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 points:
979 You may not mix implicit-parameter bindings with ordinary bindings in a
980 single <literal>let</literal>
981 expression; use two nested <literal>let</literal>s instead.
985 You may put multiple implicit-parameter bindings in a
986 single <literal>let</literal> expression; they are <emphasis>not</emphasis> treated
987 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
988 Instead they are treated as a non-recursive group, each scoping over the bindings that
989 follow. For example, consider:
991 f y = let { ?x = y; ?x = ?x+1 } in ?x
993 This function adds one to its argument.
997 You may not have an implicit-parameter binding in a <literal>where</literal> clause,
998 only in a <literal>let</literal> binding.
1002 <para> You can't have an implicit parameter in the context of a class or instance
1003 declaration. For example, both these declarations are illegal:
1005 class (?x::Int) => C a where ...
1006 instance (?x::a) => Foo [a] where ...
1008 Reason: exactly which implicit parameter you pick up depends on exactly where
1009 you invoke a function. But the ``invocation'' of instance declarations is done
1010 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1011 Easiest thing is to outlaw the offending types.</para>
1018 <sect2 id="linear-implicit-parameters">
1019 <title>Linear implicit parameters
1022 Linear implicit parameters are an idea developed by Koen Claessen,
1023 Mark Shields, and Simon PJ. They address the long-standing
1024 problem that monads seem over-kill for certain sorts of problem, notably:
1027 <listitem> <para> distributing a supply of unique names </para> </listitem>
1028 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1029 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1033 Linear implicit parameters are just like ordinary implicit parameters,
1034 except that they are "linear" -- that is, they cannot be copied, and
1035 must be explicitly "split" instead. Linear implicit parameters are
1036 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1037 (The '/' in the '%' suggests the split!)
1042 import GHC.Exts( Splittable )
1044 data NameSupply = ...
1046 splitNS :: NameSupply -> (NameSupply, NameSupply)
1047 newName :: NameSupply -> Name
1049 instance Splittable NameSupply where
1053 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1054 f env (Lam x e) = Lam x' (f env e)
1057 env' = extend env x x'
1058 ...more equations for f...
1060 Notice that the implicit parameter %ns is consumed
1062 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1063 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1067 So the translation done by the type checker makes
1068 the parameter explicit:
1070 f :: NameSupply -> Env -> Expr -> Expr
1071 f ns env (Lam x e) = Lam x' (f ns1 env e)
1073 (ns1,ns2) = splitNS ns
1075 env = extend env x x'
1077 Notice the call to 'split' introduced by the type checker.
1078 How did it know to use 'splitNS'? Because what it really did
1079 was to introduce a call to the overloaded function 'split',
1080 defined by the class <literal>Splittable</literal>:
1082 class Splittable a where
1085 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1086 split for name supplies. But we can simply write
1092 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1094 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1095 <literal>GHC.Exts</literal>.
1100 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1101 are entirely distinct implicit parameters: you
1102 can use them together and they won't intefere with each other. </para>
1105 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1107 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1108 in the context of a class or instance declaration. </para></listitem>
1112 <sect3><title>Warnings</title>
1115 The monomorphism restriction is even more important than usual.
1116 Consider the example above:
1118 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1119 f env (Lam x e) = Lam x' (f env e)
1122 env' = extend env x x'
1124 If we replaced the two occurrences of x' by (newName %ns), which is
1125 usually a harmless thing to do, we get:
1127 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1128 f env (Lam x e) = Lam (newName %ns) (f env e)
1130 env' = extend env x (newName %ns)
1132 But now the name supply is consumed in <emphasis>three</emphasis> places
1133 (the two calls to newName,and the recursive call to f), so
1134 the result is utterly different. Urk! We don't even have
1138 Well, this is an experimental change. With implicit
1139 parameters we have already lost beta reduction anyway, and
1140 (as John Launchbury puts it) we can't sensibly reason about
1141 Haskell programs without knowing their typing.
1146 <sect3><title>Recursive functions</title>
1147 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1150 foo :: %x::T => Int -> [Int]
1152 foo n = %x : foo (n-1)
1154 where T is some type in class Splittable.</para>
1156 Do you get a list of all the same T's or all different T's
1157 (assuming that split gives two distinct T's back)?
1159 If you supply the type signature, taking advantage of polymorphic
1160 recursion, you get what you'd probably expect. Here's the
1161 translated term, where the implicit param is made explicit:
1164 foo x n = let (x1,x2) = split x
1165 in x1 : foo x2 (n-1)
1167 But if you don't supply a type signature, GHC uses the Hindley
1168 Milner trick of using a single monomorphic instance of the function
1169 for the recursive calls. That is what makes Hindley Milner type inference
1170 work. So the translation becomes
1174 foom n = x : foom (n-1)
1178 Result: 'x' is not split, and you get a list of identical T's. So the
1179 semantics of the program depends on whether or not foo has a type signature.
1182 You may say that this is a good reason to dislike linear implicit parameters
1183 and you'd be right. That is why they are an experimental feature.
1189 <sect2 id="functional-dependencies">
1190 <title>Functional dependencies
1193 <para> Functional dependencies are implemented as described by Mark Jones
1194 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1195 In Proceedings of the 9th European Symposium on Programming,
1196 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1201 There should be more documentation, but there isn't (yet). Yell if you need it.
1206 <sect2 id="universal-quantification">
1207 <title>Arbitrary-rank polymorphism
1211 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1212 allows us to say exactly what this means. For example:
1220 g :: forall b. (b -> b)
1222 The two are treated identically.
1226 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1227 explicit universal quantification in
1229 For example, all the following types are legal:
1231 f1 :: forall a b. a -> b -> a
1232 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1234 f2 :: (forall a. a->a) -> Int -> Int
1235 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1237 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1239 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1240 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1241 The <literal>forall</literal> makes explicit the universal quantification that
1242 is implicitly added by Haskell.
1245 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1246 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1247 shows, the polymorphic type on the left of the function arrow can be overloaded.
1250 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1251 they have rank-2 types on the left of a function arrow.
1254 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1255 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1256 that restriction has now been lifted.)
1257 In particular, a forall-type (also called a "type scheme"),
1258 including an operational type class context, is legal:
1260 <listitem> <para> On the left of a function arrow </para> </listitem>
1261 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1262 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1263 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1264 field type signatures.</para> </listitem>
1265 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1266 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1268 There is one place you cannot put a <literal>forall</literal>:
1269 you cannot instantiate a type variable with a forall-type. So you cannot
1270 make a forall-type the argument of a type constructor. So these types are illegal:
1272 x1 :: [forall a. a->a]
1273 x2 :: (forall a. a->a, Int)
1274 x3 :: Maybe (forall a. a->a)
1276 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1277 a type variable any more!
1286 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1287 the types of the constructor arguments. Here are several examples:
1293 data T a = T1 (forall b. b -> b -> b) a
1295 data MonadT m = MkMonad { return :: forall a. a -> m a,
1296 bind :: forall a b. m a -> (a -> m b) -> m b
1299 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1305 The constructors have rank-2 types:
1311 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1312 MkMonad :: forall m. (forall a. a -> m a)
1313 -> (forall a b. m a -> (a -> m b) -> m b)
1315 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1321 Notice that you don't need to use a <literal>forall</literal> if there's an
1322 explicit context. For example in the first argument of the
1323 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1324 prefixed to the argument type. The implicit <literal>forall</literal>
1325 quantifies all type variables that are not already in scope, and are
1326 mentioned in the type quantified over.
1330 As for type signatures, implicit quantification happens for non-overloaded
1331 types too. So if you write this:
1334 data T a = MkT (Either a b) (b -> b)
1337 it's just as if you had written this:
1340 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1343 That is, since the type variable <literal>b</literal> isn't in scope, it's
1344 implicitly universally quantified. (Arguably, it would be better
1345 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1346 where that is what is wanted. Feedback welcomed.)
1350 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1351 the constructor to suitable values, just as usual. For example,
1362 a3 = MkSwizzle reverse
1365 a4 = let r x = Just x
1372 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1373 mkTs f x y = [T1 f x, T1 f y]
1379 The type of the argument can, as usual, be more general than the type
1380 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1381 does not need the <literal>Ord</literal> constraint.)
1385 When you use pattern matching, the bound variables may now have
1386 polymorphic types. For example:
1392 f :: T a -> a -> (a, Char)
1393 f (T1 w k) x = (w k x, w 'c' 'd')
1395 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1396 g (MkSwizzle s) xs f = s (map f (s xs))
1398 h :: MonadT m -> [m a] -> m [a]
1399 h m [] = return m []
1400 h m (x:xs) = bind m x $ \y ->
1401 bind m (h m xs) $ \ys ->
1408 In the function <function>h</function> we use the record selectors <literal>return</literal>
1409 and <literal>bind</literal> to extract the polymorphic bind and return functions
1410 from the <literal>MonadT</literal> data structure, rather than using pattern
1416 <title>Type inference</title>
1419 In general, type inference for arbitrary-rank types is undecideable.
1420 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1421 to get a decidable algorithm by requiring some help from the programmer.
1422 We do not yet have a formal specification of "some help" but the rule is this:
1425 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1426 provides an explicit polymorphic type for x, or GHC's type inference will assume
1427 that x's type has no foralls in it</emphasis>.
1430 What does it mean to "provide" an explicit type for x? You can do that by
1431 giving a type signature for x directly, using a pattern type signature
1432 (<xref linkend="scoped-type-variables">), thus:
1434 \ f :: (forall a. a->a) -> (f True, f 'c')
1436 Alternatively, you can give a type signature to the enclosing
1437 context, which GHC can "push down" to find the type for the variable:
1439 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1441 Here the type signature on the expression can be pushed inwards
1442 to give a type signature for f. Similarly, and more commonly,
1443 one can give a type signature for the function itself:
1445 h :: (forall a. a->a) -> (Bool,Char)
1446 h f = (f True, f 'c')
1448 You don't need to give a type signature if the lambda bound variable
1449 is a constructor argument. Here is an example we saw earlier:
1451 f :: T a -> a -> (a, Char)
1452 f (T1 w k) x = (w k x, w 'c' 'd')
1454 Here we do not need to give a type signature to <literal>w</literal>, because
1455 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1462 <sect3 id="implicit-quant">
1463 <title>Implicit quantification</title>
1466 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1467 user-written types, if and only if there is no explicit <literal>forall</literal>,
1468 GHC finds all the type variables mentioned in the type that are not already
1469 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1473 f :: forall a. a -> a
1480 h :: forall b. a -> b -> b
1486 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1489 f :: (a -> a) -> Int
1491 f :: forall a. (a -> a) -> Int
1493 f :: (forall a. a -> a) -> Int
1496 g :: (Ord a => a -> a) -> Int
1497 -- MEANS the illegal type
1498 g :: forall a. (Ord a => a -> a) -> Int
1500 g :: (forall a. Ord a => a -> a) -> Int
1502 The latter produces an illegal type, which you might think is silly,
1503 but at least the rule is simple. If you want the latter type, you
1504 can write your for-alls explicitly. Indeed, doing so is strongly advised
1510 <sect2 id="type-synonyms">
1511 <title>Liberalised type synonyms
1515 Type synonmys are like macros at the type level, and
1516 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1517 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1519 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1520 in a type synonym, thus:
1522 type Discard a = forall b. Show b => a -> b -> (a, String)
1527 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1534 You can write an unboxed tuple in a type synonym:
1536 type Pr = (# Int, Int #)
1544 You can apply a type synonym to a forall type:
1546 type Foo a = a -> a -> Bool
1548 f :: Foo (forall b. b->b)
1550 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1552 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1557 You can apply a type synonym to a partially applied type synonym:
1559 type Generic i o = forall x. i x -> o x
1562 foo :: Generic Id []
1564 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1566 foo :: forall x. x -> [x]
1574 GHC currently does kind checking before expanding synonyms (though even that
1578 After expanding type synonyms, GHC does validity checking on types, looking for
1579 the following mal-formedness which isn't detected simply by kind checking:
1582 Type constructor applied to a type involving for-alls.
1585 Unboxed tuple on left of an arrow.
1588 Partially-applied type synonym.
1592 this will be rejected:
1594 type Pr = (# Int, Int #)
1599 because GHC does not allow unboxed tuples on the left of a function arrow.
1604 <title>For-all hoisting</title>
1606 It is often convenient to use generalised type synonyms at the right hand
1607 end of an arrow, thus:
1609 type Discard a = forall b. a -> b -> a
1611 g :: Int -> Discard Int
1614 Simply expanding the type synonym would give
1616 g :: Int -> (forall b. Int -> b -> Int)
1618 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1620 g :: forall b. Int -> Int -> b -> Int
1622 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1623 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1624 performs the transformation:</emphasis>
1626 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1628 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1630 (In fact, GHC tries to retain as much synonym information as possible for use in
1631 error messages, but that is a usability issue.) This rule applies, of course, whether
1632 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1633 valid way to write <literal>g</literal>'s type signature:
1635 g :: Int -> Int -> forall b. b -> Int
1639 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1642 type Foo a = (?x::Int) => Bool -> a
1647 g :: (?x::Int) => Bool -> Bool -> Int
1653 <sect2 id="existential-quantification">
1654 <title>Existentially quantified data constructors
1658 The idea of using existential quantification in data type declarations
1659 was suggested by Laufer (I believe, thought doubtless someone will
1660 correct me), and implemented in Hope+. It's been in Lennart
1661 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1662 proved very useful. Here's the idea. Consider the declaration:
1668 data Foo = forall a. MkFoo a (a -> Bool)
1675 The data type <literal>Foo</literal> has two constructors with types:
1681 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1688 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1689 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1690 For example, the following expression is fine:
1696 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1702 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1703 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1704 isUpper</function> packages a character with a compatible function. These
1705 two things are each of type <literal>Foo</literal> and can be put in a list.
1709 What can we do with a value of type <literal>Foo</literal>?. In particular,
1710 what happens when we pattern-match on <function>MkFoo</function>?
1716 f (MkFoo val fn) = ???
1722 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1723 are compatible, the only (useful) thing we can do with them is to
1724 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1731 f (MkFoo val fn) = fn val
1737 What this allows us to do is to package heterogenous values
1738 together with a bunch of functions that manipulate them, and then treat
1739 that collection of packages in a uniform manner. You can express
1740 quite a bit of object-oriented-like programming this way.
1743 <sect3 id="existential">
1744 <title>Why existential?
1748 What has this to do with <emphasis>existential</emphasis> quantification?
1749 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1755 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1761 But Haskell programmers can safely think of the ordinary
1762 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1763 adding a new existential quantification construct.
1769 <title>Type classes</title>
1772 An easy extension (implemented in <Command>hbc</Command>) is to allow
1773 arbitrary contexts before the constructor. For example:
1779 data Baz = forall a. Eq a => Baz1 a a
1780 | forall b. Show b => Baz2 b (b -> b)
1786 The two constructors have the types you'd expect:
1792 Baz1 :: forall a. Eq a => a -> a -> Baz
1793 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1799 But when pattern matching on <function>Baz1</function> the matched values can be compared
1800 for equality, and when pattern matching on <function>Baz2</function> the first matched
1801 value can be converted to a string (as well as applying the function to it).
1802 So this program is legal:
1809 f (Baz1 p q) | p == q = "Yes"
1811 f (Baz2 v fn) = show (fn v)
1817 Operationally, in a dictionary-passing implementation, the
1818 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1819 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1820 extract it on pattern matching.
1824 Notice the way that the syntax fits smoothly with that used for
1825 universal quantification earlier.
1831 <title>Restrictions</title>
1834 There are several restrictions on the ways in which existentially-quantified
1835 constructors can be use.
1844 When pattern matching, each pattern match introduces a new,
1845 distinct, type for each existential type variable. These types cannot
1846 be unified with any other type, nor can they escape from the scope of
1847 the pattern match. For example, these fragments are incorrect:
1855 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1856 is the result of <function>f1</function>. One way to see why this is wrong is to
1857 ask what type <function>f1</function> has:
1861 f1 :: Foo -> a -- Weird!
1865 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1870 f1 :: forall a. Foo -> a -- Wrong!
1874 The original program is just plain wrong. Here's another sort of error
1878 f2 (Baz1 a b) (Baz1 p q) = a==q
1882 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1883 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1884 from the two <function>Baz1</function> constructors.
1892 You can't pattern-match on an existentially quantified
1893 constructor in a <literal>let</literal> or <literal>where</literal> group of
1894 bindings. So this is illegal:
1898 f3 x = a==b where { Baz1 a b = x }
1902 You can only pattern-match
1903 on an existentially-quantified constructor in a <literal>case</literal> expression or
1904 in the patterns of a function definition.
1906 The reason for this restriction is really an implementation one.
1907 Type-checking binding groups is already a nightmare without
1908 existentials complicating the picture. Also an existential pattern
1909 binding at the top level of a module doesn't make sense, because it's
1910 not clear how to prevent the existentially-quantified type "escaping".
1911 So for now, there's a simple-to-state restriction. We'll see how
1919 You can't use existential quantification for <literal>newtype</literal>
1920 declarations. So this is illegal:
1924 newtype T = forall a. Ord a => MkT a
1928 Reason: a value of type <literal>T</literal> must be represented as a pair
1929 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1930 That contradicts the idea that <literal>newtype</literal> should have no
1931 concrete representation. You can get just the same efficiency and effect
1932 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1933 overloading involved, then there is more of a case for allowing
1934 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1935 because the <literal>data</literal> version does carry an implementation cost,
1936 but single-field existentially quantified constructors aren't much
1937 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1938 stands, unless there are convincing reasons to change it.
1946 You can't use <literal>deriving</literal> to define instances of a
1947 data type with existentially quantified data constructors.
1949 Reason: in most cases it would not make sense. For example:#
1952 data T = forall a. MkT [a] deriving( Eq )
1955 To derive <literal>Eq</literal> in the standard way we would need to have equality
1956 between the single component of two <function>MkT</function> constructors:
1960 (MkT a) == (MkT b) = ???
1963 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1964 It's just about possible to imagine examples in which the derived instance
1965 would make sense, but it seems altogether simpler simply to prohibit such
1966 declarations. Define your own instances!
1978 <sect2 id="scoped-type-variables">
1979 <title>Scoped type variables
1983 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
1984 variable</emphasis>. For example
1990 f (xs::[a]) = ys ++ ys
1999 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2000 This brings the type variable <literal>a</literal> into scope; it scopes over
2001 all the patterns and right hand sides for this equation for <function>f</function>.
2002 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2006 Pattern type signatures are completely orthogonal to ordinary, separate
2007 type signatures. The two can be used independently or together.
2008 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2009 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2010 implicitly universally quantified. (If there are no type variables in
2011 scope, all type variables mentioned in the signature are universally
2012 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2013 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2014 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2015 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2016 it becomes possible to do so.
2020 Scoped type variables are implemented in both GHC and Hugs. Where the
2021 implementations differ from the specification below, those differences
2026 So much for the basic idea. Here are the details.
2030 <title>What a pattern type signature means</title>
2032 A type variable brought into scope by a pattern type signature is simply
2033 the name for a type. The restriction they express is that all occurrences
2034 of the same name mean the same type. For example:
2036 f :: [Int] -> Int -> Int
2037 f (xs::[a]) (y::a) = (head xs + y) :: a
2039 The pattern type signatures on the left hand side of
2040 <literal>f</literal> express the fact that <literal>xs</literal>
2041 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2042 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2043 specifies that this expression must have the same type <literal>a</literal>.
2044 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2045 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2046 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2047 rules, which specified that a pattern-bound type variable should be universally quantified.)
2048 For example, all of these are legal:</para>
2051 t (x::a) (y::a) = x+y*2
2053 f (x::a) (y::b) = [x,y] -- a unifies with b
2055 g (x::a) = x + 1::Int -- a unifies with Int
2057 h x = let k (y::a) = [x,y] -- a is free in the
2058 in k x -- environment
2060 k (x::a) True = ... -- a unifies with Int
2061 k (x::Int) False = ...
2064 w (x::a) = x -- a unifies with [b]
2070 <title>Scope and implicit quantification</title>
2078 All the type variables mentioned in a pattern,
2079 that are not already in scope,
2080 are brought into scope by the pattern. We describe this set as
2081 the <emphasis>type variables bound by the pattern</emphasis>.
2084 f (x::a) = let g (y::(a,b)) = fst y
2088 The pattern <literal>(x::a)</literal> brings the type variable
2089 <literal>a</literal> into scope, as well as the term
2090 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2091 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2092 and brings into scope the type variable <literal>b</literal>.
2098 The type variable(s) bound by the pattern have the same scope
2099 as the term variable(s) bound by the pattern. For example:
2102 f (x::a) = <...rhs of f...>
2103 (p::b, q::b) = (1,2)
2104 in <...body of let...>
2106 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2107 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2108 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2109 just like <literal>p</literal> and <literal>q</literal> do.
2110 Indeed, the newly bound type variables also scope over any ordinary, separate
2111 type signatures in the <literal>let</literal> group.
2118 The type variables bound by the pattern may be
2119 mentioned in ordinary type signatures or pattern
2120 type signatures anywhere within their scope.
2127 In ordinary type signatures, any type variable mentioned in the
2128 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2136 Ordinary type signatures do not bring any new type variables
2137 into scope (except in the type signature itself!). So this is illegal:
2144 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2145 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2146 and that is an incorrect typing.
2153 The pattern type signature is a monotype:
2158 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2162 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2163 not to type schemes.
2167 There is no implicit universal quantification on pattern type signatures (in contrast to
2168 ordinary type signatures).
2178 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2179 scope over the methods defined in the <literal>where</literal> part. For example:
2193 (Not implemented in Hugs yet, Dec 98).
2204 <title>Result type signatures</title>
2212 The result type of a function can be given a signature,
2217 f (x::a) :: [a] = [x,x,x]
2221 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2222 result type. Sometimes this is the only way of naming the type variable
2227 f :: Int -> [a] -> [a]
2228 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2229 in \xs -> map g (reverse xs `zip` xs)
2241 Result type signatures are not yet implemented in Hugs.
2247 <title>Where a pattern type signature can occur</title>
2250 A pattern type signature can occur in any pattern. For example:
2255 A pattern type signature can be on an arbitrary sub-pattern, not
2260 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2269 Pattern type signatures, including the result part, can be used
2270 in lambda abstractions:
2273 (\ (x::a, y) :: a -> x)
2280 Pattern type signatures, including the result part, can be used
2281 in <literal>case</literal> expressions:
2285 case e of { (x::a, y) :: a -> x }
2293 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2294 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2295 token or a parenthesised type of some sort). To see why,
2296 consider how one would parse this:
2310 Pattern type signatures can bind existential type variables.
2315 data T = forall a. MkT [a]
2318 f (MkT [t::a]) = MkT t3
2331 Pattern type signatures
2332 can be used in pattern bindings:
2335 f x = let (y, z::a) = x in ...
2336 f1 x = let (y, z::Int) = x in ...
2337 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2338 f3 :: (b->b) = \x -> x
2341 In all such cases, the binding is not generalised over the pattern-bound
2342 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2343 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2344 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2345 In contrast, the binding
2350 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2351 in <literal>f4</literal>'s scope.
2363 <!-- ==================== End of type system extensions ================= -->
2366 <!-- ==================== ASSERTIONS ================= -->
2368 <sect1 id="sec-assertions">
2370 <indexterm><primary>Assertions</primary></indexterm>
2374 If you want to make use of assertions in your standard Haskell code, you
2375 could define a function like the following:
2381 assert :: Bool -> a -> a
2382 assert False x = error "assertion failed!"
2389 which works, but gives you back a less than useful error message --
2390 an assertion failed, but which and where?
2394 One way out is to define an extended <function>assert</function> function which also
2395 takes a descriptive string to include in the error message and
2396 perhaps combine this with the use of a pre-processor which inserts
2397 the source location where <function>assert</function> was used.
2401 Ghc offers a helping hand here, doing all of this for you. For every
2402 use of <function>assert</function> in the user's source:
2408 kelvinToC :: Double -> Double
2409 kelvinToC k = assert (k >= 0.0) (k+273.15)
2415 Ghc will rewrite this to also include the source location where the
2422 assert pred val ==> assertError "Main.hs|15" pred val
2428 The rewrite is only performed by the compiler when it spots
2429 applications of <function>Control.Exception.assert</function>, so you
2430 can still define and use your own versions of
2431 <function>assert</function>, should you so wish. If not, import
2432 <literal>Control.Exception</literal> to make use
2433 <function>assert</function> in your code.
2437 To have the compiler ignore uses of assert, use the compiler option
2438 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
2439 option</primary></indexterm> That is, expressions of the form
2440 <literal>assert pred e</literal> will be rewritten to
2441 <literal>e</literal>.
2445 Assertion failures can be caught, see the documentation for the
2446 <literal>Control.Exception</literal> library for the details.
2452 <sect1 id="syntax-extns">
2453 <title>Syntactic extensions</title>
2455 <!-- ====================== HIERARCHICAL MODULES ======================= -->
2457 <sect2 id="hierarchical-modules">
2458 <title>Hierarchical Modules</title>
2460 <para>GHC supports a small extension to the syntax of module
2461 names: a module name is allowed to contain a dot
2462 <literal>‘.’</literal>. This is also known as the
2463 “hierarchical module namespace” extension, because
2464 it extends the normally flat Haskell module namespace into a
2465 more flexible hierarchy of modules.</para>
2467 <para>This extension has very little impact on the language
2468 itself; modules names are <emphasis>always</emphasis> fully
2469 qualified, so you can just think of the fully qualified module
2470 name as <quote>the module name</quote>. In particular, this
2471 means that the full module name must be given after the
2472 <literal>module</literal> keyword at the beginning of the
2473 module; for example, the module <literal>A.B.C</literal> must
2476 <programlisting>module A.B.C</programlisting>
2479 <para>It is a common strategy to use the <literal>as</literal>
2480 keyword to save some typing when using qualified names with
2481 hierarchical modules. For example:</para>
2484 import qualified Control.Monad.ST.Strict as ST
2487 <para>Hierarchical modules have an impact on the way that GHC
2488 searches for files. For a description, see <xref
2489 linkend="finding-hierarchical-modules">.</para>
2491 <para>GHC comes with a large collection of libraries arranged
2492 hierarchically; see the accompanying library documentation.
2493 There is an ongoing project to create and maintain a stable set
2494 of <quote>core</quote> libraries used by several Haskell
2495 compilers, and the libraries that GHC comes with represent the
2496 current status of that project. For more details, see <ulink
2497 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
2498 Libraries</ulink>.</para>
2502 <!-- ====================== PATTERN GUARDS ======================= -->
2504 <sect2 id="pattern-guards">
2505 <title>Pattern guards</title>
2508 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
2509 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.)
2513 Suppose we have an abstract data type of finite maps, with a
2517 lookup :: FiniteMap -> Int -> Maybe Int
2520 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
2521 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
2525 clunky env var1 var2 | ok1 && ok2 = val1 + val2
2526 | otherwise = var1 + var2
2528 m1 = lookup env var1
2529 m2 = lookup env var2
2530 ok1 = maybeToBool m1
2531 ok2 = maybeToBool m2
2532 val1 = expectJust m1
2533 val2 = expectJust m2
2537 The auxiliary functions are
2541 maybeToBool :: Maybe a -> Bool
2542 maybeToBool (Just x) = True
2543 maybeToBool Nothing = False
2545 expectJust :: Maybe a -> a
2546 expectJust (Just x) = x
2547 expectJust Nothing = error "Unexpected Nothing"
2551 What is <function>clunky</function> doing? The guard <literal>ok1 &&
2552 ok2</literal> checks that both lookups succeed, using
2553 <function>maybeToBool</function> to convert the <function>Maybe</function>
2554 types to booleans. The (lazily evaluated) <function>expectJust</function>
2555 calls extract the values from the results of the lookups, and binds the
2556 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
2557 respectively. If either lookup fails, then clunky takes the
2558 <literal>otherwise</literal> case and returns the sum of its arguments.
2562 This is certainly legal Haskell, but it is a tremendously verbose and
2563 un-obvious way to achieve the desired effect. Arguably, a more direct way
2564 to write clunky would be to use case expressions:
2568 clunky env var1 var1 = case lookup env var1 of
2570 Just val1 -> case lookup env var2 of
2572 Just val2 -> val1 + val2
2578 This is a bit shorter, but hardly better. Of course, we can rewrite any set
2579 of pattern-matching, guarded equations as case expressions; that is
2580 precisely what the compiler does when compiling equations! The reason that
2581 Haskell provides guarded equations is because they allow us to write down
2582 the cases we want to consider, one at a time, independently of each other.
2583 This structure is hidden in the case version. Two of the right-hand sides
2584 are really the same (<function>fail</function>), and the whole expression
2585 tends to become more and more indented.
2589 Here is how I would write clunky:
2593 clunky env var1 var1
2594 | Just val1 <- lookup env var1
2595 , Just val2 <- lookup env var2
2597 ...other equations for clunky...
2601 The semantics should be clear enough. The qualifers are matched in order.
2602 For a <literal><-</literal> qualifier, which I call a pattern guard, the
2603 right hand side is evaluated and matched against the pattern on the left.
2604 If the match fails then the whole guard fails and the next equation is
2605 tried. If it succeeds, then the appropriate binding takes place, and the
2606 next qualifier is matched, in the augmented environment. Unlike list
2607 comprehensions, however, the type of the expression to the right of the
2608 <literal><-</literal> is the same as the type of the pattern to its
2609 left. The bindings introduced by pattern guards scope over all the
2610 remaining guard qualifiers, and over the right hand side of the equation.
2614 Just as with list comprehensions, boolean expressions can be freely mixed
2615 with among the pattern guards. For example:
2626 Haskell's current guards therefore emerge as a special case, in which the
2627 qualifier list has just one element, a boolean expression.
2631 <!-- ===================== Recursive do-notation =================== -->
2633 <sect2 id="mdo-notation">
2634 <title>The recursive do-notation
2637 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
2638 "A recursive do for Haskell",
2639 Levent Erkok, John Launchbury",
2640 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
2643 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
2644 that is, the variables bound in a do-expression are visible only in the textually following
2645 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
2646 group. It turns out that several applications can benefit from recursive bindings in
2647 the do-notation, and this extension provides the necessary syntactic support.
2650 Here is a simple (yet contrived) example:
2653 justOnes = mdo xs <- Just (1:xs)
2657 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
2661 The MonadFix library introduces the <literal>MonadFix</literal> class. It's definition is:
2664 class Monad m => MonadFix m where
2665 mfix :: (a -> m a) -> m a
2668 The function <literal>mfix</literal>
2669 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
2670 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
2671 For details, see the above mentioned reference.
2674 The <literal>MonadFix</literal> library automatically declares List, Maybe, IO, and
2675 state monads (both lazy and strict) as instances of the <literal>MonadFix</literal> class.
2678 There are three important points in using the recursive-do notation:
2681 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
2682 than <literal>do</literal>).
2686 If you want to declare an instance of the <literal>MonadFix</literal> class for one of
2687 your own monads, or you need to refer to the class name <literal>MonadFix</literal> in any other way (for instance in
2688 writing a type constraint), then your program should <literal>import Control.Monad.MonadFix</literal>.
2689 Otherwise, you don't need to import any special libraries to use the mdo-notation. That is,
2690 as long as you only use the predefined instances mentioned above, the mdo-notation will
2691 be automatically available. (Note: This differs from the Hugs implementation, where
2692 <literal>MonadFix</literal> should always be imported.)
2696 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
2702 Historical note: The originial implementation of the mdo-notation, and most
2703 of the existing documents, use the names
2704 <literal>MonadRec</literal> for the class, and
2705 <literal>Control.Monad.MonadRec</literal> for the library. These names
2706 are no longer supported.
2710 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
2711 contains up to date information on recursive monadic bindings.
2716 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
2718 <sect2 id="parallel-list-comprehensions">
2719 <title>Parallel List Comprehensions</title>
2720 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
2722 <indexterm><primary>parallel list comprehensions</primary>
2725 <para>Parallel list comprehensions are a natural extension to list
2726 comprehensions. List comprehensions can be thought of as a nice
2727 syntax for writing maps and filters. Parallel comprehensions
2728 extend this to include the zipWith family.</para>
2730 <para>A parallel list comprehension has multiple independent
2731 branches of qualifier lists, each separated by a `|' symbol. For
2732 example, the following zips together two lists:</para>
2735 [ (x, y) | x <- xs | y <- ys ]
2738 <para>The behavior of parallel list comprehensions follows that of
2739 zip, in that the resulting list will have the same length as the
2740 shortest branch.</para>
2742 <para>We can define parallel list comprehensions by translation to
2743 regular comprehensions. Here's the basic idea:</para>
2745 <para>Given a parallel comprehension of the form: </para>
2748 [ e | p1 <- e11, p2 <- e12, ...
2749 | q1 <- e21, q2 <- e22, ...
2754 <para>This will be translated to: </para>
2757 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
2758 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
2763 <para>where `zipN' is the appropriate zip for the given number of
2768 <sect2 id="rebindable-syntax">
2769 <title>Rebindable syntax</title>
2772 <para>GHC allows most kinds of built-in syntax to be rebound by
2773 the user, to facilitate replacing the <literal>Prelude</literal>
2774 with a home-grown version, for example.</para>
2776 <para>You may want to define your own numeric class
2777 hierarchy. It completely defeats that purpose if the
2778 literal "1" means "<literal>Prelude.fromInteger
2779 1</literal>", which is what the Haskell Report specifies.
2780 So the <option>-fno-implicit-prelude</option> flag causes
2781 the following pieces of built-in syntax to refer to
2782 <emphasis>whatever is in scope</emphasis>, not the Prelude
2787 <para>Integer and fractional literals mean
2788 "<literal>fromInteger 1</literal>" and
2789 "<literal>fromRational 3.2</literal>", not the
2790 Prelude-qualified versions; both in expressions and in
2792 <para>However, the standard Prelude <literal>Eq</literal> class
2793 is still used for the equality test necessary for literal patterns.</para>
2797 <para>Negation (e.g. "<literal>- (f x)</literal>")
2798 means "<literal>negate (f x)</literal>" (not
2799 <literal>Prelude.negate</literal>).</para>
2803 <para>In an n+k pattern, the standard Prelude
2804 <literal>Ord</literal> class is still used for comparison,
2805 but the necessary subtraction uses whatever
2806 "<literal>(-)</literal>" is in scope (not
2807 "<literal>Prelude.(-)</literal>").</para>
2811 <para>"Do" notation is translated using whatever
2812 functions <literal>(>>=)</literal>,
2813 <literal>(>>)</literal>, <literal>fail</literal>, and
2814 <literal>return</literal>, are in scope (not the Prelude
2815 versions). List comprehensions, and parallel array
2816 comprehensions, are unaffected. </para></listitem>
2819 <para>Be warned: this is an experimental facility, with fewer checks than
2820 usual. In particular, it is essential that the functions GHC finds in scope
2821 must have the appropriate types, namely:
2823 fromInteger :: forall a. (...) => Integer -> a
2824 fromRational :: forall a. (...) => Rational -> a
2825 negate :: forall a. (...) => a -> a
2826 (-) :: forall a. (...) => a -> a -> a
2827 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
2828 (>>) :: forall m a. (...) => m a -> m b -> m b
2829 return :: forall m a. (...) => a -> m a
2830 fail :: forall m a. (...) => String -> m a
2832 (The (...) part can be any context including the empty context; that part
2834 If the functions don't have the right type, very peculiar things may
2835 happen. Use <literal>-dcore-lint</literal> to
2836 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
2841 <!-- =============================== PRAGMAS =========================== -->
2843 <sect1 id="pragmas">
2844 <title>Pragmas</title>
2846 <indexterm><primary>pragma</primary></indexterm>
2848 <para>GHC supports several pragmas, or instructions to the
2849 compiler placed in the source code. Pragmas don't normally affect
2850 the meaning of the program, but they might affect the efficiency
2851 of the generated code.</para>
2853 <para>Pragmas all take the form
2855 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2857 where <replaceable>word</replaceable> indicates the type of
2858 pragma, and is followed optionally by information specific to that
2859 type of pragma. Case is ignored in
2860 <replaceable>word</replaceable>. The various values for
2861 <replaceable>word</replaceable> that GHC understands are described
2862 in the following sections; any pragma encountered with an
2863 unrecognised <replaceable>word</replaceable> is (silently)
2866 <sect2 id="inline-pragma">
2867 <title>INLINE pragma
2869 <indexterm><primary>INLINE pragma</primary></indexterm>
2870 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2873 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2874 functions/values that are “small enough,” thus avoiding the call
2875 overhead and possibly exposing other more-wonderful optimisations.
2879 You will probably see these unfoldings (in Core syntax) in your
2884 Normally, if GHC decides a function is “too expensive” to inline, it
2885 will not do so, nor will it export that unfolding for other modules to
2890 The sledgehammer you can bring to bear is the
2891 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2894 key_function :: Int -> String -> (Bool, Double)
2896 #ifdef __GLASGOW_HASKELL__
2897 {-# INLINE key_function #-}
2901 (You don't need to do the C pre-processor carry-on unless you're going
2902 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2906 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2907 “cost” to be very low. The normal unfolding machinery will then be
2908 very keen to inline it.
2912 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2913 signature could be put.
2917 <literal>INLINE</literal> pragmas are a particularly good idea for the
2918 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2919 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2922 #ifdef __GLASGOW_HASKELL__
2923 {-# INLINE thenUs #-}
2924 {-# INLINE returnUs #-}
2932 <sect2 id="noinline-pragma">
2933 <title>NOINLINE pragma
2936 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2937 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2938 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2939 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2942 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2943 it stops the named function from being inlined by the compiler. You
2944 shouldn't ever need to do this, unless you're very cautious about code
2948 <para><literal>NOTINLINE</literal> is a synonym for
2949 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2950 by Haskell 98 as the standard way to disable inlining, so it should be
2951 used if you want your code to be portable).</para>
2955 <sect2 id="specialize-pragma">
2956 <title>SPECIALIZE pragma</title>
2958 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2959 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2960 <indexterm><primary>overloading, death to</primary></indexterm>
2962 <para>(UK spelling also accepted.) For key overloaded
2963 functions, you can create extra versions (NB: more code space)
2964 specialised to particular types. Thus, if you have an
2965 overloaded function:</para>
2968 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2971 <para>If it is heavily used on lists with
2972 <literal>Widget</literal> keys, you could specialise it as
2976 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2979 <para>To get very fancy, you can also specify a named function
2980 to use for the specialised value, as in:</para>
2983 {-# RULES hammeredLookup = blah #-}
2986 <para>where <literal>blah</literal> is an implementation of
2987 <literal>hammerdLookup</literal> written specialy for
2988 <literal>Widget</literal> lookups. It's <emphasis>Your
2989 Responsibility</emphasis> to make sure that
2990 <function>blah</function> really behaves as a specialised
2991 version of <function>hammeredLookup</function>!!!</para>
2993 <para>Note we use the <literal>RULE</literal> pragma here to
2994 indicate that <literal>hammeredLookup</literal> applied at a
2995 certain type should be replaced by <literal>blah</literal>. See
2996 <xref linkend="rules"> for more information on
2997 <literal>RULES</literal>.</para>
2999 <para>An example in which using <literal>RULES</literal> for
3000 specialisation will Win Big:
3003 toDouble :: Real a => a -> Double
3004 toDouble = fromRational . toRational
3006 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
3007 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3010 The <function>i2d</function> function is virtually one machine
3011 instruction; the default conversion—via an intermediate
3012 <literal>Rational</literal>—is obscenely expensive by
3015 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3016 be put anywhere its type signature could be put.</para>
3020 <sect2 id="specialize-instance-pragma">
3021 <title>SPECIALIZE instance pragma
3025 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3026 <indexterm><primary>overloading, death to</primary></indexterm>
3027 Same idea, except for instance declarations. For example:
3030 instance (Eq a) => Eq (Foo a) where {
3031 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3035 The pragma must occur inside the <literal>where</literal> part
3036 of the instance declaration.
3039 Compatible with HBC, by the way, except perhaps in the placement
3045 <sect2 id="line-pragma">
3050 <indexterm><primary>LINE pragma</primary></indexterm>
3051 <indexterm><primary>pragma, LINE</primary></indexterm>
3055 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
3056 automatically generated Haskell code. It lets you specify the line
3057 number and filename of the original code; for example
3063 {-# LINE 42 "Foo.vhs" #-}
3069 if you'd generated the current file from something called <filename>Foo.vhs</filename>
3070 and this line corresponds to line 42 in the original. GHC will adjust
3071 its error messages to refer to the line/file named in the <literal>LINE</literal>
3078 <title>RULES pragma</title>
3081 The RULES pragma lets you specify rewrite rules. It is described in
3082 <xref LinkEnd="rewrite-rules">.
3087 <sect2 id="deprecated-pragma">
3088 <title>DEPRECATED pragma</title>
3091 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
3092 There are two forms.
3096 You can deprecate an entire module thus:</para>
3098 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3102 When you compile any module that import <literal>Wibble</literal>, GHC will print
3103 the specified message.</para>
3108 You can deprecate a function, class, or type, with the following top-level declaration:
3111 {-# DEPRECATED f, C, T "Don't use these" #-}
3114 When you compile any module that imports and uses any of the specifed entities,
3115 GHC will print the specified message.
3119 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
3125 <!-- ======================= REWRITE RULES ======================== -->
3127 <sect1 id="rewrite-rules">
3128 <title>Rewrite rules
3130 <indexterm><primary>RULES pagma</primary></indexterm>
3131 <indexterm><primary>pragma, RULES</primary></indexterm>
3132 <indexterm><primary>rewrite rules</primary></indexterm></title>
3135 The programmer can specify rewrite rules as part of the source program
3136 (in a pragma). GHC applies these rewrite rules wherever it can.
3144 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3151 <title>Syntax</title>
3154 From a syntactic point of view:
3160 Each rule has a name, enclosed in double quotes. The name itself has
3161 no significance at all. It is only used when reporting how many times the rule fired.
3167 There may be zero or more rules in a <literal>RULES</literal> pragma.
3173 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3174 is set, so you must lay out your rules starting in the same column as the
3175 enclosing definitions.
3181 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3182 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3183 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3184 by spaces, just like in a type <literal>forall</literal>.
3190 A pattern variable may optionally have a type signature.
3191 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3192 For example, here is the <literal>foldr/build</literal> rule:
3195 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3196 foldr k z (build g) = g k z
3199 Since <function>g</function> has a polymorphic type, it must have a type signature.
3206 The left hand side of a rule must consist of a top-level variable applied
3207 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3210 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3211 "wrong2" forall f. f True = True
3214 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3221 A rule does not need to be in the same module as (any of) the
3222 variables it mentions, though of course they need to be in scope.
3228 Rules are automatically exported from a module, just as instance declarations are.
3239 <title>Semantics</title>
3242 From a semantic point of view:
3248 Rules are only applied if you use the <option>-O</option> flag.
3254 Rules are regarded as left-to-right rewrite rules.
3255 When GHC finds an expression that is a substitution instance of the LHS
3256 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3257 By "a substitution instance" we mean that the LHS can be made equal to the
3258 expression by substituting for the pattern variables.
3265 The LHS and RHS of a rule are typechecked, and must have the
3273 GHC makes absolutely no attempt to verify that the LHS and RHS
3274 of a rule have the same meaning. That is undecideable in general, and
3275 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3282 GHC makes no attempt to make sure that the rules are confluent or
3283 terminating. For example:
3286 "loop" forall x,y. f x y = f y x
3289 This rule will cause the compiler to go into an infinite loop.
3296 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3302 GHC currently uses a very simple, syntactic, matching algorithm
3303 for matching a rule LHS with an expression. It seeks a substitution
3304 which makes the LHS and expression syntactically equal modulo alpha
3305 conversion. The pattern (rule), but not the expression, is eta-expanded if
3306 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3307 But not beta conversion (that's called higher-order matching).
3311 Matching is carried out on GHC's intermediate language, which includes
3312 type abstractions and applications. So a rule only matches if the
3313 types match too. See <xref LinkEnd="rule-spec"> below.
3319 GHC keeps trying to apply the rules as it optimises the program.
3320 For example, consider:
3329 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3330 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3331 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3332 not be substituted, and the rule would not fire.
3339 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3340 that appears on the LHS of a rule</emphasis>, because once you have substituted
3341 for something you can't match against it (given the simple minded
3342 matching). So if you write the rule
3345 "map/map" forall f,g. map f . map g = map (f.g)
3348 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3349 It will only match something written with explicit use of ".".
3350 Well, not quite. It <emphasis>will</emphasis> match the expression
3356 where <function>wibble</function> is defined:
3359 wibble f g = map f . map g
3362 because <function>wibble</function> will be inlined (it's small).
3364 Later on in compilation, GHC starts inlining even things on the
3365 LHS of rules, but still leaves the rules enabled. This inlining
3366 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3373 All rules are implicitly exported from the module, and are therefore
3374 in force in any module that imports the module that defined the rule, directly
3375 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3376 in force when compiling A.) The situation is very similar to that for instance
3388 <title>List fusion</title>
3391 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3392 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3393 intermediate list should be eliminated entirely.
3397 The following are good producers:
3409 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3415 Explicit lists (e.g. <literal>[True, False]</literal>)
3421 The cons constructor (e.g <literal>3:4:[]</literal>)
3427 <function>++</function>
3433 <function>map</function>
3439 <function>filter</function>
3445 <function>iterate</function>, <function>repeat</function>
3451 <function>zip</function>, <function>zipWith</function>
3460 The following are good consumers:
3472 <function>array</function> (on its second argument)
3478 <function>length</function>
3484 <function>++</function> (on its first argument)
3490 <function>foldr</function>
3496 <function>map</function>
3502 <function>filter</function>
3508 <function>concat</function>
3514 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3520 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3521 will fuse with one but not the other)
3527 <function>partition</function>
3533 <function>head</function>
3539 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3545 <function>sequence_</function>
3551 <function>msum</function>
3557 <function>sortBy</function>
3566 So, for example, the following should generate no intermediate lists:
3569 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3575 This list could readily be extended; if there are Prelude functions that you use
3576 a lot which are not included, please tell us.
3580 If you want to write your own good consumers or producers, look at the
3581 Prelude definitions of the above functions to see how to do so.
3586 <sect2 id="rule-spec">
3587 <title>Specialisation
3591 Rewrite rules can be used to get the same effect as a feature
3592 present in earlier version of GHC:
3595 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3598 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3599 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3600 specialising the original definition of <function>fromIntegral</function> the programmer is
3601 promising that it is safe to use <function>int8ToInt16</function> instead.
3605 This feature is no longer in GHC. But rewrite rules let you do the
3610 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3614 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3615 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3616 GHC adds the type and dictionary applications to get the typed rule
3619 forall (d1::Integral Int8) (d2::Num Int16) .
3620 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3624 this rule does not need to be in the same file as fromIntegral,
3625 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3626 have an original definition available to specialise).
3632 <title>Controlling what's going on</title>
3640 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3646 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3647 If you add <option>-dppr-debug</option> you get a more detailed listing.
3653 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3656 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3657 {-# INLINE build #-}
3661 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3662 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3663 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3664 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3671 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3672 see how to write rules that will do fusion and yet give an efficient
3673 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3685 <sect1 id="generic-classes">
3686 <title>Generic classes</title>
3688 <para>(Note: support for generic classes is currently broken in
3692 The ideas behind this extension are described in detail in "Derivable type classes",
3693 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3694 An example will give the idea:
3702 fromBin :: [Int] -> (a, [Int])
3704 toBin {| Unit |} Unit = []
3705 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3706 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3707 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3709 fromBin {| Unit |} bs = (Unit, bs)
3710 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3711 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3712 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3713 (y,bs'') = fromBin bs'
3716 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3717 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3718 which are defined thus in the library module <literal>Generics</literal>:
3722 data a :+: b = Inl a | Inr b
3723 data a :*: b = a :*: b
3726 Now you can make a data type into an instance of Bin like this:
3728 instance (Bin a, Bin b) => Bin (a,b)
3729 instance Bin a => Bin [a]
3731 That is, just leave off the "where" clasuse. Of course, you can put in the
3732 where clause and over-ride whichever methods you please.
3736 <title> Using generics </title>
3737 <para>To use generics you need to</para>
3740 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3741 <option>-fgenerics</option> (to generate extra per-data-type code),
3742 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3746 <para>Import the module <literal>Generics</literal> from the
3747 <literal>lang</literal> package. This import brings into
3748 scope the data types <literal>Unit</literal>,
3749 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3750 don't need this import if you don't mention these types
3751 explicitly; for example, if you are simply giving instance
3752 declarations.)</para>
3757 <sect2> <title> Changes wrt the paper </title>
3759 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3760 can be written infix (indeed, you can now use
3761 any operator starting in a colon as an infix type constructor). Also note that
3762 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3763 Finally, note that the syntax of the type patterns in the class declaration
3764 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3765 alone would ambiguous when they appear on right hand sides (an extension we
3766 anticipate wanting).
3770 <sect2> <title>Terminology and restrictions</title>
3772 Terminology. A "generic default method" in a class declaration
3773 is one that is defined using type patterns as above.
3774 A "polymorphic default method" is a default method defined as in Haskell 98.
3775 A "generic class declaration" is a class declaration with at least one
3776 generic default method.
3784 Alas, we do not yet implement the stuff about constructor names and
3791 A generic class can have only one parameter; you can't have a generic
3792 multi-parameter class.
3798 A default method must be defined entirely using type patterns, or entirely
3799 without. So this is illegal:
3802 op :: a -> (a, Bool)
3803 op {| Unit |} Unit = (Unit, True)
3806 However it is perfectly OK for some methods of a generic class to have
3807 generic default methods and others to have polymorphic default methods.
3813 The type variable(s) in the type pattern for a generic method declaration
3814 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:
3818 op {| p :*: q |} (x :*: y) = op (x :: p)
3826 The type patterns in a generic default method must take one of the forms:
3832 where "a" and "b" are type variables. Furthermore, all the type patterns for
3833 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3834 must use the same type variables. So this is illegal:
3838 op {| a :+: b |} (Inl x) = True
3839 op {| p :+: q |} (Inr y) = False
3841 The type patterns must be identical, even in equations for different methods of the class.
3842 So this too is illegal:
3846 op1 {| a :*: b |} (x :*: y) = True
3849 op2 {| p :*: q |} (x :*: y) = False
3851 (The reason for this restriction is that we gather all the equations for a particular type consructor
3852 into a single generic instance declaration.)
3858 A generic method declaration must give a case for each of the three type constructors.
3864 The type for a generic method can be built only from:
3866 <listitem> <para> Function arrows </para> </listitem>
3867 <listitem> <para> Type variables </para> </listitem>
3868 <listitem> <para> Tuples </para> </listitem>
3869 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3871 Here are some example type signatures for generic methods:
3874 op2 :: Bool -> (a,Bool)
3875 op3 :: [Int] -> a -> a
3878 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3882 This restriction is an implementation restriction: we just havn't got around to
3883 implementing the necessary bidirectional maps over arbitrary type constructors.
3884 It would be relatively easy to add specific type constructors, such as Maybe and list,
3885 to the ones that are allowed.</para>
3890 In an instance declaration for a generic class, the idea is that the compiler
3891 will fill in the methods for you, based on the generic templates. However it can only
3896 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3901 No constructor of the instance type has unboxed fields.
3905 (Of course, these things can only arise if you are already using GHC extensions.)
3906 However, you can still give an instance declarations for types which break these rules,
3907 provided you give explicit code to override any generic default methods.
3915 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3916 what the compiler does with generic declarations.
3921 <sect2> <title> Another example </title>
3923 Just to finish with, here's another example I rather like:
3927 nCons {| Unit |} _ = 1
3928 nCons {| a :*: b |} _ = 1
3929 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3932 tag {| Unit |} _ = 1
3933 tag {| a :*: b |} _ = 1
3934 tag {| a :+: b |} (Inl x) = tag x
3935 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3941 <sect1 id="newtype-deriving">
3942 <title>Generalised derived instances for newtypes</title>
3945 When you define an abstract type using <literal>newtype</literal>, you may want
3946 the new type to inherit some instances from its representation. In
3947 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3948 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3949 other classes you have to write an explicit instance declaration. For
3950 example, if you define
3953 newtype Dollars = Dollars Int
3956 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3957 explicitly define an instance of <literal>Num</literal>:
3960 instance Num Dollars where
3961 Dollars a + Dollars b = Dollars (a+b)
3964 All the instance does is apply and remove the <literal>newtype</literal>
3965 constructor. It is particularly galling that, since the constructor
3966 doesn't appear at run-time, this instance declaration defines a
3967 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3968 dictionary, only slower!
3971 <sect2> <title> Generalising the deriving clause </title>
3973 GHC now permits such instances to be derived instead, so one can write
3975 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3978 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3979 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3980 derives an instance declaration of the form
3983 instance Num Int => Num Dollars
3986 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3990 We can also derive instances of constructor classes in a similar
3991 way. For example, suppose we have implemented state and failure monad
3992 transformers, such that
3995 instance Monad m => Monad (State s m)
3996 instance Monad m => Monad (Failure m)
3998 In Haskell 98, we can define a parsing monad by
4000 type Parser tok m a = State [tok] (Failure m) a
4003 which is automatically a monad thanks to the instance declarations
4004 above. With the extension, we can make the parser type abstract,
4005 without needing to write an instance of class <literal>Monad</literal>, via
4008 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
4011 In this case the derived instance declaration is of the form
4013 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
4016 Notice that, since <literal>Monad</literal> is a constructor class, the
4017 instance is a <emphasis>partial application</emphasis> of the new type, not the
4018 entire left hand side. We can imagine that the type declaration is
4019 ``eta-converted'' to generate the context of the instance
4024 We can even derive instances of multi-parameter classes, provided the
4025 newtype is the last class parameter. In this case, a ``partial
4026 application'' of the class appears in the <literal>deriving</literal>
4027 clause. For example, given the class
4030 class StateMonad s m | m -> s where ...
4031 instance Monad m => StateMonad s (State s m) where ...
4033 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
4035 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
4036 deriving (Monad, StateMonad [tok])
4039 The derived instance is obtained by completing the application of the
4040 class to the new type:
4043 instance StateMonad [tok] (State [tok] (Failure m)) =>
4044 StateMonad [tok] (Parser tok m)
4049 As a result of this extension, all derived instances in newtype
4050 declarations are treated uniformly (and implemented just by reusing
4051 the dictionary for the representation type), <emphasis>except</emphasis>
4052 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
4053 the newtype and its representation.
4057 <sect2> <title> A more precise specification </title>
4059 Derived instance declarations are constructed as follows. Consider the
4060 declaration (after expansion of any type synonyms)
4063 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
4066 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
4068 <literal>vk+1...vn</literal> are type variables which do not occur in any of
4069 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
4070 classes of the form <literal>C t1'...tj'</literal>. The derived instance
4071 declarations are, for each <literal>ci</literal>,
4074 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
4076 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
4077 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
4081 As an example which does <emphasis>not</emphasis> work, consider
4083 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
4085 Here we cannot derive the instance
4087 instance Monad (State s m) => Monad (NonMonad m)
4090 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
4091 and so cannot be "eta-converted" away. It is a good thing that this
4092 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
4093 not, in fact, a monad --- for the same reason. Try defining
4094 <literal>>>=</literal> with the correct type: you won't be able to.
4098 Notice also that the <emphasis>order</emphasis> of class parameters becomes
4099 important, since we can only derive instances for the last one. If the
4100 <literal>StateMonad</literal> class above were instead defined as
4103 class StateMonad m s | m -> s where ...
4106 then we would not have been able to derive an instance for the
4107 <literal>Parser</literal> type above. We hypothesise that multi-parameter
4108 classes usually have one "main" parameter for which deriving new
4109 instances is most interesting.
4118 ;;; Local Variables: ***
4120 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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