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. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-fgenerics</option></term>
114 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
116 <para>See <xref LinkEnd="generic-classes">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fno-implicit-prelude</option></term>
124 <para><indexterm><primary>-fno-implicit-prelude
125 option</primary></indexterm> GHC normally imports
126 <filename>Prelude.hi</filename> files for you. If you'd
127 rather it didn't, then give it a
128 <option>-fno-implicit-prelude</option> option. The idea
129 is that you can then import a Prelude of your own. (But
130 don't call it <literal>Prelude</literal>; the Haskell
131 module namespace is flat, and you must not conflict with
132 any Prelude module.)</para>
134 <para>Even though you have not imported the Prelude, most of
135 the built-in syntax still refers to the built-in Haskell
136 Prelude types and values, as specified by the Haskell
137 Report. For example, the type <literal>[Int]</literal>
138 still means <literal>Prelude.[] Int</literal>; tuples
139 continue to refer to the standard Prelude tuples; the
140 translation for list comprehensions continues to use
141 <literal>Prelude.map</literal> etc.</para>
143 <para>However, <option>-fno-implicit-prelude</option> does
144 change the handling of certain built-in syntax: see
145 <xref LinkEnd="rebindable-syntax">.</para>
153 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
154 <!-- included from primitives.sgml -->
158 <!-- TYPE SYSTEM EXTENSIONS -->
159 <sect1 id="type-extensions">
160 <title>Type system extensions</title>
162 <sect2 id="nullary-types">
163 <title>Data types with no constructors</title>
165 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
166 a data type with no constructors. For example:</para>
170 data T a -- T :: * -> *
173 <para>Syntactically, the declaration lacks the "= constrs" part. The
174 type can be parameterised over types of any kind, but if the kind is
175 not <literal>*</literal> then an explicit kind annotation must be used
176 (see <xref linkend="sec-kinding">).</para>
178 <para>Such data types have only one value, namely bottom.
179 Nevertheless, they can be useful when defining "phantom types".</para>
182 <sect2 id="infix-tycons">
183 <title>Infix type constructors</title>
186 GHC allows type constructors to be operators, and to be written infix, very much
187 like expressions. More specifically:
190 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
191 The lexical syntax is the same as that for data constructors.
194 Types can be written infix. For example <literal>Int :*: Bool</literal>.
198 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
199 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
202 Fixities may be declared for type constructors just as for data constructors. However,
203 one cannot distinguish between the two in a fixity declaration; a fixity declaration
204 sets the fixity for a data constructor and the corresponding type constructor. For example:
208 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
209 and similarly for <literal>:*:</literal>.
210 <literal>Int `a` Bool</literal>.
213 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
216 Data type and type-synonym declarations can be written infix. E.g.
218 data a :*: b = Foo a b
219 type a :+: b = Either a b
223 The only thing that differs between operators in types and operators in expressions is that
224 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
225 are not allowed in types. Reason: the uniform thing to do would be to make them type
226 variables, but that's not very useful. A less uniform but more useful thing would be to
227 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
228 lists. So for now we just exclude them.
235 <sect2 id="sec-kinding">
236 <title>Explicitly-kinded quantification</title>
239 Haskell infers the kind of each type variable. Sometimes it is nice to be able
240 to give the kind explicitly as (machine-checked) documentation,
241 just as it is nice to give a type signature for a function. On some occasions,
242 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
243 John Hughes had to define the data type:
245 data Set cxt a = Set [a]
246 | Unused (cxt a -> ())
248 The only use for the <literal>Unused</literal> constructor was to force the correct
249 kind for the type variable <literal>cxt</literal>.
252 GHC now instead allows you to specify the kind of a type variable directly, wherever
253 a type variable is explicitly bound. Namely:
255 <listitem><para><literal>data</literal> declarations:
257 data Set (cxt :: * -> *) a = Set [a]
258 </Screen></para></listitem>
259 <listitem><para><literal>type</literal> declarations:
261 type T (f :: * -> *) = f Int
262 </Screen></para></listitem>
263 <listitem><para><literal>class</literal> declarations:
265 class (Eq a) => C (f :: * -> *) a where ...
266 </Screen></para></listitem>
267 <listitem><para><literal>forall</literal>'s in type signatures:
269 f :: forall (cxt :: * -> *). Set cxt Int
270 </Screen></para></listitem>
275 The parentheses are required. Some of the spaces are required too, to
276 separate the lexemes. If you write <literal>(f::*->*)</literal> you
277 will get a parse error, because "<literal>::*->*</literal>" is a
278 single lexeme in Haskell.
282 As part of the same extension, you can put kind annotations in types
285 f :: (Int :: *) -> Int
286 g :: forall a. a -> (a :: *)
290 atype ::= '(' ctype '::' kind ')
292 The parentheses are required.
297 <sect2 id="class-method-types">
298 <title>Class method types
301 Haskell 98 prohibits class method types to mention constraints on the
302 class type variable, thus:
305 fromList :: [a] -> s a
306 elem :: Eq a => a -> s a -> Bool
308 The type of <literal>elem</literal> is illegal in Haskell 98, because it
309 contains the constraint <literal>Eq a</literal>, constrains only the
310 class type variable (in this case <literal>a</literal>).
313 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
318 <sect2 id="multi-param-type-classes">
319 <title>Multi-parameter type classes
323 This section documents GHC's implementation of multi-parameter type
324 classes. There's lots of background in the paper <ULink
325 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
326 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
331 I'd like to thank people who reported shorcomings in the GHC 3.02
332 implementation. Our default decisions were all conservative ones, and
333 the experience of these heroic pioneers has given useful concrete
334 examples to support several generalisations. (These appear below as
335 design choices not implemented in 3.02.)
339 I've discussed these notes with Mark Jones, and I believe that Hugs
340 will migrate towards the same design choices as I outline here.
341 Thanks to him, and to many others who have offered very useful
349 There are the following restrictions on the form of a qualified
356 forall tv1..tvn (c1, ...,cn) => type
362 (Here, I write the "foralls" explicitly, although the Haskell source
363 language omits them; in Haskell 1.4, all the free type variables of an
364 explicit source-language type signature are universally quantified,
365 except for the class type variables in a class declaration. However,
366 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
375 <emphasis>Each universally quantified type variable
376 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
378 The reason for this is that a value with a type that does not obey
379 this restriction could not be used without introducing
380 ambiguity. Here, for example, is an illegal type:
384 forall a. Eq a => Int
388 When a value with this type was used, the constraint <literal>Eq tv</literal>
389 would be introduced where <literal>tv</literal> is a fresh type variable, and
390 (in the dictionary-translation implementation) the value would be
391 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
392 can never know which instance of <literal>Eq</literal> to use because we never
393 get any more information about <literal>tv</literal>.
400 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
401 universally quantified type variables <literal>tvi</literal></emphasis>.
403 For example, this type is OK because <literal>C a b</literal> mentions the
404 universally quantified type variable <literal>b</literal>:
408 forall a. C a b => burble
412 The next type is illegal because the constraint <literal>Eq b</literal> does not
413 mention <literal>a</literal>:
417 forall a. Eq b => burble
421 The reason for this restriction is milder than the other one. The
422 excluded types are never useful or necessary (because the offending
423 context doesn't need to be witnessed at this point; it can be floated
424 out). Furthermore, floating them out increases sharing. Lastly,
425 excluding them is a conservative choice; it leaves a patch of
426 territory free in case we need it later.
436 These restrictions apply to all types, whether declared in a type signature
441 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
442 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
449 f :: Eq (m a) => [m a] -> [m a]
456 This choice recovers principal types, a property that Haskell 1.4 does not have.
462 <title>Class declarations</title>
470 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
474 class Collection c a where
475 union :: c a -> c a -> c a
486 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
487 of "acyclic" involves only the superclass relationships. For example,
493 op :: D b => a -> b -> b
496 class C a => D a where { ... }
500 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
501 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
502 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
509 <emphasis>There are no restrictions on the context in a class declaration
510 (which introduces superclasses), except that the class hierarchy must
511 be acyclic</emphasis>. So these class declarations are OK:
515 class Functor (m k) => FiniteMap m k where
518 class (Monad m, Monad (t m)) => Transform t m where
519 lift :: m a -> (t m) a
528 <emphasis>In the signature of a class operation, every constraint
529 must mention at least one type variable that is not a class type
536 class Collection c a where
537 mapC :: Collection c b => (a->b) -> c a -> c b
541 is OK because the constraint <literal>(Collection a b)</literal> mentions
542 <literal>b</literal>, even though it also mentions the class variable
543 <literal>a</literal>. On the other hand:
548 op :: Eq a => (a,b) -> (a,b)
552 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
553 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
554 example is easily fixed by moving the offending context up to the
559 class Eq a => C a where
564 A yet more relaxed rule would allow the context of a class-op signature
565 to mention only class type variables. However, that conflicts with
566 Rule 1(b) for types above.
573 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
574 the class type variables</emphasis>. For example:
580 insert :: s -> a -> s
584 is not OK, because the type of <literal>empty</literal> doesn't mention
585 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
586 types, and has the same motivation.
588 Sometimes, offending class declarations exhibit misunderstandings. For
589 example, <literal>Coll</literal> might be rewritten
595 insert :: s a -> a -> s a
599 which makes the connection between the type of a collection of
600 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
601 Occasionally this really doesn't work, in which case you can split the
609 class CollE s => Coll s a where
610 insert :: s -> a -> s
623 <sect3 id="instance-decls">
624 <title>Instance declarations</title>
632 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
637 instance context1 => C type1 where ...
638 instance context2 => C type2 where ...
642 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
644 However, if you give the command line option
645 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
646 option</primary></indexterm> then overlapping instance declarations are permitted.
647 However, GHC arranges never to commit to using an instance declaration
648 if another instance declaration also applies, either now or later.
654 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
660 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
661 (but not identical to <literal>type1</literal>), or vice versa.
665 Notice that these rules
670 make it clear which instance decl to use
671 (pick the most specific one that matches)
678 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
679 Reason: you can pick which instance decl
680 "matches" based on the type.
685 However the rules are over-conservative. Two instance declarations can overlap,
686 but it can still be clear in particular situations which to use. For example:
688 instance C (Int,a) where ...
689 instance C (a,Bool) where ...
691 These are rejected by GHC's rules, but it is clear what to do when trying
692 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
693 cannot apply. Yell if this restriction bites you.
696 GHC is also conservative about committing to an overlapping instance. For example:
698 class C a where { op :: a -> a }
699 instance C [Int] where ...
700 instance C a => C [a] where ...
702 f :: C b => [b] -> [b]
705 From the RHS of f we get the constraint <literal>C [b]</literal>. But
706 GHC does not commit to the second instance declaration, because in a paricular
707 call of f, b might be instantiate to Int, so the first instance declaration
708 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
709 GHC will instead silently pick the second instance, without complaining about
710 the problem of subsequent instantiations.
713 Regrettably, GHC doesn't guarantee to detect overlapping instance
714 declarations if they appear in different modules. GHC can "see" the
715 instance declarations in the transitive closure of all the modules
716 imported by the one being compiled, so it can "see" all instance decls
717 when it is compiling <literal>Main</literal>. However, it currently chooses not
718 to look at ones that can't possibly be of use in the module currently
719 being compiled, in the interests of efficiency. (Perhaps we should
720 change that decision, at least for <literal>Main</literal>.)
727 <emphasis>There are no restrictions on the type in an instance
728 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
729 The instance "head" is the bit after the "=>" in an instance decl. For
730 example, these are OK:
734 instance C Int a where ...
736 instance D (Int, Int) where ...
738 instance E [[a]] where ...
742 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
743 For example, this is OK:
747 instance Stateful (ST s) (MutVar s) where ...
751 The "at least one not a type variable" restriction is to ensure that
752 context reduction terminates: each reduction step removes one type
753 constructor. For example, the following would make the type checker
754 loop if it wasn't excluded:
758 instance C a => C a where ...
762 There are two situations in which the rule is a bit of a pain. First,
763 if one allows overlapping instance declarations then it's quite
764 convenient to have a "default instance" declaration that applies if
765 something more specific does not:
774 Second, sometimes you might want to use the following to get the
775 effect of a "class synonym":
779 class (C1 a, C2 a, C3 a) => C a where { }
781 instance (C1 a, C2 a, C3 a) => C a where { }
785 This allows you to write shorter signatures:
797 f :: (C1 a, C2 a, C3 a) => ...
801 I'm on the lookout for a simple rule that preserves decidability while
802 allowing these idioms. The experimental flag
803 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
804 option</primary></indexterm> lifts this restriction, allowing all the types in an
805 instance head to be type variables.
812 <emphasis>Unlike Haskell 1.4, instance heads may use type
813 synonyms</emphasis>. As always, using a type synonym is just shorthand for
814 writing the RHS of the type synonym definition. For example:
818 type Point = (Int,Int)
819 instance C Point where ...
820 instance C [Point] where ...
824 is legal. However, if you added
828 instance C (Int,Int) where ...
832 as well, then the compiler will complain about the overlapping
833 (actually, identical) instance declarations. As always, type synonyms
834 must be fully applied. You cannot, for example, write:
839 instance Monad P where ...
843 This design decision is independent of all the others, and easily
844 reversed, but it makes sense to me.
851 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
852 be type variables</emphasis>. Thus
856 instance C a b => Eq (a,b) where ...
864 instance C Int b => Foo b where ...
868 is not OK. Again, the intent here is to make sure that context
869 reduction terminates.
871 Voluminous correspondence on the Haskell mailing list has convinced me
872 that it's worth experimenting with a more liberal rule. If you use
873 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
874 types in an instance context. Termination is ensured by having a
875 fixed-depth recursion stack. If you exceed the stack depth you get a
876 sort of backtrace, and the opportunity to increase the stack depth
877 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
890 <sect2 id="implicit-parameters">
891 <title>Implicit parameters
894 <para> Implicit paramters are implemented as described in
895 "Implicit parameters: dynamic scoping with static types",
896 J Lewis, MB Shields, E Meijer, J Launchbury,
897 27th ACM Symposium on Principles of Programming Languages (POPL'00),
900 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
902 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
903 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
904 context. In Haskell, all variables are statically bound. Dynamic
905 binding of variables is a notion that goes back to Lisp, but was later
906 discarded in more modern incarnations, such as Scheme. Dynamic binding
907 can be very confusing in an untyped language, and unfortunately, typed
908 languages, in particular Hindley-Milner typed languages like Haskell,
909 only support static scoping of variables.
912 However, by a simple extension to the type class system of Haskell, we
913 can support dynamic binding. Basically, we express the use of a
914 dynamically bound variable as a constraint on the type. These
915 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
916 function uses a dynamically-bound variable <literal>?x</literal>
917 of type <literal>t'</literal>". For
918 example, the following expresses the type of a sort function,
919 implicitly parameterized by a comparison function named <literal>cmp</literal>.
921 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
923 The dynamic binding constraints are just a new form of predicate in the type class system.
926 An implicit parameter is introduced by the special form <literal>?x</literal>,
927 where <literal>x</literal> is
928 any valid identifier. Use if this construct also introduces new
929 dynamic binding constraints. For example, the following definition
930 shows how we can define an implicitly parameterized sort function in
931 terms of an explicitly parameterized <literal>sortBy</literal> function:
933 sortBy :: (a -> a -> Bool) -> [a] -> [a]
935 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
938 Dynamic binding constraints behave just like other type class
939 constraints in that they are automatically propagated. Thus, when a
940 function is used, its implicit parameters are inherited by the
941 function that called it. For example, our <literal>sort</literal> function might be used
942 to pick out the least value in a list:
944 least :: (?cmp :: a -> a -> Bool) => [a] -> a
945 least xs = fst (sort xs)
947 Without lifting a finger, the <literal>?cmp</literal> parameter is
948 propagated to become a parameter of <literal>least</literal> as well. With explicit
949 parameters, the default is that parameters must always be explicit
950 propagated. With implicit parameters, the default is to always
954 An implicit parameter differs from other type class constraints in the
955 following way: All uses of a particular implicit parameter must have
956 the same type. This means that the type of <literal>(?x, ?x)</literal>
957 is <literal>(?x::a) => (a,a)</literal>, and not
958 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
962 An implicit parameter is bound using the standard
963 <literal>let</literal> binding form, where the bindings must be a
964 collection of simple bindings to implicit-style variables (no
965 function-style bindings, and no type signatures); these bindings are
966 neither polymorphic or recursive. This form binds the implicit
967 parameters arising in the body, not the free variables as a
968 <literal>let</literal> or <literal>where</literal> would do. For
969 example, we define the <literal>min</literal> function by binding
970 <literal>cmp</literal>.</para>
973 min = let ?cmp = (<=) in least
976 Note the following additional constraints:
979 <para> You can't have an implicit parameter in the context of a class or instance
980 declaration. For example, both these declarations are illegal:
982 class (?x::Int) => C a where ...
983 instance (?x::a) => Foo [a] where ...
985 Reason: exactly which implicit parameter you pick up depends on exactly where
986 you invoke a function. But the ``invocation'' of instance declarations is done
987 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
988 Easiest thing is to outlaw the offending types.</para>
995 <sect2 id="linear-implicit-parameters">
996 <title>Linear implicit parameters
999 Linear implicit parameters are an idea developed by Koen Claessen,
1000 Mark Shields, and Simon PJ. They address the long-standing
1001 problem that monads seem over-kill for certain sorts of problem, notably:
1004 <listitem> <para> distributing a supply of unique names </para> </listitem>
1005 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1006 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1010 Linear implicit parameters are just like ordinary implicit parameters,
1011 except that they are "linear" -- that is, they cannot be copied, and
1012 must be explicitly "split" instead. Linear implicit parameters are
1013 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1014 (The '/' in the '%' suggests the split!)
1019 import GHC.Exts( Splittable )
1021 data NameSupply = ...
1023 splitNS :: NameSupply -> (NameSupply, NameSupply)
1024 newName :: NameSupply -> Name
1026 instance Splittable NameSupply where
1030 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1031 f env (Lam x e) = Lam x' (f env e)
1034 env' = extend env x x'
1035 ...more equations for f...
1037 Notice that the implicit parameter %ns is consumed
1039 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1040 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1044 So the translation done by the type checker makes
1045 the parameter explicit:
1047 f :: NameSupply -> Env -> Expr -> Expr
1048 f ns env (Lam x e) = Lam x' (f ns1 env e)
1050 (ns1,ns2) = splitNS ns
1052 env = extend env x x'
1054 Notice the call to 'split' introduced by the type checker.
1055 How did it know to use 'splitNS'? Because what it really did
1056 was to introduce a call to the overloaded function 'split',
1057 defined by the class <literal>Splittable</literal>:
1059 class Splittable a where
1062 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1063 split for name supplies. But we can simply write
1069 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1071 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1072 <literal>GHC.Exts</literal>.
1077 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1078 are entirely distinct implicit parameters: you
1079 can use them together and they won't intefere with each other. </para>
1082 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1084 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1085 in the context of a class or instance declaration. </para></listitem>
1089 <sect3><title>Warnings</title>
1092 The monomorphism restriction is even more important than usual.
1093 Consider the example above:
1095 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1096 f env (Lam x e) = Lam x' (f env e)
1099 env' = extend env x x'
1101 If we replaced the two occurrences of x' by (newName %ns), which is
1102 usually a harmless thing to do, we get:
1104 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1105 f env (Lam x e) = Lam (newName %ns) (f env e)
1107 env' = extend env x (newName %ns)
1109 But now the name supply is consumed in <emphasis>three</emphasis> places
1110 (the two calls to newName,and the recursive call to f), so
1111 the result is utterly different. Urk! We don't even have
1115 Well, this is an experimental change. With implicit
1116 parameters we have already lost beta reduction anyway, and
1117 (as John Launchbury puts it) we can't sensibly reason about
1118 Haskell programs without knowing their typing.
1125 <sect2 id="functional-dependencies">
1126 <title>Functional dependencies
1129 <para> Functional dependencies are implemented as described by Mark Jones
1130 in "Type Classes with Functional Dependencies", Mark P. Jones,
1131 In Proceedings of the 9th European Symposium on Programming,
1132 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1136 There should be more documentation, but there isn't (yet). Yell if you need it.
1141 <sect2 id="universal-quantification">
1142 <title>Arbitrary-rank polymorphism
1146 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1147 allows us to say exactly what this means. For example:
1155 g :: forall b. (b -> b)
1157 The two are treated identically.
1161 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1162 explicit universal quantification in
1164 For example, all the following types are legal:
1166 f1 :: forall a b. a -> b -> a
1167 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1169 f2 :: (forall a. a->a) -> Int -> Int
1170 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1172 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1174 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1175 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1176 The <literal>forall</literal> makes explicit the universal quantification that
1177 is implicitly added by Haskell.
1180 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1181 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1182 shows, the polymorphic type on the left of the function arrow can be overloaded.
1185 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1186 they have rank-2 types on the left of a function arrow.
1189 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1190 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1191 that restriction has now been lifted.)
1192 In particular, a forall-type (also called a "type scheme"),
1193 including an operational type class context, is legal:
1195 <listitem> <para> On the left of a function arrow </para> </listitem>
1196 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1197 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1198 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1199 field type signatures.</para> </listitem>
1200 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1201 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1203 There is one place you cannot put a <literal>forall</literal>:
1204 you cannot instantiate a type variable with a forall-type. So you cannot
1205 make a forall-type the argument of a type constructor. So these types are illegal:
1207 x1 :: [forall a. a->a]
1208 x2 :: (forall a. a->a, Int)
1209 x3 :: Maybe (forall a. a->a)
1211 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1212 a type variable any more!
1221 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1222 the types of the constructor arguments. Here are several examples:
1228 data T a = T1 (forall b. b -> b -> b) a
1230 data MonadT m = MkMonad { return :: forall a. a -> m a,
1231 bind :: forall a b. m a -> (a -> m b) -> m b
1234 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1240 The constructors have rank-2 types:
1246 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1247 MkMonad :: forall m. (forall a. a -> m a)
1248 -> (forall a b. m a -> (a -> m b) -> m b)
1250 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1256 Notice that you don't need to use a <literal>forall</literal> if there's an
1257 explicit context. For example in the first argument of the
1258 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1259 prefixed to the argument type. The implicit <literal>forall</literal>
1260 quantifies all type variables that are not already in scope, and are
1261 mentioned in the type quantified over.
1265 As for type signatures, implicit quantification happens for non-overloaded
1266 types too. So if you write this:
1269 data T a = MkT (Either a b) (b -> b)
1272 it's just as if you had written this:
1275 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1278 That is, since the type variable <literal>b</literal> isn't in scope, it's
1279 implicitly universally quantified. (Arguably, it would be better
1280 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1281 where that is what is wanted. Feedback welcomed.)
1285 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1286 the constructor to suitable values, just as usual. For example,
1297 a3 = MkSwizzle reverse
1300 a4 = let r x = Just x
1307 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1308 mkTs f x y = [T1 f x, T1 f y]
1314 The type of the argument can, as usual, be more general than the type
1315 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1316 does not need the <literal>Ord</literal> constraint.)
1320 When you use pattern matching, the bound variables may now have
1321 polymorphic types. For example:
1327 f :: T a -> a -> (a, Char)
1328 f (T1 w k) x = (w k x, w 'c' 'd')
1330 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1331 g (MkSwizzle s) xs f = s (map f (s xs))
1333 h :: MonadT m -> [m a] -> m [a]
1334 h m [] = return m []
1335 h m (x:xs) = bind m x $ \y ->
1336 bind m (h m xs) $ \ys ->
1343 In the function <function>h</function> we use the record selectors <literal>return</literal>
1344 and <literal>bind</literal> to extract the polymorphic bind and return functions
1345 from the <literal>MonadT</literal> data structure, rather than using pattern
1351 <title>Type inference</title>
1354 In general, type inference for arbitrary-rank types is undecideable.
1355 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1356 to get a decidable algorithm by requiring some help from the programmer.
1357 We do not yet have a formal specification of "some help" but the rule is this:
1360 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1361 provides an explicit polymorphic type for x, or GHC's type inference will assume
1362 that x's type has no foralls in it</emphasis>.
1365 What does it mean to "provide" an explicit type for x? You can do that by
1366 giving a type signature for x directly, using a pattern type signature
1367 (<xref linkend="scoped-type-variables">), thus:
1369 \ f :: (forall a. a->a) -> (f True, f 'c')
1371 Alternatively, you can give a type signature to the enclosing
1372 context, which GHC can "push down" to find the type for the variable:
1374 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1376 Here the type signature on the expression can be pushed inwards
1377 to give a type signature for f. Similarly, and more commonly,
1378 one can give a type signature for the function itself:
1380 h :: (forall a. a->a) -> (Bool,Char)
1381 h f = (f True, f 'c')
1383 You don't need to give a type signature if the lambda bound variable
1384 is a constructor argument. Here is an example we saw earlier:
1386 f :: T a -> a -> (a, Char)
1387 f (T1 w k) x = (w k x, w 'c' 'd')
1389 Here we do not need to give a type signature to <literal>w</literal>, because
1390 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1397 <sect3 id="implicit-quant">
1398 <title>Implicit quantification</title>
1401 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1402 user-written types, if and only if there is no explicit <literal>forall</literal>,
1403 GHC finds all the type variables mentioned in the type that are not already
1404 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1408 f :: forall a. a -> a
1415 h :: forall b. a -> b -> b
1421 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1424 f :: (a -> a) -> Int
1426 f :: forall a. (a -> a) -> Int
1428 f :: (forall a. a -> a) -> Int
1431 g :: (Ord a => a -> a) -> Int
1432 -- MEANS the illegal type
1433 g :: forall a. (Ord a => a -> a) -> Int
1435 g :: (forall a. Ord a => a -> a) -> Int
1437 The latter produces an illegal type, which you might think is silly,
1438 but at least the rule is simple. If you want the latter type, you
1439 can write your for-alls explicitly. Indeed, doing so is strongly advised
1445 <sect2 id="type-synonyms">
1446 <title>Liberalised type synonyms
1450 Type synonmys are like macros at the type level, and
1451 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1452 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1454 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1455 in a type synonym, thus:
1457 type Discard a = forall b. Show b => a -> b -> (a, String)
1462 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1469 You can write an unboxed tuple in a type synonym:
1471 type Pr = (# Int, Int #)
1479 You can apply a type synonym to a forall type:
1481 type Foo a = a -> a -> Bool
1483 f :: Foo (forall b. b->b)
1485 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1487 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1492 You can apply a type synonym to a partially applied type synonym:
1494 type Generic i o = forall x. i x -> o x
1497 foo :: Generic Id []
1499 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1501 foo :: forall x. x -> [x]
1509 GHC currently does kind checking before expanding synonyms (though even that
1513 After expanding type synonyms, GHC does validity checking on types, looking for
1514 the following mal-formedness which isn't detected simply by kind checking:
1517 Type constructor applied to a type involving for-alls.
1520 Unboxed tuple on left of an arrow.
1523 Partially-applied type synonym.
1527 this will be rejected:
1529 type Pr = (# Int, Int #)
1534 because GHC does not allow unboxed tuples on the left of a function arrow.
1539 <title>For-all hoisting</title>
1541 It is often convenient to use generalised type synonyms at the right hand
1542 end of an arrow, thus:
1544 type Discard a = forall b. a -> b -> a
1546 g :: Int -> Discard Int
1549 Simply expanding the type synonym would give
1551 g :: Int -> (forall b. Int -> b -> Int)
1553 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1555 g :: forall b. Int -> Int -> b -> Int
1557 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1558 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1559 performs the transformation:</emphasis>
1561 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1563 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1565 (In fact, GHC tries to retain as much synonym information as possible for use in
1566 error messages, but that is a usability issue.) This rule applies, of course, whether
1567 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1568 valid way to write <literal>g</literal>'s type signature:
1570 g :: Int -> Int -> forall b. b -> Int
1576 <sect2 id="existential-quantification">
1577 <title>Existentially quantified data constructors
1581 The idea of using existential quantification in data type declarations
1582 was suggested by Laufer (I believe, thought doubtless someone will
1583 correct me), and implemented in Hope+. It's been in Lennart
1584 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1585 proved very useful. Here's the idea. Consider the declaration:
1591 data Foo = forall a. MkFoo a (a -> Bool)
1598 The data type <literal>Foo</literal> has two constructors with types:
1604 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1611 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1612 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1613 For example, the following expression is fine:
1619 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1625 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1626 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1627 isUpper</function> packages a character with a compatible function. These
1628 two things are each of type <literal>Foo</literal> and can be put in a list.
1632 What can we do with a value of type <literal>Foo</literal>?. In particular,
1633 what happens when we pattern-match on <function>MkFoo</function>?
1639 f (MkFoo val fn) = ???
1645 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1646 are compatible, the only (useful) thing we can do with them is to
1647 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1654 f (MkFoo val fn) = fn val
1660 What this allows us to do is to package heterogenous values
1661 together with a bunch of functions that manipulate them, and then treat
1662 that collection of packages in a uniform manner. You can express
1663 quite a bit of object-oriented-like programming this way.
1666 <sect3 id="existential">
1667 <title>Why existential?
1671 What has this to do with <emphasis>existential</emphasis> quantification?
1672 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1678 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1684 But Haskell programmers can safely think of the ordinary
1685 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1686 adding a new existential quantification construct.
1692 <title>Type classes</title>
1695 An easy extension (implemented in <Command>hbc</Command>) is to allow
1696 arbitrary contexts before the constructor. For example:
1702 data Baz = forall a. Eq a => Baz1 a a
1703 | forall b. Show b => Baz2 b (b -> b)
1709 The two constructors have the types you'd expect:
1715 Baz1 :: forall a. Eq a => a -> a -> Baz
1716 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1722 But when pattern matching on <function>Baz1</function> the matched values can be compared
1723 for equality, and when pattern matching on <function>Baz2</function> the first matched
1724 value can be converted to a string (as well as applying the function to it).
1725 So this program is legal:
1732 f (Baz1 p q) | p == q = "Yes"
1734 f (Baz2 v fn) = show (fn v)
1740 Operationally, in a dictionary-passing implementation, the
1741 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1742 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1743 extract it on pattern matching.
1747 Notice the way that the syntax fits smoothly with that used for
1748 universal quantification earlier.
1754 <title>Restrictions</title>
1757 There are several restrictions on the ways in which existentially-quantified
1758 constructors can be use.
1767 When pattern matching, each pattern match introduces a new,
1768 distinct, type for each existential type variable. These types cannot
1769 be unified with any other type, nor can they escape from the scope of
1770 the pattern match. For example, these fragments are incorrect:
1778 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1779 is the result of <function>f1</function>. One way to see why this is wrong is to
1780 ask what type <function>f1</function> has:
1784 f1 :: Foo -> a -- Weird!
1788 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1793 f1 :: forall a. Foo -> a -- Wrong!
1797 The original program is just plain wrong. Here's another sort of error
1801 f2 (Baz1 a b) (Baz1 p q) = a==q
1805 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1806 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1807 from the two <function>Baz1</function> constructors.
1815 You can't pattern-match on an existentially quantified
1816 constructor in a <literal>let</literal> or <literal>where</literal> group of
1817 bindings. So this is illegal:
1821 f3 x = a==b where { Baz1 a b = x }
1825 You can only pattern-match
1826 on an existentially-quantified constructor in a <literal>case</literal> expression or
1827 in the patterns of a function definition.
1829 The reason for this restriction is really an implementation one.
1830 Type-checking binding groups is already a nightmare without
1831 existentials complicating the picture. Also an existential pattern
1832 binding at the top level of a module doesn't make sense, because it's
1833 not clear how to prevent the existentially-quantified type "escaping".
1834 So for now, there's a simple-to-state restriction. We'll see how
1842 You can't use existential quantification for <literal>newtype</literal>
1843 declarations. So this is illegal:
1847 newtype T = forall a. Ord a => MkT a
1851 Reason: a value of type <literal>T</literal> must be represented as a pair
1852 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1853 That contradicts the idea that <literal>newtype</literal> should have no
1854 concrete representation. You can get just the same efficiency and effect
1855 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1856 overloading involved, then there is more of a case for allowing
1857 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1858 because the <literal>data</literal> version does carry an implementation cost,
1859 but single-field existentially quantified constructors aren't much
1860 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1861 stands, unless there are convincing reasons to change it.
1869 You can't use <literal>deriving</literal> to define instances of a
1870 data type with existentially quantified data constructors.
1872 Reason: in most cases it would not make sense. For example:#
1875 data T = forall a. MkT [a] deriving( Eq )
1878 To derive <literal>Eq</literal> in the standard way we would need to have equality
1879 between the single component of two <function>MkT</function> constructors:
1883 (MkT a) == (MkT b) = ???
1886 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1887 It's just about possible to imagine examples in which the derived instance
1888 would make sense, but it seems altogether simpler simply to prohibit such
1889 declarations. Define your own instances!
1901 <sect2 id="scoped-type-variables">
1902 <title>Scoped type variables
1906 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1907 variable</emphasis>. For example
1913 f (xs::[a]) = ys ++ ys
1922 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1923 This brings the type variable <literal>a</literal> into scope; it scopes over
1924 all the patterns and right hand sides for this equation for <function>f</function>.
1925 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1929 Pattern type signatures are completely orthogonal to ordinary, separate
1930 type signatures. The two can be used independently or together.
1931 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1932 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1933 implicitly universally quantified. (If there are no type variables in
1934 scope, all type variables mentioned in the signature are universally
1935 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1936 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1937 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1938 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1939 it becomes possible to do so.
1943 Scoped type variables are implemented in both GHC and Hugs. Where the
1944 implementations differ from the specification below, those differences
1949 So much for the basic idea. Here are the details.
1953 <title>What a pattern type signature means</title>
1955 A type variable brought into scope by a pattern type signature is simply
1956 the name for a type. The restriction they express is that all occurrences
1957 of the same name mean the same type. For example:
1959 f :: [Int] -> Int -> Int
1960 f (xs::[a]) (y::a) = (head xs + y) :: a
1962 The pattern type signatures on the left hand side of
1963 <literal>f</literal> express the fact that <literal>xs</literal>
1964 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1965 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1966 specifies that this expression must have the same type <literal>a</literal>.
1967 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1968 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1969 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1970 rules, which specified that a pattern-bound type variable should be universally quantified.)
1971 For example, all of these are legal:</para>
1974 t (x::a) (y::a) = x+y*2
1976 f (x::a) (y::b) = [x,y] -- a unifies with b
1978 g (x::a) = x + 1::Int -- a unifies with Int
1980 h x = let k (y::a) = [x,y] -- a is free in the
1981 in k x -- environment
1983 k (x::a) True = ... -- a unifies with Int
1984 k (x::Int) False = ...
1987 w (x::a) = x -- a unifies with [b]
1993 <title>Scope and implicit quantification</title>
2001 All the type variables mentioned in a pattern,
2002 that are not already in scope,
2003 are brought into scope by the pattern. We describe this set as
2004 the <emphasis>type variables bound by the pattern</emphasis>.
2007 f (x::a) = let g (y::(a,b)) = fst y
2011 The pattern <literal>(x::a)</literal> brings the type variable
2012 <literal>a</literal> into scope, as well as the term
2013 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2014 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2015 and brings into scope the type variable <literal>b</literal>.
2021 The type variable(s) bound by the pattern have the same scope
2022 as the term variable(s) bound by the pattern. For example:
2025 f (x::a) = <...rhs of f...>
2026 (p::b, q::b) = (1,2)
2027 in <...body of let...>
2029 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2030 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2031 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2032 just like <literal>p</literal> and <literal>q</literal> do.
2033 Indeed, the newly bound type variables also scope over any ordinary, separate
2034 type signatures in the <literal>let</literal> group.
2041 The type variables bound by the pattern may be
2042 mentioned in ordinary type signatures or pattern
2043 type signatures anywhere within their scope.
2050 In ordinary type signatures, any type variable mentioned in the
2051 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2059 Ordinary type signatures do not bring any new type variables
2060 into scope (except in the type signature itself!). So this is illegal:
2067 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2068 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2069 and that is an incorrect typing.
2076 The pattern type signature is a monotype:
2081 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2085 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2086 not to type schemes.
2090 There is no implicit universal quantification on pattern type signatures (in contrast to
2091 ordinary type signatures).
2101 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2102 scope over the methods defined in the <literal>where</literal> part. For example:
2116 (Not implemented in Hugs yet, Dec 98).
2127 <title>Result type signatures</title>
2135 The result type of a function can be given a signature,
2140 f (x::a) :: [a] = [x,x,x]
2144 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2145 result type. Sometimes this is the only way of naming the type variable
2150 f :: Int -> [a] -> [a]
2151 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2152 in \xs -> map g (reverse xs `zip` xs)
2164 Result type signatures are not yet implemented in Hugs.
2170 <title>Where a pattern type signature can occur</title>
2173 A pattern type signature can occur in any pattern. For example:
2178 A pattern type signature can be on an arbitrary sub-pattern, not
2183 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2192 Pattern type signatures, including the result part, can be used
2193 in lambda abstractions:
2196 (\ (x::a, y) :: a -> x)
2203 Pattern type signatures, including the result part, can be used
2204 in <literal>case</literal> expressions:
2208 case e of { (x::a, y) :: a -> x }
2216 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2217 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2218 token or a parenthesised type of some sort). To see why,
2219 consider how one would parse this:
2233 Pattern type signatures can bind existential type variables.
2238 data T = forall a. MkT [a]
2241 f (MkT [t::a]) = MkT t3
2254 Pattern type signatures
2255 can be used in pattern bindings:
2258 f x = let (y, z::a) = x in ...
2259 f1 x = let (y, z::Int) = x in ...
2260 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2261 f3 :: (b->b) = \x -> x
2264 In all such cases, the binding is not generalised over the pattern-bound
2265 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2266 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2267 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2268 In contrast, the binding
2273 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2274 in <literal>f4</literal>'s scope.
2286 <!-- ==================== End of type system extensions ================= -->
2289 <!-- ==================== ASSERTIONS ================= -->
2291 <sect1 id="sec-assertions">
2293 <indexterm><primary>Assertions</primary></indexterm>
2297 If you want to make use of assertions in your standard Haskell code, you
2298 could define a function like the following:
2304 assert :: Bool -> a -> a
2305 assert False x = error "assertion failed!"
2312 which works, but gives you back a less than useful error message --
2313 an assertion failed, but which and where?
2317 One way out is to define an extended <function>assert</function> function which also
2318 takes a descriptive string to include in the error message and
2319 perhaps combine this with the use of a pre-processor which inserts
2320 the source location where <function>assert</function> was used.
2324 Ghc offers a helping hand here, doing all of this for you. For every
2325 use of <function>assert</function> in the user's source:
2331 kelvinToC :: Double -> Double
2332 kelvinToC k = assert (k >= 0.0) (k+273.15)
2338 Ghc will rewrite this to also include the source location where the
2345 assert pred val ==> assertError "Main.hs|15" pred val
2351 The rewrite is only performed by the compiler when it spots
2352 applications of <function>Control.Exception.assert</function>, so you
2353 can still define and use your own versions of
2354 <function>assert</function>, should you so wish. If not, import
2355 <literal>Control.Exception</literal> to make use
2356 <function>assert</function> in your code.
2360 To have the compiler ignore uses of assert, use the compiler option
2361 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
2362 option</primary></indexterm> That is, expressions of the form
2363 <literal>assert pred e</literal> will be rewritten to
2364 <literal>e</literal>.
2368 Assertion failures can be caught, see the documentation for the
2369 <literal>Control.Exception</literal> library for the details.
2375 <sect1 id="syntax-extns">
2376 <title>Syntactic extensions</title>
2378 <!-- ====================== HIERARCHICAL MODULES ======================= -->
2380 <sect2 id="hierarchical-modules">
2381 <title>Hierarchical Modules</title>
2383 <para>GHC supports a small extension to the syntax of module
2384 names: a module name is allowed to contain a dot
2385 <literal>‘.’</literal>. This is also known as the
2386 “hierarchical module namespace” extension, because
2387 it extends the normally flat Haskell module namespace into a
2388 more flexible hierarchy of modules.</para>
2390 <para>This extension has very little impact on the language
2391 itself; modules names are <emphasis>always</emphasis> fully
2392 qualified, so you can just think of the fully qualified module
2393 name as <quote>the module name</quote>. In particular, this
2394 means that the full module name must be given after the
2395 <literal>module</literal> keyword at the beginning of the
2396 module; for example, the module <literal>A.B.C</literal> must
2399 <programlisting>module A.B.C</programlisting>
2402 <para>It is a common strategy to use the <literal>as</literal>
2403 keyword to save some typing when using qualified names with
2404 hierarchical modules. For example:</para>
2407 import qualified Control.Monad.ST.Strict as ST
2410 <para>Hierarchical modules have an impact on the way that GHC
2411 searches for files. For a description, see <xref
2412 linkend="finding-hierarchical-modules">.</para>
2414 <para>GHC comes with a large collection of libraries arranged
2415 hierarchically; see the accompanying library documentation.
2416 There is an ongoing project to create and maintain a stable set
2417 of <quote>core</quote> libraries used by several Haskell
2418 compilers, and the libraries that GHC comes with represent the
2419 current status of that project. For more details, see <ulink
2420 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
2421 Libraries</ulink>.</para>
2425 <!-- ====================== PATTERN GUARDS ======================= -->
2427 <sect2 id="pattern-guards">
2428 <title>Pattern guards</title>
2431 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2432 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.)
2436 Suppose we have an abstract data type of finite maps, with a
2440 lookup :: FiniteMap -> Int -> Maybe Int
2443 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2444 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2448 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2449 | otherwise = var1 + var2
2451 m1 = lookup env var1
2452 m2 = lookup env var2
2453 ok1 = maybeToBool m1
2454 ok2 = maybeToBool m2
2455 val1 = expectJust m1
2456 val2 = expectJust m2
2460 The auxiliary functions are
2464 maybeToBool :: Maybe a -> Bool
2465 maybeToBool (Just x) = True
2466 maybeToBool Nothing = False
2468 expectJust :: Maybe a -> a
2469 expectJust (Just x) = x
2470 expectJust Nothing = error "Unexpected Nothing"
2474 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2475 ok2</literal> checks that both lookups succeed, using
2476 <function>maybeToBool</function> to convert the <function>Maybe</function>
2477 types to booleans. The (lazily evaluated) <function>expectJust</function>
2478 calls extract the values from the results of the lookups, and binds the
2479 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2480 respectively. If either lookup fails, then clunky takes the
2481 <literal>otherwise</literal> case and returns the sum of its arguments.
2485 This is certainly legal Haskell, but it is a tremendously verbose and
2486 un-obvious way to achieve the desired effect. Arguably, a more direct way
2487 to write clunky would be to use case expressions:
2491 clunky env var1 var1 = case lookup env var1 of
2493 Just val1 -> case lookup env var2 of
2495 Just val2 -> val1 + val2
2501 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2502 of pattern-matching, guarded equations as case expressions; that is
2503 precisely what the compiler does when compiling equations! The reason that
2504 Haskell provides guarded equations is because they allow us to write down
2505 the cases we want to consider, one at a time, independently of each other.
2506 This structure is hidden in the case version. Two of the right-hand sides
2507 are really the same (<function>fail</function>), and the whole expression
2508 tends to become more and more indented.
2512 Here is how I would write clunky:
2516 clunky env var1 var1
2517 | Just val1 <- lookup env var1
2518 , Just val2 <- lookup env var2
2520 ...other equations for clunky...
2524 The semantics should be clear enough. The qualifers are matched in order.
2525 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2526 right hand side is evaluated and matched against the pattern on the left.
2527 If the match fails then the whole guard fails and the next equation is
2528 tried. If it succeeds, then the appropriate binding takes place, and the
2529 next qualifier is matched, in the augmented environment. Unlike list
2530 comprehensions, however, the type of the expression to the right of the
2531 <literal><-</literal> is the same as the type of the pattern to its
2532 left. The bindings introduced by pattern guards scope over all the
2533 remaining guard qualifiers, and over the right hand side of the equation.
2537 Just as with list comprehensions, boolean expressions can be freely mixed
2538 with among the pattern guards. For example:
2549 Haskell's current guards therefore emerge as a special case, in which the
2550 qualifier list has just one element, a boolean expression.
2554 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2556 <sect2 id="parallel-list-comprehensions">
2557 <title>Parallel List Comprehensions</title>
2558 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2560 <indexterm><primary>parallel list comprehensions</primary>
2563 <para>Parallel list comprehensions are a natural extension to list
2564 comprehensions. List comprehensions can be thought of as a nice
2565 syntax for writing maps and filters. Parallel comprehensions
2566 extend this to include the zipWith family.</para>
2568 <para>A parallel list comprehension has multiple independent
2569 branches of qualifier lists, each separated by a `|' symbol. For
2570 example, the following zips together two lists:</para>
2573 [ (x, y) | x <- xs | y <- ys ]
2576 <para>The behavior of parallel list comprehensions follows that of
2577 zip, in that the resulting list will have the same length as the
2578 shortest branch.</para>
2580 <para>We can define parallel list comprehensions by translation to
2581 regular comprehensions. Here's the basic idea:</para>
2583 <para>Given a parallel comprehension of the form: </para>
2586 [ e | p1 <- e11, p2 <- e12, ...
2587 | q1 <- e21, q2 <- e22, ...
2592 <para>This will be translated to: </para>
2595 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2596 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2601 <para>where `zipN' is the appropriate zip for the given number of
2606 <sect2 id="rebindable-syntax">
2607 <title>Rebindable syntax</title>
2610 <para>GHC allows most kinds of built-in syntax to be rebound by
2611 the user, to facilitate replacing the <literal>Prelude</literal>
2612 with a home-grown version, for example.</para>
2614 <para>You may want to define your own numeric class
2615 hierarchy. It completely defeats that purpose if the
2616 literal "1" means "<literal>Prelude.fromInteger
2617 1</literal>", which is what the Haskell Report specifies.
2618 So the <option>-fno-implicit-prelude</option> flag causes
2619 the following pieces of built-in syntax to refer to
2620 <emphasis>whatever is in scope</emphasis>, not the Prelude
2625 <para>Integer and fractional literals mean
2626 "<literal>fromInteger 1</literal>" and
2627 "<literal>fromRational 3.2</literal>", not the
2628 Prelude-qualified versions; both in expressions and in
2633 <para>Negation (e.g. "<literal>- (f x)</literal>")
2634 means "<literal>negate (f x)</literal>" (not
2635 <literal>Prelude.negate</literal>).</para>
2639 <para>In an n+k pattern, the standard Prelude
2640 <literal>Ord</literal> class is still used for comparison,
2641 but the necessary subtraction uses whatever
2642 "<literal>(-)</literal>" is in scope (not
2643 "<literal>Prelude.(-)</literal>").</para>
2647 <para>"Do" notation is translated using whatever
2648 functions <literal>(>>=)</literal>,
2649 <literal>(>>)</literal>, <literal>fail</literal>, and
2650 <literal>return</literal>, are in scope (not the Prelude
2651 versions). List comprehensions, and parallel array
2652 comprehensions, are unaffected. </para></listitem>
2655 <para>Be warned: this is an experimental facility, with fewer checks than
2656 usual. In particular, it is essential that the functions GHC finds in scope
2657 must have the appropriate types, namely:
2659 fromInteger :: forall a. (...) => Integer -> a
2660 fromRational :: forall a. (...) => Rational -> a
2661 negate :: forall a. (...) => a -> a
2662 (-) :: forall a. (...) => a -> a -> a
2663 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
2664 (>>) :: forall m a. (...) => m a -> m b -> m b
2665 return :: forall m a. (...) => a -> m a
2666 fail :: forall m a. (...) => String -> m a
2668 (The (...) part can be any context including the empty context; that part
2670 If the functions don't have the right type, very peculiar things may
2671 happen. Use <literal>-dcore-lint</literal> to
2672 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
2677 <!-- =============================== PRAGMAS =========================== -->
2679 <sect1 id="pragmas">
2680 <title>Pragmas</title>
2682 <indexterm><primary>pragma</primary></indexterm>
2684 <para>GHC supports several pragmas, or instructions to the
2685 compiler placed in the source code. Pragmas don't normally affect
2686 the meaning of the program, but they might affect the efficiency
2687 of the generated code.</para>
2689 <para>Pragmas all take the form
2691 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2693 where <replaceable>word</replaceable> indicates the type of
2694 pragma, and is followed optionally by information specific to that
2695 type of pragma. Case is ignored in
2696 <replaceable>word</replaceable>. The various values for
2697 <replaceable>word</replaceable> that GHC understands are described
2698 in the following sections; any pragma encountered with an
2699 unrecognised <replaceable>word</replaceable> is (silently)
2702 <sect2 id="inline-pragma">
2703 <title>INLINE pragma
2705 <indexterm><primary>INLINE pragma</primary></indexterm>
2706 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2709 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2710 functions/values that are “small enough,” thus avoiding the call
2711 overhead and possibly exposing other more-wonderful optimisations.
2715 You will probably see these unfoldings (in Core syntax) in your
2720 Normally, if GHC decides a function is “too expensive” to inline, it
2721 will not do so, nor will it export that unfolding for other modules to
2726 The sledgehammer you can bring to bear is the
2727 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2730 key_function :: Int -> String -> (Bool, Double)
2732 #ifdef __GLASGOW_HASKELL__
2733 {-# INLINE key_function #-}
2737 (You don't need to do the C pre-processor carry-on unless you're going
2738 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2742 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2743 “cost” to be very low. The normal unfolding machinery will then be
2744 very keen to inline it.
2748 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2749 signature could be put.
2753 <literal>INLINE</literal> pragmas are a particularly good idea for the
2754 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2755 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2758 #ifdef __GLASGOW_HASKELL__
2759 {-# INLINE thenUs #-}
2760 {-# INLINE returnUs #-}
2768 <sect2 id="noinline-pragma">
2769 <title>NOINLINE pragma
2772 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2773 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2774 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2775 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2778 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2779 it stops the named function from being inlined by the compiler. You
2780 shouldn't ever need to do this, unless you're very cautious about code
2784 <para><literal>NOTINLINE</literal> is a synonym for
2785 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2786 by Haskell 98 as the standard way to disable inlining, so it should be
2787 used if you want your code to be portable).</para>
2791 <sect2 id="specialize-pragma">
2792 <title>SPECIALIZE pragma</title>
2794 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2795 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2796 <indexterm><primary>overloading, death to</primary></indexterm>
2798 <para>(UK spelling also accepted.) For key overloaded
2799 functions, you can create extra versions (NB: more code space)
2800 specialised to particular types. Thus, if you have an
2801 overloaded function:</para>
2804 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2807 <para>If it is heavily used on lists with
2808 <literal>Widget</literal> keys, you could specialise it as
2812 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2815 <para>To get very fancy, you can also specify a named function
2816 to use for the specialised value, as in:</para>
2819 {-# RULES hammeredLookup = blah #-}
2822 <para>where <literal>blah</literal> is an implementation of
2823 <literal>hammerdLookup</literal> written specialy for
2824 <literal>Widget</literal> lookups. It's <emphasis>Your
2825 Responsibility</emphasis> to make sure that
2826 <function>blah</function> really behaves as a specialised
2827 version of <function>hammeredLookup</function>!!!</para>
2829 <para>Note we use the <literal>RULE</literal> pragma here to
2830 indicate that <literal>hammeredLookup</literal> applied at a
2831 certain type should be replaced by <literal>blah</literal>. See
2832 <xref linkend="rules"> for more information on
2833 <literal>RULES</literal>.</para>
2835 <para>An example in which using <literal>RULES</literal> for
2836 specialisation will Win Big:
2839 toDouble :: Real a => a -> Double
2840 toDouble = fromRational . toRational
2842 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2843 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2846 The <function>i2d</function> function is virtually one machine
2847 instruction; the default conversion—via an intermediate
2848 <literal>Rational</literal>—is obscenely expensive by
2851 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2852 be put anywhere its type signature could be put.</para>
2856 <sect2 id="specialize-instance-pragma">
2857 <title>SPECIALIZE instance pragma
2861 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2862 <indexterm><primary>overloading, death to</primary></indexterm>
2863 Same idea, except for instance declarations. For example:
2866 instance (Eq a) => Eq (Foo a) where {
2867 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2871 The pragma must occur inside the <literal>where</literal> part
2872 of the instance declaration.
2875 Compatible with HBC, by the way, except perhaps in the placement
2881 <sect2 id="line-pragma">
2886 <indexterm><primary>LINE pragma</primary></indexterm>
2887 <indexterm><primary>pragma, LINE</primary></indexterm>
2891 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2892 automatically generated Haskell code. It lets you specify the line
2893 number and filename of the original code; for example
2899 {-# LINE 42 "Foo.vhs" #-}
2905 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2906 and this line corresponds to line 42 in the original. GHC will adjust
2907 its error messages to refer to the line/file named in the <literal>LINE</literal>
2914 <title>RULES pragma</title>
2917 The RULES pragma lets you specify rewrite rules. It is described in
2918 <xref LinkEnd="rewrite-rules">.
2923 <sect2 id="deprecated-pragma">
2924 <title>DEPRECATED pragma</title>
2927 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2928 There are two forms.
2932 You can deprecate an entire module thus:</para>
2934 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2938 When you compile any module that import <literal>Wibble</literal>, GHC will print
2939 the specified message.</para>
2944 You can deprecate a function, class, or type, with the following top-level declaration:
2947 {-# DEPRECATED f, C, T "Don't use these" #-}
2950 When you compile any module that imports and uses any of the specifed entities,
2951 GHC will print the specified message.
2955 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2961 <!-- ======================= REWRITE RULES ======================== -->
2963 <sect1 id="rewrite-rules">
2964 <title>Rewrite rules
2966 <indexterm><primary>RULES pagma</primary></indexterm>
2967 <indexterm><primary>pragma, RULES</primary></indexterm>
2968 <indexterm><primary>rewrite rules</primary></indexterm></title>
2971 The programmer can specify rewrite rules as part of the source program
2972 (in a pragma). GHC applies these rewrite rules wherever it can.
2980 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2987 <title>Syntax</title>
2990 From a syntactic point of view:
2996 Each rule has a name, enclosed in double quotes. The name itself has
2997 no significance at all. It is only used when reporting how many times the rule fired.
3003 There may be zero or more rules in a <literal>RULES</literal> pragma.
3009 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3010 is set, so you must lay out your rules starting in the same column as the
3011 enclosing definitions.
3017 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3018 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3019 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3020 by spaces, just like in a type <literal>forall</literal>.
3026 A pattern variable may optionally have a type signature.
3027 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3028 For example, here is the <literal>foldr/build</literal> rule:
3031 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3032 foldr k z (build g) = g k z
3035 Since <function>g</function> has a polymorphic type, it must have a type signature.
3042 The left hand side of a rule must consist of a top-level variable applied
3043 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3046 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3047 "wrong2" forall f. f True = True
3050 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3057 A rule does not need to be in the same module as (any of) the
3058 variables it mentions, though of course they need to be in scope.
3064 Rules are automatically exported from a module, just as instance declarations are.
3075 <title>Semantics</title>
3078 From a semantic point of view:
3084 Rules are only applied if you use the <option>-O</option> flag.
3090 Rules are regarded as left-to-right rewrite rules.
3091 When GHC finds an expression that is a substitution instance of the LHS
3092 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3093 By "a substitution instance" we mean that the LHS can be made equal to the
3094 expression by substituting for the pattern variables.
3101 The LHS and RHS of a rule are typechecked, and must have the
3109 GHC makes absolutely no attempt to verify that the LHS and RHS
3110 of a rule have the same meaning. That is undecideable in general, and
3111 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3118 GHC makes no attempt to make sure that the rules are confluent or
3119 terminating. For example:
3122 "loop" forall x,y. f x y = f y x
3125 This rule will cause the compiler to go into an infinite loop.
3132 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3138 GHC currently uses a very simple, syntactic, matching algorithm
3139 for matching a rule LHS with an expression. It seeks a substitution
3140 which makes the LHS and expression syntactically equal modulo alpha
3141 conversion. The pattern (rule), but not the expression, is eta-expanded if
3142 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3143 But not beta conversion (that's called higher-order matching).
3147 Matching is carried out on GHC's intermediate language, which includes
3148 type abstractions and applications. So a rule only matches if the
3149 types match too. See <xref LinkEnd="rule-spec"> below.
3155 GHC keeps trying to apply the rules as it optimises the program.
3156 For example, consider:
3165 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3166 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3167 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3168 not be substituted, and the rule would not fire.
3175 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3176 that appears on the LHS of a rule</emphasis>, because once you have substituted
3177 for something you can't match against it (given the simple minded
3178 matching). So if you write the rule
3181 "map/map" forall f,g. map f . map g = map (f.g)
3184 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3185 It will only match something written with explicit use of ".".
3186 Well, not quite. It <emphasis>will</emphasis> match the expression
3192 where <function>wibble</function> is defined:
3195 wibble f g = map f . map g
3198 because <function>wibble</function> will be inlined (it's small).
3200 Later on in compilation, GHC starts inlining even things on the
3201 LHS of rules, but still leaves the rules enabled. This inlining
3202 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3209 All rules are implicitly exported from the module, and are therefore
3210 in force in any module that imports the module that defined the rule, directly
3211 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3212 in force when compiling A.) The situation is very similar to that for instance
3224 <title>List fusion</title>
3227 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3228 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3229 intermediate list should be eliminated entirely.
3233 The following are good producers:
3245 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3251 Explicit lists (e.g. <literal>[True, False]</literal>)
3257 The cons constructor (e.g <literal>3:4:[]</literal>)
3263 <function>++</function>
3269 <function>map</function>
3275 <function>filter</function>
3281 <function>iterate</function>, <function>repeat</function>
3287 <function>zip</function>, <function>zipWith</function>
3296 The following are good consumers:
3308 <function>array</function> (on its second argument)
3314 <function>length</function>
3320 <function>++</function> (on its first argument)
3326 <function>foldr</function>
3332 <function>map</function>
3338 <function>filter</function>
3344 <function>concat</function>
3350 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3356 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3357 will fuse with one but not the other)
3363 <function>partition</function>
3369 <function>head</function>
3375 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3381 <function>sequence_</function>
3387 <function>msum</function>
3393 <function>sortBy</function>
3402 So, for example, the following should generate no intermediate lists:
3405 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3411 This list could readily be extended; if there are Prelude functions that you use
3412 a lot which are not included, please tell us.
3416 If you want to write your own good consumers or producers, look at the
3417 Prelude definitions of the above functions to see how to do so.
3422 <sect2 id="rule-spec">
3423 <title>Specialisation
3427 Rewrite rules can be used to get the same effect as a feature
3428 present in earlier version of GHC:
3431 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3434 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3435 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3436 specialising the original definition of <function>fromIntegral</function> the programmer is
3437 promising that it is safe to use <function>int8ToInt16</function> instead.
3441 This feature is no longer in GHC. But rewrite rules let you do the
3446 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3450 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3451 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3452 GHC adds the type and dictionary applications to get the typed rule
3455 forall (d1::Integral Int8) (d2::Num Int16) .
3456 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3460 this rule does not need to be in the same file as fromIntegral,
3461 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3462 have an original definition available to specialise).
3468 <title>Controlling what's going on</title>
3476 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3482 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3483 If you add <option>-dppr-debug</option> you get a more detailed listing.
3489 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3492 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3493 {-# INLINE build #-}
3497 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3498 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3499 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3500 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3507 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3508 see how to write rules that will do fusion and yet give an efficient
3509 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3521 <sect1 id="generic-classes">
3522 <title>Generic classes</title>
3524 <para>(Note: support for generic classes is currently broken in
3528 The ideas behind this extension are described in detail in "Derivable type classes",
3529 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3530 An example will give the idea:
3538 fromBin :: [Int] -> (a, [Int])
3540 toBin {| Unit |} Unit = []
3541 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3542 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3543 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3545 fromBin {| Unit |} bs = (Unit, bs)
3546 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3547 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3548 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3549 (y,bs'') = fromBin bs'
3552 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3553 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3554 which are defined thus in the library module <literal>Generics</literal>:
3558 data a :+: b = Inl a | Inr b
3559 data a :*: b = a :*: b
3562 Now you can make a data type into an instance of Bin like this:
3564 instance (Bin a, Bin b) => Bin (a,b)
3565 instance Bin a => Bin [a]
3567 That is, just leave off the "where" clasuse. Of course, you can put in the
3568 where clause and over-ride whichever methods you please.
3572 <title> Using generics </title>
3573 <para>To use generics you need to</para>
3576 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3577 <option>-fgenerics</option> (to generate extra per-data-type code),
3578 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3582 <para>Import the module <literal>Generics</literal> from the
3583 <literal>lang</literal> package. This import brings into
3584 scope the data types <literal>Unit</literal>,
3585 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3586 don't need this import if you don't mention these types
3587 explicitly; for example, if you are simply giving instance
3588 declarations.)</para>
3593 <sect2> <title> Changes wrt the paper </title>
3595 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3596 can be written infix (indeed, you can now use
3597 any operator starting in a colon as an infix type constructor). Also note that
3598 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3599 Finally, note that the syntax of the type patterns in the class declaration
3600 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3601 alone would ambiguous when they appear on right hand sides (an extension we
3602 anticipate wanting).
3606 <sect2> <title>Terminology and restrictions</title>
3608 Terminology. A "generic default method" in a class declaration
3609 is one that is defined using type patterns as above.
3610 A "polymorphic default method" is a default method defined as in Haskell 98.
3611 A "generic class declaration" is a class declaration with at least one
3612 generic default method.
3620 Alas, we do not yet implement the stuff about constructor names and
3627 A generic class can have only one parameter; you can't have a generic
3628 multi-parameter class.
3634 A default method must be defined entirely using type patterns, or entirely
3635 without. So this is illegal:
3638 op :: a -> (a, Bool)
3639 op {| Unit |} Unit = (Unit, True)
3642 However it is perfectly OK for some methods of a generic class to have
3643 generic default methods and others to have polymorphic default methods.
3649 The type variable(s) in the type pattern for a generic method declaration
3650 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:
3654 op {| p :*: q |} (x :*: y) = op (x :: p)
3662 The type patterns in a generic default method must take one of the forms:
3668 where "a" and "b" are type variables. Furthermore, all the type patterns for
3669 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3670 must use the same type variables. So this is illegal:
3674 op {| a :+: b |} (Inl x) = True
3675 op {| p :+: q |} (Inr y) = False
3677 The type patterns must be identical, even in equations for different methods of the class.
3678 So this too is illegal:
3682 op1 {| a :*: b |} (x :*: y) = True
3685 op2 {| p :*: q |} (x :*: y) = False
3687 (The reason for this restriction is that we gather all the equations for a particular type consructor
3688 into a single generic instance declaration.)
3694 A generic method declaration must give a case for each of the three type constructors.
3700 The type for a generic method can be built only from:
3702 <listitem> <para> Function arrows </para> </listitem>
3703 <listitem> <para> Type variables </para> </listitem>
3704 <listitem> <para> Tuples </para> </listitem>
3705 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3707 Here are some example type signatures for generic methods:
3710 op2 :: Bool -> (a,Bool)
3711 op3 :: [Int] -> a -> a
3714 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3718 This restriction is an implementation restriction: we just havn't got around to
3719 implementing the necessary bidirectional maps over arbitrary type constructors.
3720 It would be relatively easy to add specific type constructors, such as Maybe and list,
3721 to the ones that are allowed.</para>
3726 In an instance declaration for a generic class, the idea is that the compiler
3727 will fill in the methods for you, based on the generic templates. However it can only
3732 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3737 No constructor of the instance type has unboxed fields.
3741 (Of course, these things can only arise if you are already using GHC extensions.)
3742 However, you can still give an instance declarations for types which break these rules,
3743 provided you give explicit code to override any generic default methods.
3751 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3752 what the compiler does with generic declarations.
3757 <sect2> <title> Another example </title>
3759 Just to finish with, here's another example I rather like:
3763 nCons {| Unit |} _ = 1
3764 nCons {| a :*: b |} _ = 1
3765 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3768 tag {| Unit |} _ = 1
3769 tag {| a :*: b |} _ = 1
3770 tag {| a :+: b |} (Inl x) = tag x
3771 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3777 <sect1 id="newtype-deriving">
3778 <title>Generalised derived instances for newtypes</title>
3781 When you define an abstract type using <literal>newtype</literal>, you may want
3782 the new type to inherit some instances from its representation. In
3783 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3784 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3785 other classes you have to write an explicit instance declaration. For
3786 example, if you define
3789 newtype Dollars = Dollars Int
3792 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3793 explicitly define an instance of <literal>Num</literal>:
3796 instance Num Dollars where
3797 Dollars a + Dollars b = Dollars (a+b)
3800 All the instance does is apply and remove the <literal>newtype</literal>
3801 constructor. It is particularly galling that, since the constructor
3802 doesn't appear at run-time, this instance declaration defines a
3803 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3804 dictionary, only slower!
3807 <sect2> <title> Generalising the deriving clause </title>
3809 GHC now permits such instances to be derived instead, so one can write
3811 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3814 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3815 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3816 derives an instance declaration of the form
3819 instance Num Int => Num Dollars
3822 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3826 We can also derive instances of constructor classes in a similar
3827 way. For example, suppose we have implemented state and failure monad
3828 transformers, such that
3831 instance Monad m => Monad (State s m)
3832 instance Monad m => Monad (Failure m)
3834 In Haskell 98, we can define a parsing monad by
3836 type Parser tok m a = State [tok] (Failure m) a
3839 which is automatically a monad thanks to the instance declarations
3840 above. With the extension, we can make the parser type abstract,
3841 without needing to write an instance of class <literal>Monad</literal>, via
3844 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3847 In this case the derived instance declaration is of the form
3849 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3852 Notice that, since <literal>Monad</literal> is a constructor class, the
3853 instance is a <emphasis>partial application</emphasis> of the new type, not the
3854 entire left hand side. We can imagine that the type declaration is
3855 ``eta-converted'' to generate the context of the instance
3860 We can even derive instances of multi-parameter classes, provided the
3861 newtype is the last class parameter. In this case, a ``partial
3862 application'' of the class appears in the <literal>deriving</literal>
3863 clause. For example, given the class
3866 class StateMonad s m | m -> s where ...
3867 instance Monad m => StateMonad s (State s m) where ...
3869 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3871 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3872 deriving (Monad, StateMonad [tok])
3875 The derived instance is obtained by completing the application of the
3876 class to the new type:
3879 instance StateMonad [tok] (State [tok] (Failure m)) =>
3880 StateMonad [tok] (Parser tok m)
3885 As a result of this extension, all derived instances in newtype
3886 declarations are treated uniformly (and implemented just by reusing
3887 the dictionary for the representation type), <emphasis>except</emphasis>
3888 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3889 the newtype and its representation.
3893 <sect2> <title> A more precise specification </title>
3895 Derived instance declarations are constructed as follows. Consider the
3896 declaration (after expansion of any type synonyms)
3899 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3902 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3904 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3905 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3906 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3907 declarations are, for each <literal>ci</literal>,
3910 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3912 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3913 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3917 As an example which does <emphasis>not</emphasis> work, consider
3919 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3921 Here we cannot derive the instance
3923 instance Monad (State s m) => Monad (NonMonad m)
3926 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3927 and so cannot be "eta-converted" away. It is a good thing that this
3928 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3929 not, in fact, a monad --- for the same reason. Try defining
3930 <literal>>>=</literal> with the correct type: you won't be able to.
3934 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3935 important, since we can only derive instances for the last one. If the
3936 <literal>StateMonad</literal> class above were instead defined as
3939 class StateMonad m s | m -> s where ...
3942 then we would not have been able to derive an instance for the
3943 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3944 classes usually have one "main" parameter for which deriving new
3945 instances is most interesting.
3953 ;;; Local Variables: ***
3955 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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