2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
6 <indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-fgenerics</option></term>
114 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
116 <para>See <xref LinkEnd="generic-classes">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fno-implicit-prelude</option></term>
124 <para><indexterm><primary>-fno-implicit-prelude
125 option</primary></indexterm> GHC normally imports
126 <filename>Prelude.hi</filename> files for you. If you'd
127 rather it didn't, then give it a
128 <option>-fno-implicit-prelude</option> option. The idea
129 is that you can then import a Prelude of your own. (But
130 don't call it <literal>Prelude</literal>; the Haskell
131 module namespace is flat, and you must not conflict with
132 any Prelude module.)</para>
134 <para>Even though you have not imported the Prelude, most of
135 the built-in syntax still refers to the built-in Haskell
136 Prelude types and values, as specified by the Haskell
137 Report. For example, the type <literal>[Int]</literal>
138 still means <literal>Prelude.[] Int</literal>; tuples
139 continue to refer to the standard Prelude tuples; the
140 translation for list comprehensions continues to use
141 <literal>Prelude.map</literal> etc.</para>
143 <para>However, <option>-fno-implicit-prelude</option> does
144 change the handling of certain built-in syntax: see
145 <xref LinkEnd="rebindable-syntax">.</para>
153 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
154 <!-- included from primitives.sgml -->
158 <!-- TYPE SYSTEM EXTENSIONS -->
159 <sect1 id="type-extensions">
160 <title>Type system extensions</title>
162 <sect2 id="nullary-types">
163 <title>Data types with no constructors</title>
165 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
166 a data type with no constructors. For example:</para>
170 data T a -- T :: * -> *
173 <para>Syntactically, the declaration lacks the "= constrs" part. The
174 type can be parameterised over types of any kind, but if the kind is
175 not <literal>*</literal> then an explicit kind annotation must be used
176 (see <xref linkend="sec-kinding">).</para>
178 <para>Such data types have only one value, namely bottom.
179 Nevertheless, they can be useful when defining "phantom types".</para>
182 <sect2 id="infix-tycons">
183 <title>Infix type constructors</title>
186 GHC allows type constructors to be operators, and to be written infix, very much
187 like expressions. More specifically:
190 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
191 The lexical syntax is the same as that for data constructors.
194 Types can be written infix. For example <literal>Int :*: Bool</literal>.
198 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
199 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
202 Fixities may be declared for type constructors just as for data constructors. However,
203 one cannot distinguish between the two in a fixity declaration; a fixity declaration
204 sets the fixity for a data constructor and the corresponding type constructor. For example:
208 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
209 and similarly for <literal>:*:</literal>.
210 <literal>Int `a` Bool</literal>.
213 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
216 Data type and type-synonym declarations can be written infix. E.g.
218 data a :*: b = Foo a b
219 type a :+: b = Either a b
223 The only thing that differs between operators in types and operators in expressions is that
224 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
225 are not allowed in types. Reason: the uniform thing to do would be to make them type
226 variables, but that's not very useful. A less uniform but more useful thing would be to
227 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
228 lists. So for now we just exclude them.
235 <sect2 id="sec-kinding">
236 <title>Explicitly-kinded quantification</title>
239 Haskell infers the kind of each type variable. Sometimes it is nice to be able
240 to give the kind explicitly as (machine-checked) documentation,
241 just as it is nice to give a type signature for a function. On some occasions,
242 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
243 John Hughes had to define the data type:
245 data Set cxt a = Set [a]
246 | Unused (cxt a -> ())
248 The only use for the <literal>Unused</literal> constructor was to force the correct
249 kind for the type variable <literal>cxt</literal>.
252 GHC now instead allows you to specify the kind of a type variable directly, wherever
253 a type variable is explicitly bound. Namely:
255 <listitem><para><literal>data</literal> declarations:
257 data Set (cxt :: * -> *) a = Set [a]
258 </Screen></para></listitem>
259 <listitem><para><literal>type</literal> declarations:
261 type T (f :: * -> *) = f Int
262 </Screen></para></listitem>
263 <listitem><para><literal>class</literal> declarations:
265 class (Eq a) => C (f :: * -> *) a where ...
266 </Screen></para></listitem>
267 <listitem><para><literal>forall</literal>'s in type signatures:
269 f :: forall (cxt :: * -> *). Set cxt Int
270 </Screen></para></listitem>
275 The parentheses are required. Some of the spaces are required too, to
276 separate the lexemes. If you write <literal>(f::*->*)</literal> you
277 will get a parse error, because "<literal>::*->*</literal>" is a
278 single lexeme in Haskell.
282 As part of the same extension, you can put kind annotations in types
285 f :: (Int :: *) -> Int
286 g :: forall a. a -> (a :: *)
290 atype ::= '(' ctype '::' kind ')
292 The parentheses are required.
297 <sect2 id="class-method-types">
298 <title>Class method types
301 Haskell 98 prohibits class method types to mention constraints on the
302 class type variable, thus:
305 fromList :: [a] -> s a
306 elem :: Eq a => a -> s a -> Bool
308 The type of <literal>elem</literal> is illegal in Haskell 98, because it
309 contains the constraint <literal>Eq a</literal>, constrains only the
310 class type variable (in this case <literal>a</literal>).
313 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
318 <sect2 id="multi-param-type-classes">
319 <title>Multi-parameter type classes
323 This section documents GHC's implementation of multi-parameter type
324 classes. There's lots of background in the paper <ULink
325 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
326 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
331 I'd like to thank people who reported shorcomings in the GHC 3.02
332 implementation. Our default decisions were all conservative ones, and
333 the experience of these heroic pioneers has given useful concrete
334 examples to support several generalisations. (These appear below as
335 design choices not implemented in 3.02.)
339 I've discussed these notes with Mark Jones, and I believe that Hugs
340 will migrate towards the same design choices as I outline here.
341 Thanks to him, and to many others who have offered very useful
349 There are the following restrictions on the form of a qualified
356 forall tv1..tvn (c1, ...,cn) => type
362 (Here, I write the "foralls" explicitly, although the Haskell source
363 language omits them; in Haskell 1.4, all the free type variables of an
364 explicit source-language type signature are universally quantified,
365 except for the class type variables in a class declaration. However,
366 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
375 <emphasis>Each universally quantified type variable
376 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
378 The reason for this is that a value with a type that does not obey
379 this restriction could not be used without introducing
380 ambiguity. Here, for example, is an illegal type:
384 forall a. Eq a => Int
388 When a value with this type was used, the constraint <literal>Eq tv</literal>
389 would be introduced where <literal>tv</literal> is a fresh type variable, and
390 (in the dictionary-translation implementation) the value would be
391 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
392 can never know which instance of <literal>Eq</literal> to use because we never
393 get any more information about <literal>tv</literal>.
400 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
401 universally quantified type variables <literal>tvi</literal></emphasis>.
403 For example, this type is OK because <literal>C a b</literal> mentions the
404 universally quantified type variable <literal>b</literal>:
408 forall a. C a b => burble
412 The next type is illegal because the constraint <literal>Eq b</literal> does not
413 mention <literal>a</literal>:
417 forall a. Eq b => burble
421 The reason for this restriction is milder than the other one. The
422 excluded types are never useful or necessary (because the offending
423 context doesn't need to be witnessed at this point; it can be floated
424 out). Furthermore, floating them out increases sharing. Lastly,
425 excluding them is a conservative choice; it leaves a patch of
426 territory free in case we need it later.
436 These restrictions apply to all types, whether declared in a type signature
441 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
442 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
449 f :: Eq (m a) => [m a] -> [m a]
456 This choice recovers principal types, a property that Haskell 1.4 does not have.
462 <title>Class declarations</title>
470 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
474 class Collection c a where
475 union :: c a -> c a -> c a
486 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
487 of "acyclic" involves only the superclass relationships. For example,
493 op :: D b => a -> b -> b
496 class C a => D a where { ... }
500 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
501 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
502 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
509 <emphasis>There are no restrictions on the context in a class declaration
510 (which introduces superclasses), except that the class hierarchy must
511 be acyclic</emphasis>. So these class declarations are OK:
515 class Functor (m k) => FiniteMap m k where
518 class (Monad m, Monad (t m)) => Transform t m where
519 lift :: m a -> (t m) a
528 <emphasis>In the signature of a class operation, every constraint
529 must mention at least one type variable that is not a class type
536 class Collection c a where
537 mapC :: Collection c b => (a->b) -> c a -> c b
541 is OK because the constraint <literal>(Collection a b)</literal> mentions
542 <literal>b</literal>, even though it also mentions the class variable
543 <literal>a</literal>. On the other hand:
548 op :: Eq a => (a,b) -> (a,b)
552 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
553 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
554 example is easily fixed by moving the offending context up to the
559 class Eq a => C a where
564 A yet more relaxed rule would allow the context of a class-op signature
565 to mention only class type variables. However, that conflicts with
566 Rule 1(b) for types above.
573 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
574 the class type variables</emphasis>. For example:
580 insert :: s -> a -> s
584 is not OK, because the type of <literal>empty</literal> doesn't mention
585 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
586 types, and has the same motivation.
588 Sometimes, offending class declarations exhibit misunderstandings. For
589 example, <literal>Coll</literal> might be rewritten
595 insert :: s a -> a -> s a
599 which makes the connection between the type of a collection of
600 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
601 Occasionally this really doesn't work, in which case you can split the
609 class CollE s => Coll s a where
610 insert :: s -> a -> s
623 <sect3 id="instance-decls">
624 <title>Instance declarations</title>
632 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
637 instance context1 => C type1 where ...
638 instance context2 => C type2 where ...
642 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
644 However, if you give the command line option
645 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
646 option</primary></indexterm> then overlapping instance declarations are permitted.
647 However, GHC arranges never to commit to using an instance declaration
648 if another instance declaration also applies, either now or later.
654 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
660 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
661 (but not identical to <literal>type1</literal>), or vice versa.
665 Notice that these rules
670 make it clear which instance decl to use
671 (pick the most specific one that matches)
678 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
679 Reason: you can pick which instance decl
680 "matches" based on the type.
685 However the rules are over-conservative. Two instance declarations can overlap,
686 but it can still be clear in particular situations which to use. For example:
688 instance C (Int,a) where ...
689 instance C (a,Bool) where ...
691 These are rejected by GHC's rules, but it is clear what to do when trying
692 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
693 cannot apply. Yell if this restriction bites you.
696 GHC is also conservative about committing to an overlapping instance. For example:
698 class C a where { op :: a -> a }
699 instance C [Int] where ...
700 instance C a => C [a] where ...
702 f :: C b => [b] -> [b]
705 From the RHS of f we get the constraint <literal>C [b]</literal>. But
706 GHC does not commit to the second instance declaration, because in a paricular
707 call of f, b might be instantiate to Int, so the first instance declaration
708 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
709 GHC will instead silently pick the second instance, without complaining about
710 the problem of subsequent instantiations.
713 Regrettably, GHC doesn't guarantee to detect overlapping instance
714 declarations if they appear in different modules. GHC can "see" the
715 instance declarations in the transitive closure of all the modules
716 imported by the one being compiled, so it can "see" all instance decls
717 when it is compiling <literal>Main</literal>. However, it currently chooses not
718 to look at ones that can't possibly be of use in the module currently
719 being compiled, in the interests of efficiency. (Perhaps we should
720 change that decision, at least for <literal>Main</literal>.)
727 <emphasis>There are no restrictions on the type in an instance
728 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
729 The instance "head" is the bit after the "=>" in an instance decl. For
730 example, these are OK:
734 instance C Int a where ...
736 instance D (Int, Int) where ...
738 instance E [[a]] where ...
742 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
743 For example, this is OK:
747 instance Stateful (ST s) (MutVar s) where ...
751 The "at least one not a type variable" restriction is to ensure that
752 context reduction terminates: each reduction step removes one type
753 constructor. For example, the following would make the type checker
754 loop if it wasn't excluded:
758 instance C a => C a where ...
762 There are two situations in which the rule is a bit of a pain. First,
763 if one allows overlapping instance declarations then it's quite
764 convenient to have a "default instance" declaration that applies if
765 something more specific does not:
774 Second, sometimes you might want to use the following to get the
775 effect of a "class synonym":
779 class (C1 a, C2 a, C3 a) => C a where { }
781 instance (C1 a, C2 a, C3 a) => C a where { }
785 This allows you to write shorter signatures:
797 f :: (C1 a, C2 a, C3 a) => ...
801 I'm on the lookout for a simple rule that preserves decidability while
802 allowing these idioms. The experimental flag
803 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
804 option</primary></indexterm> lifts this restriction, allowing all the types in an
805 instance head to be type variables.
812 <emphasis>Unlike Haskell 1.4, instance heads may use type
813 synonyms</emphasis>. As always, using a type synonym is just shorthand for
814 writing the RHS of the type synonym definition. For example:
818 type Point = (Int,Int)
819 instance C Point where ...
820 instance C [Point] where ...
824 is legal. However, if you added
828 instance C (Int,Int) where ...
832 as well, then the compiler will complain about the overlapping
833 (actually, identical) instance declarations. As always, type synonyms
834 must be fully applied. You cannot, for example, write:
839 instance Monad P where ...
843 This design decision is independent of all the others, and easily
844 reversed, but it makes sense to me.
851 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
852 be type variables</emphasis>. Thus
856 instance C a b => Eq (a,b) where ...
864 instance C Int b => Foo b where ...
868 is not OK. Again, the intent here is to make sure that context
869 reduction terminates.
871 Voluminous correspondence on the Haskell mailing list has convinced me
872 that it's worth experimenting with a more liberal rule. If you use
873 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
874 types in an instance context. Termination is ensured by having a
875 fixed-depth recursion stack. If you exceed the stack depth you get a
876 sort of backtrace, and the opportunity to increase the stack depth
877 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
890 <sect2 id="implicit-parameters">
891 <title>Implicit parameters
894 <para> Implicit paramters are implemented as described in
895 "Implicit parameters: dynamic scoping with static types",
896 J Lewis, MB Shields, E Meijer, J Launchbury,
897 27th ACM Symposium on Principles of Programming Languages (POPL'00),
900 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
902 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
903 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
904 context. In Haskell, all variables are statically bound. Dynamic
905 binding of variables is a notion that goes back to Lisp, but was later
906 discarded in more modern incarnations, such as Scheme. Dynamic binding
907 can be very confusing in an untyped language, and unfortunately, typed
908 languages, in particular Hindley-Milner typed languages like Haskell,
909 only support static scoping of variables.
912 However, by a simple extension to the type class system of Haskell, we
913 can support dynamic binding. Basically, we express the use of a
914 dynamically bound variable as a constraint on the type. These
915 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
916 function uses a dynamically-bound variable <literal>?x</literal>
917 of type <literal>t'</literal>". For
918 example, the following expresses the type of a sort function,
919 implicitly parameterized by a comparison function named <literal>cmp</literal>.
921 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
923 The dynamic binding constraints are just a new form of predicate in the type class system.
926 An implicit parameter is introduced by the special form <literal>?x</literal>,
927 where <literal>x</literal> is
928 any valid identifier. Use if this construct also introduces new
929 dynamic binding constraints. For example, the following definition
930 shows how we can define an implicitly parameterized sort function in
931 terms of an explicitly parameterized <literal>sortBy</literal> function:
933 sortBy :: (a -> a -> Bool) -> [a] -> [a]
935 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
938 Dynamic binding constraints behave just like other type class
939 constraints in that they are automatically propagated. Thus, when a
940 function is used, its implicit parameters are inherited by the
941 function that called it. For example, our <literal>sort</literal> function might be used
942 to pick out the least value in a list:
944 least :: (?cmp :: a -> a -> Bool) => [a] -> a
945 least xs = fst (sort xs)
947 Without lifting a finger, the <literal>?cmp</literal> parameter is
948 propagated to become a parameter of <literal>least</literal> as well. With explicit
949 parameters, the default is that parameters must always be explicit
950 propagated. With implicit parameters, the default is to always
954 An implicit parameter differs from other type class constraints in the
955 following way: All uses of a particular implicit parameter must have
956 the same type. This means that the type of <literal>(?x, ?x)</literal>
957 is <literal>(?x::a) => (a,a)</literal>, and not
958 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
962 An implicit parameter is bound using the standard
963 <literal>let</literal> binding form, where the bindings must be a
964 collection of simple bindings to implicit-style variables (no
965 function-style bindings, and no type signatures); these bindings are
966 neither polymorphic or recursive. This form binds the implicit
967 parameters arising in the body, not the free variables as a
968 <literal>let</literal> or <literal>where</literal> would do. For
969 example, we define the <literal>min</literal> function by binding
970 <literal>cmp</literal>.</para>
973 min = let ?cmp = (<=) in least
976 Note the following additional constraints:
979 <para> You can't have an implicit parameter in the context of a class or instance
980 declaration. For example, both these declarations are illegal:
982 class (?x::Int) => C a where ...
983 instance (?x::a) => Foo [a] where ...
985 Reason: exactly which implicit parameter you pick up depends on exactly where
986 you invoke a function. But the ``invocation'' of instance declarations is done
987 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
988 Easiest thing is to outlaw the offending types.</para>
995 <sect2 id="linear-implicit-parameters">
996 <title>Linear implicit parameters
999 Linear implicit parameters are an idea developed by Koen Claessen,
1000 Mark Shields, and Simon PJ. They address the long-standing
1001 problem that monads seem over-kill for certain sorts of problem, notably:
1004 <listitem> <para> distributing a supply of unique names </para> </listitem>
1005 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1006 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1010 Linear implicit parameters are just like ordinary implicit parameters,
1011 except that they are "linear" -- that is, they cannot be copied, and
1012 must be explicitly "split" instead. Linear implicit parameters are
1013 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1014 (The '/' in the '%' suggests the split!)
1019 import GHC.Exts( Splittable )
1021 data NameSupply = ...
1023 splitNS :: NameSupply -> (NameSupply, NameSupply)
1024 newName :: NameSupply -> Name
1026 instance Splittable NameSupply where
1030 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1031 f env (Lam x e) = Lam x' (f env e)
1034 env' = extend env x x'
1035 ...more equations for f...
1037 Notice that the implicit parameter %ns is consumed
1039 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1040 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1044 So the translation done by the type checker makes
1045 the parameter explicit:
1047 f :: NameSupply -> Env -> Expr -> Expr
1048 f ns env (Lam x e) = Lam x' (f ns1 env e)
1050 (ns1,ns2) = splitNS ns
1052 env = extend env x x'
1054 Notice the call to 'split' introduced by the type checker.
1055 How did it know to use 'splitNS'? Because what it really did
1056 was to introduce a call to the overloaded function 'split',
1057 defined by the class <literal>Splittable</literal>:
1059 class Splittable a where
1062 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1063 split for name supplies. But we can simply write
1069 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1071 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1072 <literal>GHC.Exts</literal>.
1077 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1078 are entirely distinct implicit parameters: you
1079 can use them together and they won't intefere with each other. </para>
1082 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1084 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1085 in the context of a class or instance declaration. </para></listitem>
1089 <sect3><title>Warnings</title>
1092 The monomorphism restriction is even more important than usual.
1093 Consider the example above:
1095 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1096 f env (Lam x e) = Lam x' (f env e)
1099 env' = extend env x x'
1101 If we replaced the two occurrences of x' by (newName %ns), which is
1102 usually a harmless thing to do, we get:
1104 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1105 f env (Lam x e) = Lam (newName %ns) (f env e)
1107 env' = extend env x (newName %ns)
1109 But now the name supply is consumed in <emphasis>three</emphasis> places
1110 (the two calls to newName,and the recursive call to f), so
1111 the result is utterly different. Urk! We don't even have
1115 Well, this is an experimental change. With implicit
1116 parameters we have already lost beta reduction anyway, and
1117 (as John Launchbury puts it) we can't sensibly reason about
1118 Haskell programs without knowing their typing.
1125 <sect2 id="functional-dependencies">
1126 <title>Functional dependencies
1129 <para> Functional dependencies are implemented as described by Mark Jones
1130 in "Type Classes with Functional Dependencies", Mark P. Jones,
1131 In Proceedings of the 9th European Symposium on Programming,
1132 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1136 There should be more documentation, but there isn't (yet). Yell if you need it.
1141 <sect2 id="universal-quantification">
1142 <title>Arbitrary-rank polymorphism
1146 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1147 allows us to say exactly what this means. For example:
1155 g :: forall b. (b -> b)
1157 The two are treated identically.
1161 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1162 explicit universal quantification in
1164 For example, all the following types are legal:
1166 f1 :: forall a b. a -> b -> a
1167 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1169 f2 :: (forall a. a->a) -> Int -> Int
1170 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1172 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1174 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1175 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1176 The <literal>forall</literal> makes explicit the universal quantification that
1177 is implicitly added by Haskell.
1180 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1181 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1182 shows, the polymorphic type on the left of the function arrow can be overloaded.
1185 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1186 they have rank-2 types on the left of a function arrow.
1189 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1190 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1191 that restriction has now been lifted.)
1192 In particular, a forall-type (also called a "type scheme"),
1193 including an operational type class context, is legal:
1195 <listitem> <para> On the left of a function arrow </para> </listitem>
1196 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1197 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1198 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1199 field type signatures.</para> </listitem>
1200 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1201 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1203 There is one place you cannot put a <literal>forall</literal>:
1204 you cannot instantiate a type variable with a forall-type. So you cannot
1205 make a forall-type the argument of a type constructor. So these types are illegal:
1207 x1 :: [forall a. a->a]
1208 x2 :: (forall a. a->a, Int)
1209 x3 :: Maybe (forall a. a->a)
1211 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1212 a type variable any more!
1221 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1222 the types of the constructor arguments. Here are several examples:
1228 data T a = T1 (forall b. b -> b -> b) a
1230 data MonadT m = MkMonad { return :: forall a. a -> m a,
1231 bind :: forall a b. m a -> (a -> m b) -> m b
1234 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1240 The constructors have rank-2 types:
1246 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1247 MkMonad :: forall m. (forall a. a -> m a)
1248 -> (forall a b. m a -> (a -> m b) -> m b)
1250 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1256 Notice that you don't need to use a <literal>forall</literal> if there's an
1257 explicit context. For example in the first argument of the
1258 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1259 prefixed to the argument type. The implicit <literal>forall</literal>
1260 quantifies all type variables that are not already in scope, and are
1261 mentioned in the type quantified over.
1265 As for type signatures, implicit quantification happens for non-overloaded
1266 types too. So if you write this:
1269 data T a = MkT (Either a b) (b -> b)
1272 it's just as if you had written this:
1275 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1278 That is, since the type variable <literal>b</literal> isn't in scope, it's
1279 implicitly universally quantified. (Arguably, it would be better
1280 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1281 where that is what is wanted. Feedback welcomed.)
1285 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1286 the constructor to suitable values, just as usual. For example,
1297 a3 = MkSwizzle reverse
1300 a4 = let r x = Just x
1307 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1308 mkTs f x y = [T1 f x, T1 f y]
1314 The type of the argument can, as usual, be more general than the type
1315 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1316 does not need the <literal>Ord</literal> constraint.)
1320 When you use pattern matching, the bound variables may now have
1321 polymorphic types. For example:
1327 f :: T a -> a -> (a, Char)
1328 f (T1 w k) x = (w k x, w 'c' 'd')
1330 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1331 g (MkSwizzle s) xs f = s (map f (s xs))
1333 h :: MonadT m -> [m a] -> m [a]
1334 h m [] = return m []
1335 h m (x:xs) = bind m x $ \y ->
1336 bind m (h m xs) $ \ys ->
1343 In the function <function>h</function> we use the record selectors <literal>return</literal>
1344 and <literal>bind</literal> to extract the polymorphic bind and return functions
1345 from the <literal>MonadT</literal> data structure, rather than using pattern
1351 <title>Type inference</title>
1354 In general, type inference for arbitrary-rank types is undecideable.
1355 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1356 to get a decidable algorithm by requiring some help from the programmer.
1357 We do not yet have a formal specification of "some help" but the rule is this:
1360 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1361 provides an explicit polymorphic type for x, or GHC's type inference will assume
1362 that x's type has no foralls in it</emphasis>.
1365 What does it mean to "provide" an explicit type for x? You can do that by
1366 giving a type signature for x directly, using a pattern type signature
1367 (<xref linkend="scoped-type-variables">), thus:
1369 \ f :: (forall a. a->a) -> (f True, f 'c')
1371 Alternatively, you can give a type signature to the enclosing
1372 context, which GHC can "push down" to find the type for the variable:
1374 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1376 Here the type signature on the expression can be pushed inwards
1377 to give a type signature for f. Similarly, and more commonly,
1378 one can give a type signature for the function itself:
1380 h :: (forall a. a->a) -> (Bool,Char)
1381 h f = (f True, f 'c')
1383 You don't need to give a type signature if the lambda bound variable
1384 is a constructor argument. Here is an example we saw earlier:
1386 f :: T a -> a -> (a, Char)
1387 f (T1 w k) x = (w k x, w 'c' 'd')
1389 Here we do not need to give a type signature to <literal>w</literal>, because
1390 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1397 <sect3 id="implicit-quant">
1398 <title>Implicit quantification</title>
1401 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1402 user-written types, if and only if there is no explicit <literal>forall</literal>,
1403 GHC finds all the type variables mentioned in the type that are not already
1404 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1408 f :: forall a. a -> a
1415 h :: forall b. a -> b -> b
1421 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1424 f :: (a -> a) -> Int
1426 f :: forall a. (a -> a) -> Int
1428 f :: (forall a. a -> a) -> Int
1431 g :: (Ord a => a -> a) -> Int
1432 -- MEANS the illegal type
1433 g :: forall a. (Ord a => a -> a) -> Int
1435 g :: (forall a. Ord a => a -> a) -> Int
1437 The latter produces an illegal type, which you might think is silly,
1438 but at least the rule is simple. If you want the latter type, you
1439 can write your for-alls explicitly. Indeed, doing so is strongly advised
1445 <sect2 id="type-synonyms">
1446 <title>Liberalised type synonyms
1450 Type synonmys are like macros at the type level, and
1451 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1452 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1454 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1455 in a type synonym, thus:
1457 type Discard a = forall b. Show b => a -> b -> (a, String)
1462 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1469 You can write an unboxed tuple in a type synonym:
1471 type Pr = (# Int, Int #)
1479 You can apply a type synonym to a forall type:
1481 type Foo a = a -> a -> Bool
1483 f :: Foo (forall b. b->b)
1485 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1487 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1492 You can apply a type synonym to a partially applied type synonym:
1494 type Generic i o = forall x. i x -> o x
1497 foo :: Generic Id []
1499 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1501 foo :: forall x. x -> [x]
1509 GHC currently does kind checking before expanding synonyms (though even that
1513 After expanding type synonyms, GHC does validity checking on types, looking for
1514 the following mal-formedness which isn't detected simply by kind checking:
1517 Type constructor applied to a type involving for-alls.
1520 Unboxed tuple on left of an arrow.
1523 Partially-applied type synonym.
1527 this will be rejected:
1529 type Pr = (# Int, Int #)
1534 because GHC does not allow unboxed tuples on the left of a function arrow.
1539 <title>For-all hoisting</title>
1541 It is often convenient to use generalised type synonyms at the right hand
1542 end of an arrow, thus:
1544 type Discard a = forall b. a -> b -> a
1546 g :: Int -> Discard Int
1549 Simply expanding the type synonym would give
1551 g :: Int -> (forall b. Int -> b -> Int)
1553 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1555 g :: forall b. Int -> Int -> b -> Int
1557 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1558 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1559 performs the transformation:</emphasis>
1561 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1563 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1565 (In fact, GHC tries to retain as much synonym information as possible for use in
1566 error messages, but that is a usability issue.) This rule applies, of course, whether
1567 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1568 valid way to write <literal>g</literal>'s type signature:
1570 g :: Int -> Int -> forall b. b -> Int
1574 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1577 type Foo a = (?x::Int) => Bool -> a
1582 g :: (?x::Int) => Bool -> Bool -> Int
1588 <sect2 id="existential-quantification">
1589 <title>Existentially quantified data constructors
1593 The idea of using existential quantification in data type declarations
1594 was suggested by Laufer (I believe, thought doubtless someone will
1595 correct me), and implemented in Hope+. It's been in Lennart
1596 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1597 proved very useful. Here's the idea. Consider the declaration:
1603 data Foo = forall a. MkFoo a (a -> Bool)
1610 The data type <literal>Foo</literal> has two constructors with types:
1616 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1623 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1624 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1625 For example, the following expression is fine:
1631 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1637 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1638 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1639 isUpper</function> packages a character with a compatible function. These
1640 two things are each of type <literal>Foo</literal> and can be put in a list.
1644 What can we do with a value of type <literal>Foo</literal>?. In particular,
1645 what happens when we pattern-match on <function>MkFoo</function>?
1651 f (MkFoo val fn) = ???
1657 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1658 are compatible, the only (useful) thing we can do with them is to
1659 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1666 f (MkFoo val fn) = fn val
1672 What this allows us to do is to package heterogenous values
1673 together with a bunch of functions that manipulate them, and then treat
1674 that collection of packages in a uniform manner. You can express
1675 quite a bit of object-oriented-like programming this way.
1678 <sect3 id="existential">
1679 <title>Why existential?
1683 What has this to do with <emphasis>existential</emphasis> quantification?
1684 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1690 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1696 But Haskell programmers can safely think of the ordinary
1697 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1698 adding a new existential quantification construct.
1704 <title>Type classes</title>
1707 An easy extension (implemented in <Command>hbc</Command>) is to allow
1708 arbitrary contexts before the constructor. For example:
1714 data Baz = forall a. Eq a => Baz1 a a
1715 | forall b. Show b => Baz2 b (b -> b)
1721 The two constructors have the types you'd expect:
1727 Baz1 :: forall a. Eq a => a -> a -> Baz
1728 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1734 But when pattern matching on <function>Baz1</function> the matched values can be compared
1735 for equality, and when pattern matching on <function>Baz2</function> the first matched
1736 value can be converted to a string (as well as applying the function to it).
1737 So this program is legal:
1744 f (Baz1 p q) | p == q = "Yes"
1746 f (Baz2 v fn) = show (fn v)
1752 Operationally, in a dictionary-passing implementation, the
1753 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1754 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1755 extract it on pattern matching.
1759 Notice the way that the syntax fits smoothly with that used for
1760 universal quantification earlier.
1766 <title>Restrictions</title>
1769 There are several restrictions on the ways in which existentially-quantified
1770 constructors can be use.
1779 When pattern matching, each pattern match introduces a new,
1780 distinct, type for each existential type variable. These types cannot
1781 be unified with any other type, nor can they escape from the scope of
1782 the pattern match. For example, these fragments are incorrect:
1790 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1791 is the result of <function>f1</function>. One way to see why this is wrong is to
1792 ask what type <function>f1</function> has:
1796 f1 :: Foo -> a -- Weird!
1800 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1805 f1 :: forall a. Foo -> a -- Wrong!
1809 The original program is just plain wrong. Here's another sort of error
1813 f2 (Baz1 a b) (Baz1 p q) = a==q
1817 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1818 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1819 from the two <function>Baz1</function> constructors.
1827 You can't pattern-match on an existentially quantified
1828 constructor in a <literal>let</literal> or <literal>where</literal> group of
1829 bindings. So this is illegal:
1833 f3 x = a==b where { Baz1 a b = x }
1837 You can only pattern-match
1838 on an existentially-quantified constructor in a <literal>case</literal> expression or
1839 in the patterns of a function definition.
1841 The reason for this restriction is really an implementation one.
1842 Type-checking binding groups is already a nightmare without
1843 existentials complicating the picture. Also an existential pattern
1844 binding at the top level of a module doesn't make sense, because it's
1845 not clear how to prevent the existentially-quantified type "escaping".
1846 So for now, there's a simple-to-state restriction. We'll see how
1854 You can't use existential quantification for <literal>newtype</literal>
1855 declarations. So this is illegal:
1859 newtype T = forall a. Ord a => MkT a
1863 Reason: a value of type <literal>T</literal> must be represented as a pair
1864 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1865 That contradicts the idea that <literal>newtype</literal> should have no
1866 concrete representation. You can get just the same efficiency and effect
1867 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1868 overloading involved, then there is more of a case for allowing
1869 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1870 because the <literal>data</literal> version does carry an implementation cost,
1871 but single-field existentially quantified constructors aren't much
1872 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1873 stands, unless there are convincing reasons to change it.
1881 You can't use <literal>deriving</literal> to define instances of a
1882 data type with existentially quantified data constructors.
1884 Reason: in most cases it would not make sense. For example:#
1887 data T = forall a. MkT [a] deriving( Eq )
1890 To derive <literal>Eq</literal> in the standard way we would need to have equality
1891 between the single component of two <function>MkT</function> constructors:
1895 (MkT a) == (MkT b) = ???
1898 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1899 It's just about possible to imagine examples in which the derived instance
1900 would make sense, but it seems altogether simpler simply to prohibit such
1901 declarations. Define your own instances!
1913 <sect2 id="scoped-type-variables">
1914 <title>Scoped type variables
1918 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1919 variable</emphasis>. For example
1925 f (xs::[a]) = ys ++ ys
1934 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
1935 This brings the type variable <literal>a</literal> into scope; it scopes over
1936 all the patterns and right hand sides for this equation for <function>f</function>.
1937 In particular, it is in scope at the type signature for <VarName>y</VarName>.
1941 Pattern type signatures are completely orthogonal to ordinary, separate
1942 type signatures. The two can be used independently or together.
1943 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
1944 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
1945 implicitly universally quantified. (If there are no type variables in
1946 scope, all type variables mentioned in the signature are universally
1947 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
1948 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
1949 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
1950 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
1951 it becomes possible to do so.
1955 Scoped type variables are implemented in both GHC and Hugs. Where the
1956 implementations differ from the specification below, those differences
1961 So much for the basic idea. Here are the details.
1965 <title>What a pattern type signature means</title>
1967 A type variable brought into scope by a pattern type signature is simply
1968 the name for a type. The restriction they express is that all occurrences
1969 of the same name mean the same type. For example:
1971 f :: [Int] -> Int -> Int
1972 f (xs::[a]) (y::a) = (head xs + y) :: a
1974 The pattern type signatures on the left hand side of
1975 <literal>f</literal> express the fact that <literal>xs</literal>
1976 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
1977 must have this same type. The type signature on the expression <literal>(head xs)</literal>
1978 specifies that this expression must have the same type <literal>a</literal>.
1979 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
1980 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
1981 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
1982 rules, which specified that a pattern-bound type variable should be universally quantified.)
1983 For example, all of these are legal:</para>
1986 t (x::a) (y::a) = x+y*2
1988 f (x::a) (y::b) = [x,y] -- a unifies with b
1990 g (x::a) = x + 1::Int -- a unifies with Int
1992 h x = let k (y::a) = [x,y] -- a is free in the
1993 in k x -- environment
1995 k (x::a) True = ... -- a unifies with Int
1996 k (x::Int) False = ...
1999 w (x::a) = x -- a unifies with [b]
2005 <title>Scope and implicit quantification</title>
2013 All the type variables mentioned in a pattern,
2014 that are not already in scope,
2015 are brought into scope by the pattern. We describe this set as
2016 the <emphasis>type variables bound by the pattern</emphasis>.
2019 f (x::a) = let g (y::(a,b)) = fst y
2023 The pattern <literal>(x::a)</literal> brings the type variable
2024 <literal>a</literal> into scope, as well as the term
2025 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2026 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2027 and brings into scope the type variable <literal>b</literal>.
2033 The type variable(s) bound by the pattern have the same scope
2034 as the term variable(s) bound by the pattern. For example:
2037 f (x::a) = <...rhs of f...>
2038 (p::b, q::b) = (1,2)
2039 in <...body of let...>
2041 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2042 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2043 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2044 just like <literal>p</literal> and <literal>q</literal> do.
2045 Indeed, the newly bound type variables also scope over any ordinary, separate
2046 type signatures in the <literal>let</literal> group.
2053 The type variables bound by the pattern may be
2054 mentioned in ordinary type signatures or pattern
2055 type signatures anywhere within their scope.
2062 In ordinary type signatures, any type variable mentioned in the
2063 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2071 Ordinary type signatures do not bring any new type variables
2072 into scope (except in the type signature itself!). So this is illegal:
2079 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2080 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2081 and that is an incorrect typing.
2088 The pattern type signature is a monotype:
2093 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2097 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2098 not to type schemes.
2102 There is no implicit universal quantification on pattern type signatures (in contrast to
2103 ordinary type signatures).
2113 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2114 scope over the methods defined in the <literal>where</literal> part. For example:
2128 (Not implemented in Hugs yet, Dec 98).
2139 <title>Result type signatures</title>
2147 The result type of a function can be given a signature,
2152 f (x::a) :: [a] = [x,x,x]
2156 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2157 result type. Sometimes this is the only way of naming the type variable
2162 f :: Int -> [a] -> [a]
2163 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2164 in \xs -> map g (reverse xs `zip` xs)
2176 Result type signatures are not yet implemented in Hugs.
2182 <title>Where a pattern type signature can occur</title>
2185 A pattern type signature can occur in any pattern. For example:
2190 A pattern type signature can be on an arbitrary sub-pattern, not
2195 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2204 Pattern type signatures, including the result part, can be used
2205 in lambda abstractions:
2208 (\ (x::a, y) :: a -> x)
2215 Pattern type signatures, including the result part, can be used
2216 in <literal>case</literal> expressions:
2220 case e of { (x::a, y) :: a -> x }
2228 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2229 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2230 token or a parenthesised type of some sort). To see why,
2231 consider how one would parse this:
2245 Pattern type signatures can bind existential type variables.
2250 data T = forall a. MkT [a]
2253 f (MkT [t::a]) = MkT t3
2266 Pattern type signatures
2267 can be used in pattern bindings:
2270 f x = let (y, z::a) = x in ...
2271 f1 x = let (y, z::Int) = x in ...
2272 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2273 f3 :: (b->b) = \x -> x
2276 In all such cases, the binding is not generalised over the pattern-bound
2277 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2278 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2279 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2280 In contrast, the binding
2285 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2286 in <literal>f4</literal>'s scope.
2298 <!-- ==================== End of type system extensions ================= -->
2301 <!-- ==================== ASSERTIONS ================= -->
2303 <sect1 id="sec-assertions">
2305 <indexterm><primary>Assertions</primary></indexterm>
2309 If you want to make use of assertions in your standard Haskell code, you
2310 could define a function like the following:
2316 assert :: Bool -> a -> a
2317 assert False x = error "assertion failed!"
2324 which works, but gives you back a less than useful error message --
2325 an assertion failed, but which and where?
2329 One way out is to define an extended <function>assert</function> function which also
2330 takes a descriptive string to include in the error message and
2331 perhaps combine this with the use of a pre-processor which inserts
2332 the source location where <function>assert</function> was used.
2336 Ghc offers a helping hand here, doing all of this for you. For every
2337 use of <function>assert</function> in the user's source:
2343 kelvinToC :: Double -> Double
2344 kelvinToC k = assert (k >= 0.0) (k+273.15)
2350 Ghc will rewrite this to also include the source location where the
2357 assert pred val ==> assertError "Main.hs|15" pred val
2363 The rewrite is only performed by the compiler when it spots
2364 applications of <function>Control.Exception.assert</function>, so you
2365 can still define and use your own versions of
2366 <function>assert</function>, should you so wish. If not, import
2367 <literal>Control.Exception</literal> to make use
2368 <function>assert</function> in your code.
2372 To have the compiler ignore uses of assert, use the compiler option
2373 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
2374 option</primary></indexterm> That is, expressions of the form
2375 <literal>assert pred e</literal> will be rewritten to
2376 <literal>e</literal>.
2380 Assertion failures can be caught, see the documentation for the
2381 <literal>Control.Exception</literal> library for the details.
2387 <sect1 id="syntax-extns">
2388 <title>Syntactic extensions</title>
2390 <!-- ====================== HIERARCHICAL MODULES ======================= -->
2392 <sect2 id="hierarchical-modules">
2393 <title>Hierarchical Modules</title>
2395 <para>GHC supports a small extension to the syntax of module
2396 names: a module name is allowed to contain a dot
2397 <literal>‘.’</literal>. This is also known as the
2398 “hierarchical module namespace” extension, because
2399 it extends the normally flat Haskell module namespace into a
2400 more flexible hierarchy of modules.</para>
2402 <para>This extension has very little impact on the language
2403 itself; modules names are <emphasis>always</emphasis> fully
2404 qualified, so you can just think of the fully qualified module
2405 name as <quote>the module name</quote>. In particular, this
2406 means that the full module name must be given after the
2407 <literal>module</literal> keyword at the beginning of the
2408 module; for example, the module <literal>A.B.C</literal> must
2411 <programlisting>module A.B.C</programlisting>
2414 <para>It is a common strategy to use the <literal>as</literal>
2415 keyword to save some typing when using qualified names with
2416 hierarchical modules. For example:</para>
2419 import qualified Control.Monad.ST.Strict as ST
2422 <para>Hierarchical modules have an impact on the way that GHC
2423 searches for files. For a description, see <xref
2424 linkend="finding-hierarchical-modules">.</para>
2426 <para>GHC comes with a large collection of libraries arranged
2427 hierarchically; see the accompanying library documentation.
2428 There is an ongoing project to create and maintain a stable set
2429 of <quote>core</quote> libraries used by several Haskell
2430 compilers, and the libraries that GHC comes with represent the
2431 current status of that project. For more details, see <ulink
2432 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
2433 Libraries</ulink>.</para>
2437 <!-- ====================== PATTERN GUARDS ======================= -->
2439 <sect2 id="pattern-guards">
2440 <title>Pattern guards</title>
2443 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2444 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.)
2448 Suppose we have an abstract data type of finite maps, with a
2452 lookup :: FiniteMap -> Int -> Maybe Int
2455 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2456 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2460 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2461 | otherwise = var1 + var2
2463 m1 = lookup env var1
2464 m2 = lookup env var2
2465 ok1 = maybeToBool m1
2466 ok2 = maybeToBool m2
2467 val1 = expectJust m1
2468 val2 = expectJust m2
2472 The auxiliary functions are
2476 maybeToBool :: Maybe a -> Bool
2477 maybeToBool (Just x) = True
2478 maybeToBool Nothing = False
2480 expectJust :: Maybe a -> a
2481 expectJust (Just x) = x
2482 expectJust Nothing = error "Unexpected Nothing"
2486 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2487 ok2</literal> checks that both lookups succeed, using
2488 <function>maybeToBool</function> to convert the <function>Maybe</function>
2489 types to booleans. The (lazily evaluated) <function>expectJust</function>
2490 calls extract the values from the results of the lookups, and binds the
2491 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2492 respectively. If either lookup fails, then clunky takes the
2493 <literal>otherwise</literal> case and returns the sum of its arguments.
2497 This is certainly legal Haskell, but it is a tremendously verbose and
2498 un-obvious way to achieve the desired effect. Arguably, a more direct way
2499 to write clunky would be to use case expressions:
2503 clunky env var1 var1 = case lookup env var1 of
2505 Just val1 -> case lookup env var2 of
2507 Just val2 -> val1 + val2
2513 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2514 of pattern-matching, guarded equations as case expressions; that is
2515 precisely what the compiler does when compiling equations! The reason that
2516 Haskell provides guarded equations is because they allow us to write down
2517 the cases we want to consider, one at a time, independently of each other.
2518 This structure is hidden in the case version. Two of the right-hand sides
2519 are really the same (<function>fail</function>), and the whole expression
2520 tends to become more and more indented.
2524 Here is how I would write clunky:
2528 clunky env var1 var1
2529 | Just val1 <- lookup env var1
2530 , Just val2 <- lookup env var2
2532 ...other equations for clunky...
2536 The semantics should be clear enough. The qualifers are matched in order.
2537 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2538 right hand side is evaluated and matched against the pattern on the left.
2539 If the match fails then the whole guard fails and the next equation is
2540 tried. If it succeeds, then the appropriate binding takes place, and the
2541 next qualifier is matched, in the augmented environment. Unlike list
2542 comprehensions, however, the type of the expression to the right of the
2543 <literal><-</literal> is the same as the type of the pattern to its
2544 left. The bindings introduced by pattern guards scope over all the
2545 remaining guard qualifiers, and over the right hand side of the equation.
2549 Just as with list comprehensions, boolean expressions can be freely mixed
2550 with among the pattern guards. For example:
2561 Haskell's current guards therefore emerge as a special case, in which the
2562 qualifier list has just one element, a boolean expression.
2566 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2568 <sect2 id="parallel-list-comprehensions">
2569 <title>Parallel List Comprehensions</title>
2570 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2572 <indexterm><primary>parallel list comprehensions</primary>
2575 <para>Parallel list comprehensions are a natural extension to list
2576 comprehensions. List comprehensions can be thought of as a nice
2577 syntax for writing maps and filters. Parallel comprehensions
2578 extend this to include the zipWith family.</para>
2580 <para>A parallel list comprehension has multiple independent
2581 branches of qualifier lists, each separated by a `|' symbol. For
2582 example, the following zips together two lists:</para>
2585 [ (x, y) | x <- xs | y <- ys ]
2588 <para>The behavior of parallel list comprehensions follows that of
2589 zip, in that the resulting list will have the same length as the
2590 shortest branch.</para>
2592 <para>We can define parallel list comprehensions by translation to
2593 regular comprehensions. Here's the basic idea:</para>
2595 <para>Given a parallel comprehension of the form: </para>
2598 [ e | p1 <- e11, p2 <- e12, ...
2599 | q1 <- e21, q2 <- e22, ...
2604 <para>This will be translated to: </para>
2607 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2608 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2613 <para>where `zipN' is the appropriate zip for the given number of
2618 <sect2 id="rebindable-syntax">
2619 <title>Rebindable syntax</title>
2622 <para>GHC allows most kinds of built-in syntax to be rebound by
2623 the user, to facilitate replacing the <literal>Prelude</literal>
2624 with a home-grown version, for example.</para>
2626 <para>You may want to define your own numeric class
2627 hierarchy. It completely defeats that purpose if the
2628 literal "1" means "<literal>Prelude.fromInteger
2629 1</literal>", which is what the Haskell Report specifies.
2630 So the <option>-fno-implicit-prelude</option> flag causes
2631 the following pieces of built-in syntax to refer to
2632 <emphasis>whatever is in scope</emphasis>, not the Prelude
2637 <para>Integer and fractional literals mean
2638 "<literal>fromInteger 1</literal>" and
2639 "<literal>fromRational 3.2</literal>", not the
2640 Prelude-qualified versions; both in expressions and in
2642 <para>However, the standard Prelude <literal>Eq</literal> class
2643 is still used for the equality test necessary for literal patterns.</para>
2647 <para>Negation (e.g. "<literal>- (f x)</literal>")
2648 means "<literal>negate (f x)</literal>" (not
2649 <literal>Prelude.negate</literal>).</para>
2653 <para>In an n+k pattern, the standard Prelude
2654 <literal>Ord</literal> class is still used for comparison,
2655 but the necessary subtraction uses whatever
2656 "<literal>(-)</literal>" is in scope (not
2657 "<literal>Prelude.(-)</literal>").</para>
2661 <para>"Do" notation is translated using whatever
2662 functions <literal>(>>=)</literal>,
2663 <literal>(>>)</literal>, <literal>fail</literal>, and
2664 <literal>return</literal>, are in scope (not the Prelude
2665 versions). List comprehensions, and parallel array
2666 comprehensions, are unaffected. </para></listitem>
2669 <para>Be warned: this is an experimental facility, with fewer checks than
2670 usual. In particular, it is essential that the functions GHC finds in scope
2671 must have the appropriate types, namely:
2673 fromInteger :: forall a. (...) => Integer -> a
2674 fromRational :: forall a. (...) => Rational -> a
2675 negate :: forall a. (...) => a -> a
2676 (-) :: forall a. (...) => a -> a -> a
2677 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
2678 (>>) :: forall m a. (...) => m a -> m b -> m b
2679 return :: forall m a. (...) => a -> m a
2680 fail :: forall m a. (...) => String -> m a
2682 (The (...) part can be any context including the empty context; that part
2684 If the functions don't have the right type, very peculiar things may
2685 happen. Use <literal>-dcore-lint</literal> to
2686 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
2691 <!-- =============================== PRAGMAS =========================== -->
2693 <sect1 id="pragmas">
2694 <title>Pragmas</title>
2696 <indexterm><primary>pragma</primary></indexterm>
2698 <para>GHC supports several pragmas, or instructions to the
2699 compiler placed in the source code. Pragmas don't normally affect
2700 the meaning of the program, but they might affect the efficiency
2701 of the generated code.</para>
2703 <para>Pragmas all take the form
2705 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2707 where <replaceable>word</replaceable> indicates the type of
2708 pragma, and is followed optionally by information specific to that
2709 type of pragma. Case is ignored in
2710 <replaceable>word</replaceable>. The various values for
2711 <replaceable>word</replaceable> that GHC understands are described
2712 in the following sections; any pragma encountered with an
2713 unrecognised <replaceable>word</replaceable> is (silently)
2716 <sect2 id="inline-pragma">
2717 <title>INLINE pragma
2719 <indexterm><primary>INLINE pragma</primary></indexterm>
2720 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2723 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2724 functions/values that are “small enough,” thus avoiding the call
2725 overhead and possibly exposing other more-wonderful optimisations.
2729 You will probably see these unfoldings (in Core syntax) in your
2734 Normally, if GHC decides a function is “too expensive” to inline, it
2735 will not do so, nor will it export that unfolding for other modules to
2740 The sledgehammer you can bring to bear is the
2741 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2744 key_function :: Int -> String -> (Bool, Double)
2746 #ifdef __GLASGOW_HASKELL__
2747 {-# INLINE key_function #-}
2751 (You don't need to do the C pre-processor carry-on unless you're going
2752 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2756 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2757 “cost” to be very low. The normal unfolding machinery will then be
2758 very keen to inline it.
2762 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2763 signature could be put.
2767 <literal>INLINE</literal> pragmas are a particularly good idea for the
2768 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2769 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2772 #ifdef __GLASGOW_HASKELL__
2773 {-# INLINE thenUs #-}
2774 {-# INLINE returnUs #-}
2782 <sect2 id="noinline-pragma">
2783 <title>NOINLINE pragma
2786 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2787 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2788 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2789 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2792 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2793 it stops the named function from being inlined by the compiler. You
2794 shouldn't ever need to do this, unless you're very cautious about code
2798 <para><literal>NOTINLINE</literal> is a synonym for
2799 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2800 by Haskell 98 as the standard way to disable inlining, so it should be
2801 used if you want your code to be portable).</para>
2805 <sect2 id="specialize-pragma">
2806 <title>SPECIALIZE pragma</title>
2808 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2809 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2810 <indexterm><primary>overloading, death to</primary></indexterm>
2812 <para>(UK spelling also accepted.) For key overloaded
2813 functions, you can create extra versions (NB: more code space)
2814 specialised to particular types. Thus, if you have an
2815 overloaded function:</para>
2818 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2821 <para>If it is heavily used on lists with
2822 <literal>Widget</literal> keys, you could specialise it as
2826 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2829 <para>To get very fancy, you can also specify a named function
2830 to use for the specialised value, as in:</para>
2833 {-# RULES hammeredLookup = blah #-}
2836 <para>where <literal>blah</literal> is an implementation of
2837 <literal>hammerdLookup</literal> written specialy for
2838 <literal>Widget</literal> lookups. It's <emphasis>Your
2839 Responsibility</emphasis> to make sure that
2840 <function>blah</function> really behaves as a specialised
2841 version of <function>hammeredLookup</function>!!!</para>
2843 <para>Note we use the <literal>RULE</literal> pragma here to
2844 indicate that <literal>hammeredLookup</literal> applied at a
2845 certain type should be replaced by <literal>blah</literal>. See
2846 <xref linkend="rules"> for more information on
2847 <literal>RULES</literal>.</para>
2849 <para>An example in which using <literal>RULES</literal> for
2850 specialisation will Win Big:
2853 toDouble :: Real a => a -> Double
2854 toDouble = fromRational . toRational
2856 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2857 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2860 The <function>i2d</function> function is virtually one machine
2861 instruction; the default conversion—via an intermediate
2862 <literal>Rational</literal>—is obscenely expensive by
2865 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2866 be put anywhere its type signature could be put.</para>
2870 <sect2 id="specialize-instance-pragma">
2871 <title>SPECIALIZE instance pragma
2875 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2876 <indexterm><primary>overloading, death to</primary></indexterm>
2877 Same idea, except for instance declarations. For example:
2880 instance (Eq a) => Eq (Foo a) where {
2881 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2885 The pragma must occur inside the <literal>where</literal> part
2886 of the instance declaration.
2889 Compatible with HBC, by the way, except perhaps in the placement
2895 <sect2 id="line-pragma">
2900 <indexterm><primary>LINE pragma</primary></indexterm>
2901 <indexterm><primary>pragma, LINE</primary></indexterm>
2905 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2906 automatically generated Haskell code. It lets you specify the line
2907 number and filename of the original code; for example
2913 {-# LINE 42 "Foo.vhs" #-}
2919 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2920 and this line corresponds to line 42 in the original. GHC will adjust
2921 its error messages to refer to the line/file named in the <literal>LINE</literal>
2928 <title>RULES pragma</title>
2931 The RULES pragma lets you specify rewrite rules. It is described in
2932 <xref LinkEnd="rewrite-rules">.
2937 <sect2 id="deprecated-pragma">
2938 <title>DEPRECATED pragma</title>
2941 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2942 There are two forms.
2946 You can deprecate an entire module thus:</para>
2948 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2952 When you compile any module that import <literal>Wibble</literal>, GHC will print
2953 the specified message.</para>
2958 You can deprecate a function, class, or type, with the following top-level declaration:
2961 {-# DEPRECATED f, C, T "Don't use these" #-}
2964 When you compile any module that imports and uses any of the specifed entities,
2965 GHC will print the specified message.
2969 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2975 <!-- ======================= REWRITE RULES ======================== -->
2977 <sect1 id="rewrite-rules">
2978 <title>Rewrite rules
2980 <indexterm><primary>RULES pagma</primary></indexterm>
2981 <indexterm><primary>pragma, RULES</primary></indexterm>
2982 <indexterm><primary>rewrite rules</primary></indexterm></title>
2985 The programmer can specify rewrite rules as part of the source program
2986 (in a pragma). GHC applies these rewrite rules wherever it can.
2994 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3001 <title>Syntax</title>
3004 From a syntactic point of view:
3010 Each rule has a name, enclosed in double quotes. The name itself has
3011 no significance at all. It is only used when reporting how many times the rule fired.
3017 There may be zero or more rules in a <literal>RULES</literal> pragma.
3023 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3024 is set, so you must lay out your rules starting in the same column as the
3025 enclosing definitions.
3031 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3032 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3033 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3034 by spaces, just like in a type <literal>forall</literal>.
3040 A pattern variable may optionally have a type signature.
3041 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3042 For example, here is the <literal>foldr/build</literal> rule:
3045 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3046 foldr k z (build g) = g k z
3049 Since <function>g</function> has a polymorphic type, it must have a type signature.
3056 The left hand side of a rule must consist of a top-level variable applied
3057 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3060 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3061 "wrong2" forall f. f True = True
3064 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3071 A rule does not need to be in the same module as (any of) the
3072 variables it mentions, though of course they need to be in scope.
3078 Rules are automatically exported from a module, just as instance declarations are.
3089 <title>Semantics</title>
3092 From a semantic point of view:
3098 Rules are only applied if you use the <option>-O</option> flag.
3104 Rules are regarded as left-to-right rewrite rules.
3105 When GHC finds an expression that is a substitution instance of the LHS
3106 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3107 By "a substitution instance" we mean that the LHS can be made equal to the
3108 expression by substituting for the pattern variables.
3115 The LHS and RHS of a rule are typechecked, and must have the
3123 GHC makes absolutely no attempt to verify that the LHS and RHS
3124 of a rule have the same meaning. That is undecideable in general, and
3125 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3132 GHC makes no attempt to make sure that the rules are confluent or
3133 terminating. For example:
3136 "loop" forall x,y. f x y = f y x
3139 This rule will cause the compiler to go into an infinite loop.
3146 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3152 GHC currently uses a very simple, syntactic, matching algorithm
3153 for matching a rule LHS with an expression. It seeks a substitution
3154 which makes the LHS and expression syntactically equal modulo alpha
3155 conversion. The pattern (rule), but not the expression, is eta-expanded if
3156 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3157 But not beta conversion (that's called higher-order matching).
3161 Matching is carried out on GHC's intermediate language, which includes
3162 type abstractions and applications. So a rule only matches if the
3163 types match too. See <xref LinkEnd="rule-spec"> below.
3169 GHC keeps trying to apply the rules as it optimises the program.
3170 For example, consider:
3179 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3180 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3181 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3182 not be substituted, and the rule would not fire.
3189 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3190 that appears on the LHS of a rule</emphasis>, because once you have substituted
3191 for something you can't match against it (given the simple minded
3192 matching). So if you write the rule
3195 "map/map" forall f,g. map f . map g = map (f.g)
3198 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3199 It will only match something written with explicit use of ".".
3200 Well, not quite. It <emphasis>will</emphasis> match the expression
3206 where <function>wibble</function> is defined:
3209 wibble f g = map f . map g
3212 because <function>wibble</function> will be inlined (it's small).
3214 Later on in compilation, GHC starts inlining even things on the
3215 LHS of rules, but still leaves the rules enabled. This inlining
3216 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3223 All rules are implicitly exported from the module, and are therefore
3224 in force in any module that imports the module that defined the rule, directly
3225 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3226 in force when compiling A.) The situation is very similar to that for instance
3238 <title>List fusion</title>
3241 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3242 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3243 intermediate list should be eliminated entirely.
3247 The following are good producers:
3259 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3265 Explicit lists (e.g. <literal>[True, False]</literal>)
3271 The cons constructor (e.g <literal>3:4:[]</literal>)
3277 <function>++</function>
3283 <function>map</function>
3289 <function>filter</function>
3295 <function>iterate</function>, <function>repeat</function>
3301 <function>zip</function>, <function>zipWith</function>
3310 The following are good consumers:
3322 <function>array</function> (on its second argument)
3328 <function>length</function>
3334 <function>++</function> (on its first argument)
3340 <function>foldr</function>
3346 <function>map</function>
3352 <function>filter</function>
3358 <function>concat</function>
3364 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3370 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3371 will fuse with one but not the other)
3377 <function>partition</function>
3383 <function>head</function>
3389 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3395 <function>sequence_</function>
3401 <function>msum</function>
3407 <function>sortBy</function>
3416 So, for example, the following should generate no intermediate lists:
3419 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3425 This list could readily be extended; if there are Prelude functions that you use
3426 a lot which are not included, please tell us.
3430 If you want to write your own good consumers or producers, look at the
3431 Prelude definitions of the above functions to see how to do so.
3436 <sect2 id="rule-spec">
3437 <title>Specialisation
3441 Rewrite rules can be used to get the same effect as a feature
3442 present in earlier version of GHC:
3445 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3448 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3449 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3450 specialising the original definition of <function>fromIntegral</function> the programmer is
3451 promising that it is safe to use <function>int8ToInt16</function> instead.
3455 This feature is no longer in GHC. But rewrite rules let you do the
3460 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3464 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3465 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3466 GHC adds the type and dictionary applications to get the typed rule
3469 forall (d1::Integral Int8) (d2::Num Int16) .
3470 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3474 this rule does not need to be in the same file as fromIntegral,
3475 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3476 have an original definition available to specialise).
3482 <title>Controlling what's going on</title>
3490 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3496 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3497 If you add <option>-dppr-debug</option> you get a more detailed listing.
3503 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3506 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3507 {-# INLINE build #-}
3511 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3512 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3513 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3514 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3521 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3522 see how to write rules that will do fusion and yet give an efficient
3523 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3535 <sect1 id="generic-classes">
3536 <title>Generic classes</title>
3538 <para>(Note: support for generic classes is currently broken in
3542 The ideas behind this extension are described in detail in "Derivable type classes",
3543 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3544 An example will give the idea:
3552 fromBin :: [Int] -> (a, [Int])
3554 toBin {| Unit |} Unit = []
3555 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3556 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3557 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3559 fromBin {| Unit |} bs = (Unit, bs)
3560 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3561 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3562 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3563 (y,bs'') = fromBin bs'
3566 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3567 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3568 which are defined thus in the library module <literal>Generics</literal>:
3572 data a :+: b = Inl a | Inr b
3573 data a :*: b = a :*: b
3576 Now you can make a data type into an instance of Bin like this:
3578 instance (Bin a, Bin b) => Bin (a,b)
3579 instance Bin a => Bin [a]
3581 That is, just leave off the "where" clasuse. Of course, you can put in the
3582 where clause and over-ride whichever methods you please.
3586 <title> Using generics </title>
3587 <para>To use generics you need to</para>
3590 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3591 <option>-fgenerics</option> (to generate extra per-data-type code),
3592 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3596 <para>Import the module <literal>Generics</literal> from the
3597 <literal>lang</literal> package. This import brings into
3598 scope the data types <literal>Unit</literal>,
3599 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3600 don't need this import if you don't mention these types
3601 explicitly; for example, if you are simply giving instance
3602 declarations.)</para>
3607 <sect2> <title> Changes wrt the paper </title>
3609 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3610 can be written infix (indeed, you can now use
3611 any operator starting in a colon as an infix type constructor). Also note that
3612 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3613 Finally, note that the syntax of the type patterns in the class declaration
3614 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3615 alone would ambiguous when they appear on right hand sides (an extension we
3616 anticipate wanting).
3620 <sect2> <title>Terminology and restrictions</title>
3622 Terminology. A "generic default method" in a class declaration
3623 is one that is defined using type patterns as above.
3624 A "polymorphic default method" is a default method defined as in Haskell 98.
3625 A "generic class declaration" is a class declaration with at least one
3626 generic default method.
3634 Alas, we do not yet implement the stuff about constructor names and
3641 A generic class can have only one parameter; you can't have a generic
3642 multi-parameter class.
3648 A default method must be defined entirely using type patterns, or entirely
3649 without. So this is illegal:
3652 op :: a -> (a, Bool)
3653 op {| Unit |} Unit = (Unit, True)
3656 However it is perfectly OK for some methods of a generic class to have
3657 generic default methods and others to have polymorphic default methods.
3663 The type variable(s) in the type pattern for a generic method declaration
3664 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:
3668 op {| p :*: q |} (x :*: y) = op (x :: p)
3676 The type patterns in a generic default method must take one of the forms:
3682 where "a" and "b" are type variables. Furthermore, all the type patterns for
3683 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3684 must use the same type variables. So this is illegal:
3688 op {| a :+: b |} (Inl x) = True
3689 op {| p :+: q |} (Inr y) = False
3691 The type patterns must be identical, even in equations for different methods of the class.
3692 So this too is illegal:
3696 op1 {| a :*: b |} (x :*: y) = True
3699 op2 {| p :*: q |} (x :*: y) = False
3701 (The reason for this restriction is that we gather all the equations for a particular type consructor
3702 into a single generic instance declaration.)
3708 A generic method declaration must give a case for each of the three type constructors.
3714 The type for a generic method can be built only from:
3716 <listitem> <para> Function arrows </para> </listitem>
3717 <listitem> <para> Type variables </para> </listitem>
3718 <listitem> <para> Tuples </para> </listitem>
3719 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3721 Here are some example type signatures for generic methods:
3724 op2 :: Bool -> (a,Bool)
3725 op3 :: [Int] -> a -> a
3728 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3732 This restriction is an implementation restriction: we just havn't got around to
3733 implementing the necessary bidirectional maps over arbitrary type constructors.
3734 It would be relatively easy to add specific type constructors, such as Maybe and list,
3735 to the ones that are allowed.</para>
3740 In an instance declaration for a generic class, the idea is that the compiler
3741 will fill in the methods for you, based on the generic templates. However it can only
3746 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3751 No constructor of the instance type has unboxed fields.
3755 (Of course, these things can only arise if you are already using GHC extensions.)
3756 However, you can still give an instance declarations for types which break these rules,
3757 provided you give explicit code to override any generic default methods.
3765 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3766 what the compiler does with generic declarations.
3771 <sect2> <title> Another example </title>
3773 Just to finish with, here's another example I rather like:
3777 nCons {| Unit |} _ = 1
3778 nCons {| a :*: b |} _ = 1
3779 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3782 tag {| Unit |} _ = 1
3783 tag {| a :*: b |} _ = 1
3784 tag {| a :+: b |} (Inl x) = tag x
3785 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3791 <sect1 id="newtype-deriving">
3792 <title>Generalised derived instances for newtypes</title>
3795 When you define an abstract type using <literal>newtype</literal>, you may want
3796 the new type to inherit some instances from its representation. In
3797 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3798 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3799 other classes you have to write an explicit instance declaration. For
3800 example, if you define
3803 newtype Dollars = Dollars Int
3806 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3807 explicitly define an instance of <literal>Num</literal>:
3810 instance Num Dollars where
3811 Dollars a + Dollars b = Dollars (a+b)
3814 All the instance does is apply and remove the <literal>newtype</literal>
3815 constructor. It is particularly galling that, since the constructor
3816 doesn't appear at run-time, this instance declaration defines a
3817 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3818 dictionary, only slower!
3821 <sect2> <title> Generalising the deriving clause </title>
3823 GHC now permits such instances to be derived instead, so one can write
3825 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3828 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3829 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3830 derives an instance declaration of the form
3833 instance Num Int => Num Dollars
3836 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3840 We can also derive instances of constructor classes in a similar
3841 way. For example, suppose we have implemented state and failure monad
3842 transformers, such that
3845 instance Monad m => Monad (State s m)
3846 instance Monad m => Monad (Failure m)
3848 In Haskell 98, we can define a parsing monad by
3850 type Parser tok m a = State [tok] (Failure m) a
3853 which is automatically a monad thanks to the instance declarations
3854 above. With the extension, we can make the parser type abstract,
3855 without needing to write an instance of class <literal>Monad</literal>, via
3858 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3861 In this case the derived instance declaration is of the form
3863 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3866 Notice that, since <literal>Monad</literal> is a constructor class, the
3867 instance is a <emphasis>partial application</emphasis> of the new type, not the
3868 entire left hand side. We can imagine that the type declaration is
3869 ``eta-converted'' to generate the context of the instance
3874 We can even derive instances of multi-parameter classes, provided the
3875 newtype is the last class parameter. In this case, a ``partial
3876 application'' of the class appears in the <literal>deriving</literal>
3877 clause. For example, given the class
3880 class StateMonad s m | m -> s where ...
3881 instance Monad m => StateMonad s (State s m) where ...
3883 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3885 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3886 deriving (Monad, StateMonad [tok])
3889 The derived instance is obtained by completing the application of the
3890 class to the new type:
3893 instance StateMonad [tok] (State [tok] (Failure m)) =>
3894 StateMonad [tok] (Parser tok m)
3899 As a result of this extension, all derived instances in newtype
3900 declarations are treated uniformly (and implemented just by reusing
3901 the dictionary for the representation type), <emphasis>except</emphasis>
3902 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3903 the newtype and its representation.
3907 <sect2> <title> A more precise specification </title>
3909 Derived instance declarations are constructed as follows. Consider the
3910 declaration (after expansion of any type synonyms)
3913 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3916 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3918 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3919 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3920 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3921 declarations are, for each <literal>ci</literal>,
3924 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3926 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3927 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3931 As an example which does <emphasis>not</emphasis> work, consider
3933 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3935 Here we cannot derive the instance
3937 instance Monad (State s m) => Monad (NonMonad m)
3940 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3941 and so cannot be "eta-converted" away. It is a good thing that this
3942 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3943 not, in fact, a monad --- for the same reason. Try defining
3944 <literal>>>=</literal> with the correct type: you won't be able to.
3948 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3949 important, since we can only derive instances for the last one. If the
3950 <literal>StateMonad</literal> class above were instead defined as
3953 class StateMonad m s | m -> s where ...
3956 then we would not have been able to derive an instance for the
3957 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3958 classes usually have one "main" parameter for which deriving new
3959 instances is most interesting.
3967 ;;; Local Variables: ***
3969 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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