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 “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1131 In Proceedings of the 9th European Symposium on Programming,
1132 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1137 There should be more documentation, but there isn't (yet). Yell if you need it.
1142 <sect2 id="universal-quantification">
1143 <title>Arbitrary-rank polymorphism
1147 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1148 allows us to say exactly what this means. For example:
1156 g :: forall b. (b -> b)
1158 The two are treated identically.
1162 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1163 explicit universal quantification in
1165 For example, all the following types are legal:
1167 f1 :: forall a b. a -> b -> a
1168 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1170 f2 :: (forall a. a->a) -> Int -> Int
1171 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1173 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1175 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1176 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1177 The <literal>forall</literal> makes explicit the universal quantification that
1178 is implicitly added by Haskell.
1181 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1182 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1183 shows, the polymorphic type on the left of the function arrow can be overloaded.
1186 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1187 they have rank-2 types on the left of a function arrow.
1190 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1191 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1192 that restriction has now been lifted.)
1193 In particular, a forall-type (also called a "type scheme"),
1194 including an operational type class context, is legal:
1196 <listitem> <para> On the left of a function arrow </para> </listitem>
1197 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1198 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1199 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1200 field type signatures.</para> </listitem>
1201 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1202 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1204 There is one place you cannot put a <literal>forall</literal>:
1205 you cannot instantiate a type variable with a forall-type. So you cannot
1206 make a forall-type the argument of a type constructor. So these types are illegal:
1208 x1 :: [forall a. a->a]
1209 x2 :: (forall a. a->a, Int)
1210 x3 :: Maybe (forall a. a->a)
1212 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1213 a type variable any more!
1222 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1223 the types of the constructor arguments. Here are several examples:
1229 data T a = T1 (forall b. b -> b -> b) a
1231 data MonadT m = MkMonad { return :: forall a. a -> m a,
1232 bind :: forall a b. m a -> (a -> m b) -> m b
1235 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1241 The constructors have rank-2 types:
1247 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1248 MkMonad :: forall m. (forall a. a -> m a)
1249 -> (forall a b. m a -> (a -> m b) -> m b)
1251 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1257 Notice that you don't need to use a <literal>forall</literal> if there's an
1258 explicit context. For example in the first argument of the
1259 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1260 prefixed to the argument type. The implicit <literal>forall</literal>
1261 quantifies all type variables that are not already in scope, and are
1262 mentioned in the type quantified over.
1266 As for type signatures, implicit quantification happens for non-overloaded
1267 types too. So if you write this:
1270 data T a = MkT (Either a b) (b -> b)
1273 it's just as if you had written this:
1276 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1279 That is, since the type variable <literal>b</literal> isn't in scope, it's
1280 implicitly universally quantified. (Arguably, it would be better
1281 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1282 where that is what is wanted. Feedback welcomed.)
1286 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1287 the constructor to suitable values, just as usual. For example,
1298 a3 = MkSwizzle reverse
1301 a4 = let r x = Just x
1308 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1309 mkTs f x y = [T1 f x, T1 f y]
1315 The type of the argument can, as usual, be more general than the type
1316 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1317 does not need the <literal>Ord</literal> constraint.)
1321 When you use pattern matching, the bound variables may now have
1322 polymorphic types. For example:
1328 f :: T a -> a -> (a, Char)
1329 f (T1 w k) x = (w k x, w 'c' 'd')
1331 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1332 g (MkSwizzle s) xs f = s (map f (s xs))
1334 h :: MonadT m -> [m a] -> m [a]
1335 h m [] = return m []
1336 h m (x:xs) = bind m x $ \y ->
1337 bind m (h m xs) $ \ys ->
1344 In the function <function>h</function> we use the record selectors <literal>return</literal>
1345 and <literal>bind</literal> to extract the polymorphic bind and return functions
1346 from the <literal>MonadT</literal> data structure, rather than using pattern
1352 <title>Type inference</title>
1355 In general, type inference for arbitrary-rank types is undecideable.
1356 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1357 to get a decidable algorithm by requiring some help from the programmer.
1358 We do not yet have a formal specification of "some help" but the rule is this:
1361 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1362 provides an explicit polymorphic type for x, or GHC's type inference will assume
1363 that x's type has no foralls in it</emphasis>.
1366 What does it mean to "provide" an explicit type for x? You can do that by
1367 giving a type signature for x directly, using a pattern type signature
1368 (<xref linkend="scoped-type-variables">), thus:
1370 \ f :: (forall a. a->a) -> (f True, f 'c')
1372 Alternatively, you can give a type signature to the enclosing
1373 context, which GHC can "push down" to find the type for the variable:
1375 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1377 Here the type signature on the expression can be pushed inwards
1378 to give a type signature for f. Similarly, and more commonly,
1379 one can give a type signature for the function itself:
1381 h :: (forall a. a->a) -> (Bool,Char)
1382 h f = (f True, f 'c')
1384 You don't need to give a type signature if the lambda bound variable
1385 is a constructor argument. Here is an example we saw earlier:
1387 f :: T a -> a -> (a, Char)
1388 f (T1 w k) x = (w k x, w 'c' 'd')
1390 Here we do not need to give a type signature to <literal>w</literal>, because
1391 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1398 <sect3 id="implicit-quant">
1399 <title>Implicit quantification</title>
1402 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1403 user-written types, if and only if there is no explicit <literal>forall</literal>,
1404 GHC finds all the type variables mentioned in the type that are not already
1405 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1409 f :: forall a. a -> a
1416 h :: forall b. a -> b -> b
1422 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1425 f :: (a -> a) -> Int
1427 f :: forall a. (a -> a) -> Int
1429 f :: (forall a. a -> a) -> Int
1432 g :: (Ord a => a -> a) -> Int
1433 -- MEANS the illegal type
1434 g :: forall a. (Ord a => a -> a) -> Int
1436 g :: (forall a. Ord a => a -> a) -> Int
1438 The latter produces an illegal type, which you might think is silly,
1439 but at least the rule is simple. If you want the latter type, you
1440 can write your for-alls explicitly. Indeed, doing so is strongly advised
1446 <sect2 id="type-synonyms">
1447 <title>Liberalised type synonyms
1451 Type synonmys are like macros at the type level, and
1452 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1453 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1455 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1456 in a type synonym, thus:
1458 type Discard a = forall b. Show b => a -> b -> (a, String)
1463 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1470 You can write an unboxed tuple in a type synonym:
1472 type Pr = (# Int, Int #)
1480 You can apply a type synonym to a forall type:
1482 type Foo a = a -> a -> Bool
1484 f :: Foo (forall b. b->b)
1486 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1488 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1493 You can apply a type synonym to a partially applied type synonym:
1495 type Generic i o = forall x. i x -> o x
1498 foo :: Generic Id []
1500 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1502 foo :: forall x. x -> [x]
1510 GHC currently does kind checking before expanding synonyms (though even that
1514 After expanding type synonyms, GHC does validity checking on types, looking for
1515 the following mal-formedness which isn't detected simply by kind checking:
1518 Type constructor applied to a type involving for-alls.
1521 Unboxed tuple on left of an arrow.
1524 Partially-applied type synonym.
1528 this will be rejected:
1530 type Pr = (# Int, Int #)
1535 because GHC does not allow unboxed tuples on the left of a function arrow.
1540 <title>For-all hoisting</title>
1542 It is often convenient to use generalised type synonyms at the right hand
1543 end of an arrow, thus:
1545 type Discard a = forall b. a -> b -> a
1547 g :: Int -> Discard Int
1550 Simply expanding the type synonym would give
1552 g :: Int -> (forall b. Int -> b -> Int)
1554 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1556 g :: forall b. Int -> Int -> b -> Int
1558 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1559 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1560 performs the transformation:</emphasis>
1562 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1564 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1566 (In fact, GHC tries to retain as much synonym information as possible for use in
1567 error messages, but that is a usability issue.) This rule applies, of course, whether
1568 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1569 valid way to write <literal>g</literal>'s type signature:
1571 g :: Int -> Int -> forall b. b -> Int
1575 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1578 type Foo a = (?x::Int) => Bool -> a
1583 g :: (?x::Int) => Bool -> Bool -> Int
1589 <sect2 id="existential-quantification">
1590 <title>Existentially quantified data constructors
1594 The idea of using existential quantification in data type declarations
1595 was suggested by Laufer (I believe, thought doubtless someone will
1596 correct me), and implemented in Hope+. It's been in Lennart
1597 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1598 proved very useful. Here's the idea. Consider the declaration:
1604 data Foo = forall a. MkFoo a (a -> Bool)
1611 The data type <literal>Foo</literal> has two constructors with types:
1617 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1624 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1625 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1626 For example, the following expression is fine:
1632 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1638 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1639 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1640 isUpper</function> packages a character with a compatible function. These
1641 two things are each of type <literal>Foo</literal> and can be put in a list.
1645 What can we do with a value of type <literal>Foo</literal>?. In particular,
1646 what happens when we pattern-match on <function>MkFoo</function>?
1652 f (MkFoo val fn) = ???
1658 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1659 are compatible, the only (useful) thing we can do with them is to
1660 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1667 f (MkFoo val fn) = fn val
1673 What this allows us to do is to package heterogenous values
1674 together with a bunch of functions that manipulate them, and then treat
1675 that collection of packages in a uniform manner. You can express
1676 quite a bit of object-oriented-like programming this way.
1679 <sect3 id="existential">
1680 <title>Why existential?
1684 What has this to do with <emphasis>existential</emphasis> quantification?
1685 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1691 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1697 But Haskell programmers can safely think of the ordinary
1698 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1699 adding a new existential quantification construct.
1705 <title>Type classes</title>
1708 An easy extension (implemented in <Command>hbc</Command>) is to allow
1709 arbitrary contexts before the constructor. For example:
1715 data Baz = forall a. Eq a => Baz1 a a
1716 | forall b. Show b => Baz2 b (b -> b)
1722 The two constructors have the types you'd expect:
1728 Baz1 :: forall a. Eq a => a -> a -> Baz
1729 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1735 But when pattern matching on <function>Baz1</function> the matched values can be compared
1736 for equality, and when pattern matching on <function>Baz2</function> the first matched
1737 value can be converted to a string (as well as applying the function to it).
1738 So this program is legal:
1745 f (Baz1 p q) | p == q = "Yes"
1747 f (Baz2 v fn) = show (fn v)
1753 Operationally, in a dictionary-passing implementation, the
1754 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1755 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1756 extract it on pattern matching.
1760 Notice the way that the syntax fits smoothly with that used for
1761 universal quantification earlier.
1767 <title>Restrictions</title>
1770 There are several restrictions on the ways in which existentially-quantified
1771 constructors can be use.
1780 When pattern matching, each pattern match introduces a new,
1781 distinct, type for each existential type variable. These types cannot
1782 be unified with any other type, nor can they escape from the scope of
1783 the pattern match. For example, these fragments are incorrect:
1791 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1792 is the result of <function>f1</function>. One way to see why this is wrong is to
1793 ask what type <function>f1</function> has:
1797 f1 :: Foo -> a -- Weird!
1801 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1806 f1 :: forall a. Foo -> a -- Wrong!
1810 The original program is just plain wrong. Here's another sort of error
1814 f2 (Baz1 a b) (Baz1 p q) = a==q
1818 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1819 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1820 from the two <function>Baz1</function> constructors.
1828 You can't pattern-match on an existentially quantified
1829 constructor in a <literal>let</literal> or <literal>where</literal> group of
1830 bindings. So this is illegal:
1834 f3 x = a==b where { Baz1 a b = x }
1838 You can only pattern-match
1839 on an existentially-quantified constructor in a <literal>case</literal> expression or
1840 in the patterns of a function definition.
1842 The reason for this restriction is really an implementation one.
1843 Type-checking binding groups is already a nightmare without
1844 existentials complicating the picture. Also an existential pattern
1845 binding at the top level of a module doesn't make sense, because it's
1846 not clear how to prevent the existentially-quantified type "escaping".
1847 So for now, there's a simple-to-state restriction. We'll see how
1855 You can't use existential quantification for <literal>newtype</literal>
1856 declarations. So this is illegal:
1860 newtype T = forall a. Ord a => MkT a
1864 Reason: a value of type <literal>T</literal> must be represented as a pair
1865 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1866 That contradicts the idea that <literal>newtype</literal> should have no
1867 concrete representation. You can get just the same efficiency and effect
1868 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1869 overloading involved, then there is more of a case for allowing
1870 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1871 because the <literal>data</literal> version does carry an implementation cost,
1872 but single-field existentially quantified constructors aren't much
1873 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1874 stands, unless there are convincing reasons to change it.
1882 You can't use <literal>deriving</literal> to define instances of a
1883 data type with existentially quantified data constructors.
1885 Reason: in most cases it would not make sense. For example:#
1888 data T = forall a. MkT [a] deriving( Eq )
1891 To derive <literal>Eq</literal> in the standard way we would need to have equality
1892 between the single component of two <function>MkT</function> constructors:
1896 (MkT a) == (MkT b) = ???
1899 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1900 It's just about possible to imagine examples in which the derived instance
1901 would make sense, but it seems altogether simpler simply to prohibit such
1902 declarations. Define your own instances!
1914 <sect2 id="scoped-type-variables">
1915 <title>Scoped type variables
1919 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1920 variable</emphasis>. For example
1926 f (xs::[a]) = ys ++ ys
1935 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1936 This brings the type variable <literal>a</literal> into scope; it scopes over
1937 all the patterns and right hand sides for this equation for <function>f</function>.
1938 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1942 Pattern type signatures are completely orthogonal to ordinary, separate
1943 type signatures. The two can be used independently or together.
1944 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1945 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1946 implicitly universally quantified. (If there are no type variables in
1947 scope, all type variables mentioned in the signature are universally
1948 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1949 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1950 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1951 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1952 it becomes possible to do so.
1956 Scoped type variables are implemented in both GHC and Hugs. Where the
1957 implementations differ from the specification below, those differences
1962 So much for the basic idea. Here are the details.
1966 <title>What a pattern type signature means</title>
1968 A type variable brought into scope by a pattern type signature is simply
1969 the name for a type. The restriction they express is that all occurrences
1970 of the same name mean the same type. For example:
1972 f :: [Int] -> Int -> Int
1973 f (xs::[a]) (y::a) = (head xs + y) :: a
1975 The pattern type signatures on the left hand side of
1976 <literal>f</literal> express the fact that <literal>xs</literal>
1977 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1978 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1979 specifies that this expression must have the same type <literal>a</literal>.
1980 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1981 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1982 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1983 rules, which specified that a pattern-bound type variable should be universally quantified.)
1984 For example, all of these are legal:</para>
1987 t (x::a) (y::a) = x+y*2
1989 f (x::a) (y::b) = [x,y] -- a unifies with b
1991 g (x::a) = x + 1::Int -- a unifies with Int
1993 h x = let k (y::a) = [x,y] -- a is free in the
1994 in k x -- environment
1996 k (x::a) True = ... -- a unifies with Int
1997 k (x::Int) False = ...
2000 w (x::a) = x -- a unifies with [b]
2006 <title>Scope and implicit quantification</title>
2014 All the type variables mentioned in a pattern,
2015 that are not already in scope,
2016 are brought into scope by the pattern. We describe this set as
2017 the <emphasis>type variables bound by the pattern</emphasis>.
2020 f (x::a) = let g (y::(a,b)) = fst y
2024 The pattern <literal>(x::a)</literal> brings the type variable
2025 <literal>a</literal> into scope, as well as the term
2026 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2027 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2028 and brings into scope the type variable <literal>b</literal>.
2034 The type variable(s) bound by the pattern have the same scope
2035 as the term variable(s) bound by the pattern. For example:
2038 f (x::a) = <...rhs of f...>
2039 (p::b, q::b) = (1,2)
2040 in <...body of let...>
2042 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2043 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2044 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2045 just like <literal>p</literal> and <literal>q</literal> do.
2046 Indeed, the newly bound type variables also scope over any ordinary, separate
2047 type signatures in the <literal>let</literal> group.
2054 The type variables bound by the pattern may be
2055 mentioned in ordinary type signatures or pattern
2056 type signatures anywhere within their scope.
2063 In ordinary type signatures, any type variable mentioned in the
2064 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2072 Ordinary type signatures do not bring any new type variables
2073 into scope (except in the type signature itself!). So this is illegal:
2080 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2081 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2082 and that is an incorrect typing.
2089 The pattern type signature is a monotype:
2094 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2098 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2099 not to type schemes.
2103 There is no implicit universal quantification on pattern type signatures (in contrast to
2104 ordinary type signatures).
2114 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2115 scope over the methods defined in the <literal>where</literal> part. For example:
2129 (Not implemented in Hugs yet, Dec 98).
2140 <title>Result type signatures</title>
2148 The result type of a function can be given a signature,
2153 f (x::a) :: [a] = [x,x,x]
2157 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2158 result type. Sometimes this is the only way of naming the type variable
2163 f :: Int -> [a] -> [a]
2164 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2165 in \xs -> map g (reverse xs `zip` xs)
2177 Result type signatures are not yet implemented in Hugs.
2183 <title>Where a pattern type signature can occur</title>
2186 A pattern type signature can occur in any pattern. For example:
2191 A pattern type signature can be on an arbitrary sub-pattern, not
2196 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2205 Pattern type signatures, including the result part, can be used
2206 in lambda abstractions:
2209 (\ (x::a, y) :: a -> x)
2216 Pattern type signatures, including the result part, can be used
2217 in <literal>case</literal> expressions:
2221 case e of { (x::a, y) :: a -> x }
2229 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2230 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2231 token or a parenthesised type of some sort). To see why,
2232 consider how one would parse this:
2246 Pattern type signatures can bind existential type variables.
2251 data T = forall a. MkT [a]
2254 f (MkT [t::a]) = MkT t3
2267 Pattern type signatures
2268 can be used in pattern bindings:
2271 f x = let (y, z::a) = x in ...
2272 f1 x = let (y, z::Int) = x in ...
2273 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2274 f3 :: (b->b) = \x -> x
2277 In all such cases, the binding is not generalised over the pattern-bound
2278 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2279 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2280 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2281 In contrast, the binding
2286 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2287 in <literal>f4</literal>'s scope.
2299 <!-- ==================== End of type system extensions ================= -->
2302 <!-- ==================== ASSERTIONS ================= -->
2304 <sect1 id="sec-assertions">
2306 <indexterm><primary>Assertions</primary></indexterm>
2310 If you want to make use of assertions in your standard Haskell code, you
2311 could define a function like the following:
2317 assert :: Bool -> a -> a
2318 assert False x = error "assertion failed!"
2325 which works, but gives you back a less than useful error message --
2326 an assertion failed, but which and where?
2330 One way out is to define an extended <function>assert</function> function which also
2331 takes a descriptive string to include in the error message and
2332 perhaps combine this with the use of a pre-processor which inserts
2333 the source location where <function>assert</function> was used.
2337 Ghc offers a helping hand here, doing all of this for you. For every
2338 use of <function>assert</function> in the user's source:
2344 kelvinToC :: Double -> Double
2345 kelvinToC k = assert (k >= 0.0) (k+273.15)
2351 Ghc will rewrite this to also include the source location where the
2358 assert pred val ==> assertError "Main.hs|15" pred val
2364 The rewrite is only performed by the compiler when it spots
2365 applications of <function>Control.Exception.assert</function>, so you
2366 can still define and use your own versions of
2367 <function>assert</function>, should you so wish. If not, import
2368 <literal>Control.Exception</literal> to make use
2369 <function>assert</function> in your code.
2373 To have the compiler ignore uses of assert, use the compiler option
2374 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
2375 option</primary></indexterm> That is, expressions of the form
2376 <literal>assert pred e</literal> will be rewritten to
2377 <literal>e</literal>.
2381 Assertion failures can be caught, see the documentation for the
2382 <literal>Control.Exception</literal> library for the details.
2388 <sect1 id="syntax-extns">
2389 <title>Syntactic extensions</title>
2391 <!-- ====================== HIERARCHICAL MODULES ======================= -->
2393 <sect2 id="hierarchical-modules">
2394 <title>Hierarchical Modules</title>
2396 <para>GHC supports a small extension to the syntax of module
2397 names: a module name is allowed to contain a dot
2398 <literal>‘.’</literal>. This is also known as the
2399 “hierarchical module namespace” extension, because
2400 it extends the normally flat Haskell module namespace into a
2401 more flexible hierarchy of modules.</para>
2403 <para>This extension has very little impact on the language
2404 itself; modules names are <emphasis>always</emphasis> fully
2405 qualified, so you can just think of the fully qualified module
2406 name as <quote>the module name</quote>. In particular, this
2407 means that the full module name must be given after the
2408 <literal>module</literal> keyword at the beginning of the
2409 module; for example, the module <literal>A.B.C</literal> must
2412 <programlisting>module A.B.C</programlisting>
2415 <para>It is a common strategy to use the <literal>as</literal>
2416 keyword to save some typing when using qualified names with
2417 hierarchical modules. For example:</para>
2420 import qualified Control.Monad.ST.Strict as ST
2423 <para>Hierarchical modules have an impact on the way that GHC
2424 searches for files. For a description, see <xref
2425 linkend="finding-hierarchical-modules">.</para>
2427 <para>GHC comes with a large collection of libraries arranged
2428 hierarchically; see the accompanying library documentation.
2429 There is an ongoing project to create and maintain a stable set
2430 of <quote>core</quote> libraries used by several Haskell
2431 compilers, and the libraries that GHC comes with represent the
2432 current status of that project. For more details, see <ulink
2433 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
2434 Libraries</ulink>.</para>
2438 <!-- ====================== PATTERN GUARDS ======================= -->
2440 <sect2 id="pattern-guards">
2441 <title>Pattern guards</title>
2444 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2445 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.)
2449 Suppose we have an abstract data type of finite maps, with a
2453 lookup :: FiniteMap -> Int -> Maybe Int
2456 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2457 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2461 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2462 | otherwise = var1 + var2
2464 m1 = lookup env var1
2465 m2 = lookup env var2
2466 ok1 = maybeToBool m1
2467 ok2 = maybeToBool m2
2468 val1 = expectJust m1
2469 val2 = expectJust m2
2473 The auxiliary functions are
2477 maybeToBool :: Maybe a -> Bool
2478 maybeToBool (Just x) = True
2479 maybeToBool Nothing = False
2481 expectJust :: Maybe a -> a
2482 expectJust (Just x) = x
2483 expectJust Nothing = error "Unexpected Nothing"
2487 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2488 ok2</literal> checks that both lookups succeed, using
2489 <function>maybeToBool</function> to convert the <function>Maybe</function>
2490 types to booleans. The (lazily evaluated) <function>expectJust</function>
2491 calls extract the values from the results of the lookups, and binds the
2492 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2493 respectively. If either lookup fails, then clunky takes the
2494 <literal>otherwise</literal> case and returns the sum of its arguments.
2498 This is certainly legal Haskell, but it is a tremendously verbose and
2499 un-obvious way to achieve the desired effect. Arguably, a more direct way
2500 to write clunky would be to use case expressions:
2504 clunky env var1 var1 = case lookup env var1 of
2506 Just val1 -> case lookup env var2 of
2508 Just val2 -> val1 + val2
2514 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2515 of pattern-matching, guarded equations as case expressions; that is
2516 precisely what the compiler does when compiling equations! The reason that
2517 Haskell provides guarded equations is because they allow us to write down
2518 the cases we want to consider, one at a time, independently of each other.
2519 This structure is hidden in the case version. Two of the right-hand sides
2520 are really the same (<function>fail</function>), and the whole expression
2521 tends to become more and more indented.
2525 Here is how I would write clunky:
2529 clunky env var1 var1
2530 | Just val1 <- lookup env var1
2531 , Just val2 <- lookup env var2
2533 ...other equations for clunky...
2537 The semantics should be clear enough. The qualifers are matched in order.
2538 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2539 right hand side is evaluated and matched against the pattern on the left.
2540 If the match fails then the whole guard fails and the next equation is
2541 tried. If it succeeds, then the appropriate binding takes place, and the
2542 next qualifier is matched, in the augmented environment. Unlike list
2543 comprehensions, however, the type of the expression to the right of the
2544 <literal><-</literal> is the same as the type of the pattern to its
2545 left. The bindings introduced by pattern guards scope over all the
2546 remaining guard qualifiers, and over the right hand side of the equation.
2550 Just as with list comprehensions, boolean expressions can be freely mixed
2551 with among the pattern guards. For example:
2562 Haskell's current guards therefore emerge as a special case, in which the
2563 qualifier list has just one element, a boolean expression.
2567 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2569 <sect2 id="parallel-list-comprehensions">
2570 <title>Parallel List Comprehensions</title>
2571 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2573 <indexterm><primary>parallel list comprehensions</primary>
2576 <para>Parallel list comprehensions are a natural extension to list
2577 comprehensions. List comprehensions can be thought of as a nice
2578 syntax for writing maps and filters. Parallel comprehensions
2579 extend this to include the zipWith family.</para>
2581 <para>A parallel list comprehension has multiple independent
2582 branches of qualifier lists, each separated by a `|' symbol. For
2583 example, the following zips together two lists:</para>
2586 [ (x, y) | x <- xs | y <- ys ]
2589 <para>The behavior of parallel list comprehensions follows that of
2590 zip, in that the resulting list will have the same length as the
2591 shortest branch.</para>
2593 <para>We can define parallel list comprehensions by translation to
2594 regular comprehensions. Here's the basic idea:</para>
2596 <para>Given a parallel comprehension of the form: </para>
2599 [ e | p1 <- e11, p2 <- e12, ...
2600 | q1 <- e21, q2 <- e22, ...
2605 <para>This will be translated to: </para>
2608 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2609 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2614 <para>where `zipN' is the appropriate zip for the given number of
2619 <sect2 id="rebindable-syntax">
2620 <title>Rebindable syntax</title>
2623 <para>GHC allows most kinds of built-in syntax to be rebound by
2624 the user, to facilitate replacing the <literal>Prelude</literal>
2625 with a home-grown version, for example.</para>
2627 <para>You may want to define your own numeric class
2628 hierarchy. It completely defeats that purpose if the
2629 literal "1" means "<literal>Prelude.fromInteger
2630 1</literal>", which is what the Haskell Report specifies.
2631 So the <option>-fno-implicit-prelude</option> flag causes
2632 the following pieces of built-in syntax to refer to
2633 <emphasis>whatever is in scope</emphasis>, not the Prelude
2638 <para>Integer and fractional literals mean
2639 "<literal>fromInteger 1</literal>" and
2640 "<literal>fromRational 3.2</literal>", not the
2641 Prelude-qualified versions; both in expressions and in
2643 <para>However, the standard Prelude <literal>Eq</literal> class
2644 is still used for the equality test necessary for literal patterns.</para>
2648 <para>Negation (e.g. "<literal>- (f x)</literal>")
2649 means "<literal>negate (f x)</literal>" (not
2650 <literal>Prelude.negate</literal>).</para>
2654 <para>In an n+k pattern, the standard Prelude
2655 <literal>Ord</literal> class is still used for comparison,
2656 but the necessary subtraction uses whatever
2657 "<literal>(-)</literal>" is in scope (not
2658 "<literal>Prelude.(-)</literal>").</para>
2662 <para>"Do" notation is translated using whatever
2663 functions <literal>(>>=)</literal>,
2664 <literal>(>>)</literal>, <literal>fail</literal>, and
2665 <literal>return</literal>, are in scope (not the Prelude
2666 versions). List comprehensions, and parallel array
2667 comprehensions, are unaffected. </para></listitem>
2670 <para>Be warned: this is an experimental facility, with fewer checks than
2671 usual. In particular, it is essential that the functions GHC finds in scope
2672 must have the appropriate types, namely:
2674 fromInteger :: forall a. (...) => Integer -> a
2675 fromRational :: forall a. (...) => Rational -> a
2676 negate :: forall a. (...) => a -> a
2677 (-) :: forall a. (...) => a -> a -> a
2678 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
2679 (>>) :: forall m a. (...) => m a -> m b -> m b
2680 return :: forall m a. (...) => a -> m a
2681 fail :: forall m a. (...) => String -> m a
2683 (The (...) part can be any context including the empty context; that part
2685 If the functions don't have the right type, very peculiar things may
2686 happen. Use <literal>-dcore-lint</literal> to
2687 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
2692 <!-- =============================== PRAGMAS =========================== -->
2694 <sect1 id="pragmas">
2695 <title>Pragmas</title>
2697 <indexterm><primary>pragma</primary></indexterm>
2699 <para>GHC supports several pragmas, or instructions to the
2700 compiler placed in the source code. Pragmas don't normally affect
2701 the meaning of the program, but they might affect the efficiency
2702 of the generated code.</para>
2704 <para>Pragmas all take the form
2706 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2708 where <replaceable>word</replaceable> indicates the type of
2709 pragma, and is followed optionally by information specific to that
2710 type of pragma. Case is ignored in
2711 <replaceable>word</replaceable>. The various values for
2712 <replaceable>word</replaceable> that GHC understands are described
2713 in the following sections; any pragma encountered with an
2714 unrecognised <replaceable>word</replaceable> is (silently)
2717 <sect2 id="inline-pragma">
2718 <title>INLINE pragma
2720 <indexterm><primary>INLINE pragma</primary></indexterm>
2721 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2724 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2725 functions/values that are “small enough,” thus avoiding the call
2726 overhead and possibly exposing other more-wonderful optimisations.
2730 You will probably see these unfoldings (in Core syntax) in your
2735 Normally, if GHC decides a function is “too expensive” to inline, it
2736 will not do so, nor will it export that unfolding for other modules to
2741 The sledgehammer you can bring to bear is the
2742 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2745 key_function :: Int -> String -> (Bool, Double)
2747 #ifdef __GLASGOW_HASKELL__
2748 {-# INLINE key_function #-}
2752 (You don't need to do the C pre-processor carry-on unless you're going
2753 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2757 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2758 “cost” to be very low. The normal unfolding machinery will then be
2759 very keen to inline it.
2763 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2764 signature could be put.
2768 <literal>INLINE</literal> pragmas are a particularly good idea for the
2769 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2770 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2773 #ifdef __GLASGOW_HASKELL__
2774 {-# INLINE thenUs #-}
2775 {-# INLINE returnUs #-}
2783 <sect2 id="noinline-pragma">
2784 <title>NOINLINE pragma
2787 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2788 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2789 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2790 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2793 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2794 it stops the named function from being inlined by the compiler. You
2795 shouldn't ever need to do this, unless you're very cautious about code
2799 <para><literal>NOTINLINE</literal> is a synonym for
2800 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2801 by Haskell 98 as the standard way to disable inlining, so it should be
2802 used if you want your code to be portable).</para>
2806 <sect2 id="specialize-pragma">
2807 <title>SPECIALIZE pragma</title>
2809 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2810 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2811 <indexterm><primary>overloading, death to</primary></indexterm>
2813 <para>(UK spelling also accepted.) For key overloaded
2814 functions, you can create extra versions (NB: more code space)
2815 specialised to particular types. Thus, if you have an
2816 overloaded function:</para>
2819 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2822 <para>If it is heavily used on lists with
2823 <literal>Widget</literal> keys, you could specialise it as
2827 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2830 <para>To get very fancy, you can also specify a named function
2831 to use for the specialised value, as in:</para>
2834 {-# RULES hammeredLookup = blah #-}
2837 <para>where <literal>blah</literal> is an implementation of
2838 <literal>hammerdLookup</literal> written specialy for
2839 <literal>Widget</literal> lookups. It's <emphasis>Your
2840 Responsibility</emphasis> to make sure that
2841 <function>blah</function> really behaves as a specialised
2842 version of <function>hammeredLookup</function>!!!</para>
2844 <para>Note we use the <literal>RULE</literal> pragma here to
2845 indicate that <literal>hammeredLookup</literal> applied at a
2846 certain type should be replaced by <literal>blah</literal>. See
2847 <xref linkend="rules"> for more information on
2848 <literal>RULES</literal>.</para>
2850 <para>An example in which using <literal>RULES</literal> for
2851 specialisation will Win Big:
2854 toDouble :: Real a => a -> Double
2855 toDouble = fromRational . toRational
2857 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2858 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2861 The <function>i2d</function> function is virtually one machine
2862 instruction; the default conversion—via an intermediate
2863 <literal>Rational</literal>—is obscenely expensive by
2866 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2867 be put anywhere its type signature could be put.</para>
2871 <sect2 id="specialize-instance-pragma">
2872 <title>SPECIALIZE instance pragma
2876 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2877 <indexterm><primary>overloading, death to</primary></indexterm>
2878 Same idea, except for instance declarations. For example:
2881 instance (Eq a) => Eq (Foo a) where {
2882 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2886 The pragma must occur inside the <literal>where</literal> part
2887 of the instance declaration.
2890 Compatible with HBC, by the way, except perhaps in the placement
2896 <sect2 id="line-pragma">
2901 <indexterm><primary>LINE pragma</primary></indexterm>
2902 <indexterm><primary>pragma, LINE</primary></indexterm>
2906 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2907 automatically generated Haskell code. It lets you specify the line
2908 number and filename of the original code; for example
2914 {-# LINE 42 "Foo.vhs" #-}
2920 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2921 and this line corresponds to line 42 in the original. GHC will adjust
2922 its error messages to refer to the line/file named in the <literal>LINE</literal>
2929 <title>RULES pragma</title>
2932 The RULES pragma lets you specify rewrite rules. It is described in
2933 <xref LinkEnd="rewrite-rules">.
2938 <sect2 id="deprecated-pragma">
2939 <title>DEPRECATED pragma</title>
2942 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2943 There are two forms.
2947 You can deprecate an entire module thus:</para>
2949 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2953 When you compile any module that import <literal>Wibble</literal>, GHC will print
2954 the specified message.</para>
2959 You can deprecate a function, class, or type, with the following top-level declaration:
2962 {-# DEPRECATED f, C, T "Don't use these" #-}
2965 When you compile any module that imports and uses any of the specifed entities,
2966 GHC will print the specified message.
2970 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2976 <!-- ======================= REWRITE RULES ======================== -->
2978 <sect1 id="rewrite-rules">
2979 <title>Rewrite rules
2981 <indexterm><primary>RULES pagma</primary></indexterm>
2982 <indexterm><primary>pragma, RULES</primary></indexterm>
2983 <indexterm><primary>rewrite rules</primary></indexterm></title>
2986 The programmer can specify rewrite rules as part of the source program
2987 (in a pragma). GHC applies these rewrite rules wherever it can.
2995 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3002 <title>Syntax</title>
3005 From a syntactic point of view:
3011 Each rule has a name, enclosed in double quotes. The name itself has
3012 no significance at all. It is only used when reporting how many times the rule fired.
3018 There may be zero or more rules in a <literal>RULES</literal> pragma.
3024 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3025 is set, so you must lay out your rules starting in the same column as the
3026 enclosing definitions.
3032 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3033 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3034 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3035 by spaces, just like in a type <literal>forall</literal>.
3041 A pattern variable may optionally have a type signature.
3042 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3043 For example, here is the <literal>foldr/build</literal> rule:
3046 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3047 foldr k z (build g) = g k z
3050 Since <function>g</function> has a polymorphic type, it must have a type signature.
3057 The left hand side of a rule must consist of a top-level variable applied
3058 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3061 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3062 "wrong2" forall f. f True = True
3065 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3072 A rule does not need to be in the same module as (any of) the
3073 variables it mentions, though of course they need to be in scope.
3079 Rules are automatically exported from a module, just as instance declarations are.
3090 <title>Semantics</title>
3093 From a semantic point of view:
3099 Rules are only applied if you use the <option>-O</option> flag.
3105 Rules are regarded as left-to-right rewrite rules.
3106 When GHC finds an expression that is a substitution instance of the LHS
3107 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3108 By "a substitution instance" we mean that the LHS can be made equal to the
3109 expression by substituting for the pattern variables.
3116 The LHS and RHS of a rule are typechecked, and must have the
3124 GHC makes absolutely no attempt to verify that the LHS and RHS
3125 of a rule have the same meaning. That is undecideable in general, and
3126 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3133 GHC makes no attempt to make sure that the rules are confluent or
3134 terminating. For example:
3137 "loop" forall x,y. f x y = f y x
3140 This rule will cause the compiler to go into an infinite loop.
3147 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3153 GHC currently uses a very simple, syntactic, matching algorithm
3154 for matching a rule LHS with an expression. It seeks a substitution
3155 which makes the LHS and expression syntactically equal modulo alpha
3156 conversion. The pattern (rule), but not the expression, is eta-expanded if
3157 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3158 But not beta conversion (that's called higher-order matching).
3162 Matching is carried out on GHC's intermediate language, which includes
3163 type abstractions and applications. So a rule only matches if the
3164 types match too. See <xref LinkEnd="rule-spec"> below.
3170 GHC keeps trying to apply the rules as it optimises the program.
3171 For example, consider:
3180 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3181 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3182 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3183 not be substituted, and the rule would not fire.
3190 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3191 that appears on the LHS of a rule</emphasis>, because once you have substituted
3192 for something you can't match against it (given the simple minded
3193 matching). So if you write the rule
3196 "map/map" forall f,g. map f . map g = map (f.g)
3199 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3200 It will only match something written with explicit use of ".".
3201 Well, not quite. It <emphasis>will</emphasis> match the expression
3207 where <function>wibble</function> is defined:
3210 wibble f g = map f . map g
3213 because <function>wibble</function> will be inlined (it's small).
3215 Later on in compilation, GHC starts inlining even things on the
3216 LHS of rules, but still leaves the rules enabled. This inlining
3217 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3224 All rules are implicitly exported from the module, and are therefore
3225 in force in any module that imports the module that defined the rule, directly
3226 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3227 in force when compiling A.) The situation is very similar to that for instance
3239 <title>List fusion</title>
3242 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3243 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3244 intermediate list should be eliminated entirely.
3248 The following are good producers:
3260 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3266 Explicit lists (e.g. <literal>[True, False]</literal>)
3272 The cons constructor (e.g <literal>3:4:[]</literal>)
3278 <function>++</function>
3284 <function>map</function>
3290 <function>filter</function>
3296 <function>iterate</function>, <function>repeat</function>
3302 <function>zip</function>, <function>zipWith</function>
3311 The following are good consumers:
3323 <function>array</function> (on its second argument)
3329 <function>length</function>
3335 <function>++</function> (on its first argument)
3341 <function>foldr</function>
3347 <function>map</function>
3353 <function>filter</function>
3359 <function>concat</function>
3365 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3371 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3372 will fuse with one but not the other)
3378 <function>partition</function>
3384 <function>head</function>
3390 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3396 <function>sequence_</function>
3402 <function>msum</function>
3408 <function>sortBy</function>
3417 So, for example, the following should generate no intermediate lists:
3420 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3426 This list could readily be extended; if there are Prelude functions that you use
3427 a lot which are not included, please tell us.
3431 If you want to write your own good consumers or producers, look at the
3432 Prelude definitions of the above functions to see how to do so.
3437 <sect2 id="rule-spec">
3438 <title>Specialisation
3442 Rewrite rules can be used to get the same effect as a feature
3443 present in earlier version of GHC:
3446 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3449 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3450 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3451 specialising the original definition of <function>fromIntegral</function> the programmer is
3452 promising that it is safe to use <function>int8ToInt16</function> instead.
3456 This feature is no longer in GHC. But rewrite rules let you do the
3461 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3465 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3466 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3467 GHC adds the type and dictionary applications to get the typed rule
3470 forall (d1::Integral Int8) (d2::Num Int16) .
3471 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3475 this rule does not need to be in the same file as fromIntegral,
3476 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3477 have an original definition available to specialise).
3483 <title>Controlling what's going on</title>
3491 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3497 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3498 If you add <option>-dppr-debug</option> you get a more detailed listing.
3504 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3507 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3508 {-# INLINE build #-}
3512 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3513 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3514 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3515 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3522 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3523 see how to write rules that will do fusion and yet give an efficient
3524 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3536 <sect1 id="generic-classes">
3537 <title>Generic classes</title>
3539 <para>(Note: support for generic classes is currently broken in
3543 The ideas behind this extension are described in detail in "Derivable type classes",
3544 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3545 An example will give the idea:
3553 fromBin :: [Int] -> (a, [Int])
3555 toBin {| Unit |} Unit = []
3556 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3557 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3558 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3560 fromBin {| Unit |} bs = (Unit, bs)
3561 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3562 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3563 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3564 (y,bs'') = fromBin bs'
3567 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3568 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3569 which are defined thus in the library module <literal>Generics</literal>:
3573 data a :+: b = Inl a | Inr b
3574 data a :*: b = a :*: b
3577 Now you can make a data type into an instance of Bin like this:
3579 instance (Bin a, Bin b) => Bin (a,b)
3580 instance Bin a => Bin [a]
3582 That is, just leave off the "where" clasuse. Of course, you can put in the
3583 where clause and over-ride whichever methods you please.
3587 <title> Using generics </title>
3588 <para>To use generics you need to</para>
3591 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3592 <option>-fgenerics</option> (to generate extra per-data-type code),
3593 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3597 <para>Import the module <literal>Generics</literal> from the
3598 <literal>lang</literal> package. This import brings into
3599 scope the data types <literal>Unit</literal>,
3600 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3601 don't need this import if you don't mention these types
3602 explicitly; for example, if you are simply giving instance
3603 declarations.)</para>
3608 <sect2> <title> Changes wrt the paper </title>
3610 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3611 can be written infix (indeed, you can now use
3612 any operator starting in a colon as an infix type constructor). Also note that
3613 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3614 Finally, note that the syntax of the type patterns in the class declaration
3615 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3616 alone would ambiguous when they appear on right hand sides (an extension we
3617 anticipate wanting).
3621 <sect2> <title>Terminology and restrictions</title>
3623 Terminology. A "generic default method" in a class declaration
3624 is one that is defined using type patterns as above.
3625 A "polymorphic default method" is a default method defined as in Haskell 98.
3626 A "generic class declaration" is a class declaration with at least one
3627 generic default method.
3635 Alas, we do not yet implement the stuff about constructor names and
3642 A generic class can have only one parameter; you can't have a generic
3643 multi-parameter class.
3649 A default method must be defined entirely using type patterns, or entirely
3650 without. So this is illegal:
3653 op :: a -> (a, Bool)
3654 op {| Unit |} Unit = (Unit, True)
3657 However it is perfectly OK for some methods of a generic class to have
3658 generic default methods and others to have polymorphic default methods.
3664 The type variable(s) in the type pattern for a generic method declaration
3665 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:
3669 op {| p :*: q |} (x :*: y) = op (x :: p)
3677 The type patterns in a generic default method must take one of the forms:
3683 where "a" and "b" are type variables. Furthermore, all the type patterns for
3684 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3685 must use the same type variables. So this is illegal:
3689 op {| a :+: b |} (Inl x) = True
3690 op {| p :+: q |} (Inr y) = False
3692 The type patterns must be identical, even in equations for different methods of the class.
3693 So this too is illegal:
3697 op1 {| a :*: b |} (x :*: y) = True
3700 op2 {| p :*: q |} (x :*: y) = False
3702 (The reason for this restriction is that we gather all the equations for a particular type consructor
3703 into a single generic instance declaration.)
3709 A generic method declaration must give a case for each of the three type constructors.
3715 The type for a generic method can be built only from:
3717 <listitem> <para> Function arrows </para> </listitem>
3718 <listitem> <para> Type variables </para> </listitem>
3719 <listitem> <para> Tuples </para> </listitem>
3720 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3722 Here are some example type signatures for generic methods:
3725 op2 :: Bool -> (a,Bool)
3726 op3 :: [Int] -> a -> a
3729 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3733 This restriction is an implementation restriction: we just havn't got around to
3734 implementing the necessary bidirectional maps over arbitrary type constructors.
3735 It would be relatively easy to add specific type constructors, such as Maybe and list,
3736 to the ones that are allowed.</para>
3741 In an instance declaration for a generic class, the idea is that the compiler
3742 will fill in the methods for you, based on the generic templates. However it can only
3747 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3752 No constructor of the instance type has unboxed fields.
3756 (Of course, these things can only arise if you are already using GHC extensions.)
3757 However, you can still give an instance declarations for types which break these rules,
3758 provided you give explicit code to override any generic default methods.
3766 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3767 what the compiler does with generic declarations.
3772 <sect2> <title> Another example </title>
3774 Just to finish with, here's another example I rather like:
3778 nCons {| Unit |} _ = 1
3779 nCons {| a :*: b |} _ = 1
3780 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3783 tag {| Unit |} _ = 1
3784 tag {| a :*: b |} _ = 1
3785 tag {| a :+: b |} (Inl x) = tag x
3786 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3792 <sect1 id="newtype-deriving">
3793 <title>Generalised derived instances for newtypes</title>
3796 When you define an abstract type using <literal>newtype</literal>, you may want
3797 the new type to inherit some instances from its representation. In
3798 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3799 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3800 other classes you have to write an explicit instance declaration. For
3801 example, if you define
3804 newtype Dollars = Dollars Int
3807 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3808 explicitly define an instance of <literal>Num</literal>:
3811 instance Num Dollars where
3812 Dollars a + Dollars b = Dollars (a+b)
3815 All the instance does is apply and remove the <literal>newtype</literal>
3816 constructor. It is particularly galling that, since the constructor
3817 doesn't appear at run-time, this instance declaration defines a
3818 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3819 dictionary, only slower!
3822 <sect2> <title> Generalising the deriving clause </title>
3824 GHC now permits such instances to be derived instead, so one can write
3826 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3829 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3830 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3831 derives an instance declaration of the form
3834 instance Num Int => Num Dollars
3837 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3841 We can also derive instances of constructor classes in a similar
3842 way. For example, suppose we have implemented state and failure monad
3843 transformers, such that
3846 instance Monad m => Monad (State s m)
3847 instance Monad m => Monad (Failure m)
3849 In Haskell 98, we can define a parsing monad by
3851 type Parser tok m a = State [tok] (Failure m) a
3854 which is automatically a monad thanks to the instance declarations
3855 above. With the extension, we can make the parser type abstract,
3856 without needing to write an instance of class <literal>Monad</literal>, via
3859 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3862 In this case the derived instance declaration is of the form
3864 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3867 Notice that, since <literal>Monad</literal> is a constructor class, the
3868 instance is a <emphasis>partial application</emphasis> of the new type, not the
3869 entire left hand side. We can imagine that the type declaration is
3870 ``eta-converted'' to generate the context of the instance
3875 We can even derive instances of multi-parameter classes, provided the
3876 newtype is the last class parameter. In this case, a ``partial
3877 application'' of the class appears in the <literal>deriving</literal>
3878 clause. For example, given the class
3881 class StateMonad s m | m -> s where ...
3882 instance Monad m => StateMonad s (State s m) where ...
3884 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3886 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3887 deriving (Monad, StateMonad [tok])
3890 The derived instance is obtained by completing the application of the
3891 class to the new type:
3894 instance StateMonad [tok] (State [tok] (Failure m)) =>
3895 StateMonad [tok] (Parser tok m)
3900 As a result of this extension, all derived instances in newtype
3901 declarations are treated uniformly (and implemented just by reusing
3902 the dictionary for the representation type), <emphasis>except</emphasis>
3903 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3904 the newtype and its representation.
3908 <sect2> <title> A more precise specification </title>
3910 Derived instance declarations are constructed as follows. Consider the
3911 declaration (after expansion of any type synonyms)
3914 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3917 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3919 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3920 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3921 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3922 declarations are, for each <literal>ci</literal>,
3925 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3927 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3928 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3932 As an example which does <emphasis>not</emphasis> work, consider
3934 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3936 Here we cannot derive the instance
3938 instance Monad (State s m) => Monad (NonMonad m)
3941 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3942 and so cannot be "eta-converted" away. It is a good thing that this
3943 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3944 not, in fact, a monad --- for the same reason. Try defining
3945 <literal>>>=</literal> with the correct type: you won't be able to.
3949 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3950 important, since we can only derive instances for the last one. If the
3951 <literal>StateMonad</literal> class above were instead defined as
3954 class StateMonad m s | m -> s where ...
3957 then we would not have been able to derive an instance for the
3958 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3959 classes usually have one "main" parameter for which deriving new
3960 instances is most interesting.
3968 ;;; Local Variables: ***
3970 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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