (forall a. a->a, Int)
1109 x3 :: Maybe (forall a. a->a)
1111 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1112 a type variable any more!
1121 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1122 the types of the constructor arguments. Here are several examples:
1128 data T a = T1 (forall b. b -> b -> b) a
1130 data MonadT m = MkMonad { return :: forall a. a -> m a,
1131 bind :: forall a b. m a -> (a -> m b) -> m b
1134 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1140 The constructors have rank-2 types:
1146 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1147 MkMonad :: forall m. (forall a. a -> m a)
1148 -> (forall a b. m a -> (a -> m b) -> m b)
1150 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1156 Notice that you don't need to use a <literal>forall</literal> if there's an
1157 explicit context. For example in the first argument of the
1158 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1159 prefixed to the argument type. The implicit <literal>forall</literal>
1160 quantifies all type variables that are not already in scope, and are
1161 mentioned in the type quantified over.
1165 As for type signatures, implicit quantification happens for non-overloaded
1166 types too. So if you write this:
1169 data T a = MkT (Either a b) (b -> b)
1172 it's just as if you had written this:
1175 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1178 That is, since the type variable <literal>b</literal> isn't in scope, it's
1179 implicitly universally quantified. (Arguably, it would be better
1180 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1181 where that is what is wanted. Feedback welcomed.)
1185 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1186 the constructor to suitable values, just as usual. For example,
1197 a3 = MkSwizzle reverse
1200 a4 = let r x = Just x
1207 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1208 mkTs f x y = [T1 f x, T1 f y]
1214 The type of the argument can, as usual, be more general than the type
1215 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1216 does not need the <literal>Ord</literal> constraint.)
1220 When you use pattern matching, the bound variables may now have
1221 polymorphic types. For example:
1227 f :: T a -> a -> (a, Char)
1228 f (T1 w k) x = (w k x, w 'c' 'd')
1230 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1231 g (MkSwizzle s) xs f = s (map f (s xs))
1233 h :: MonadT m -> [m a] -> m [a]
1234 h m [] = return m []
1235 h m (x:xs) = bind m x $ \y ->
1236 bind m (h m xs) $ \ys ->
1243 In the function <function>h</function> we use the record selectors <literal>return</literal>
1244 and <literal>bind</literal> to extract the polymorphic bind and return functions
1245 from the <literal>MonadT</literal> data structure, rather than using pattern
1251 <title>Type inference</title>
1254 In general, type inference for arbitrary-rank types is undecideable.
1255 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1256 to get a decidable algorithm by requiring some help from the programmer.
1257 We do not yet have a formal specification of "some help" but the rule is this:
1260 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1261 provides an explicit polymorphic type for x, or GHC's type inference will assume
1262 that x's type has no foralls in it</emphasis>.
1265 What does it mean to "provide" an explicit type for x? You can do that by
1266 giving a type signature for x directly, using a pattern type signature
1267 (<xref linkend="scoped-type-variables">), thus:
1269 \ f :: (forall a. a->a) -> (f True, f 'c')
1271 Alternatively, you can give a type signature to the enclosing
1272 context, which GHC can "push down" to find the type for the variable:
1274 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1276 Here the type signature on the expression can be pushed inwards
1277 to give a type signature for f. Similarly, and more commonly,
1278 one can give a type signature for the function itself:
1280 h :: (forall a. a->a) -> (Bool,Char)
1281 h f = (f True, f 'c')
1283 You don't need to give a type signature if the lambda bound variable
1284 is a constructor argument. Here is an example we saw earlier:
1286 f :: T a -> a -> (a, Char)
1287 f (T1 w k) x = (w k x, w 'c' 'd')
1289 Here we do not need to give a type signature to <literal>w</literal>, because
1290 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1297 <sect3 id="implicit-quant">
1298 <title>Implicit quantification</title>
1301 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1302 user-written types, if and only if there is no explicit <literal>forall</literal>,
1303 GHC finds all the type variables mentioned in the type that are not already
1304 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1308 f :: forall a. a -> a
1315 h :: forall b. a -> b -> b
1321 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1324 f :: (a -> a) -> Int
1326 f :: forall a. (a -> a) -> Int
1328 f :: (forall a. a -> a) -> Int
1331 g :: (Ord a => a -> a) -> Int
1332 -- MEANS the illegal type
1333 g :: forall a. (Ord a => a -> a) -> Int
1335 g :: (forall a. Ord a => a -> a) -> Int
1337 The latter produces an illegal type, which you might think is silly,
1338 but at least the rule is simple. If you want the latter type, you
1339 can write your for-alls explicitly. Indeed, doing so is strongly advised
1346 <title>Liberalised type synonyms
1350 Type synonmys are like macros at the type level, and
1351 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1352 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1354 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1355 in a type synonym, thus:
1357 type Discard a = forall b. Show b => a -> b -> (a, String)
1362 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1369 You can write an unboxed tuple in a type synonym:
1371 type Pr = (# Int, Int #)
1379 You can apply a type synonym to a forall type:
1381 type Foo a = a -> a -> Bool
1383 f :: Foo (forall b. b->b)
1385 After epxanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1387 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1392 You can apply a type synonym to a partially applied type synonym:
1394 type Generic i o = forall x. i x -> o x
1397 foo :: Generic Id []
1399 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1401 foo :: forall x. x -> [x]
1409 GHC currently does kind checking before expanding synonyms (though even that
1413 After expanding type synonyms, GHC does validity checking on types, looking for
1414 the following mal-formedness which isn't detected simply by kind checking:
1417 Type constructor applied to a type involving for-alls.
1420 Unboxed tuple on left of an arrow.
1423 Partially-applied type synonym.
1427 this will be rejected:
1429 type Pr = (# Int, Int #)
1434 because GHC does not allow unboxed tuples on the left of a function arrow.
1439 <title>For-all hoisting</title>
1441 It is often convenient to use generalised type synonyms at the right hand
1442 end of an arrow, thus:
1444 type Discard a = forall b. a -> b -> a
1446 g :: Int -> Discard Int
1449 Simply expanding the type synonym would give
1451 g :: Int -> (forall b. Int -> b -> Int)
1453 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1455 g :: forall b. Int -> Int -> b -> Int
1457 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1458 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1459 performs the transformation:</emphasis>
1461 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1463 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1465 (In fact, GHC tries to retain as much synonym information as possible for use in
1466 error messages, but that is a usability issue.) This rule applies, of course, whether
1467 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1468 valid way to write <literal>g</literal>'s type signature:
1470 g :: Int -> Int -> forall b. b -> Int
1476 <sect2 id="existential-quantification">
1477 <title>Existentially quantified data constructors
1481 The idea of using existential quantification in data type declarations
1482 was suggested by Laufer (I believe, thought doubtless someone will
1483 correct me), and implemented in Hope+. It's been in Lennart
1484 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1485 proved very useful. Here's the idea. Consider the declaration:
1491 data Foo = forall a. MkFoo a (a -> Bool)
1498 The data type <literal>Foo</literal> has two constructors with types:
1504 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1511 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1512 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1513 For example, the following expression is fine:
1519 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1525 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1526 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1527 isUpper</function> packages a character with a compatible function. These
1528 two things are each of type <literal>Foo</literal> and can be put in a list.
1532 What can we do with a value of type <literal>Foo</literal>?. In particular,
1533 what happens when we pattern-match on <function>MkFoo</function>?
1539 f (MkFoo val fn) = ???
1545 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1546 are compatible, the only (useful) thing we can do with them is to
1547 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1554 f (MkFoo val fn) = fn val
1560 What this allows us to do is to package heterogenous values
1561 together with a bunch of functions that manipulate them, and then treat
1562 that collection of packages in a uniform manner. You can express
1563 quite a bit of object-oriented-like programming this way.
1566 <sect3 id="existential">
1567 <title>Why existential?
1571 What has this to do with <emphasis>existential</emphasis> quantification?
1572 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1578 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1584 But Haskell programmers can safely think of the ordinary
1585 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1586 adding a new existential quantification construct.
1592 <title>Type classes</title>
1595 An easy extension (implemented in <Command>hbc</Command>) is to allow
1596 arbitrary contexts before the constructor. For example:
1602 data Baz = forall a. Eq a => Baz1 a a
1603 | forall b. Show b => Baz2 b (b -> b)
1609 The two constructors have the types you'd expect:
1615 Baz1 :: forall a. Eq a => a -> a -> Baz
1616 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1622 But when pattern matching on <function>Baz1</function> the matched values can be compared
1623 for equality, and when pattern matching on <function>Baz2</function> the first matched
1624 value can be converted to a string (as well as applying the function to it).
1625 So this program is legal:
1632 f (Baz1 p q) | p == q = "Yes"
1634 f (Baz2 v fn) = show (fn v)
1640 Operationally, in a dictionary-passing implementation, the
1641 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1642 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1643 extract it on pattern matching.
1647 Notice the way that the syntax fits smoothly with that used for
1648 universal quantification earlier.
1654 <title>Restrictions</title>
1657 There are several restrictions on the ways in which existentially-quantified
1658 constructors can be use.
1667 When pattern matching, each pattern match introduces a new,
1668 distinct, type for each existential type variable. These types cannot
1669 be unified with any other type, nor can they escape from the scope of
1670 the pattern match. For example, these fragments are incorrect:
1678 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1679 is the result of <function>f1</function>. One way to see why this is wrong is to
1680 ask what type <function>f1</function> has:
1684 f1 :: Foo -> a -- Weird!
1688 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1693 f1 :: forall a. Foo -> a -- Wrong!
1697 The original program is just plain wrong. Here's another sort of error
1701 f2 (Baz1 a b) (Baz1 p q) = a==q
1705 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1706 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1707 from the two <function>Baz1</function> constructors.
1715 You can't pattern-match on an existentially quantified
1716 constructor in a <literal>let</literal> or <literal>where</literal> group of
1717 bindings. So this is illegal:
1721 f3 x = a==b where { Baz1 a b = x }
1725 You can only pattern-match
1726 on an existentially-quantified constructor in a <literal>case</literal> expression or
1727 in the patterns of a function definition.
1729 The reason for this restriction is really an implementation one.
1730 Type-checking binding groups is already a nightmare without
1731 existentials complicating the picture. Also an existential pattern
1732 binding at the top level of a module doesn't make sense, because it's
1733 not clear how to prevent the existentially-quantified type "escaping".
1734 So for now, there's a simple-to-state restriction. We'll see how
1742 You can't use existential quantification for <literal>newtype</literal>
1743 declarations. So this is illegal:
1747 newtype T = forall a. Ord a => MkT a
1751 Reason: a value of type <literal>T</literal> must be represented as a pair
1752 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1753 That contradicts the idea that <literal>newtype</literal> should have no
1754 concrete representation. You can get just the same efficiency and effect
1755 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1756 overloading involved, then there is more of a case for allowing
1757 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1758 because the <literal>data</literal> version does carry an implementation cost,
1759 but single-field existentially quantified constructors aren't much
1760 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1761 stands, unless there are convincing reasons to change it.
1769 You can't use <literal>deriving</literal> to define instances of a
1770 data type with existentially quantified data constructors.
1772 Reason: in most cases it would not make sense. For example:#
1775 data T = forall a. MkT [a] deriving( Eq )
1778 To derive <literal>Eq</literal> in the standard way we would need to have equality
1779 between the single component of two <function>MkT</function> constructors:
1783 (MkT a) == (MkT b) = ???
1786 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1787 It's just about possible to imagine examples in which the derived instance
1788 would make sense, but it seems altogether simpler simply to prohibit such
1789 declarations. Define your own instances!
1801 <sect2 id="scoped-type-variables">
1802 <title>Scoped Type Variables
1806 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1807 variable</emphasis>. For example
1813 f (xs::[a]) = ys ++ ys
1822 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1823 This brings the type variable <literal>a</literal> into scope; it scopes over
1824 all the patterns and right hand sides for this equation for <function>f</function>.
1825 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1829 Pattern type signatures are completely orthogonal to ordinary, separate
1830 type signatures. The two can be used independently or together.
1831 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1832 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1833 implicitly universally quantified. (If there are no type variables in
1834 scope, all type variables mentioned in the signature are universally
1835 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1836 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1837 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1838 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1839 it becomes possible to do so.
1843 Scoped type variables are implemented in both GHC and Hugs. Where the
1844 implementations differ from the specification below, those differences
1849 So much for the basic idea. Here are the details.
1853 <title>What a pattern type signature means</title>
1855 A type variable brought into scope by a pattern type signature is simply
1856 the name for a type. The restriction they express is that all occurrences
1857 of the same name mean the same type. For example:
1859 f :: [Int] -> Int -> Int
1860 f (xs::[a]) (y::a) = (head xs + y) :: a
1862 The pattern type signatures on the left hand side of
1863 <literal>f</literal> express the fact that <literal>xs</literal>
1864 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1865 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1866 specifies that this expression must have the same type <literal>a</literal>.
1867 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1868 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1869 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1870 rules, which specified that a pattern-bound type variable should be universally quantified.)
1871 For example, all of these are legal:</para>
1874 t (x::a) (y::a) = x+y*2
1876 f (x::a) (y::b) = [x,y] -- a unifies with b
1878 g (x::a) = x + 1::Int -- a unifies with Int
1880 h x = let k (y::a) = [x,y] -- a is free in the
1881 in k x -- environment
1883 k (x::a) True = ... -- a unifies with Int
1884 k (x::Int) False = ...
1887 w (x::a) = x -- a unifies with [b]
1893 <title>Scope and implicit quantification</title>
1901 All the type variables mentioned in a pattern,
1902 that are not already in scope,
1903 are brought into scope by the pattern. We describe this set as
1904 the <emphasis>type variables bound by the pattern</emphasis>.
1907 f (x::a) = let g (y::(a,b)) = fst y
1911 The pattern <literal>(x::a)</literal> brings the type variable
1912 <literal>a</literal> into scope, as well as the term
1913 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
1914 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
1915 and brings into scope the type variable <literal>b</literal>.
1921 The type variable(s) bound by the pattern have the same scope
1922 as the term variable(s) bound by the pattern. For example:
1925 f (x::a) = <...rhs of f...>
1926 (p::b, q::b) = (1,2)
1927 in <...body of let...>
1929 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
1930 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
1931 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
1932 just like <literal>p</literal> and <literal>q</literal> do.
1933 Indeed, the newly bound type variables also scope over any ordinary, separate
1934 type signatures in the <literal>let</literal> group.
1941 The type variables bound by the pattern may be
1942 mentioned in ordinary type signatures or pattern
1943 type signatures anywhere within their scope.
1950 In ordinary type signatures, any type variable mentioned in the
1951 signature that is in scope is <emphasis>not</emphasis> universally quantified.
1959 Ordinary type signatures do not bring any new type variables
1960 into scope (except in the type signature itself!). So this is illegal:
1967 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
1968 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
1969 and that is an incorrect typing.
1976 The pattern type signature is a monotype:
1981 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
1985 The type variables bound by a pattern type signature can only be instantiated to monotypes,
1986 not to type schemes.
1990 There is no implicit universal quantification on pattern type signatures (in contrast to
1991 ordinary type signatures).
2001 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2002 scope over the methods defined in the <literal>where</literal> part. For example:
2016 (Not implemented in Hugs yet, Dec 98).
2027 <title>Result type signatures</title>
2035 The result type of a function can be given a signature,
2040 f (x::a) :: [a] = [x,x,x]
2044 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2045 result type. Sometimes this is the only way of naming the type variable
2050 f :: Int -> [a] -> [a]
2051 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2052 in \xs -> map g (reverse xs `zip` xs)
2064 Result type signatures are not yet implemented in Hugs.
2070 <title>Where a pattern type signature can occur</title>
2073 A pattern type signature can occur in any pattern. For example:
2078 A pattern type signature can be on an arbitrary sub-pattern, not
2083 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2092 Pattern type signatures, including the result part, can be used
2093 in lambda abstractions:
2096 (\ (x::a, y) :: a -> x)
2103 Pattern type signatures, including the result part, can be used
2104 in <literal>case</literal> expressions:
2108 case e of { (x::a, y) :: a -> x }
2116 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2117 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2118 token or a parenthesised type of some sort). To see why,
2119 consider how one would parse this:
2133 Pattern type signatures can bind existential type variables.
2138 data T = forall a. MkT [a]
2141 f (MkT [t::a]) = MkT t3
2154 Pattern type signatures
2155 can be used in pattern bindings:
2158 f x = let (y, z::a) = x in ...
2159 f1 x = let (y, z::Int) = x in ...
2160 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2161 f3 :: (b->b) = \x -> x
2164 In all such cases, the binding is not generalised over the pattern-bound
2165 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2166 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2167 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2168 In contrast, the binding
2173 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2174 in <literal>f4</literal>'s scope.
2184 <sect2 id="sec-kinding">
2185 <title>Explicitly-kinded quantification</title>
2188 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2189 to give the kind explicitly as (machine-checked) documentation,
2190 just as it is nice to give a type signature for a function. On some occasions,
2191 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2192 John Hughes had to define the data type:
2194 data Set cxt a = Set [a]
2195 | Unused (cxt a -> ())
2197 The only use for the <literal>Unused</literal> constructor was to force the correct
2198 kind for the type variable <literal>cxt</literal>.
2201 GHC now instead allows you to specify the kind of a type variable directly, wherever
2202 a type variable is explicitly bound. Namely:
2204 <listitem><para><literal>data</literal> declarations:
2206 data Set (cxt :: * -> *) a = Set [a]
2207 </Screen></para></listitem>
2208 <listitem><para><literal>type</literal> declarations:
2210 type T (f :: * -> *) = f Int
2211 </Screen></para></listitem>
2212 <listitem><para><literal>class</literal> declarations:
2214 class (Eq a) => C (f :: * -> *) a where ...
2215 </Screen></para></listitem>
2216 <listitem><para><literal>forall</literal>'s in type signatures:
2218 f :: forall (cxt :: * -> *). Set cxt Int
2219 </Screen></para></listitem>
2224 The parentheses are required. Some of the spaces are required too, to
2225 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2226 will get a parse error, because "<literal>::*->*</literal>" is a
2227 single lexeme in Haskell.
2231 As part of the same extension, you can put kind annotations in types
2234 f :: (Int :: *) -> Int
2235 g :: forall a. a -> (a :: *)
2239 atype ::= '(' ctype '::' kind ')
2241 The parentheses are required.
2246 <!-- ==================== End of type system extensions ================= -->
2249 <!-- ==================== ASSERTIONS ================= -->
2251 <sect1 id="sec-assertions">
2253 <indexterm><primary>Assertions</primary></indexterm>
2257 If you want to make use of assertions in your standard Haskell code, you
2258 could define a function like the following:
2264 assert :: Bool -> a -> a
2265 assert False x = error "assertion failed!"
2272 which works, but gives you back a less than useful error message --
2273 an assertion failed, but which and where?
2277 One way out is to define an extended <function>assert</function> function which also
2278 takes a descriptive string to include in the error message and
2279 perhaps combine this with the use of a pre-processor which inserts
2280 the source location where <function>assert</function> was used.
2284 Ghc offers a helping hand here, doing all of this for you. For every
2285 use of <function>assert</function> in the user's source:
2291 kelvinToC :: Double -> Double
2292 kelvinToC k = assert (k >= 0.0) (k+273.15)
2298 Ghc will rewrite this to also include the source location where the
2305 assert pred val ==> assertError "Main.hs|15" pred val
2311 The rewrite is only performed by the compiler when it spots
2312 applications of <function>Exception.assert</function>, so you can still define and
2313 use your own versions of <function>assert</function>, should you so wish. If not,
2314 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2318 To have the compiler ignore uses of assert, use the compiler option
2319 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2320 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2324 Assertion failures can be caught, see the documentation for the
2325 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2331 <!-- ====================== PATTERN GUARDS ======================= -->
2333 <sect1 id="pattern-guards">
2334 <title>Pattern guards</title>
2337 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2338 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.)
2342 Suppose we have an abstract data type of finite maps, with a
2346 lookup :: FiniteMap -> Int -> Maybe Int
2349 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2350 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2354 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2355 | otherwise = var1 + var2
2357 m1 = lookup env var1
2358 m2 = lookup env var2
2359 ok1 = maybeToBool m1
2360 ok2 = maybeToBool m2
2361 val1 = expectJust m1
2362 val2 = expectJust m2
2366 The auxiliary functions are
2370 maybeToBool :: Maybe a -> Bool
2371 maybeToBool (Just x) = True
2372 maybeToBool Nothing = False
2374 expectJust :: Maybe a -> a
2375 expectJust (Just x) = x
2376 expectJust Nothing = error "Unexpected Nothing"
2380 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2381 ok2</literal> checks that both lookups succeed, using
2382 <function>maybeToBool</function> to convert the <function>Maybe</function>
2383 types to booleans. The (lazily evaluated) <function>expectJust</function>
2384 calls extract the values from the results of the lookups, and binds the
2385 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2386 respectively. If either lookup fails, then clunky takes the
2387 <literal>otherwise</literal> case and returns the sum of its arguments.
2391 This is certainly legal Haskell, but it is a tremendously verbose and
2392 un-obvious way to achieve the desired effect. Arguably, a more direct way
2393 to write clunky would be to use case expressions:
2397 clunky env var1 var1 = case lookup env var1 of
2399 Just val1 -> case lookup env var2 of
2401 Just val2 -> val1 + val2
2407 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2408 of pattern-matching, guarded equations as case expressions; that is
2409 precisely what the compiler does when compiling equations! The reason that
2410 Haskell provides guarded equations is because they allow us to write down
2411 the cases we want to consider, one at a time, independently of each other.
2412 This structure is hidden in the case version. Two of the right-hand sides
2413 are really the same (<function>fail</function>), and the whole expression
2414 tends to become more and more indented.
2418 Here is how I would write clunky:
2422 clunky env var1 var1
2423 | Just val1 <- lookup env var1
2424 , Just val2 <- lookup env var2
2426 ...other equations for clunky...
2430 The semantics should be clear enough. The qualifers are matched in order.
2431 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2432 right hand side is evaluated and matched against the pattern on the left.
2433 If the match fails then the whole guard fails and the next equation is
2434 tried. If it succeeds, then the appropriate binding takes place, and the
2435 next qualifier is matched, in the augmented environment. Unlike list
2436 comprehensions, however, the type of the expression to the right of the
2437 <literal><-</literal> is the same as the type of the pattern to its
2438 left. The bindings introduced by pattern guards scope over all the
2439 remaining guard qualifiers, and over the right hand side of the equation.
2443 Just as with list comprehensions, boolean expressions can be freely mixed
2444 with among the pattern guards. For example:
2455 Haskell's current guards therefore emerge as a special case, in which the
2456 qualifier list has just one element, a boolean expression.
2460 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2462 <sect1 id="parallel-list-comprehensions">
2463 <title>Parallel List Comprehensions</title>
2464 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2466 <indexterm><primary>parallel list comprehensions</primary>
2469 <para>Parallel list comprehensions are a natural extension to list
2470 comprehensions. List comprehensions can be thought of as a nice
2471 syntax for writing maps and filters. Parallel comprehensions
2472 extend this to include the zipWith family.</para>
2474 <para>A parallel list comprehension has multiple independent
2475 branches of qualifier lists, each separated by a `|' symbol. For
2476 example, the following zips together two lists:</para>
2479 [ (x, y) | x <- xs | y <- ys ]
2482 <para>The behavior of parallel list comprehensions follows that of
2483 zip, in that the resulting list will have the same length as the
2484 shortest branch.</para>
2486 <para>We can define parallel list comprehensions by translation to
2487 regular comprehensions. Here's the basic idea:</para>
2489 <para>Given a parallel comprehension of the form: </para>
2492 [ e | p1 <- e11, p2 <- e12, ...
2493 | q1 <- e21, q2 <- e22, ...
2498 <para>This will be translated to: </para>
2501 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2502 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2507 <para>where `zipN' is the appropriate zip for the given number of
2512 <!-- =============================== PRAGMAS =========================== -->
2514 <sect1 id="pragmas">
2515 <title>Pragmas</title>
2517 <indexterm><primary>pragma</primary></indexterm>
2519 <para>GHC supports several pragmas, or instructions to the
2520 compiler placed in the source code. Pragmas don't normally affect
2521 the meaning of the program, but they might affect the efficiency
2522 of the generated code.</para>
2524 <para>Pragmas all take the form
2526 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2528 where <replaceable>word</replaceable> indicates the type of
2529 pragma, and is followed optionally by information specific to that
2530 type of pragma. Case is ignored in
2531 <replaceable>word</replaceable>. The various values for
2532 <replaceable>word</replaceable> that GHC understands are described
2533 in the following sections; any pragma encountered with an
2534 unrecognised <replaceable>word</replaceable> is (silently)
2537 <sect2 id="inline-pragma">
2538 <title>INLINE pragma
2540 <indexterm><primary>INLINE pragma</primary></indexterm>
2541 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2544 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2545 functions/values that are “small enough,” thus avoiding the call
2546 overhead and possibly exposing other more-wonderful optimisations.
2550 You will probably see these unfoldings (in Core syntax) in your
2555 Normally, if GHC decides a function is “too expensive” to inline, it
2556 will not do so, nor will it export that unfolding for other modules to
2561 The sledgehammer you can bring to bear is the
2562 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2565 key_function :: Int -> String -> (Bool, Double)
2567 #ifdef __GLASGOW_HASKELL__
2568 {-# INLINE key_function #-}
2572 (You don't need to do the C pre-processor carry-on unless you're going
2573 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2577 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2578 “cost” to be very low. The normal unfolding machinery will then be
2579 very keen to inline it.
2583 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2584 signature could be put.
2588 <literal>INLINE</literal> pragmas are a particularly good idea for the
2589 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2590 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2593 #ifdef __GLASGOW_HASKELL__
2594 {-# INLINE thenUs #-}
2595 {-# INLINE returnUs #-}
2603 <sect2 id="noinline-pragma">
2604 <title>NOINLINE pragma
2607 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2608 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2609 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2610 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2613 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2614 it stops the named function from being inlined by the compiler. You
2615 shouldn't ever need to do this, unless you're very cautious about code
2619 <para><literal>NOTINLINE</literal> is a synonym for
2620 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2621 by Haskell 98 as the standard way to disable inlining, so it should be
2622 used if you want your code to be portable).</para>
2626 <sect2 id="specialize-pragma">
2627 <title>SPECIALIZE pragma</title>
2629 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2630 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2631 <indexterm><primary>overloading, death to</primary></indexterm>
2633 <para>(UK spelling also accepted.) For key overloaded
2634 functions, you can create extra versions (NB: more code space)
2635 specialised to particular types. Thus, if you have an
2636 overloaded function:</para>
2639 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2642 <para>If it is heavily used on lists with
2643 <literal>Widget</literal> keys, you could specialise it as
2647 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2650 <para>To get very fancy, you can also specify a named function
2651 to use for the specialised value, as in:</para>
2654 {-# RULES hammeredLookup = blah #-}
2657 <para>where <literal>blah</literal> is an implementation of
2658 <literal>hammerdLookup</literal> written specialy for
2659 <literal>Widget</literal> lookups. It's <emphasis>Your
2660 Responsibility</emphasis> to make sure that
2661 <function>blah</function> really behaves as a specialised
2662 version of <function>hammeredLookup</function>!!!</para>
2664 <para>Note we use the <literal>RULE</literal> pragma here to
2665 indicate that <literal>hammeredLookup</literal> applied at a
2666 certain type should be replaced by <literal>blah</literal>. See
2667 <xref linkend="rules"> for more information on
2668 <literal>RULES</literal>.</para>
2670 <para>An example in which using <literal>RULES</literal> for
2671 specialisation will Win Big:
2674 toDouble :: Real a => a -> Double
2675 toDouble = fromRational . toRational
2677 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2678 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2681 The <function>i2d</function> function is virtually one machine
2682 instruction; the default conversion—via an intermediate
2683 <literal>Rational</literal>—is obscenely expensive by
2686 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2687 be put anywhere its type signature could be put.</para>
2691 <sect2 id="specialize-instance-pragma">
2692 <title>SPECIALIZE instance pragma
2696 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2697 <indexterm><primary>overloading, death to</primary></indexterm>
2698 Same idea, except for instance declarations. For example:
2701 instance (Eq a) => Eq (Foo a) where {
2702 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2706 The pragma must occur inside the <literal>where</literal> part
2707 of the instance declaration.
2710 Compatible with HBC, by the way, except perhaps in the placement
2716 <sect2 id="line-pragma">
2721 <indexterm><primary>LINE pragma</primary></indexterm>
2722 <indexterm><primary>pragma, LINE</primary></indexterm>
2726 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2727 automatically generated Haskell code. It lets you specify the line
2728 number and filename of the original code; for example
2734 {-# LINE 42 "Foo.vhs" #-}
2740 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2741 and this line corresponds to line 42 in the original. GHC will adjust
2742 its error messages to refer to the line/file named in the <literal>LINE</literal>
2749 <title>RULES pragma</title>
2752 The RULES pragma lets you specify rewrite rules. It is described in
2753 <xref LinkEnd="rewrite-rules">.
2758 <sect2 id="deprecated-pragma">
2759 <title>DEPRECATED pragma</title>
2762 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2763 There are two forms.
2767 You can deprecate an entire module thus:</para>
2769 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2773 When you compile any module that import <literal>Wibble</literal>, GHC will print
2774 the specified message.</para>
2779 You can deprecate a function, class, or type, with the following top-level declaration:
2782 {-# DEPRECATED f, C, T "Don't use these" #-}
2785 When you compile any module that imports and uses any of the specifed entities,
2786 GHC will print the specified message.
2790 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2796 <!-- ======================= REWRITE RULES ======================== -->
2798 <sect1 id="rewrite-rules">
2799 <title>Rewrite rules
2801 <indexterm><primary>RULES pagma</primary></indexterm>
2802 <indexterm><primary>pragma, RULES</primary></indexterm>
2803 <indexterm><primary>rewrite rules</primary></indexterm></title>
2806 The programmer can specify rewrite rules as part of the source program
2807 (in a pragma). GHC applies these rewrite rules wherever it can.
2815 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2822 <title>Syntax</title>
2825 From a syntactic point of view:
2831 Each rule has a name, enclosed in double quotes. The name itself has
2832 no significance at all. It is only used when reporting how many times the rule fired.
2838 There may be zero or more rules in a <literal>RULES</literal> pragma.
2844 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2845 is set, so you must lay out your rules starting in the same column as the
2846 enclosing definitions.
2852 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2853 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2854 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2855 by spaces, just like in a type <literal>forall</literal>.
2861 A pattern variable may optionally have a type signature.
2862 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2863 For example, here is the <literal>foldr/build</literal> rule:
2866 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2867 foldr k z (build g) = g k z
2870 Since <function>g</function> has a polymorphic type, it must have a type signature.
2877 The left hand side of a rule must consist of a top-level variable applied
2878 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2881 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2882 "wrong2" forall f. f True = True
2885 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2892 A rule does not need to be in the same module as (any of) the
2893 variables it mentions, though of course they need to be in scope.
2899 Rules are automatically exported from a module, just as instance declarations are.
2910 <title>Semantics</title>
2913 From a semantic point of view:
2919 Rules are only applied if you use the <option>-O</option> flag.
2925 Rules are regarded as left-to-right rewrite rules.
2926 When GHC finds an expression that is a substitution instance of the LHS
2927 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
2928 By "a substitution instance" we mean that the LHS can be made equal to the
2929 expression by substituting for the pattern variables.
2936 The LHS and RHS of a rule are typechecked, and must have the
2944 GHC makes absolutely no attempt to verify that the LHS and RHS
2945 of a rule have the same meaning. That is undecideable in general, and
2946 infeasible in most interesting cases. The responsibility is entirely the programmer's!
2953 GHC makes no attempt to make sure that the rules are confluent or
2954 terminating. For example:
2957 "loop" forall x,y. f x y = f y x
2960 This rule will cause the compiler to go into an infinite loop.
2967 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
2973 GHC currently uses a very simple, syntactic, matching algorithm
2974 for matching a rule LHS with an expression. It seeks a substitution
2975 which makes the LHS and expression syntactically equal modulo alpha
2976 conversion. The pattern (rule), but not the expression, is eta-expanded if
2977 necessary. (Eta-expanding the epression can lead to laziness bugs.)
2978 But not beta conversion (that's called higher-order matching).
2982 Matching is carried out on GHC's intermediate language, which includes
2983 type abstractions and applications. So a rule only matches if the
2984 types match too. See <xref LinkEnd="rule-spec"> below.
2990 GHC keeps trying to apply the rules as it optimises the program.
2991 For example, consider:
3000 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3001 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3002 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3003 not be substituted, and the rule would not fire.
3010 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3011 that appears on the LHS of a rule</emphasis>, because once you have substituted
3012 for something you can't match against it (given the simple minded
3013 matching). So if you write the rule
3016 "map/map" forall f,g. map f . map g = map (f.g)
3019 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3020 It will only match something written with explicit use of ".".
3021 Well, not quite. It <emphasis>will</emphasis> match the expression
3027 where <function>wibble</function> is defined:
3030 wibble f g = map f . map g
3033 because <function>wibble</function> will be inlined (it's small).
3035 Later on in compilation, GHC starts inlining even things on the
3036 LHS of rules, but still leaves the rules enabled. This inlining
3037 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3044 All rules are implicitly exported from the module, and are therefore
3045 in force in any module that imports the module that defined the rule, directly
3046 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3047 in force when compiling A.) The situation is very similar to that for instance
3059 <title>List fusion</title>
3062 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3063 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3064 intermediate list should be eliminated entirely.
3068 The following are good producers:
3080 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3086 Explicit lists (e.g. <literal>[True, False]</literal>)
3092 The cons constructor (e.g <literal>3:4:[]</literal>)
3098 <function>++</function>
3104 <function>map</function>
3110 <function>filter</function>
3116 <function>iterate</function>, <function>repeat</function>
3122 <function>zip</function>, <function>zipWith</function>
3131 The following are good consumers:
3143 <function>array</function> (on its second argument)
3149 <function>length</function>
3155 <function>++</function> (on its first argument)
3161 <function>foldr</function>
3167 <function>map</function>
3173 <function>filter</function>
3179 <function>concat</function>
3185 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3191 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3192 will fuse with one but not the other)
3198 <function>partition</function>
3204 <function>head</function>
3210 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3216 <function>sequence_</function>
3222 <function>msum</function>
3228 <function>sortBy</function>
3237 So, for example, the following should generate no intermediate lists:
3240 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3246 This list could readily be extended; if there are Prelude functions that you use
3247 a lot which are not included, please tell us.
3251 If you want to write your own good consumers or producers, look at the
3252 Prelude definitions of the above functions to see how to do so.
3257 <sect2 id="rule-spec">
3258 <title>Specialisation
3262 Rewrite rules can be used to get the same effect as a feature
3263 present in earlier version of GHC:
3266 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3269 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3270 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3271 specialising the original definition of <function>fromIntegral</function> the programmer is
3272 promising that it is safe to use <function>int8ToInt16</function> instead.
3276 This feature is no longer in GHC. But rewrite rules let you do the
3281 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3285 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3286 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3287 GHC adds the type and dictionary applications to get the typed rule
3290 forall (d1::Integral Int8) (d2::Num Int16) .
3291 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3295 this rule does not need to be in the same file as fromIntegral,
3296 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3297 have an original definition available to specialise).
3303 <title>Controlling what's going on</title>
3311 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3317 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3318 If you add <option>-dppr-debug</option> you get a more detailed listing.
3324 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3327 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3328 {-# INLINE build #-}
3332 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3333 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3334 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3335 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3342 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3343 see how to write rules that will do fusion and yet give an efficient
3344 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3356 <sect1 id="generic-classes">
3357 <title>Generic classes</title>
3359 <para>(Note: support for generic classes is currently broken in
3363 The ideas behind this extension are described in detail in "Derivable type classes",
3364 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3365 An example will give the idea:
3373 fromBin :: [Int] -> (a, [Int])
3375 toBin {| Unit |} Unit = []
3376 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3377 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3378 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3380 fromBin {| Unit |} bs = (Unit, bs)
3381 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3382 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3383 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3384 (y,bs'') = fromBin bs'
3387 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3388 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3389 which are defined thus in the library module <literal>Generics</literal>:
3393 data a :+: b = Inl a | Inr b
3394 data a :*: b = a :*: b
3397 Now you can make a data type into an instance of Bin like this:
3399 instance (Bin a, Bin b) => Bin (a,b)
3400 instance Bin a => Bin [a]
3402 That is, just leave off the "where" clasuse. Of course, you can put in the
3403 where clause and over-ride whichever methods you please.
3407 <title> Using generics </title>
3408 <para>To use generics you need to</para>
3411 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3412 <option>-fgenerics</option> (to generate extra per-data-type code),
3413 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3417 <para>Import the module <literal>Generics</literal> from the
3418 <literal>lang</literal> package. This import brings into
3419 scope the data types <literal>Unit</literal>,
3420 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3421 don't need this import if you don't mention these types
3422 explicitly; for example, if you are simply giving instance
3423 declarations.)</para>
3428 <sect2> <title> Changes wrt the paper </title>
3430 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3431 can be written infix (indeed, you can now use
3432 any operator starting in a colon as an infix type constructor). Also note that
3433 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3434 Finally, note that the syntax of the type patterns in the class declaration
3435 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3436 alone would ambiguous when they appear on right hand sides (an extension we
3437 anticipate wanting).
3441 <sect2> <title>Terminology and restrictions</title>
3443 Terminology. A "generic default method" in a class declaration
3444 is one that is defined using type patterns as above.
3445 A "polymorphic default method" is a default method defined as in Haskell 98.
3446 A "generic class declaration" is a class declaration with at least one
3447 generic default method.
3455 Alas, we do not yet implement the stuff about constructor names and
3462 A generic class can have only one parameter; you can't have a generic
3463 multi-parameter class.
3469 A default method must be defined entirely using type patterns, or entirely
3470 without. So this is illegal:
3473 op :: a -> (a, Bool)
3474 op {| Unit |} Unit = (Unit, True)
3477 However it is perfectly OK for some methods of a generic class to have
3478 generic default methods and others to have polymorphic default methods.
3484 The type variable(s) in the type pattern for a generic method declaration
3485 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:
3489 op {| p :*: q |} (x :*: y) = op (x :: p)
3497 The type patterns in a generic default method must take one of the forms:
3503 where "a" and "b" are type variables. Furthermore, all the type patterns for
3504 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3505 must use the same type variables. So this is illegal:
3509 op {| a :+: b |} (Inl x) = True
3510 op {| p :+: q |} (Inr y) = False
3512 The type patterns must be identical, even in equations for different methods of the class.
3513 So this too is illegal:
3517 op1 {| a :*: b |} (x :*: y) = True
3520 op2 {| p :*: q |} (x :*: y) = False
3522 (The reason for this restriction is that we gather all the equations for a particular type consructor
3523 into a single generic instance declaration.)
3529 A generic method declaration must give a case for each of the three type constructors.
3535 The type for a generic method can be built only from:
3537 <listitem> <para> Function arrows </para> </listitem>
3538 <listitem> <para> Type variables </para> </listitem>
3539 <listitem> <para> Tuples </para> </listitem>
3540 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3542 Here are some example type signatures for generic methods:
3545 op2 :: Bool -> (a,Bool)
3546 op3 :: [Int] -> a -> a
3549 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3553 This restriction is an implementation restriction: we just havn't got around to
3554 implementing the necessary bidirectional maps over arbitrary type constructors.
3555 It would be relatively easy to add specific type constructors, such as Maybe and list,
3556 to the ones that are allowed.</para>
3561 In an instance declaration for a generic class, the idea is that the compiler
3562 will fill in the methods for you, based on the generic templates. However it can only
3567 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3572 No constructor of the instance type has unboxed fields.
3576 (Of course, these things can only arise if you are already using GHC extensions.)
3577 However, you can still give an instance declarations for types which break these rules,
3578 provided you give explicit code to override any generic default methods.
3586 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3587 what the compiler does with generic declarations.
3592 <sect2> <title> Another example </title>
3594 Just to finish with, here's another example I rather like:
3598 nCons {| Unit |} _ = 1
3599 nCons {| a :*: b |} _ = 1
3600 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3603 tag {| Unit |} _ = 1
3604 tag {| a :*: b |} _ = 1
3605 tag {| a :+: b |} (Inl x) = tag x
3606 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3612 <sect1 id="newtype-deriving">
3613 <title>Generalised derived instances for newtypes</title>
3616 When you define an abstract type using <literal>newtype</literal>, you may want
3617 the new type to inherit some instances from its representation. In
3618 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3619 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3620 other classes you have to write an explicit instance declaration. For
3621 example, if you define
3624 newtype Dollars = Dollars Int
3627 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3628 explicitly define an instance of <literal>Num</literal>:
3631 instance Num Dollars where
3632 Dollars a + Dollars b = Dollars (a+b)
3635 All the instance does is apply and remove the <literal>newtype</literal>
3636 constructor. It is particularly galling that, since the constructor
3637 doesn't appear at run-time, this instance declaration defines a
3638 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3639 dictionary, only slower!
3642 <sect2> <title> Generalising the deriving clause </title>
3644 GHC now permits such instances to be derived instead, so one can write
3646 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3649 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3650 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3651 derives an instance declaration of the form
3654 instance Num Int => Num Dollars
3657 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3661 We can also derive instances of constructor classes in a similar
3662 way. For example, suppose we have implemented state and failure monad
3663 transformers, such that
3666 instance Monad m => Monad (State s m)
3667 instance Monad m => Monad (Failure m)
3669 In Haskell 98, we can define a parsing monad by
3671 type Parser tok m a = State [tok] (Failure m) a
3674 which is automatically a monad thanks to the instance declarations
3675 above. With the extension, we can make the parser type abstract,
3676 without needing to write an instance of class <literal>Monad</literal>, via
3679 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3682 In this case the derived instance declaration is of the form
3684 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3687 Notice that, since <literal>Monad</literal> is a constructor class, the
3688 instance is a <emphasis>partial application</emphasis> of the new type, not the
3689 entire left hand side. We can imagine that the type declaration is
3690 ``eta-converted'' to generate the context of the instance
3695 We can even derive instances of multi-parameter classes, provided the
3696 newtype is the last class parameter. In this case, a ``partial
3697 application'' of the class appears in the <literal>deriving</literal>
3698 clause. For example, given the class
3701 class StateMonad s m | m -> s where ...
3702 instance Monad m => StateMonad s (State s m) where ...
3704 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3706 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3707 deriving (Monad, StateMonad [tok])
3710 The derived instance is obtained by completing the application of the
3711 class to the new type:
3714 instance StateMonad [tok] (State [tok] (Failure m)) =>
3715 StateMonad [tok] (Parser tok m)
3720 As a result of this extension, all derived instances in newtype
3721 declarations are treated uniformly (and implemented just by reusing
3722 the dictionary for the representation type), <emphasis>except</emphasis>
3723 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3724 the newtype and its representation.
3728 <sect2> <title> A more precise specification </title>
3730 Derived instance declarations are constructed as follows. Consider the
3731 declaration (after expansion of any type synonyms)
3734 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3737 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3739 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3740 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3741 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3742 declarations are, for each <literal>ci</literal>,
3745 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3747 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3748 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3752 As an example which does <emphasis>not</emphasis> work, consider
3754 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3756 Here we cannot derive the instance
3758 instance Monad (State s m) => Monad (NonMonad m)
3761 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3762 and so cannot be "eta-converted" away. It is a good thing that this
3763 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3764 not, in fact, a monad --- for the same reason. Try defining
3765 <literal>>>=</literal> with the correct type: you won't be able to.
3769 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3770 important, since we can only derive instances for the last one. If the
3771 <literal>StateMonad</literal> class above were instead defined as
3774 class StateMonad m s | m -> s where ...
3777 then we would not have been able to derive an instance for the
3778 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3779 classes usually have one "main" parameter for which deriving new
3780 instances is most interesting.
3788 ;;; Local Variables: ***
3790 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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