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 Executive summary of our extensions:
25 <term>Unboxed types and primitive operations:</Term>
27 <para>You can get right down to the raw machine types and
28 operations; included in this are “primitive
29 arrays” (direct access to Big Wads of Bytes). Please
30 see <XRef LinkEnd="glasgow-unboxed"> and following.</para>
35 <term>Type system extensions:</term>
37 <para> GHC supports a large number of extensions to Haskell's
38 type system. Specifically:</para>
42 <term>Multi-parameter type classes:</term>
44 <para><xref LinkEnd="multi-param-type-classes"></para>
49 <term>Functional dependencies:</term>
51 <para><xref LinkEnd="functional-dependencies"></para>
56 <term>Implicit parameters:</term>
58 <para><xref LinkEnd="implicit-parameters"></para>
63 <term>Local universal quantification:</term>
65 <para><xref LinkEnd="universal-quantification"></para>
70 <term>Extistentially quantification in data types:</term>
72 <para><xref LinkEnd="existential-quantification"></para>
77 <term>Scoped type variables:</term>
79 <para>Scoped type variables enable the programmer to
80 supply type signatures for some nested declarations,
81 where this would not be legal in Haskell 98. Details in
82 <xref LinkEnd="scoped-type-variables">.</para>
90 <term>Pattern guards</term>
92 <para>Instead of being a boolean expression, a guard is a list
93 of qualifiers, exactly as in a list comprehension. See <xref
94 LinkEnd="pattern-guards">.</para>
99 <term>Foreign calling:</term>
101 <para>Just what it sounds like. We provide
102 <emphasis>lots</emphasis> of rope that you can dangle around
103 your neck. Please see <xref LinkEnd="ffi">.</para>
110 <para>Pragmas are special instructions to the compiler placed
111 in the source file. The pragmas GHC supports are described in
112 <xref LinkEnd="pragmas">.</para>
117 <term>Rewrite rules:</term>
119 <para>The programmer can specify rewrite rules as part of the
120 source program (in a pragma). GHC applies these rewrite rules
121 wherever it can. Details in <xref
122 LinkEnd="rewrite-rules">.</para>
127 <term>Generic classes:</term>
129 <para>Generic class declarations allow you to define a class
130 whose methods say how to work over an arbitrary data type.
131 Then it's really easy to make any new type into an instance of
132 the class. This generalises the rather ad-hoc "deriving"
133 feature of Haskell 98. Details in <xref
134 LinkEnd="generic-classes">.</para>
140 Before you get too carried away working at the lowest level (e.g.,
141 sloshing <literal>MutableByteArray#</literal>s around your
142 program), you may wish to check if there are libraries that provide a
143 “Haskellised veneer” over the features you want. See
144 <xref linkend="book-hslibs">.
147 <sect1 id="options-language">
148 <title>Language options</title>
150 <indexterm><primary>language</primary><secondary>option</secondary>
152 <indexterm><primary>options</primary><secondary>language</secondary>
154 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
157 <para> These flags control what variation of the language are
158 permitted. Leaving out all of them gives you standard Haskell
164 <term><option>-fglasgow-exts</option>:</term>
165 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
167 <para>This simultaneously enables all of the extensions to
168 Haskell 98 described in <xref
169 linkend="ghc-language-features">, except where otherwise
175 <term><option>-fno-monomorphism-restriction</option>:</term>
176 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
178 <para> Switch off the Haskell 98 monomorphism restriction.
179 Independent of the <option>-fglasgow-exts</option>
185 <term><option>-fallow-overlapping-instances</option></term>
186 <term><option>-fallow-undecidable-instances</option></term>
187 <term><option>-fcontext-stack</option></term>
188 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
189 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
190 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
192 <para> See <xref LinkEnd="instance-decls">. Only relevant
193 if you also use <option>-fglasgow-exts</option>.</para>
198 <term><option>-finline-phase</option></term>
199 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
201 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
202 you also use <option>-fglasgow-exts</option>.</para>
207 <term><option>-fgenerics</option></term>
208 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
210 <para>See <xref LinkEnd="generic-classes">. Independent of
211 <option>-fglasgow-exts</option>.</para>
216 <term><option>-fno-implicit-prelude</option></term>
218 <para><indexterm><primary>-fno-implicit-prelude
219 option</primary></indexterm> GHC normally imports
220 <filename>Prelude.hi</filename> files for you. If you'd
221 rather it didn't, then give it a
222 <option>-fno-implicit-prelude</option> option. The idea
223 is that you can then import a Prelude of your own. (But
224 don't call it <literal>Prelude</literal>; the Haskell
225 module namespace is flat, and you must not conflict with
226 any Prelude module.)</para>
228 <para>Even though you have not imported the Prelude, all
229 the built-in syntax still refers to the built-in Haskell
230 Prelude types and values, as specified by the Haskell
231 Report. For example, the type <literal>[Int]</literal>
232 still means <literal>Prelude.[] Int</literal>; tuples
233 continue to refer to the standard Prelude tuples; the
234 translation for list comprehensions continues to use
235 <literal>Prelude.map</literal> etc.</para>
237 <para> With one group of exceptions! You may want to
238 define your own numeric class hierarchy. It completely
239 defeats that purpose if the literal "1" means
240 "<literal>Prelude.fromInteger 1</literal>", which is what
241 the Haskell Report specifies. So the
242 <option>-fno-implicit-prelude</option> flag causes the
243 following pieces of built-in syntax to refer to whatever
244 is in scope, not the Prelude versions:</para>
248 <para>Integer and fractional literals mean
249 "<literal>fromInteger 1</literal>" and
250 "<literal>fromRational 3.2</literal>", not the
251 Prelude-qualified versions; both in expressions and in
256 <para>Negation (e.g. "<literal>- (f x)</literal>")
257 means "<literal>negate (f x)</literal>" (not
258 <literal>Prelude.negate</literal>).</para>
262 <para>In an n+k pattern, the standard Prelude
263 <literal>Ord</literal> class is used for comparison,
264 but the necessary subtraction uses whatever
265 "<literal>(-)</literal>" is in scope (not
266 "<literal>Prelude.(-)</literal>").</para>
276 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
279 <sect1 id="glasgow-ST-monad">
280 <title>Primitive state-transformer monad</title>
283 <indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
284 <indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
288 This monad underlies our implementation of arrays, mutable and
289 immutable, and our implementation of I/O, including “C calls”.
293 The <literal>ST</literal> library, which provides access to the
294 <function>ST</function> monad, is described in <xref
300 <sect1 id="glasgow-prim-arrays">
301 <title>Primitive arrays, mutable and otherwise
305 <indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
306 <indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
310 GHC knows about quite a few flavours of Large Swathes of Bytes.
314 First, GHC distinguishes between primitive arrays of (boxed) Haskell
315 objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
316 <literal>ByteArray#</literal>).
320 Second, it distinguishes between…
324 <term>Immutable:</term>
327 Arrays that do not change (as with “standard” Haskell arrays); you
328 can only read from them. Obviously, they do not need the care and
329 attention of the state-transformer monad.
334 <term>Mutable:</term>
337 Arrays that may be changed or “mutated.” All the operations on them
338 live within the state-transformer monad and the updates happen
339 <emphasis>in-place</emphasis>.
344 <term>“Static” (in C land):</term>
347 A C routine may pass an <literal>Addr#</literal> pointer back into Haskell land. There
348 are then primitive operations with which you may merrily grab values
349 over in C land, by indexing off the “static” pointer.
354 <term>“Stable” pointers:</term>
357 If, for some reason, you wish to hand a Haskell pointer (i.e.,
358 <emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
359 pointer “stable,” so that the garbage collector won't forget that it
360 exists. That is, GHC provides a safe way to pass Haskell pointers to
365 Please see <xref LinkEnd="sec-stable-pointers"> for more details.
370 <term>“Foreign objects”:</term>
373 A “foreign object” is a safe way to pass an external object (a
374 C-allocated pointer, say) to Haskell and have Haskell do the Right
375 Thing when it no longer references the object. So, for example, C
376 could pass a large bitmap over to Haskell and say “please free this
377 memory when you're done with it.”
381 Please see <xref LinkEnd="sec-ForeignObj"> for more details.
389 The libraries documentatation gives more details on all these
390 “primitive array” types and the operations on them.
396 <sect1 id="pattern-guards">
397 <title>Pattern guards</title>
400 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
401 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.)
405 Suppose we have an abstract data type of finite maps, with a
409 lookup :: FiniteMap -> Int -> Maybe Int
412 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
413 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
417 clunky env var1 var2 | ok1 && ok2 = val1 + val2
418 | otherwise = var1 + var2
429 The auxiliary functions are
433 maybeToBool :: Maybe a -> Bool
434 maybeToBool (Just x) = True
435 maybeToBool Nothing = False
437 expectJust :: Maybe a -> a
438 expectJust (Just x) = x
439 expectJust Nothing = error "Unexpected Nothing"
443 What is <function>clunky</function> doing? The guard <literal>ok1 &&
444 ok2</literal> checks that both lookups succeed, using
445 <function>maybeToBool</function> to convert the <function>Maybe</function>
446 types to booleans. The (lazily evaluated) <function>expectJust</function>
447 calls extract the values from the results of the lookups, and binds the
448 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
449 respectively. If either lookup fails, then clunky takes the
450 <literal>otherwise</literal> case and returns the sum of its arguments.
454 This is certainly legal Haskell, but it is a tremendously verbose and
455 un-obvious way to achieve the desired effect. Arguably, a more direct way
456 to write clunky would be to use case expressions:
460 clunky env var1 var1 = case lookup env var1 of
462 Just val1 -> case lookup env var2 of
464 Just val2 -> val1 + val2
470 This is a bit shorter, but hardly better. Of course, we can rewrite any set
471 of pattern-matching, guarded equations as case expressions; that is
472 precisely what the compiler does when compiling equations! The reason that
473 Haskell provides guarded equations is because they allow us to write down
474 the cases we want to consider, one at a time, independently of each other.
475 This structure is hidden in the case version. Two of the right-hand sides
476 are really the same (<function>fail</function>), and the whole expression
477 tends to become more and more indented.
481 Here is how I would write clunky:
486 | Just val1 <- lookup env var1
487 , Just val2 <- lookup env var2
489 ...other equations for clunky...
493 The semantics should be clear enough. The qualifers are matched in order.
494 For a <literal><-</literal> qualifier, which I call a pattern guard, the
495 right hand side is evaluated and matched against the pattern on the left.
496 If the match fails then the whole guard fails and the next equation is
497 tried. If it succeeds, then the appropriate binding takes place, and the
498 next qualifier is matched, in the augmented environment. Unlike list
499 comprehensions, however, the type of the expression to the right of the
500 <literal><-</literal> is the same as the type of the pattern to its
501 left. The bindings introduced by pattern guards scope over all the
502 remaining guard qualifiers, and over the right hand side of the equation.
506 Just as with list comprehensions, boolean expressions can be freely mixed
507 with among the pattern guards. For example:
518 Haskell's current guards therefore emerge as a special case, in which the
519 qualifier list has just one element, a boolean expression.
524 <title>The foreign interface</title>
526 <para>The foreign interface consists of the following components:</para>
530 <para>The Foreign Function Interface language specification
531 (included in this manual, in <xref linkend="ffi">).</para>
535 <para>The <literal>Foreign</literal> module (see <xref
536 linkend="sec-Foreign">) collects together several interfaces
537 which are useful in specifying foreign language
538 interfaces, including the following:</para>
542 <para>The <literal>ForeignObj</literal> module (see <xref
543 linkend="sec-ForeignObj">), for managing pointers from
544 Haskell into the outside world.</para>
548 <para>The <literal>StablePtr</literal> module (see <xref
549 linkend="sec-stable-pointers">), for managing pointers
550 into Haskell from the outside world.</para>
554 <para>The <literal>CTypes</literal> module (see <xref
555 linkend="sec-CTypes">) gives Haskell equivalents for the
556 standard C datatypes, for use in making Haskell bindings
557 to existing C libraries.</para>
561 <para>The <literal>CTypesISO</literal> module (see <xref
562 linkend="sec-CTypesISO">) gives Haskell equivalents for C
563 types defined by the ISO C standard.</para>
567 <para>The <literal>Storable</literal> library, for
568 primitive marshalling of data types between Haskell and
569 the foreign language.</para>
576 <para>The following sections also give some hints and tips on the use
577 of the foreign function interface in GHC.</para>
579 <sect2 id="glasgow-foreign-headers">
580 <title>Using function headers
584 <indexterm><primary>C calls, function headers</primary></indexterm>
588 When generating C (using the <option>-fvia-C</option> directive), one can assist the
589 C compiler in detecting type errors by using the <Command>-#include</Command> directive
590 to provide <filename>.h</filename> files containing function headers.
602 void initialiseEFS (HsInt size);
603 HsInt terminateEFS (void);
604 HsForeignObj emptyEFS(void);
605 HsForeignObj updateEFS (HsForeignObj a, HsInt i, HsInt x);
606 HsInt lookupEFS (HsForeignObj a, HsInt i);
610 <para>The types <literal>HsInt</literal>,
611 <literal>HsForeignObj</literal> etc. are described in <xref
612 linkend="sec-mapping-table">.</para>
614 <para>Note that this approach is only
615 <emphasis>essential</emphasis> for returning
616 <literal>float</literal>s (or if <literal>sizeof(int) !=
617 sizeof(int *)</literal> on your architecture) but is a Good
618 Thing for anyone who cares about writing solid code. You're
619 crazy not to do it.</para>
625 <sect1 id="multi-param-type-classes">
626 <title>Multi-parameter type classes
630 This section documents GHC's implementation of multi-parameter type
631 classes. There's lots of background in the paper <ULink
632 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
633 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
638 I'd like to thank people who reported shorcomings in the GHC 3.02
639 implementation. Our default decisions were all conservative ones, and
640 the experience of these heroic pioneers has given useful concrete
641 examples to support several generalisations. (These appear below as
642 design choices not implemented in 3.02.)
646 I've discussed these notes with Mark Jones, and I believe that Hugs
647 will migrate towards the same design choices as I outline here.
648 Thanks to him, and to many others who have offered very useful
656 There are the following restrictions on the form of a qualified
663 forall tv1..tvn (c1, ...,cn) => type
669 (Here, I write the "foralls" explicitly, although the Haskell source
670 language omits them; in Haskell 1.4, all the free type variables of an
671 explicit source-language type signature are universally quantified,
672 except for the class type variables in a class declaration. However,
673 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
682 <emphasis>Each universally quantified type variable
683 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
685 The reason for this is that a value with a type that does not obey
686 this restriction could not be used without introducing
687 ambiguity. Here, for example, is an illegal type:
691 forall a. Eq a => Int
695 When a value with this type was used, the constraint <literal>Eq tv</literal>
696 would be introduced where <literal>tv</literal> is a fresh type variable, and
697 (in the dictionary-translation implementation) the value would be
698 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
699 can never know which instance of <literal>Eq</literal> to use because we never
700 get any more information about <literal>tv</literal>.
707 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
708 universally quantified type variables <literal>tvi</literal></emphasis>.
710 For example, this type is OK because <literal>C a b</literal> mentions the
711 universally quantified type variable <literal>b</literal>:
715 forall a. C a b => burble
719 The next type is illegal because the constraint <literal>Eq b</literal> does not
720 mention <literal>a</literal>:
724 forall a. Eq b => burble
728 The reason for this restriction is milder than the other one. The
729 excluded types are never useful or necessary (because the offending
730 context doesn't need to be witnessed at this point; it can be floated
731 out). Furthermore, floating them out increases sharing. Lastly,
732 excluding them is a conservative choice; it leaves a patch of
733 territory free in case we need it later.
743 These restrictions apply to all types, whether declared in a type signature
748 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
749 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
756 f :: Eq (m a) => [m a] -> [m a]
763 This choice recovers principal types, a property that Haskell 1.4 does not have.
769 <title>Class declarations</title>
777 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
781 class Collection c a where
782 union :: c a -> c a -> c a
793 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
794 of "acyclic" involves only the superclass relationships. For example,
800 op :: D b => a -> b -> b
803 class C a => D a where { ... }
807 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
808 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
809 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
816 <emphasis>There are no restrictions on the context in a class declaration
817 (which introduces superclasses), except that the class hierarchy must
818 be acyclic</emphasis>. So these class declarations are OK:
822 class Functor (m k) => FiniteMap m k where
825 class (Monad m, Monad (t m)) => Transform t m where
826 lift :: m a -> (t m) a
835 <emphasis>In the signature of a class operation, every constraint
836 must mention at least one type variable that is not a class type
843 class Collection c a where
844 mapC :: Collection c b => (a->b) -> c a -> c b
848 is OK because the constraint <literal>(Collection a b)</literal> mentions
849 <literal>b</literal>, even though it also mentions the class variable
850 <literal>a</literal>. On the other hand:
855 op :: Eq a => (a,b) -> (a,b)
859 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
860 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
861 example is easily fixed by moving the offending context up to the
866 class Eq a => C a where
871 A yet more relaxed rule would allow the context of a class-op signature
872 to mention only class type variables. However, that conflicts with
873 Rule 1(b) for types above.
880 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
881 the class type variables</emphasis>. For example:
887 insert :: s -> a -> s
891 is not OK, because the type of <literal>empty</literal> doesn't mention
892 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
893 types, and has the same motivation.
895 Sometimes, offending class declarations exhibit misunderstandings. For
896 example, <literal>Coll</literal> might be rewritten
902 insert :: s a -> a -> s a
906 which makes the connection between the type of a collection of
907 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
908 Occasionally this really doesn't work, in which case you can split the
916 class CollE s => Coll s a where
917 insert :: s -> a -> s
930 <sect2 id="instance-decls">
931 <title>Instance declarations</title>
939 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
944 instance context1 => C type1 where ...
945 instance context2 => C type2 where ...
949 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
951 However, if you give the command line option
952 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
953 option</primary></indexterm> then two overlapping instance declarations are permitted
961 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
967 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
968 (but not identical to <literal>type1</literal>)
981 Notice that these rules
988 make it clear which instance decl to use
989 (pick the most specific one that matches)
996 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
997 Reason: you can pick which instance decl
998 "matches" based on the type.
1005 Regrettably, GHC doesn't guarantee to detect overlapping instance
1006 declarations if they appear in different modules. GHC can "see" the
1007 instance declarations in the transitive closure of all the modules
1008 imported by the one being compiled, so it can "see" all instance decls
1009 when it is compiling <literal>Main</literal>. However, it currently chooses not
1010 to look at ones that can't possibly be of use in the module currently
1011 being compiled, in the interests of efficiency. (Perhaps we should
1012 change that decision, at least for <literal>Main</literal>.)
1019 <emphasis>There are no restrictions on the type in an instance
1020 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1021 The instance "head" is the bit after the "=>" in an instance decl. For
1022 example, these are OK:
1026 instance C Int a where ...
1028 instance D (Int, Int) where ...
1030 instance E [[a]] where ...
1034 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1035 For example, this is OK:
1039 instance Stateful (ST s) (MutVar s) where ...
1043 The "at least one not a type variable" restriction is to ensure that
1044 context reduction terminates: each reduction step removes one type
1045 constructor. For example, the following would make the type checker
1046 loop if it wasn't excluded:
1050 instance C a => C a where ...
1054 There are two situations in which the rule is a bit of a pain. First,
1055 if one allows overlapping instance declarations then it's quite
1056 convenient to have a "default instance" declaration that applies if
1057 something more specific does not:
1066 Second, sometimes you might want to use the following to get the
1067 effect of a "class synonym":
1071 class (C1 a, C2 a, C3 a) => C a where { }
1073 instance (C1 a, C2 a, C3 a) => C a where { }
1077 This allows you to write shorter signatures:
1089 f :: (C1 a, C2 a, C3 a) => ...
1093 I'm on the lookout for a simple rule that preserves decidability while
1094 allowing these idioms. The experimental flag
1095 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1096 option</primary></indexterm> lifts this restriction, allowing all the types in an
1097 instance head to be type variables.
1104 <emphasis>Unlike Haskell 1.4, instance heads may use type
1105 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1106 writing the RHS of the type synonym definition. For example:
1110 type Point = (Int,Int)
1111 instance C Point where ...
1112 instance C [Point] where ...
1116 is legal. However, if you added
1120 instance C (Int,Int) where ...
1124 as well, then the compiler will complain about the overlapping
1125 (actually, identical) instance declarations. As always, type synonyms
1126 must be fully applied. You cannot, for example, write:
1131 instance Monad P where ...
1135 This design decision is independent of all the others, and easily
1136 reversed, but it makes sense to me.
1143 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1144 be type variables</emphasis>. Thus
1148 instance C a b => Eq (a,b) where ...
1156 instance C Int b => Foo b where ...
1160 is not OK. Again, the intent here is to make sure that context
1161 reduction terminates.
1163 Voluminous correspondence on the Haskell mailing list has convinced me
1164 that it's worth experimenting with a more liberal rule. If you use
1165 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1166 types in an instance context. Termination is ensured by having a
1167 fixed-depth recursion stack. If you exceed the stack depth you get a
1168 sort of backtrace, and the opportunity to increase the stack depth
1169 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1182 <sect1 id="implicit-parameters">
1183 <title>Implicit parameters
1186 <para> Implicit paramters are implemented as described in
1187 "Implicit parameters: dynamic scoping with static types",
1188 J Lewis, MB Shields, E Meijer, J Launchbury,
1189 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1194 There should be more documentation, but there isn't (yet). Yell if you need it.
1198 <para> You can't have an implicit parameter in the context of a class or instance
1199 declaration. For example, both these declarations are illegal:
1201 class (?x::Int) => C a where ...
1202 instance (?x::a) => Foo [a] where ...
1204 Reason: exactly which implicit parameter you pick up depends on exactly where
1205 you invoke a function. But the ``invocation'' of instance declarations is done
1206 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1207 Easiest thing is to outlaw the offending types.</para>
1215 <sect1 id="functional-dependencies">
1216 <title>Functional dependencies
1219 <para> Functional dependencies are implemented as described by Mark Jones
1220 in "Type Classes with Functional Dependencies", Mark P. Jones,
1221 In Proceedings of the 9th European Symposium on Programming,
1222 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1226 There should be more documentation, but there isn't (yet). Yell if you need it.
1231 <sect1 id="universal-quantification">
1232 <title>Explicit universal quantification
1236 GHC's type system supports explicit universal quantification in
1237 constructor fields and function arguments. This is useful for things
1238 like defining <literal>runST</literal> from the state-thread world.
1239 GHC's syntax for this now agrees with Hugs's, namely:
1245 forall a b. (Ord a, Eq b) => a -> b -> a
1251 The context is, of course, optional. You can't use <literal>forall</literal> as
1252 a type variable any more!
1256 Haskell type signatures are implicitly quantified. The <literal>forall</literal>
1257 allows us to say exactly what this means. For example:
1275 g :: forall b. (b -> b)
1281 The two are treated identically.
1285 <title>Universally-quantified data type fields
1289 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1290 the types of the constructor arguments. Here are several examples:
1296 data T a = T1 (forall b. b -> b -> b) a
1298 data MonadT m = MkMonad { return :: forall a. a -> m a,
1299 bind :: forall a b. m a -> (a -> m b) -> m b
1302 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1308 The constructors now have so-called <emphasis>rank 2</emphasis> polymorphic
1309 types, in which there is a for-all in the argument types.:
1315 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1316 MkMonad :: forall m. (forall a. a -> m a)
1317 -> (forall a b. m a -> (a -> m b) -> m b)
1319 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1325 Notice that you don't need to use a <literal>forall</literal> if there's an
1326 explicit context. For example in the first argument of the
1327 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1328 prefixed to the argument type. The implicit <literal>forall</literal>
1329 quantifies all type variables that are not already in scope, and are
1330 mentioned in the type quantified over.
1334 As for type signatures, implicit quantification happens for non-overloaded
1335 types too. So if you write this:
1338 data T a = MkT (Either a b) (b -> b)
1341 it's just as if you had written this:
1344 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1347 That is, since the type variable <literal>b</literal> isn't in scope, it's
1348 implicitly universally quantified. (Arguably, it would be better
1349 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1350 where that is what is wanted. Feedback welcomed.)
1356 <title>Construction </title>
1359 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1360 the constructor to suitable values, just as usual. For example,
1366 (T1 (\xy->x) 3) :: T Int
1368 (MkSwizzle sort) :: Swizzle
1369 (MkSwizzle reverse) :: Swizzle
1376 MkMonad r b) :: MonadT Maybe
1382 The type of the argument can, as usual, be more general than the type
1383 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1384 does not need the <literal>Ord</literal> constraint.)
1390 <title>Pattern matching</title>
1393 When you use pattern matching, the bound variables may now have
1394 polymorphic types. For example:
1400 f :: T a -> a -> (a, Char)
1401 f (T1 f k) x = (f k x, f 'c' 'd')
1403 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1404 g (MkSwizzle s) xs f = s (map f (s xs))
1406 h :: MonadT m -> [m a] -> m [a]
1407 h m [] = return m []
1408 h m (x:xs) = bind m x $ \y ->
1409 bind m (h m xs) $ \ys ->
1416 In the function <function>h</function> we use the record selectors <literal>return</literal>
1417 and <literal>bind</literal> to extract the polymorphic bind and return functions
1418 from the <literal>MonadT</literal> data structure, rather than using pattern
1423 You cannot pattern-match against an argument that is polymorphic.
1427 newtype TIM s a = TIM (ST s (Maybe a))
1429 runTIM :: (forall s. TIM s a) -> Maybe a
1430 runTIM (TIM m) = runST m
1436 Here the pattern-match fails, because you can't pattern-match against
1437 an argument of type <literal>(forall s. TIM s a)</literal>. Instead you
1438 must bind the variable and pattern match in the right hand side:
1441 runTIM :: (forall s. TIM s a) -> Maybe a
1442 runTIM tm = case tm of { TIM m -> runST m }
1445 The <literal>tm</literal> on the right hand side is (invisibly) instantiated, like
1446 any polymorphic value at its occurrence site, and now you can pattern-match
1453 <title>The partial-application restriction</title>
1456 There is really only one way in which data structures with polymorphic
1457 components might surprise you: you must not partially apply them.
1458 For example, this is illegal:
1464 map MkSwizzle [sort, reverse]
1470 The restriction is this: <emphasis>every subexpression of the program must
1471 have a type that has no for-alls, except that in a function
1472 application (f e1…en) the partial applications are not subject to
1473 this rule</emphasis>. The restriction makes type inference feasible.
1477 In the illegal example, the sub-expression <literal>MkSwizzle</literal> has the
1478 polymorphic type <literal>(Ord b => [b] -> [b]) -> Swizzle</literal> and is not
1479 a sub-expression of an enclosing application. On the other hand, this
1486 map (T1 (\a b -> a)) [1,2,3]
1492 even though it involves a partial application of <function>T1</function>, because
1493 the sub-expression <literal>T1 (\a b -> a)</literal> has type <literal>Int -> T
1500 <title>Type signatures
1504 Once you have data constructors with universally-quantified fields, or
1505 constants such as <Constant>runST</Constant> that have rank-2 types, it isn't long
1506 before you discover that you need more! Consider:
1512 mkTs f x y = [T1 f x, T1 f y]
1518 <function>mkTs</function> is a fuction that constructs some values of type
1519 <literal>T</literal>, using some pieces passed to it. The trouble is that since
1520 <literal>f</literal> is a function argument, Haskell assumes that it is
1521 monomorphic, so we'll get a type error when applying <function>T1</function> to
1522 it. This is a rather silly example, but the problem really bites in
1523 practice. Lots of people trip over the fact that you can't make
1524 "wrappers functions" for <Constant>runST</Constant> for exactly the same reason.
1525 In short, it is impossible to build abstractions around functions with
1530 The solution is fairly clear. We provide the ability to give a rank-2
1531 type signature for <emphasis>ordinary</emphasis> functions (not only data
1532 constructors), thus:
1538 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1539 mkTs f x y = [T1 f x, T1 f y]
1545 This type signature tells the compiler to attribute <literal>f</literal> with
1546 the polymorphic type <literal>(forall b. b -> b -> b)</literal> when type
1547 checking the body of <function>mkTs</function>, so now the application of
1548 <function>T1</function> is fine.
1552 There are two restrictions:
1561 You can only define a rank 2 type, specified by the following
1566 rank2type ::= [forall tyvars .] [context =>] funty
1567 funty ::= ([forall tyvars .] [context =>] ty) -> funty
1569 ty ::= ...current Haskell monotype syntax...
1573 Informally, the universal quantification must all be right at the beginning,
1574 or at the top level of a function argument.
1581 There is a restriction on the definition of a function whose
1582 type signature is a rank-2 type: the polymorphic arguments must be
1583 matched on the left hand side of the "<literal>=</literal>" sign. You can't
1584 define <function>mkTs</function> like this:
1588 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1589 mkTs = \ f x y -> [T1 f x, T1 f y]
1594 The same partial-application rule applies to ordinary functions with
1595 rank-2 types as applied to data constructors.
1608 <title>Type synonyms and hoisting
1612 GHC also allows you to write a <literal>forall</literal> in a type synonym, thus:
1614 type Discard a = forall b. a -> b -> a
1619 However, it is often convenient to use these sort of synonyms at the right hand
1620 end of an arrow, thus:
1622 type Discard a = forall b. a -> b -> a
1624 g :: Int -> Discard Int
1627 Simply expanding the type synonym would give
1629 g :: Int -> (forall b. Int -> b -> Int)
1631 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1633 g :: forall b. Int -> Int -> b -> Int
1635 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1636 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1637 performs the transformation:</emphasis>
1639 <emphasis>type1</emphasis> -> forall a. <emphasis>type2</emphasis>
1641 forall a. <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1643 (In fact, GHC tries to retain as much synonym information as possible for use in
1644 error messages, but that is a usability issue.) This rule applies, of course, whether
1645 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1646 valid way to write <literal>g</literal>'s type signature:
1648 g :: Int -> Int -> forall b. b -> Int
1655 <sect1 id="existential-quantification">
1656 <title>Existentially quantified data constructors
1660 The idea of using existential quantification in data type declarations
1661 was suggested by Laufer (I believe, thought doubtless someone will
1662 correct me), and implemented in Hope+. It's been in Lennart
1663 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1664 proved very useful. Here's the idea. Consider the declaration:
1670 data Foo = forall a. MkFoo a (a -> Bool)
1677 The data type <literal>Foo</literal> has two constructors with types:
1683 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1690 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1691 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1692 For example, the following expression is fine:
1698 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1704 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1705 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1706 isUpper</function> packages a character with a compatible function. These
1707 two things are each of type <literal>Foo</literal> and can be put in a list.
1711 What can we do with a value of type <literal>Foo</literal>?. In particular,
1712 what happens when we pattern-match on <function>MkFoo</function>?
1718 f (MkFoo val fn) = ???
1724 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1725 are compatible, the only (useful) thing we can do with them is to
1726 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1733 f (MkFoo val fn) = fn val
1739 What this allows us to do is to package heterogenous values
1740 together with a bunch of functions that manipulate them, and then treat
1741 that collection of packages in a uniform manner. You can express
1742 quite a bit of object-oriented-like programming this way.
1745 <sect2 id="existential">
1746 <title>Why existential?
1750 What has this to do with <emphasis>existential</emphasis> quantification?
1751 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1757 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1763 But Haskell programmers can safely think of the ordinary
1764 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1765 adding a new existential quantification construct.
1771 <title>Type classes</title>
1774 An easy extension (implemented in <Command>hbc</Command>) is to allow
1775 arbitrary contexts before the constructor. For example:
1781 data Baz = forall a. Eq a => Baz1 a a
1782 | forall b. Show b => Baz2 b (b -> b)
1788 The two constructors have the types you'd expect:
1794 Baz1 :: forall a. Eq a => a -> a -> Baz
1795 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1801 But when pattern matching on <function>Baz1</function> the matched values can be compared
1802 for equality, and when pattern matching on <function>Baz2</function> the first matched
1803 value can be converted to a string (as well as applying the function to it).
1804 So this program is legal:
1811 f (Baz1 p q) | p == q = "Yes"
1813 f (Baz1 v fn) = show (fn v)
1819 Operationally, in a dictionary-passing implementation, the
1820 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1821 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1822 extract it on pattern matching.
1826 Notice the way that the syntax fits smoothly with that used for
1827 universal quantification earlier.
1833 <title>Restrictions</title>
1836 There are several restrictions on the ways in which existentially-quantified
1837 constructors can be use.
1846 When pattern matching, each pattern match introduces a new,
1847 distinct, type for each existential type variable. These types cannot
1848 be unified with any other type, nor can they escape from the scope of
1849 the pattern match. For example, these fragments are incorrect:
1857 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1858 is the result of <function>f1</function>. One way to see why this is wrong is to
1859 ask what type <function>f1</function> has:
1863 f1 :: Foo -> a -- Weird!
1867 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1872 f1 :: forall a. Foo -> a -- Wrong!
1876 The original program is just plain wrong. Here's another sort of error
1880 f2 (Baz1 a b) (Baz1 p q) = a==q
1884 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1885 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1886 from the two <function>Baz1</function> constructors.
1894 You can't pattern-match on an existentially quantified
1895 constructor in a <literal>let</literal> or <literal>where</literal> group of
1896 bindings. So this is illegal:
1900 f3 x = a==b where { Baz1 a b = x }
1904 You can only pattern-match
1905 on an existentially-quantified constructor in a <literal>case</literal> expression or
1906 in the patterns of a function definition.
1908 The reason for this restriction is really an implementation one.
1909 Type-checking binding groups is already a nightmare without
1910 existentials complicating the picture. Also an existential pattern
1911 binding at the top level of a module doesn't make sense, because it's
1912 not clear how to prevent the existentially-quantified type "escaping".
1913 So for now, there's a simple-to-state restriction. We'll see how
1921 You can't use existential quantification for <literal>newtype</literal>
1922 declarations. So this is illegal:
1926 newtype T = forall a. Ord a => MkT a
1930 Reason: a value of type <literal>T</literal> must be represented as a pair
1931 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1932 That contradicts the idea that <literal>newtype</literal> should have no
1933 concrete representation. You can get just the same efficiency and effect
1934 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1935 overloading involved, then there is more of a case for allowing
1936 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1937 because the <literal>data</literal> version does carry an implementation cost,
1938 but single-field existentially quantified constructors aren't much
1939 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1940 stands, unless there are convincing reasons to change it.
1948 You can't use <literal>deriving</literal> to define instances of a
1949 data type with existentially quantified data constructors.
1951 Reason: in most cases it would not make sense. For example:#
1954 data T = forall a. MkT [a] deriving( Eq )
1957 To derive <literal>Eq</literal> in the standard way we would need to have equality
1958 between the single component of two <function>MkT</function> constructors:
1962 (MkT a) == (MkT b) = ???
1965 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1966 It's just about possible to imagine examples in which the derived instance
1967 would make sense, but it seems altogether simpler simply to prohibit such
1968 declarations. Define your own instances!
1980 <sect1 id="sec-assertions">
1982 <indexterm><primary>Assertions</primary></indexterm>
1986 If you want to make use of assertions in your standard Haskell code, you
1987 could define a function like the following:
1993 assert :: Bool -> a -> a
1994 assert False x = error "assertion failed!"
2001 which works, but gives you back a less than useful error message --
2002 an assertion failed, but which and where?
2006 One way out is to define an extended <function>assert</function> function which also
2007 takes a descriptive string to include in the error message and
2008 perhaps combine this with the use of a pre-processor which inserts
2009 the source location where <function>assert</function> was used.
2013 Ghc offers a helping hand here, doing all of this for you. For every
2014 use of <function>assert</function> in the user's source:
2020 kelvinToC :: Double -> Double
2021 kelvinToC k = assert (k >= 0.0) (k+273.15)
2027 Ghc will rewrite this to also include the source location where the
2034 assert pred val ==> assertError "Main.hs|15" pred val
2040 The rewrite is only performed by the compiler when it spots
2041 applications of <function>Exception.assert</function>, so you can still define and
2042 use your own versions of <function>assert</function>, should you so wish. If not,
2043 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2047 To have the compiler ignore uses of assert, use the compiler option
2048 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2049 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2053 Assertion failures can be caught, see the documentation for the
2054 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2060 <sect1 id="scoped-type-variables">
2061 <title>Scoped Type Variables
2065 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2066 variable</emphasis>. For example
2072 f (xs::[a]) = ys ++ ys
2081 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2082 This brings the type variable <literal>a</literal> into scope; it scopes over
2083 all the patterns and right hand sides for this equation for <function>f</function>.
2084 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2088 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2089 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2090 implicitly universally quantified. (If there are no type variables in
2091 scope, all type variables mentioned in the signature are universally
2092 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2093 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2094 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2095 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2096 it becomes possible to do so.
2100 Scoped type variables are implemented in both GHC and Hugs. Where the
2101 implementations differ from the specification below, those differences
2106 So much for the basic idea. Here are the details.
2110 <title>Scope and implicit quantification</title>
2118 All the type variables mentioned in the patterns for a single
2119 function definition equation, that are not already in scope,
2120 are brought into scope by the patterns. We describe this set as
2121 the <emphasis>type variables bound by the equation</emphasis>.
2128 The type variables thus brought into scope may be mentioned
2129 in ordinary type signatures or pattern type signatures anywhere within
2137 In ordinary type signatures, any type variable mentioned in the
2138 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2145 Ordinary type signatures do not bring any new type variables
2146 into scope (except in the type signature itself!). So this is illegal:
2155 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2156 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2157 and that is an incorrect typing.
2164 There is no implicit universal quantification on pattern type
2165 signatures, nor may one write an explicit <literal>forall</literal> type in a pattern
2166 type signature. The pattern type signature is a monotype.
2174 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2175 scope over the methods defined in the <literal>where</literal> part. For example:
2189 (Not implemented in Hugs yet, Dec 98).
2200 <title>Polymorphism</title>
2208 Pattern type signatures are completely orthogonal to ordinary, separate
2209 type signatures. The two can be used independently or together. There is
2210 no scoping associated with the names of the type variables in a separate type signature.
2215 f (xs::[b]) = reverse xs
2224 The function must be polymorphic in the type variables
2225 bound by all its equations. Operationally, the type variables bound
2226 by one equation must not:
2233 Be unified with a type (such as <literal>Int</literal>, or <literal>[a]</literal>).
2239 Be unified with a type variable free in the environment.
2245 Be unified with each other. (They may unify with the type variables
2246 bound by another equation for the same function, of course.)
2253 For example, the following all fail to type check:
2257 f (x::a) (y::b) = [x,y] -- a unifies with b
2259 g (x::a) = x + 1::Int -- a unifies with Int
2261 h x = let k (y::a) = [x,y] -- a is free in the
2262 in k x -- environment
2264 k (x::a) True = ... -- a unifies with Int
2265 k (x::Int) False = ...
2268 w (x::a) = x -- a unifies with [b]
2277 The pattern-bound type variable may, however, be constrained
2278 by the context of the principal type, thus:
2282 f (x::a) (y::a) = x+y*2
2286 gets the inferred type: <literal>forall a. Num a => a -> a -> a</literal>.
2297 <title>Result type signatures</title>
2305 The result type of a function can be given a signature,
2310 f (x::a) :: [a] = [x,x,x]
2314 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2315 result type. Sometimes this is the only way of naming the type variable
2320 f :: Int -> [a] -> [a]
2321 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2322 in \xs -> map g (reverse xs `zip` xs)
2334 Result type signatures are not yet implemented in Hugs.
2340 <title>Pattern signatures on other constructs</title>
2348 A pattern type signature can be on an arbitrary sub-pattern, not
2353 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2362 Pattern type signatures, including the result part, can be used
2363 in lambda abstractions:
2367 (\ (x::a, y) :: a -> x)
2371 Type variables bound by these patterns must be polymorphic in
2372 the sense defined above.
2377 f1 (x::c) = f1 x -- ok
2378 f2 = \(x::c) -> f2 x -- not ok
2382 Here, <function>f1</function> is OK, but <function>f2</function> is not, because <VarName>c</VarName> gets unified
2383 with a type variable free in the environment, in this
2384 case, the type of <function>f2</function>, which is in the environment when
2385 the lambda abstraction is checked.
2392 Pattern type signatures, including the result part, can be used
2393 in <literal>case</literal> expressions:
2397 case e of { (x::a, y) :: a -> x }
2401 The pattern-bound type variables must, as usual,
2402 be polymorphic in the following sense: each case alternative,
2403 considered as a lambda abstraction, must be polymorphic.
2408 case (True,False) of { (x::a, y) -> x }
2412 Even though the context is that of a pair of booleans,
2413 the alternative itself is polymorphic. Of course, it is
2418 case (True,False) of { (x::Bool, y) -> x }
2427 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2428 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2429 token or a parenthesised type of some sort). To see why,
2430 consider how one would parse this:
2443 Pattern type signatures that bind new type variables
2444 may not be used in pattern bindings at all.
2449 f x = let (y, z::a) = x in ...
2453 But these are OK, because they do not bind fresh type variables:
2457 f1 x = let (y, z::Int) = x in ...
2458 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2462 However a single variable is considered a degenerate function binding,
2463 rather than a degerate pattern binding, so this is permitted, even
2464 though it binds a type variable:
2468 f :: (b->b) = \(x::b) -> x
2477 Such degnerate function bindings do not fall under the monomorphism
2484 g :: a -> a -> Bool = \x y. x==y
2490 Here <function>g</function> has type <literal>forall a. Eq a => a -> a -> Bool</literal>, just as if
2491 <function>g</function> had a separate type signature. Lacking a type signature, <function>g</function>
2492 would get a monomorphic type.
2498 <title>Existentials</title>
2506 Pattern type signatures can bind existential type variables.
2511 data T = forall a. MkT [a]
2514 f (MkT [t::a]) = MkT t3
2531 <sect1 id="pragmas">
2536 GHC supports several pragmas, or instructions to the compiler placed
2537 in the source code. Pragmas don't affect the meaning of the program,
2538 but they might affect the efficiency of the generated code.
2541 <sect2 id="inline-pragma">
2542 <title>INLINE pragma
2544 <indexterm><primary>INLINE pragma</primary></indexterm>
2545 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2548 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2549 functions/values that are “small enough,” thus avoiding the call
2550 overhead and possibly exposing other more-wonderful optimisations.
2554 You will probably see these unfoldings (in Core syntax) in your
2559 Normally, if GHC decides a function is “too expensive” to inline, it
2560 will not do so, nor will it export that unfolding for other modules to
2565 The sledgehammer you can bring to bear is the
2566 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2569 key_function :: Int -> String -> (Bool, Double)
2571 #ifdef __GLASGOW_HASKELL__
2572 {-# INLINE key_function #-}
2576 (You don't need to do the C pre-processor carry-on unless you're going
2577 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2581 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2582 “cost” to be very low. The normal unfolding machinery will then be
2583 very keen to inline it.
2587 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2588 signature could be put.
2592 <literal>INLINE</literal> pragmas are a particularly good idea for the
2593 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2594 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2597 #ifdef __GLASGOW_HASKELL__
2598 {-# INLINE thenUs #-}
2599 {-# INLINE returnUs #-}
2607 <sect2 id="noinline-pragma">
2608 <title>NOINLINE pragma
2612 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2613 <indexterm><primary>pragma, NOINLINE</primary></indexterm>
2617 The <literal>NOINLINE</literal> pragma does exactly what you'd expect: it stops the
2618 named function from being inlined by the compiler. You shouldn't ever
2619 need to do this, unless you're very cautious about code size.
2624 <sect2 id="specialize-pragma">
2625 <title>SPECIALIZE pragma</title>
2627 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2628 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2629 <indexterm><primary>overloading, death to</primary></indexterm>
2631 <para>(UK spelling also accepted.) For key overloaded
2632 functions, you can create extra versions (NB: more code space)
2633 specialised to particular types. Thus, if you have an
2634 overloaded function:</para>
2637 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2640 <para>If it is heavily used on lists with
2641 <literal>Widget</literal> keys, you could specialise it as
2645 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2648 <para>To get very fancy, you can also specify a named function
2649 to use for the specialised value, as in:</para>
2652 {-# RULES hammeredLookup = blah #-}
2655 <para>where <literal>blah</literal> is an implementation of
2656 <literal>hammerdLookup</literal> written specialy for
2657 <literal>Widget</literal> lookups. It's <emphasis>Your
2658 Responsibility</emphasis> to make sure that
2659 <function>blah</function> really behaves as a specialised
2660 version of <function>hammeredLookup</function>!!!</para>
2662 <para>Note we use the <literal>RULE</literal> pragma here to
2663 indicate that <literal>hammeredLookup</literal> applied at a
2664 certain type should be replaced by <literal>blah</literal>. See
2665 <xref linkend="rules"> for more information on
2666 <literal>RULES</literal>.</para>
2668 <para>An example in which using <literal>RULES</literal> for
2669 specialisation will Win Big:
2672 toDouble :: Real a => a -> Double
2673 toDouble = fromRational . toRational
2675 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2676 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2679 The <function>i2d</function> function is virtually one machine
2680 instruction; the default conversion—via an intermediate
2681 <literal>Rational</literal>—is obscenely expensive by
2684 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2685 be put anywhere its type signature could be put.</para>
2689 <sect2 id="specialize-instance-pragma">
2690 <title>SPECIALIZE instance pragma
2694 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2695 <indexterm><primary>overloading, death to</primary></indexterm>
2696 Same idea, except for instance declarations. For example:
2699 instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
2701 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
2704 Compatible with HBC, by the way.
2709 <sect2 id="line-pragma">
2714 <indexterm><primary>LINE pragma</primary></indexterm>
2715 <indexterm><primary>pragma, LINE</primary></indexterm>
2719 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2720 automatically generated Haskell code. It lets you specify the line
2721 number and filename of the original code; for example
2727 {-# LINE 42 "Foo.vhs" #-}
2733 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2734 and this line corresponds to line 42 in the original. GHC will adjust
2735 its error messages to refer to the line/file named in the <literal>LINE</literal>
2742 <title>RULES pragma</title>
2745 The RULES pragma lets you specify rewrite rules. It is described in
2746 <xref LinkEnd="rewrite-rules">.
2753 <sect1 id="rewrite-rules">
2754 <title>Rewrite rules
2756 <indexterm><primary>RULES pagma</primary></indexterm>
2757 <indexterm><primary>pragma, RULES</primary></indexterm>
2758 <indexterm><primary>rewrite rules</primary></indexterm></title>
2761 The programmer can specify rewrite rules as part of the source program
2762 (in a pragma). GHC applies these rewrite rules wherever it can.
2770 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2777 <title>Syntax</title>
2780 From a syntactic point of view:
2786 Each rule has a name, enclosed in double quotes. The name itself has
2787 no significance at all. It is only used when reporting how many times the rule fired.
2793 There may be zero or more rules in a <literal>RULES</literal> pragma.
2799 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2800 is set, so you must lay out your rules starting in the same column as the
2801 enclosing definitions.
2807 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2808 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2809 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2810 by spaces, just like in a type <literal>forall</literal>.
2816 A pattern variable may optionally have a type signature.
2817 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2818 For example, here is the <literal>foldr/build</literal> rule:
2821 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2822 foldr k z (build g) = g k z
2825 Since <function>g</function> has a polymorphic type, it must have a type signature.
2832 The left hand side of a rule must consist of a top-level variable applied
2833 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2836 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2837 "wrong2" forall f. f True = True
2840 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2847 A rule does not need to be in the same module as (any of) the
2848 variables it mentions, though of course they need to be in scope.
2854 Rules are automatically exported from a module, just as instance declarations are.
2865 <title>Semantics</title>
2868 From a semantic point of view:
2874 Rules are only applied if you use the <option>-O</option> flag.
2880 Rules are regarded as left-to-right rewrite rules.
2881 When GHC finds an expression that is a substitution instance of the LHS
2882 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
2883 By "a substitution instance" we mean that the LHS can be made equal to the
2884 expression by substituting for the pattern variables.
2891 The LHS and RHS of a rule are typechecked, and must have the
2899 GHC makes absolutely no attempt to verify that the LHS and RHS
2900 of a rule have the same meaning. That is undecideable in general, and
2901 infeasible in most interesting cases. The responsibility is entirely the programmer's!
2908 GHC makes no attempt to make sure that the rules are confluent or
2909 terminating. For example:
2912 "loop" forall x,y. f x y = f y x
2915 This rule will cause the compiler to go into an infinite loop.
2922 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
2928 GHC currently uses a very simple, syntactic, matching algorithm
2929 for matching a rule LHS with an expression. It seeks a substitution
2930 which makes the LHS and expression syntactically equal modulo alpha
2931 conversion. The pattern (rule), but not the expression, is eta-expanded if
2932 necessary. (Eta-expanding the epression can lead to laziness bugs.)
2933 But not beta conversion (that's called higher-order matching).
2937 Matching is carried out on GHC's intermediate language, which includes
2938 type abstractions and applications. So a rule only matches if the
2939 types match too. See <xref LinkEnd="rule-spec"> below.
2945 GHC keeps trying to apply the rules as it optimises the program.
2946 For example, consider:
2955 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
2956 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
2957 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
2958 not be substituted, and the rule would not fire.
2965 In the earlier phases of compilation, GHC inlines <emphasis>nothing
2966 that appears on the LHS of a rule</emphasis>, because once you have substituted
2967 for something you can't match against it (given the simple minded
2968 matching). So if you write the rule
2971 "map/map" forall f,g. map f . map g = map (f.g)
2974 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
2975 It will only match something written with explicit use of ".".
2976 Well, not quite. It <emphasis>will</emphasis> match the expression
2982 where <function>wibble</function> is defined:
2985 wibble f g = map f . map g
2988 because <function>wibble</function> will be inlined (it's small).
2990 Later on in compilation, GHC starts inlining even things on the
2991 LHS of rules, but still leaves the rules enabled. This inlining
2992 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
2999 All rules are implicitly exported from the module, and are therefore
3000 in force in any module that imports the module that defined the rule, directly
3001 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3002 in force when compiling A.) The situation is very similar to that for instance
3014 <title>List fusion</title>
3017 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3018 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3019 intermediate list should be eliminated entirely.
3023 The following are good producers:
3035 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3041 Explicit lists (e.g. <literal>[True, False]</literal>)
3047 The cons constructor (e.g <literal>3:4:[]</literal>)
3053 <function>++</function>
3059 <function>map</function>
3065 <function>filter</function>
3071 <function>iterate</function>, <function>repeat</function>
3077 <function>zip</function>, <function>zipWith</function>
3086 The following are good consumers:
3098 <function>array</function> (on its second argument)
3104 <function>length</function>
3110 <function>++</function> (on its first argument)
3116 <function>map</function>
3122 <function>filter</function>
3128 <function>concat</function>
3134 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3140 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3141 will fuse with one but not the other)
3147 <function>partition</function>
3153 <function>head</function>
3159 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3165 <function>sequence_</function>
3171 <function>msum</function>
3177 <function>sortBy</function>
3186 So, for example, the following should generate no intermediate lists:
3189 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3195 This list could readily be extended; if there are Prelude functions that you use
3196 a lot which are not included, please tell us.
3200 If you want to write your own good consumers or producers, look at the
3201 Prelude definitions of the above functions to see how to do so.
3206 <sect2 id="rule-spec">
3207 <title>Specialisation
3211 Rewrite rules can be used to get the same effect as a feature
3212 present in earlier version of GHC:
3215 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3218 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3219 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3220 specialising the original definition of <function>fromIntegral</function> the programmer is
3221 promising that it is safe to use <function>int8ToInt16</function> instead.
3225 This feature is no longer in GHC. But rewrite rules let you do the
3230 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3234 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3235 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3236 GHC adds the type and dictionary applications to get the typed rule
3239 forall (d1::Integral Int8) (d2::Num Int16) .
3240 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3244 this rule does not need to be in the same file as fromIntegral,
3245 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3246 have an original definition available to specialise).
3252 <title>Controlling what's going on</title>
3260 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3266 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3267 If you add <option>-dppr-debug</option> you get a more detailed listing.
3273 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3276 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3277 {-# INLINE build #-}
3281 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3282 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3283 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3284 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3291 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3292 see how to write rules that will do fusion and yet give an efficient
3293 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3305 <sect1 id="generic-classes">
3306 <title>Generic classes</title>
3309 The ideas behind this extension are described in detail in "Derivable type classes",
3310 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3311 An example will give the idea:
3319 fromBin :: [Int] -> (a, [Int])
3321 toBin {| Unit |} Unit = []
3322 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3323 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3324 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3326 fromBin {| Unit |} bs = (Unit, bs)
3327 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3328 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3329 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3330 (y,bs'') = fromBin bs'
3333 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3334 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3335 which are defined thus in the library module <literal>Generics</literal>:
3339 data a :+: b = Inl a | Inr b
3340 data a :*: b = a :*: b
3343 Now you can make a data type into an instance of Bin like this:
3345 instance (Bin a, Bin b) => Bin (a,b)
3346 instance Bin a => Bin [a]
3348 That is, just leave off the "where" clasuse. Of course, you can put in the
3349 where clause and over-ride whichever methods you please.
3353 <title> Using generics </title>
3354 <para>To use generics you need to</para>
3357 <para>Use the <option>-fgenerics</option> flag.</para>
3360 <para>Import the module <literal>Generics</literal> from the
3361 <literal>lang</literal> package. This import brings into
3362 scope the data types <literal>Unit</literal>,
3363 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3364 don't need this import if you don't mention these types
3365 explicitly; for example, if you are simply giving instance
3366 declarations.)</para>
3371 <sect2> <title> Changes wrt the paper </title>
3373 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3374 can be written infix (indeed, you can now use
3375 any operator starting in a colon as an infix type constructor). Also note that
3376 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3377 Finally, note that the syntax of the type patterns in the class declaration
3378 uses "<literal>{|</literal>" and "<literal>{|</literal>" brackets; curly braces
3379 alone would ambiguous when they appear on right hand sides (an extension we
3380 anticipate wanting).
3384 <sect2> <title>Terminology and restrictions</title>
3386 Terminology. A "generic default method" in a class declaration
3387 is one that is defined using type patterns as above.
3388 A "polymorphic default method" is a default method defined as in Haskell 98.
3389 A "generic class declaration" is a class declaration with at least one
3390 generic default method.
3398 Alas, we do not yet implement the stuff about constructor names and
3405 A generic class can have only one parameter; you can't have a generic
3406 multi-parameter class.
3412 A default method must be defined entirely using type patterns, or entirely
3413 without. So this is illegal:
3416 op :: a -> (a, Bool)
3417 op {| Unit |} Unit = (Unit, True)
3420 However it is perfectly OK for some methods of a generic class to have
3421 generic default methods and others to have polymorphic default methods.
3427 The type variable(s) in the type pattern for a generic method declaration
3428 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:
3432 op {| p :*: q |} (x :*: y) = op (x :: p)
3440 The type patterns in a generic default method must take one of the forms:
3446 where "a" and "b" are type variables. Furthermore, all the type patterns for
3447 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3448 must use the same type variables. So this is illegal:
3452 op {| a :+: b |} (Inl x) = True
3453 op {| p :+: q |} (Inr y) = False
3455 The type patterns must be identical, even in equations for different methods of the class.
3456 So this too is illegal:
3460 op {| a :*: b |} (Inl x) = True
3463 op {| p :*: q |} (Inr y) = False
3465 (The reason for this restriction is that we gather all the equations for a particular type consructor
3466 into a single generic instance declaration.)
3472 A generic method declaration must give a case for each of the three type constructors.
3478 The type for a generic method can be built only from:
3480 <listitem> <para> Function arrows </para> </listitem>
3481 <listitem> <para> Type variables </para> </listitem>
3482 <listitem> <para> Tuples </para> </listitem>
3483 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3485 Here are some example type signatures for generic methods:
3488 op2 :: Bool -> (a,Bool)
3489 op3 :: [Int] -> a -> a
3492 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3496 This restriction is an implementation restriction: we just havn't got around to
3497 implementing the necessary bidirectional maps over arbitrary type constructors.
3498 It would be relatively easy to add specific type constructors, such as Maybe and list,
3499 to the ones that are allowed.</para>
3504 In an instance declaration for a generic class, the idea is that the compiler
3505 will fill in the methods for you, based on the generic templates. However it can only
3510 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3515 No constructor of the instance type has unboxed fields.
3519 (Of course, these things can only arise if you are already using GHC extensions.)
3520 However, you can still give an instance declarations for types which break these rules,
3521 provided you give explicit code to override any generic default methods.
3529 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3530 what the compiler does with generic declarations.
3535 <sect2> <title> Another example </title>
3537 Just to finish with, here's another example I rather like:
3541 nCons {| Unit |} _ = 1
3542 nCons {| a :*: b |} _ = 1
3543 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3546 tag {| Unit |} _ = 1
3547 tag {| a :*: b |} _ = 1
3548 tag {| a :+: b |} (Inl x) = tag x
3549 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3556 ;;; Local Variables: ***
3558 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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