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>Data types with no constructors</term>
101 <para>See <xref LinkEnd="nullary-types">.</para>
106 <term>Parallel list comprehensions</term>
108 <para>An extension to the list comprehension syntax to support
109 <literal>zipWith</literal>-like functionality. See <xref
110 linkend="parallel-list-comprehensions">.</para>
115 <term>Foreign calling:</term>
117 <para>Just what it sounds like. We provide
118 <emphasis>lots</emphasis> of rope that you can dangle around
119 your neck. Please see <xref LinkEnd="ffi">.</para>
126 <para>Pragmas are special instructions to the compiler placed
127 in the source file. The pragmas GHC supports are described in
128 <xref LinkEnd="pragmas">.</para>
133 <term>Rewrite rules:</term>
135 <para>The programmer can specify rewrite rules as part of the
136 source program (in a pragma). GHC applies these rewrite rules
137 wherever it can. Details in <xref
138 LinkEnd="rewrite-rules">.</para>
143 <term>Generic classes:</term>
145 <para>(Note: support for generic classes is currently broken
148 <para>Generic class declarations allow you to define a class
149 whose methods say how to work over an arbitrary data type.
150 Then it's really easy to make any new type into an instance of
151 the class. This generalises the rather ad-hoc "deriving"
152 feature of Haskell 98. Details in <xref
153 LinkEnd="generic-classes">.</para>
159 Before you get too carried away working at the lowest level (e.g.,
160 sloshing <literal>MutableByteArray#</literal>s around your
161 program), you may wish to check if there are libraries that provide a
162 “Haskellised veneer” over the features you want. See
163 <xref linkend="book-hslibs">.
166 <sect1 id="options-language">
167 <title>Language options</title>
169 <indexterm><primary>language</primary><secondary>option</secondary>
171 <indexterm><primary>options</primary><secondary>language</secondary>
173 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
176 <para> These flags control what variation of the language are
177 permitted. Leaving out all of them gives you standard Haskell
183 <term><option>-fglasgow-exts</option>:</term>
184 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
186 <para>This simultaneously enables all of the extensions to
187 Haskell 98 described in <xref
188 linkend="ghc-language-features">, except where otherwise
194 <term><option>-fno-monomorphism-restriction</option>:</term>
195 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
197 <para> Switch off the Haskell 98 monomorphism restriction.
198 Independent of the <option>-fglasgow-exts</option>
204 <term><option>-fallow-overlapping-instances</option></term>
205 <term><option>-fallow-undecidable-instances</option></term>
206 <term><option>-fcontext-stack</option></term>
207 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
208 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
209 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
211 <para> See <xref LinkEnd="instance-decls">. Only relevant
212 if you also use <option>-fglasgow-exts</option>.</para>
217 <term><option>-finline-phase</option></term>
218 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
220 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
221 you also use <option>-fglasgow-exts</option>.</para>
226 <term><option>-fgenerics</option></term>
227 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
229 <para>See <xref LinkEnd="generic-classes">. Independent of
230 <option>-fglasgow-exts</option>.</para>
235 <term><option>-fno-implicit-prelude</option></term>
237 <para><indexterm><primary>-fno-implicit-prelude
238 option</primary></indexterm> GHC normally imports
239 <filename>Prelude.hi</filename> files for you. If you'd
240 rather it didn't, then give it a
241 <option>-fno-implicit-prelude</option> option. The idea
242 is that you can then import a Prelude of your own. (But
243 don't call it <literal>Prelude</literal>; the Haskell
244 module namespace is flat, and you must not conflict with
245 any Prelude module.)</para>
247 <para>Even though you have not imported the Prelude, all
248 the built-in syntax still refers to the built-in Haskell
249 Prelude types and values, as specified by the Haskell
250 Report. For example, the type <literal>[Int]</literal>
251 still means <literal>Prelude.[] Int</literal>; tuples
252 continue to refer to the standard Prelude tuples; the
253 translation for list comprehensions continues to use
254 <literal>Prelude.map</literal> etc.</para>
256 <para> With one group of exceptions! You may want to
257 define your own numeric class hierarchy. It completely
258 defeats that purpose if the literal "1" means
259 "<literal>Prelude.fromInteger 1</literal>", which is what
260 the Haskell Report specifies. So the
261 <option>-fno-implicit-prelude</option> flag causes the
262 following pieces of built-in syntax to refer to <emphasis>whatever
263 is in scope</emphasis>, not the Prelude versions:</para>
267 <para>Integer and fractional literals mean
268 "<literal>fromInteger 1</literal>" and
269 "<literal>fromRational 3.2</literal>", not the
270 Prelude-qualified versions; both in expressions and in
275 <para>Negation (e.g. "<literal>- (f x)</literal>")
276 means "<literal>negate (f x)</literal>" (not
277 <literal>Prelude.negate</literal>).</para>
281 <para>In an n+k pattern, the standard Prelude
282 <literal>Ord</literal> class is still used for comparison,
283 but the necessary subtraction uses whatever
284 "<literal>(-)</literal>" is in scope (not
285 "<literal>Prelude.(-)</literal>").</para>
289 <para>Note: Negative literals, such as <literal>-3</literal>, are
290 specified by (a careful reading of) the Haskell Report as
291 meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
292 However, GHC deviates from this slightly, and treats them as meaning
293 <literal>fromInteger (-3)</literal>. One particular effect of this
294 slightly-non-standard reading is that there is no difficulty with
295 the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
296 it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
297 would be <literal>negate (fromInteger 2147483648)</literal>,
298 and the call to <literal>fromInteger</literal> would overflow
299 (at type <literal>Int</literal>, remember).
308 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
311 <sect1 id="glasgow-ST-monad">
312 <title>Primitive state-transformer monad</title>
315 <indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
316 <indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
320 This monad underlies our implementation of arrays, mutable and
321 immutable, and our implementation of I/O, including “C calls”.
325 The <literal>ST</literal> library, which provides access to the
326 <function>ST</function> monad, is described in <xref
332 <sect1 id="glasgow-prim-arrays">
333 <title>Primitive arrays, mutable and otherwise
337 <indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
338 <indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
342 GHC knows about quite a few flavours of Large Swathes of Bytes.
346 First, GHC distinguishes between primitive arrays of (boxed) Haskell
347 objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
348 <literal>ByteArray#</literal>).
352 Second, it distinguishes between…
356 <term>Immutable:</term>
359 Arrays that do not change (as with “standard” Haskell arrays); you
360 can only read from them. Obviously, they do not need the care and
361 attention of the state-transformer monad.
366 <term>Mutable:</term>
369 Arrays that may be changed or “mutated.” All the operations on them
370 live within the state-transformer monad and the updates happen
371 <emphasis>in-place</emphasis>.
376 <term>“Static” (in C land):</term>
379 A C routine may pass an <literal>Addr#</literal> pointer back into Haskell land. There
380 are then primitive operations with which you may merrily grab values
381 over in C land, by indexing off the “static” pointer.
386 <term>“Stable” pointers:</term>
389 If, for some reason, you wish to hand a Haskell pointer (i.e.,
390 <emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
391 pointer “stable,” so that the garbage collector won't forget that it
392 exists. That is, GHC provides a safe way to pass Haskell pointers to
397 Please see <xref LinkEnd="sec-stable-pointers"> for more details.
402 <term>“Foreign objects”:</term>
405 A “foreign object” is a safe way to pass an external object (a
406 C-allocated pointer, say) to Haskell and have Haskell do the Right
407 Thing when it no longer references the object. So, for example, C
408 could pass a large bitmap over to Haskell and say “please free this
409 memory when you're done with it.”
413 Please see <xref LinkEnd="sec-ForeignObj"> for more details.
421 The libraries documentatation gives more details on all these
422 “primitive array” types and the operations on them.
428 <sect1 id="nullary-types">
429 <title>Data types with no constructors</title>
431 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
432 a data type with no constructors. For example:</para>
435 data T a -- T :: * -> *
437 <para>Syntactically, the declaration lacks the "= constrs" part. The
438 type can be parameterised, but only over ordinary types, of kind *; since
439 Haskell does not have kind signatures, you cannot parameterise over higher-kinded
442 <para>Such data types have only one value, namely bottom.
443 Nevertheless, they can be useful when defining "phantom types".</para>
446 <sect1 id="pattern-guards">
447 <title>Pattern guards</title>
450 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
451 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.)
455 Suppose we have an abstract data type of finite maps, with a
459 lookup :: FiniteMap -> Int -> Maybe Int
462 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
463 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
467 clunky env var1 var2 | ok1 && ok2 = val1 + val2
468 | otherwise = var1 + var2
479 The auxiliary functions are
483 maybeToBool :: Maybe a -> Bool
484 maybeToBool (Just x) = True
485 maybeToBool Nothing = False
487 expectJust :: Maybe a -> a
488 expectJust (Just x) = x
489 expectJust Nothing = error "Unexpected Nothing"
493 What is <function>clunky</function> doing? The guard <literal>ok1 &&
494 ok2</literal> checks that both lookups succeed, using
495 <function>maybeToBool</function> to convert the <function>Maybe</function>
496 types to booleans. The (lazily evaluated) <function>expectJust</function>
497 calls extract the values from the results of the lookups, and binds the
498 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
499 respectively. If either lookup fails, then clunky takes the
500 <literal>otherwise</literal> case and returns the sum of its arguments.
504 This is certainly legal Haskell, but it is a tremendously verbose and
505 un-obvious way to achieve the desired effect. Arguably, a more direct way
506 to write clunky would be to use case expressions:
510 clunky env var1 var1 = case lookup env var1 of
512 Just val1 -> case lookup env var2 of
514 Just val2 -> val1 + val2
520 This is a bit shorter, but hardly better. Of course, we can rewrite any set
521 of pattern-matching, guarded equations as case expressions; that is
522 precisely what the compiler does when compiling equations! The reason that
523 Haskell provides guarded equations is because they allow us to write down
524 the cases we want to consider, one at a time, independently of each other.
525 This structure is hidden in the case version. Two of the right-hand sides
526 are really the same (<function>fail</function>), and the whole expression
527 tends to become more and more indented.
531 Here is how I would write clunky:
536 | Just val1 <- lookup env var1
537 , Just val2 <- lookup env var2
539 ...other equations for clunky...
543 The semantics should be clear enough. The qualifers are matched in order.
544 For a <literal><-</literal> qualifier, which I call a pattern guard, the
545 right hand side is evaluated and matched against the pattern on the left.
546 If the match fails then the whole guard fails and the next equation is
547 tried. If it succeeds, then the appropriate binding takes place, and the
548 next qualifier is matched, in the augmented environment. Unlike list
549 comprehensions, however, the type of the expression to the right of the
550 <literal><-</literal> is the same as the type of the pattern to its
551 left. The bindings introduced by pattern guards scope over all the
552 remaining guard qualifiers, and over the right hand side of the equation.
556 Just as with list comprehensions, boolean expressions can be freely mixed
557 with among the pattern guards. For example:
568 Haskell's current guards therefore emerge as a special case, in which the
569 qualifier list has just one element, a boolean expression.
573 <sect1 id="parallel-list-comprehensions">
574 <title>Parallel List Comprehensions</title>
575 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
577 <indexterm><primary>parallel list comprehensions</primary>
580 <para>Parallel list comprehensions are a natural extension to list
581 comprehensions. List comprehensions can be thought of as a nice
582 syntax for writing maps and filters. Parallel comprehensions
583 extend this to include the zipWith family.</para>
585 <para>A parallel list comprehension has multiple independent
586 branches of qualifier lists, each separated by a `|' symbol. For
587 example, the following zips together two lists:</para>
590 [ (x, y) | x <- xs | y <- ys ]
593 <para>The behavior of parallel list comprehensions follows that of
594 zip, in that the resulting list will have the same length as the
595 shortest branch.</para>
597 <para>We can define parallel list comprehensions by translation to
598 regular comprehensions. Here's the basic idea:</para>
600 <para>Given a parallel comprehension of the form: </para>
603 [ e | p1 <- e11, p2 <- e12, ...
604 | q1 <- e21, q2 <- e22, ...
609 <para>This will be translated to: </para>
612 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
613 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
618 <para>where `zipN' is the appropriate zip for the given number of
623 <sect1 id="multi-param-type-classes">
624 <title>Multi-parameter type classes
628 This section documents GHC's implementation of multi-parameter type
629 classes. There's lots of background in the paper <ULink
630 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
631 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
636 I'd like to thank people who reported shorcomings in the GHC 3.02
637 implementation. Our default decisions were all conservative ones, and
638 the experience of these heroic pioneers has given useful concrete
639 examples to support several generalisations. (These appear below as
640 design choices not implemented in 3.02.)
644 I've discussed these notes with Mark Jones, and I believe that Hugs
645 will migrate towards the same design choices as I outline here.
646 Thanks to him, and to many others who have offered very useful
654 There are the following restrictions on the form of a qualified
661 forall tv1..tvn (c1, ...,cn) => type
667 (Here, I write the "foralls" explicitly, although the Haskell source
668 language omits them; in Haskell 1.4, all the free type variables of an
669 explicit source-language type signature are universally quantified,
670 except for the class type variables in a class declaration. However,
671 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
680 <emphasis>Each universally quantified type variable
681 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
683 The reason for this is that a value with a type that does not obey
684 this restriction could not be used without introducing
685 ambiguity. Here, for example, is an illegal type:
689 forall a. Eq a => Int
693 When a value with this type was used, the constraint <literal>Eq tv</literal>
694 would be introduced where <literal>tv</literal> is a fresh type variable, and
695 (in the dictionary-translation implementation) the value would be
696 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
697 can never know which instance of <literal>Eq</literal> to use because we never
698 get any more information about <literal>tv</literal>.
705 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
706 universally quantified type variables <literal>tvi</literal></emphasis>.
708 For example, this type is OK because <literal>C a b</literal> mentions the
709 universally quantified type variable <literal>b</literal>:
713 forall a. C a b => burble
717 The next type is illegal because the constraint <literal>Eq b</literal> does not
718 mention <literal>a</literal>:
722 forall a. Eq b => burble
726 The reason for this restriction is milder than the other one. The
727 excluded types are never useful or necessary (because the offending
728 context doesn't need to be witnessed at this point; it can be floated
729 out). Furthermore, floating them out increases sharing. Lastly,
730 excluding them is a conservative choice; it leaves a patch of
731 territory free in case we need it later.
741 These restrictions apply to all types, whether declared in a type signature
746 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
747 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
754 f :: Eq (m a) => [m a] -> [m a]
761 This choice recovers principal types, a property that Haskell 1.4 does not have.
767 <title>Class declarations</title>
775 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
779 class Collection c a where
780 union :: c a -> c a -> c a
791 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
792 of "acyclic" involves only the superclass relationships. For example,
798 op :: D b => a -> b -> b
801 class C a => D a where { ... }
805 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
806 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
807 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
814 <emphasis>There are no restrictions on the context in a class declaration
815 (which introduces superclasses), except that the class hierarchy must
816 be acyclic</emphasis>. So these class declarations are OK:
820 class Functor (m k) => FiniteMap m k where
823 class (Monad m, Monad (t m)) => Transform t m where
824 lift :: m a -> (t m) a
833 <emphasis>In the signature of a class operation, every constraint
834 must mention at least one type variable that is not a class type
841 class Collection c a where
842 mapC :: Collection c b => (a->b) -> c a -> c b
846 is OK because the constraint <literal>(Collection a b)</literal> mentions
847 <literal>b</literal>, even though it also mentions the class variable
848 <literal>a</literal>. On the other hand:
853 op :: Eq a => (a,b) -> (a,b)
857 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
858 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
859 example is easily fixed by moving the offending context up to the
864 class Eq a => C a where
869 A yet more relaxed rule would allow the context of a class-op signature
870 to mention only class type variables. However, that conflicts with
871 Rule 1(b) for types above.
878 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
879 the class type variables</emphasis>. For example:
885 insert :: s -> a -> s
889 is not OK, because the type of <literal>empty</literal> doesn't mention
890 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
891 types, and has the same motivation.
893 Sometimes, offending class declarations exhibit misunderstandings. For
894 example, <literal>Coll</literal> might be rewritten
900 insert :: s a -> a -> s a
904 which makes the connection between the type of a collection of
905 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
906 Occasionally this really doesn't work, in which case you can split the
914 class CollE s => Coll s a where
915 insert :: s -> a -> s
928 <sect2 id="instance-decls">
929 <title>Instance declarations</title>
937 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
942 instance context1 => C type1 where ...
943 instance context2 => C type2 where ...
947 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
949 However, if you give the command line option
950 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
951 option</primary></indexterm> then two overlapping instance declarations are permitted
959 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
965 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
966 (but not identical to <literal>type1</literal>)
979 Notice that these rules
986 make it clear which instance decl to use
987 (pick the most specific one that matches)
994 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
995 Reason: you can pick which instance decl
996 "matches" based on the type.
1003 Regrettably, GHC doesn't guarantee to detect overlapping instance
1004 declarations if they appear in different modules. GHC can "see" the
1005 instance declarations in the transitive closure of all the modules
1006 imported by the one being compiled, so it can "see" all instance decls
1007 when it is compiling <literal>Main</literal>. However, it currently chooses not
1008 to look at ones that can't possibly be of use in the module currently
1009 being compiled, in the interests of efficiency. (Perhaps we should
1010 change that decision, at least for <literal>Main</literal>.)
1017 <emphasis>There are no restrictions on the type in an instance
1018 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1019 The instance "head" is the bit after the "=>" in an instance decl. For
1020 example, these are OK:
1024 instance C Int a where ...
1026 instance D (Int, Int) where ...
1028 instance E [[a]] where ...
1032 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1033 For example, this is OK:
1037 instance Stateful (ST s) (MutVar s) where ...
1041 The "at least one not a type variable" restriction is to ensure that
1042 context reduction terminates: each reduction step removes one type
1043 constructor. For example, the following would make the type checker
1044 loop if it wasn't excluded:
1048 instance C a => C a where ...
1052 There are two situations in which the rule is a bit of a pain. First,
1053 if one allows overlapping instance declarations then it's quite
1054 convenient to have a "default instance" declaration that applies if
1055 something more specific does not:
1064 Second, sometimes you might want to use the following to get the
1065 effect of a "class synonym":
1069 class (C1 a, C2 a, C3 a) => C a where { }
1071 instance (C1 a, C2 a, C3 a) => C a where { }
1075 This allows you to write shorter signatures:
1087 f :: (C1 a, C2 a, C3 a) => ...
1091 I'm on the lookout for a simple rule that preserves decidability while
1092 allowing these idioms. The experimental flag
1093 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1094 option</primary></indexterm> lifts this restriction, allowing all the types in an
1095 instance head to be type variables.
1102 <emphasis>Unlike Haskell 1.4, instance heads may use type
1103 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1104 writing the RHS of the type synonym definition. For example:
1108 type Point = (Int,Int)
1109 instance C Point where ...
1110 instance C [Point] where ...
1114 is legal. However, if you added
1118 instance C (Int,Int) where ...
1122 as well, then the compiler will complain about the overlapping
1123 (actually, identical) instance declarations. As always, type synonyms
1124 must be fully applied. You cannot, for example, write:
1129 instance Monad P where ...
1133 This design decision is independent of all the others, and easily
1134 reversed, but it makes sense to me.
1141 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1142 be type variables</emphasis>. Thus
1146 instance C a b => Eq (a,b) where ...
1154 instance C Int b => Foo b where ...
1158 is not OK. Again, the intent here is to make sure that context
1159 reduction terminates.
1161 Voluminous correspondence on the Haskell mailing list has convinced me
1162 that it's worth experimenting with a more liberal rule. If you use
1163 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1164 types in an instance context. Termination is ensured by having a
1165 fixed-depth recursion stack. If you exceed the stack depth you get a
1166 sort of backtrace, and the opportunity to increase the stack depth
1167 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1180 <sect1 id="implicit-parameters">
1181 <title>Implicit parameters
1184 <para> Implicit paramters are implemented as described in
1185 "Implicit parameters: dynamic scoping with static types",
1186 J Lewis, MB Shields, E Meijer, J Launchbury,
1187 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1192 There should be more documentation, but there isn't (yet). Yell if you need it.
1196 <para> You can't have an implicit parameter in the context of a class or instance
1197 declaration. For example, both these declarations are illegal:
1199 class (?x::Int) => C a where ...
1200 instance (?x::a) => Foo [a] where ...
1202 Reason: exactly which implicit parameter you pick up depends on exactly where
1203 you invoke a function. But the ``invocation'' of instance declarations is done
1204 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1205 Easiest thing is to outlaw the offending types.</para>
1213 <sect1 id="functional-dependencies">
1214 <title>Functional dependencies
1217 <para> Functional dependencies are implemented as described by Mark Jones
1218 in "Type Classes with Functional Dependencies", Mark P. Jones,
1219 In Proceedings of the 9th European Symposium on Programming,
1220 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1224 There should be more documentation, but there isn't (yet). Yell if you need it.
1229 <sect1 id="universal-quantification">
1230 <title>Explicit universal quantification
1234 GHC's type system supports explicit universal quantification in
1235 constructor fields and function arguments. This is useful for things
1236 like defining <literal>runST</literal> from the state-thread world.
1237 GHC's syntax for this now agrees with Hugs's, namely:
1243 forall a b. (Ord a, Eq b) => a -> b -> a
1249 The context is, of course, optional. You can't use <literal>forall</literal> as
1250 a type variable any more!
1254 Haskell type signatures are implicitly quantified. The <literal>forall</literal>
1255 allows us to say exactly what this means. For example:
1273 g :: forall b. (b -> b)
1279 The two are treated identically.
1283 <title>Universally-quantified data type fields
1287 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1288 the types of the constructor arguments. Here are several examples:
1294 data T a = T1 (forall b. b -> b -> b) a
1296 data MonadT m = MkMonad { return :: forall a. a -> m a,
1297 bind :: forall a b. m a -> (a -> m b) -> m b
1300 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1306 The constructors now have so-called <emphasis>rank 2</emphasis> polymorphic
1307 types, in which there is a for-all in the argument types.:
1313 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1314 MkMonad :: forall m. (forall a. a -> m a)
1315 -> (forall a b. m a -> (a -> m b) -> m b)
1317 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1323 Notice that you don't need to use a <literal>forall</literal> if there's an
1324 explicit context. For example in the first argument of the
1325 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1326 prefixed to the argument type. The implicit <literal>forall</literal>
1327 quantifies all type variables that are not already in scope, and are
1328 mentioned in the type quantified over.
1332 As for type signatures, implicit quantification happens for non-overloaded
1333 types too. So if you write this:
1336 data T a = MkT (Either a b) (b -> b)
1339 it's just as if you had written this:
1342 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1345 That is, since the type variable <literal>b</literal> isn't in scope, it's
1346 implicitly universally quantified. (Arguably, it would be better
1347 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1348 where that is what is wanted. Feedback welcomed.)
1354 <title>Construction </title>
1357 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1358 the constructor to suitable values, just as usual. For example,
1364 (T1 (\xy->x) 3) :: T Int
1366 (MkSwizzle sort) :: Swizzle
1367 (MkSwizzle reverse) :: Swizzle
1374 MkMonad r b) :: MonadT Maybe
1380 The type of the argument can, as usual, be more general than the type
1381 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1382 does not need the <literal>Ord</literal> constraint.)
1388 <title>Pattern matching</title>
1391 When you use pattern matching, the bound variables may now have
1392 polymorphic types. For example:
1398 f :: T a -> a -> (a, Char)
1399 f (T1 f k) x = (f k x, f 'c' 'd')
1401 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1402 g (MkSwizzle s) xs f = s (map f (s xs))
1404 h :: MonadT m -> [m a] -> m [a]
1405 h m [] = return m []
1406 h m (x:xs) = bind m x $ \y ->
1407 bind m (h m xs) $ \ys ->
1414 In the function <function>h</function> we use the record selectors <literal>return</literal>
1415 and <literal>bind</literal> to extract the polymorphic bind and return functions
1416 from the <literal>MonadT</literal> data structure, rather than using pattern
1421 You cannot pattern-match against an argument that is polymorphic.
1425 newtype TIM s a = TIM (ST s (Maybe a))
1427 runTIM :: (forall s. TIM s a) -> Maybe a
1428 runTIM (TIM m) = runST m
1434 Here the pattern-match fails, because you can't pattern-match against
1435 an argument of type <literal>(forall s. TIM s a)</literal>. Instead you
1436 must bind the variable and pattern match in the right hand side:
1439 runTIM :: (forall s. TIM s a) -> Maybe a
1440 runTIM tm = case tm of { TIM m -> runST m }
1443 The <literal>tm</literal> on the right hand side is (invisibly) instantiated, like
1444 any polymorphic value at its occurrence site, and now you can pattern-match
1451 <title>The partial-application restriction</title>
1454 There is really only one way in which data structures with polymorphic
1455 components might surprise you: you must not partially apply them.
1456 For example, this is illegal:
1462 map MkSwizzle [sort, reverse]
1468 The restriction is this: <emphasis>every subexpression of the program must
1469 have a type that has no for-alls, except that in a function
1470 application (f e1…en) the partial applications are not subject to
1471 this rule</emphasis>. The restriction makes type inference feasible.
1475 In the illegal example, the sub-expression <literal>MkSwizzle</literal> has the
1476 polymorphic type <literal>(Ord b => [b] -> [b]) -> Swizzle</literal> and is not
1477 a sub-expression of an enclosing application. On the other hand, this
1484 map (T1 (\a b -> a)) [1,2,3]
1490 even though it involves a partial application of <function>T1</function>, because
1491 the sub-expression <literal>T1 (\a b -> a)</literal> has type <literal>Int -> T
1498 <title>Type signatures
1502 Once you have data constructors with universally-quantified fields, or
1503 constants such as <Constant>runST</Constant> that have rank-2 types, it isn't long
1504 before you discover that you need more! Consider:
1510 mkTs f x y = [T1 f x, T1 f y]
1516 <function>mkTs</function> is a fuction that constructs some values of type
1517 <literal>T</literal>, using some pieces passed to it. The trouble is that since
1518 <literal>f</literal> is a function argument, Haskell assumes that it is
1519 monomorphic, so we'll get a type error when applying <function>T1</function> to
1520 it. This is a rather silly example, but the problem really bites in
1521 practice. Lots of people trip over the fact that you can't make
1522 "wrappers functions" for <Constant>runST</Constant> for exactly the same reason.
1523 In short, it is impossible to build abstractions around functions with
1528 The solution is fairly clear. We provide the ability to give a rank-2
1529 type signature for <emphasis>ordinary</emphasis> functions (not only data
1530 constructors), thus:
1536 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1537 mkTs f x y = [T1 f x, T1 f y]
1543 This type signature tells the compiler to attribute <literal>f</literal> with
1544 the polymorphic type <literal>(forall b. b -> b -> b)</literal> when type
1545 checking the body of <function>mkTs</function>, so now the application of
1546 <function>T1</function> is fine.
1550 There are two restrictions:
1559 You can only define a rank 2 type, specified by the following
1564 rank2type ::= [forall tyvars .] [context =>] funty
1565 funty ::= ([forall tyvars .] [context =>] ty) -> funty
1567 ty ::= ...current Haskell monotype syntax...
1571 Informally, the universal quantification must all be right at the beginning,
1572 or at the top level of a function argument.
1579 There is a restriction on the definition of a function whose
1580 type signature is a rank-2 type: the polymorphic arguments must be
1581 matched on the left hand side of the "<literal>=</literal>" sign. You can't
1582 define <function>mkTs</function> like this:
1586 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1587 mkTs = \ f x y -> [T1 f x, T1 f y]
1592 The same partial-application rule applies to ordinary functions with
1593 rank-2 types as applied to data constructors.
1606 <title>Type synonyms and hoisting
1610 GHC also allows you to write a <literal>forall</literal> in a type synonym, thus:
1612 type Discard a = forall b. a -> b -> a
1617 However, it is often convenient to use these sort of synonyms at the right hand
1618 end of an arrow, thus:
1620 type Discard a = forall b. a -> b -> a
1622 g :: Int -> Discard Int
1625 Simply expanding the type synonym would give
1627 g :: Int -> (forall b. Int -> b -> Int)
1629 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1631 g :: forall b. Int -> Int -> b -> Int
1633 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1634 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1635 performs the transformation:</emphasis>
1637 <emphasis>type1</emphasis> -> forall a. <emphasis>type2</emphasis>
1639 forall a. <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1641 (In fact, GHC tries to retain as much synonym information as possible for use in
1642 error messages, but that is a usability issue.) This rule applies, of course, whether
1643 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1644 valid way to write <literal>g</literal>'s type signature:
1646 g :: Int -> Int -> forall b. b -> Int
1653 <sect1 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 <sect2 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 (Baz1 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 <sect1 id="sec-assertions">
1980 <indexterm><primary>Assertions</primary></indexterm>
1984 If you want to make use of assertions in your standard Haskell code, you
1985 could define a function like the following:
1991 assert :: Bool -> a -> a
1992 assert False x = error "assertion failed!"
1999 which works, but gives you back a less than useful error message --
2000 an assertion failed, but which and where?
2004 One way out is to define an extended <function>assert</function> function which also
2005 takes a descriptive string to include in the error message and
2006 perhaps combine this with the use of a pre-processor which inserts
2007 the source location where <function>assert</function> was used.
2011 Ghc offers a helping hand here, doing all of this for you. For every
2012 use of <function>assert</function> in the user's source:
2018 kelvinToC :: Double -> Double
2019 kelvinToC k = assert (k >= 0.0) (k+273.15)
2025 Ghc will rewrite this to also include the source location where the
2032 assert pred val ==> assertError "Main.hs|15" pred val
2038 The rewrite is only performed by the compiler when it spots
2039 applications of <function>Exception.assert</function>, so you can still define and
2040 use your own versions of <function>assert</function>, should you so wish. If not,
2041 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2045 To have the compiler ignore uses of assert, use the compiler option
2046 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2047 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2051 Assertion failures can be caught, see the documentation for the
2052 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2058 <sect1 id="scoped-type-variables">
2059 <title>Scoped Type Variables
2063 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2064 variable</emphasis>. For example
2070 f (xs::[a]) = ys ++ ys
2079 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2080 This brings the type variable <literal>a</literal> into scope; it scopes over
2081 all the patterns and right hand sides for this equation for <function>f</function>.
2082 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2086 Pattern type signatures are completely orthogonal to ordinary, separate
2087 type signatures. The two can be used independently or together.
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>What a pattern type signature means</title>
2112 A type variable brought into scope by a pattern type signature is simply
2113 the name for a type. The restriction they express is that all occurrences
2114 of the same name mean the same type. For example:
2116 f :: [Int] -> Int -> Int
2117 f (xs::[a]) (y::a) = (head xs + y) :: a
2119 The pattern type signatures on the left hand side of
2120 <literal>f</literal> express the fact that <literal>xs</literal>
2121 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2122 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2123 specifies that this expression must have the same type <literal>a</literal>.
2124 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2125 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2126 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2127 rules, which specified that a pattern-bound type variable should be universally quantified.)
2128 For example, all of these are legal:</para>
2131 t (x::a) (y::a) = x+y*2
2133 f (x::a) (y::b) = [x,y] -- a unifies with b
2135 g (x::a) = x + 1::Int -- a unifies with Int
2137 h x = let k (y::a) = [x,y] -- a is free in the
2138 in k x -- environment
2140 k (x::a) True = ... -- a unifies with Int
2141 k (x::Int) False = ...
2144 w (x::a) = x -- a unifies with [b]
2150 <title>Scope and implicit quantification</title>
2158 All the type variables mentioned in a pattern,
2159 that are not already in scope,
2160 are brought into scope by the pattern. We describe this set as
2161 the <emphasis>type variables bound by the pattern</emphasis>.
2164 f (x::a) = let g (y::(a,b)) = fst y
2168 The pattern <literal>(x::a)</literal> brings the type variable
2169 <literal>a</literal> into scope, as well as the term
2170 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2171 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2172 and brings into scope the type variable <literal>b</literal>.
2178 The type variable(s) bound by the pattern have the same scope
2179 as the term variable(s) bound by the pattern. For example:
2182 f (x::a) = <...rhs of f...>
2183 (p::b, q::b) = (1,2)
2184 in <...body of let...>
2186 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2187 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2188 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2189 just like <literal>p</literal> and <literal>q</literal> do.
2190 Indeed, the newly bound type variables also scope over any ordinary, separate
2191 type signatures in the <literal>let</literal> group.
2198 The type variables bound by the pattern may be
2199 mentioned in ordinary type signatures or pattern
2200 type signatures anywhere within their scope.
2207 In ordinary type signatures, any type variable mentioned in the
2208 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2216 Ordinary type signatures do not bring any new type variables
2217 into scope (except in the type signature itself!). So this is illegal:
2224 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2225 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2226 and that is an incorrect typing.
2233 The pattern type signature is a monotype:
2238 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2242 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2243 not to type schemes.
2247 There is no implicit universal quantification on pattern type signatures (in contrast to
2248 ordinary type signatures).
2258 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2259 scope over the methods defined in the <literal>where</literal> part. For example:
2273 (Not implemented in Hugs yet, Dec 98).
2284 <title>Result type signatures</title>
2292 The result type of a function can be given a signature,
2297 f (x::a) :: [a] = [x,x,x]
2301 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2302 result type. Sometimes this is the only way of naming the type variable
2307 f :: Int -> [a] -> [a]
2308 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2309 in \xs -> map g (reverse xs `zip` xs)
2321 Result type signatures are not yet implemented in Hugs.
2327 <title>Where a pattern type signature can occur</title>
2330 A pattern type signature can occur in any pattern. For example:
2335 A pattern type signature can be on an arbitrary sub-pattern, not
2340 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2349 Pattern type signatures, including the result part, can be used
2350 in lambda abstractions:
2353 (\ (x::a, y) :: a -> x)
2360 Pattern type signatures, including the result part, can be used
2361 in <literal>case</literal> expressions:
2365 case e of { (x::a, y) :: a -> x }
2373 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2374 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2375 token or a parenthesised type of some sort). To see why,
2376 consider how one would parse this:
2390 Pattern type signatures can bind existential type variables.
2395 data T = forall a. MkT [a]
2398 f (MkT [t::a]) = MkT t3
2411 Pattern type signatures
2412 can be used in pattern bindings:
2415 f x = let (y, z::a) = x in ...
2416 f1 x = let (y, z::Int) = x in ...
2417 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2418 f3 :: (b->b) = \x -> x
2421 In all such cases, the binding is not generalised over the pattern-bound
2422 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2423 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2424 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2425 In contrast, the binding
2430 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2431 in <literal>f4</literal>'s scope.
2443 <sect1 id="pragmas">
2444 <title>Pragmas</title>
2446 <indexterm><primary>pragma</primary></indexterm>
2448 <para>GHC supports several pragmas, or instructions to the
2449 compiler placed in the source code. Pragmas don't normally affect
2450 the meaning of the program, but they might affect the efficiency
2451 of the generated code.</para>
2453 <para>Pragmas all take the form
2455 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2457 where <replaceable>word</replaceable> indicates the type of
2458 pragma, and is followed optionally by information specific to that
2459 type of pragma. Case is ignored in
2460 <replaceable>word</replaceable>. The various values for
2461 <replaceable>word</replaceable> that GHC understands are described
2462 in the following sections; any pragma encountered with an
2463 unrecognised <replaceable>word</replaceable> is (silently)
2466 <sect2 id="inline-pragma">
2467 <title>INLINE pragma
2469 <indexterm><primary>INLINE pragma</primary></indexterm>
2470 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2473 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2474 functions/values that are “small enough,” thus avoiding the call
2475 overhead and possibly exposing other more-wonderful optimisations.
2479 You will probably see these unfoldings (in Core syntax) in your
2484 Normally, if GHC decides a function is “too expensive” to inline, it
2485 will not do so, nor will it export that unfolding for other modules to
2490 The sledgehammer you can bring to bear is the
2491 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2494 key_function :: Int -> String -> (Bool, Double)
2496 #ifdef __GLASGOW_HASKELL__
2497 {-# INLINE key_function #-}
2501 (You don't need to do the C pre-processor carry-on unless you're going
2502 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2506 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2507 “cost” to be very low. The normal unfolding machinery will then be
2508 very keen to inline it.
2512 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2513 signature could be put.
2517 <literal>INLINE</literal> pragmas are a particularly good idea for the
2518 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2519 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2522 #ifdef __GLASGOW_HASKELL__
2523 {-# INLINE thenUs #-}
2524 {-# INLINE returnUs #-}
2532 <sect2 id="noinline-pragma">
2533 <title>NOINLINE pragma
2536 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2537 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2538 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2539 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2542 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2543 it stops the named function from being inlined by the compiler. You
2544 shouldn't ever need to do this, unless you're very cautious about code
2548 <para><literal>NOTINLINE</literal> is a synonym for
2549 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2550 by Haskell 98 as the standard way to disable inlining, so it should be
2551 used if you want your code to be portable).</para>
2555 <sect2 id="specialize-pragma">
2556 <title>SPECIALIZE pragma</title>
2558 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2559 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2560 <indexterm><primary>overloading, death to</primary></indexterm>
2562 <para>(UK spelling also accepted.) For key overloaded
2563 functions, you can create extra versions (NB: more code space)
2564 specialised to particular types. Thus, if you have an
2565 overloaded function:</para>
2568 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2571 <para>If it is heavily used on lists with
2572 <literal>Widget</literal> keys, you could specialise it as
2576 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2579 <para>To get very fancy, you can also specify a named function
2580 to use for the specialised value, as in:</para>
2583 {-# RULES hammeredLookup = blah #-}
2586 <para>where <literal>blah</literal> is an implementation of
2587 <literal>hammerdLookup</literal> written specialy for
2588 <literal>Widget</literal> lookups. It's <emphasis>Your
2589 Responsibility</emphasis> to make sure that
2590 <function>blah</function> really behaves as a specialised
2591 version of <function>hammeredLookup</function>!!!</para>
2593 <para>Note we use the <literal>RULE</literal> pragma here to
2594 indicate that <literal>hammeredLookup</literal> applied at a
2595 certain type should be replaced by <literal>blah</literal>. See
2596 <xref linkend="rules"> for more information on
2597 <literal>RULES</literal>.</para>
2599 <para>An example in which using <literal>RULES</literal> for
2600 specialisation will Win Big:
2603 toDouble :: Real a => a -> Double
2604 toDouble = fromRational . toRational
2606 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2607 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2610 The <function>i2d</function> function is virtually one machine
2611 instruction; the default conversion—via an intermediate
2612 <literal>Rational</literal>—is obscenely expensive by
2615 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2616 be put anywhere its type signature could be put.</para>
2620 <sect2 id="specialize-instance-pragma">
2621 <title>SPECIALIZE instance pragma
2625 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2626 <indexterm><primary>overloading, death to</primary></indexterm>
2627 Same idea, except for instance declarations. For example:
2630 instance (Eq a) => Eq (Foo a) where {
2631 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2635 The pragma must occur inside the <literal>where</literal> part
2636 of the instance declaration.
2639 Compatible with HBC, by the way, except perhaps in the placement
2645 <sect2 id="line-pragma">
2650 <indexterm><primary>LINE pragma</primary></indexterm>
2651 <indexterm><primary>pragma, LINE</primary></indexterm>
2655 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2656 automatically generated Haskell code. It lets you specify the line
2657 number and filename of the original code; for example
2663 {-# LINE 42 "Foo.vhs" #-}
2669 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2670 and this line corresponds to line 42 in the original. GHC will adjust
2671 its error messages to refer to the line/file named in the <literal>LINE</literal>
2678 <title>RULES pragma</title>
2681 The RULES pragma lets you specify rewrite rules. It is described in
2682 <xref LinkEnd="rewrite-rules">.
2687 <sect2 id="deprecated-pragma">
2688 <title>DEPRECATED pragma</title>
2691 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2692 There are two forms.
2696 You can deprecate an entire module thus:</para>
2698 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2702 When you compile any module that import <literal>Wibble</literal>, GHC will print
2703 the specified message.</para>
2708 You can deprecate a function, class, or type, with the following top-level declaration:
2711 {-# DEPRECATED f, C, T "Don't use these" #-}
2714 When you compile any module that imports and uses any of the specifed entities,
2715 GHC will print the specified message.
2719 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2725 <sect1 id="rewrite-rules">
2726 <title>Rewrite rules
2728 <indexterm><primary>RULES pagma</primary></indexterm>
2729 <indexterm><primary>pragma, RULES</primary></indexterm>
2730 <indexterm><primary>rewrite rules</primary></indexterm></title>
2733 The programmer can specify rewrite rules as part of the source program
2734 (in a pragma). GHC applies these rewrite rules wherever it can.
2742 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2749 <title>Syntax</title>
2752 From a syntactic point of view:
2758 Each rule has a name, enclosed in double quotes. The name itself has
2759 no significance at all. It is only used when reporting how many times the rule fired.
2765 There may be zero or more rules in a <literal>RULES</literal> pragma.
2771 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2772 is set, so you must lay out your rules starting in the same column as the
2773 enclosing definitions.
2779 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2780 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2781 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2782 by spaces, just like in a type <literal>forall</literal>.
2788 A pattern variable may optionally have a type signature.
2789 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2790 For example, here is the <literal>foldr/build</literal> rule:
2793 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2794 foldr k z (build g) = g k z
2797 Since <function>g</function> has a polymorphic type, it must have a type signature.
2804 The left hand side of a rule must consist of a top-level variable applied
2805 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2808 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2809 "wrong2" forall f. f True = True
2812 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2819 A rule does not need to be in the same module as (any of) the
2820 variables it mentions, though of course they need to be in scope.
2826 Rules are automatically exported from a module, just as instance declarations are.
2837 <title>Semantics</title>
2840 From a semantic point of view:
2846 Rules are only applied if you use the <option>-O</option> flag.
2852 Rules are regarded as left-to-right rewrite rules.
2853 When GHC finds an expression that is a substitution instance of the LHS
2854 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
2855 By "a substitution instance" we mean that the LHS can be made equal to the
2856 expression by substituting for the pattern variables.
2863 The LHS and RHS of a rule are typechecked, and must have the
2871 GHC makes absolutely no attempt to verify that the LHS and RHS
2872 of a rule have the same meaning. That is undecideable in general, and
2873 infeasible in most interesting cases. The responsibility is entirely the programmer's!
2880 GHC makes no attempt to make sure that the rules are confluent or
2881 terminating. For example:
2884 "loop" forall x,y. f x y = f y x
2887 This rule will cause the compiler to go into an infinite loop.
2894 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
2900 GHC currently uses a very simple, syntactic, matching algorithm
2901 for matching a rule LHS with an expression. It seeks a substitution
2902 which makes the LHS and expression syntactically equal modulo alpha
2903 conversion. The pattern (rule), but not the expression, is eta-expanded if
2904 necessary. (Eta-expanding the epression can lead to laziness bugs.)
2905 But not beta conversion (that's called higher-order matching).
2909 Matching is carried out on GHC's intermediate language, which includes
2910 type abstractions and applications. So a rule only matches if the
2911 types match too. See <xref LinkEnd="rule-spec"> below.
2917 GHC keeps trying to apply the rules as it optimises the program.
2918 For example, consider:
2927 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
2928 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
2929 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
2930 not be substituted, and the rule would not fire.
2937 In the earlier phases of compilation, GHC inlines <emphasis>nothing
2938 that appears on the LHS of a rule</emphasis>, because once you have substituted
2939 for something you can't match against it (given the simple minded
2940 matching). So if you write the rule
2943 "map/map" forall f,g. map f . map g = map (f.g)
2946 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
2947 It will only match something written with explicit use of ".".
2948 Well, not quite. It <emphasis>will</emphasis> match the expression
2954 where <function>wibble</function> is defined:
2957 wibble f g = map f . map g
2960 because <function>wibble</function> will be inlined (it's small).
2962 Later on in compilation, GHC starts inlining even things on the
2963 LHS of rules, but still leaves the rules enabled. This inlining
2964 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
2971 All rules are implicitly exported from the module, and are therefore
2972 in force in any module that imports the module that defined the rule, directly
2973 or indirectly. (That is, if A imports B, which imports C, then C's rules are
2974 in force when compiling A.) The situation is very similar to that for instance
2986 <title>List fusion</title>
2989 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
2990 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
2991 intermediate list should be eliminated entirely.
2995 The following are good producers:
3007 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3013 Explicit lists (e.g. <literal>[True, False]</literal>)
3019 The cons constructor (e.g <literal>3:4:[]</literal>)
3025 <function>++</function>
3031 <function>map</function>
3037 <function>filter</function>
3043 <function>iterate</function>, <function>repeat</function>
3049 <function>zip</function>, <function>zipWith</function>
3058 The following are good consumers:
3070 <function>array</function> (on its second argument)
3076 <function>length</function>
3082 <function>++</function> (on its first argument)
3088 <function>foldr</function>
3094 <function>map</function>
3100 <function>filter</function>
3106 <function>concat</function>
3112 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3118 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3119 will fuse with one but not the other)
3125 <function>partition</function>
3131 <function>head</function>
3137 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3143 <function>sequence_</function>
3149 <function>msum</function>
3155 <function>sortBy</function>
3164 So, for example, the following should generate no intermediate lists:
3167 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3173 This list could readily be extended; if there are Prelude functions that you use
3174 a lot which are not included, please tell us.
3178 If you want to write your own good consumers or producers, look at the
3179 Prelude definitions of the above functions to see how to do so.
3184 <sect2 id="rule-spec">
3185 <title>Specialisation
3189 Rewrite rules can be used to get the same effect as a feature
3190 present in earlier version of GHC:
3193 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3196 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3197 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3198 specialising the original definition of <function>fromIntegral</function> the programmer is
3199 promising that it is safe to use <function>int8ToInt16</function> instead.
3203 This feature is no longer in GHC. But rewrite rules let you do the
3208 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3212 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3213 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3214 GHC adds the type and dictionary applications to get the typed rule
3217 forall (d1::Integral Int8) (d2::Num Int16) .
3218 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3222 this rule does not need to be in the same file as fromIntegral,
3223 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3224 have an original definition available to specialise).
3230 <title>Controlling what's going on</title>
3238 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3244 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3245 If you add <option>-dppr-debug</option> you get a more detailed listing.
3251 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3254 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3255 {-# INLINE build #-}
3259 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3260 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3261 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3262 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3269 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3270 see how to write rules that will do fusion and yet give an efficient
3271 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3283 <sect1 id="generic-classes">
3284 <title>Generic classes</title>
3286 <para>(Note: support for generic classes is currently broken in
3290 The ideas behind this extension are described in detail in "Derivable type classes",
3291 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3292 An example will give the idea:
3300 fromBin :: [Int] -> (a, [Int])
3302 toBin {| Unit |} Unit = []
3303 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3304 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3305 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3307 fromBin {| Unit |} bs = (Unit, bs)
3308 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3309 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3310 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3311 (y,bs'') = fromBin bs'
3314 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3315 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3316 which are defined thus in the library module <literal>Generics</literal>:
3320 data a :+: b = Inl a | Inr b
3321 data a :*: b = a :*: b
3324 Now you can make a data type into an instance of Bin like this:
3326 instance (Bin a, Bin b) => Bin (a,b)
3327 instance Bin a => Bin [a]
3329 That is, just leave off the "where" clasuse. Of course, you can put in the
3330 where clause and over-ride whichever methods you please.
3334 <title> Using generics </title>
3335 <para>To use generics you need to</para>
3338 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3339 <option>-fgenerics</option> (to generate extra per-data-type code),
3340 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3344 <para>Import the module <literal>Generics</literal> from the
3345 <literal>lang</literal> package. This import brings into
3346 scope the data types <literal>Unit</literal>,
3347 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3348 don't need this import if you don't mention these types
3349 explicitly; for example, if you are simply giving instance
3350 declarations.)</para>
3355 <sect2> <title> Changes wrt the paper </title>
3357 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3358 can be written infix (indeed, you can now use
3359 any operator starting in a colon as an infix type constructor). Also note that
3360 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3361 Finally, note that the syntax of the type patterns in the class declaration
3362 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3363 alone would ambiguous when they appear on right hand sides (an extension we
3364 anticipate wanting).
3368 <sect2> <title>Terminology and restrictions</title>
3370 Terminology. A "generic default method" in a class declaration
3371 is one that is defined using type patterns as above.
3372 A "polymorphic default method" is a default method defined as in Haskell 98.
3373 A "generic class declaration" is a class declaration with at least one
3374 generic default method.
3382 Alas, we do not yet implement the stuff about constructor names and
3389 A generic class can have only one parameter; you can't have a generic
3390 multi-parameter class.
3396 A default method must be defined entirely using type patterns, or entirely
3397 without. So this is illegal:
3400 op :: a -> (a, Bool)
3401 op {| Unit |} Unit = (Unit, True)
3404 However it is perfectly OK for some methods of a generic class to have
3405 generic default methods and others to have polymorphic default methods.
3411 The type variable(s) in the type pattern for a generic method declaration
3412 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:
3416 op {| p :*: q |} (x :*: y) = op (x :: p)
3424 The type patterns in a generic default method must take one of the forms:
3430 where "a" and "b" are type variables. Furthermore, all the type patterns for
3431 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3432 must use the same type variables. So this is illegal:
3436 op {| a :+: b |} (Inl x) = True
3437 op {| p :+: q |} (Inr y) = False
3439 The type patterns must be identical, even in equations for different methods of the class.
3440 So this too is illegal:
3444 op1 {| a :*: b |} (x :*: y) = True
3447 op2 {| p :*: q |} (x :*: y) = False
3449 (The reason for this restriction is that we gather all the equations for a particular type consructor
3450 into a single generic instance declaration.)
3456 A generic method declaration must give a case for each of the three type constructors.
3462 The type for a generic method can be built only from:
3464 <listitem> <para> Function arrows </para> </listitem>
3465 <listitem> <para> Type variables </para> </listitem>
3466 <listitem> <para> Tuples </para> </listitem>
3467 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3469 Here are some example type signatures for generic methods:
3472 op2 :: Bool -> (a,Bool)
3473 op3 :: [Int] -> a -> a
3476 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3480 This restriction is an implementation restriction: we just havn't got around to
3481 implementing the necessary bidirectional maps over arbitrary type constructors.
3482 It would be relatively easy to add specific type constructors, such as Maybe and list,
3483 to the ones that are allowed.</para>
3488 In an instance declaration for a generic class, the idea is that the compiler
3489 will fill in the methods for you, based on the generic templates. However it can only
3494 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3499 No constructor of the instance type has unboxed fields.
3503 (Of course, these things can only arise if you are already using GHC extensions.)
3504 However, you can still give an instance declarations for types which break these rules,
3505 provided you give explicit code to override any generic default methods.
3513 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3514 what the compiler does with generic declarations.
3519 <sect2> <title> Another example </title>
3521 Just to finish with, here's another example I rather like:
3525 nCons {| Unit |} _ = 1
3526 nCons {| a :*: b |} _ = 1
3527 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3530 tag {| Unit |} _ = 1
3531 tag {| a :*: b |} _ = 1
3532 tag {| a :+: b |} (Inl x) = tag x
3533 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3540 ;;; Local Variables: ***
3542 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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