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 <emphasis>whatever
244 is in scope</emphasis>, 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 still used for comparison,
264 but the necessary subtraction uses whatever
265 "<literal>(-)</literal>" is in scope (not
266 "<literal>Prelude.(-)</literal>").</para>
270 <para>Note: Negative literals, such as <literal>-3</literal>, are
271 specified by (a careful reading of) the Haskell Report as
272 meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
273 However, GHC deviates from this slightly, and treats them as meaning
274 <literal>fromInteger (-3)</literal>. One particular effect of this
275 slightly-non-standard reading is that there is no difficulty with
276 the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
277 it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
278 would be <literal>negate (fromInteger 21474836483)</literal>,
279 and the call to <literal>fromInteger</literal> would overflow (at type <literal>Int</literal>, remember).
288 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
291 <sect1 id="glasgow-ST-monad">
292 <title>Primitive state-transformer monad</title>
295 <indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
296 <indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
300 This monad underlies our implementation of arrays, mutable and
301 immutable, and our implementation of I/O, including “C calls”.
305 The <literal>ST</literal> library, which provides access to the
306 <function>ST</function> monad, is described in <xref
312 <sect1 id="glasgow-prim-arrays">
313 <title>Primitive arrays, mutable and otherwise
317 <indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
318 <indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
322 GHC knows about quite a few flavours of Large Swathes of Bytes.
326 First, GHC distinguishes between primitive arrays of (boxed) Haskell
327 objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
328 <literal>ByteArray#</literal>).
332 Second, it distinguishes between…
336 <term>Immutable:</term>
339 Arrays that do not change (as with “standard” Haskell arrays); you
340 can only read from them. Obviously, they do not need the care and
341 attention of the state-transformer monad.
346 <term>Mutable:</term>
349 Arrays that may be changed or “mutated.” All the operations on them
350 live within the state-transformer monad and the updates happen
351 <emphasis>in-place</emphasis>.
356 <term>“Static” (in C land):</term>
359 A C routine may pass an <literal>Addr#</literal> pointer back into Haskell land. There
360 are then primitive operations with which you may merrily grab values
361 over in C land, by indexing off the “static” pointer.
366 <term>“Stable” pointers:</term>
369 If, for some reason, you wish to hand a Haskell pointer (i.e.,
370 <emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
371 pointer “stable,” so that the garbage collector won't forget that it
372 exists. That is, GHC provides a safe way to pass Haskell pointers to
377 Please see <xref LinkEnd="sec-stable-pointers"> for more details.
382 <term>“Foreign objects”:</term>
385 A “foreign object” is a safe way to pass an external object (a
386 C-allocated pointer, say) to Haskell and have Haskell do the Right
387 Thing when it no longer references the object. So, for example, C
388 could pass a large bitmap over to Haskell and say “please free this
389 memory when you're done with it.”
393 Please see <xref LinkEnd="sec-ForeignObj"> for more details.
401 The libraries documentatation gives more details on all these
402 “primitive array” types and the operations on them.
408 <sect1 id="pattern-guards">
409 <title>Pattern guards</title>
412 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
413 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.)
417 Suppose we have an abstract data type of finite maps, with a
421 lookup :: FiniteMap -> Int -> Maybe Int
424 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
425 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
429 clunky env var1 var2 | ok1 && ok2 = val1 + val2
430 | otherwise = var1 + var2
441 The auxiliary functions are
445 maybeToBool :: Maybe a -> Bool
446 maybeToBool (Just x) = True
447 maybeToBool Nothing = False
449 expectJust :: Maybe a -> a
450 expectJust (Just x) = x
451 expectJust Nothing = error "Unexpected Nothing"
455 What is <function>clunky</function> doing? The guard <literal>ok1 &&
456 ok2</literal> checks that both lookups succeed, using
457 <function>maybeToBool</function> to convert the <function>Maybe</function>
458 types to booleans. The (lazily evaluated) <function>expectJust</function>
459 calls extract the values from the results of the lookups, and binds the
460 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
461 respectively. If either lookup fails, then clunky takes the
462 <literal>otherwise</literal> case and returns the sum of its arguments.
466 This is certainly legal Haskell, but it is a tremendously verbose and
467 un-obvious way to achieve the desired effect. Arguably, a more direct way
468 to write clunky would be to use case expressions:
472 clunky env var1 var1 = case lookup env var1 of
474 Just val1 -> case lookup env var2 of
476 Just val2 -> val1 + val2
482 This is a bit shorter, but hardly better. Of course, we can rewrite any set
483 of pattern-matching, guarded equations as case expressions; that is
484 precisely what the compiler does when compiling equations! The reason that
485 Haskell provides guarded equations is because they allow us to write down
486 the cases we want to consider, one at a time, independently of each other.
487 This structure is hidden in the case version. Two of the right-hand sides
488 are really the same (<function>fail</function>), and the whole expression
489 tends to become more and more indented.
493 Here is how I would write clunky:
498 | Just val1 <- lookup env var1
499 , Just val2 <- lookup env var2
501 ...other equations for clunky...
505 The semantics should be clear enough. The qualifers are matched in order.
506 For a <literal><-</literal> qualifier, which I call a pattern guard, the
507 right hand side is evaluated and matched against the pattern on the left.
508 If the match fails then the whole guard fails and the next equation is
509 tried. If it succeeds, then the appropriate binding takes place, and the
510 next qualifier is matched, in the augmented environment. Unlike list
511 comprehensions, however, the type of the expression to the right of the
512 <literal><-</literal> is the same as the type of the pattern to its
513 left. The bindings introduced by pattern guards scope over all the
514 remaining guard qualifiers, and over the right hand side of the equation.
518 Just as with list comprehensions, boolean expressions can be freely mixed
519 with among the pattern guards. For example:
530 Haskell's current guards therefore emerge as a special case, in which the
531 qualifier list has just one element, a boolean expression.
536 <title>The foreign interface</title>
538 <para>The foreign interface consists of the following components:</para>
542 <para>The Foreign Function Interface language specification
543 (included in this manual, in <xref linkend="ffi">).</para>
547 <para>The <literal>Foreign</literal> module (see <xref
548 linkend="sec-Foreign">) collects together several interfaces
549 which are useful in specifying foreign language
550 interfaces, including the following:</para>
554 <para>The <literal>ForeignObj</literal> module (see <xref
555 linkend="sec-ForeignObj">), for managing pointers from
556 Haskell into the outside world.</para>
560 <para>The <literal>StablePtr</literal> module (see <xref
561 linkend="sec-stable-pointers">), for managing pointers
562 into Haskell from the outside world.</para>
566 <para>The <literal>CTypes</literal> module (see <xref
567 linkend="sec-CTypes">) gives Haskell equivalents for the
568 standard C datatypes, for use in making Haskell bindings
569 to existing C libraries.</para>
573 <para>The <literal>CTypesISO</literal> module (see <xref
574 linkend="sec-CTypesISO">) gives Haskell equivalents for C
575 types defined by the ISO C standard.</para>
579 <para>The <literal>Storable</literal> library, for
580 primitive marshalling of data types between Haskell and
581 the foreign language.</para>
588 <para>The following sections also give some hints and tips on the use
589 of the foreign function interface in GHC.</para>
591 <sect2 id="glasgow-foreign-headers">
592 <title>Using function headers
596 <indexterm><primary>C calls, function headers</primary></indexterm>
600 When generating C (using the <option>-fvia-C</option> directive), one can assist the
601 C compiler in detecting type errors by using the <Command>-#include</Command> directive
602 to provide <filename>.h</filename> files containing function headers.
614 void initialiseEFS (HsInt size);
615 HsInt terminateEFS (void);
616 HsForeignObj emptyEFS(void);
617 HsForeignObj updateEFS (HsForeignObj a, HsInt i, HsInt x);
618 HsInt lookupEFS (HsForeignObj a, HsInt i);
622 <para>The types <literal>HsInt</literal>,
623 <literal>HsForeignObj</literal> etc. are described in <xref
624 linkend="sec-mapping-table">.</para>
626 <para>Note that this approach is only
627 <emphasis>essential</emphasis> for returning
628 <literal>float</literal>s (or if <literal>sizeof(int) !=
629 sizeof(int *)</literal> on your architecture) but is a Good
630 Thing for anyone who cares about writing solid code. You're
631 crazy not to do it.</para>
637 <sect1 id="multi-param-type-classes">
638 <title>Multi-parameter type classes
642 This section documents GHC's implementation of multi-parameter type
643 classes. There's lots of background in the paper <ULink
644 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
645 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
650 I'd like to thank people who reported shorcomings in the GHC 3.02
651 implementation. Our default decisions were all conservative ones, and
652 the experience of these heroic pioneers has given useful concrete
653 examples to support several generalisations. (These appear below as
654 design choices not implemented in 3.02.)
658 I've discussed these notes with Mark Jones, and I believe that Hugs
659 will migrate towards the same design choices as I outline here.
660 Thanks to him, and to many others who have offered very useful
668 There are the following restrictions on the form of a qualified
675 forall tv1..tvn (c1, ...,cn) => type
681 (Here, I write the "foralls" explicitly, although the Haskell source
682 language omits them; in Haskell 1.4, all the free type variables of an
683 explicit source-language type signature are universally quantified,
684 except for the class type variables in a class declaration. However,
685 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
694 <emphasis>Each universally quantified type variable
695 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
697 The reason for this is that a value with a type that does not obey
698 this restriction could not be used without introducing
699 ambiguity. Here, for example, is an illegal type:
703 forall a. Eq a => Int
707 When a value with this type was used, the constraint <literal>Eq tv</literal>
708 would be introduced where <literal>tv</literal> is a fresh type variable, and
709 (in the dictionary-translation implementation) the value would be
710 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
711 can never know which instance of <literal>Eq</literal> to use because we never
712 get any more information about <literal>tv</literal>.
719 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
720 universally quantified type variables <literal>tvi</literal></emphasis>.
722 For example, this type is OK because <literal>C a b</literal> mentions the
723 universally quantified type variable <literal>b</literal>:
727 forall a. C a b => burble
731 The next type is illegal because the constraint <literal>Eq b</literal> does not
732 mention <literal>a</literal>:
736 forall a. Eq b => burble
740 The reason for this restriction is milder than the other one. The
741 excluded types are never useful or necessary (because the offending
742 context doesn't need to be witnessed at this point; it can be floated
743 out). Furthermore, floating them out increases sharing. Lastly,
744 excluding them is a conservative choice; it leaves a patch of
745 territory free in case we need it later.
755 These restrictions apply to all types, whether declared in a type signature
760 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
761 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
768 f :: Eq (m a) => [m a] -> [m a]
775 This choice recovers principal types, a property that Haskell 1.4 does not have.
781 <title>Class declarations</title>
789 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
793 class Collection c a where
794 union :: c a -> c a -> c a
805 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
806 of "acyclic" involves only the superclass relationships. For example,
812 op :: D b => a -> b -> b
815 class C a => D a where { ... }
819 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
820 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
821 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
828 <emphasis>There are no restrictions on the context in a class declaration
829 (which introduces superclasses), except that the class hierarchy must
830 be acyclic</emphasis>. So these class declarations are OK:
834 class Functor (m k) => FiniteMap m k where
837 class (Monad m, Monad (t m)) => Transform t m where
838 lift :: m a -> (t m) a
847 <emphasis>In the signature of a class operation, every constraint
848 must mention at least one type variable that is not a class type
855 class Collection c a where
856 mapC :: Collection c b => (a->b) -> c a -> c b
860 is OK because the constraint <literal>(Collection a b)</literal> mentions
861 <literal>b</literal>, even though it also mentions the class variable
862 <literal>a</literal>. On the other hand:
867 op :: Eq a => (a,b) -> (a,b)
871 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
872 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
873 example is easily fixed by moving the offending context up to the
878 class Eq a => C a where
883 A yet more relaxed rule would allow the context of a class-op signature
884 to mention only class type variables. However, that conflicts with
885 Rule 1(b) for types above.
892 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
893 the class type variables</emphasis>. For example:
899 insert :: s -> a -> s
903 is not OK, because the type of <literal>empty</literal> doesn't mention
904 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
905 types, and has the same motivation.
907 Sometimes, offending class declarations exhibit misunderstandings. For
908 example, <literal>Coll</literal> might be rewritten
914 insert :: s a -> a -> s a
918 which makes the connection between the type of a collection of
919 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
920 Occasionally this really doesn't work, in which case you can split the
928 class CollE s => Coll s a where
929 insert :: s -> a -> s
942 <sect2 id="instance-decls">
943 <title>Instance declarations</title>
951 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
956 instance context1 => C type1 where ...
957 instance context2 => C type2 where ...
961 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
963 However, if you give the command line option
964 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
965 option</primary></indexterm> then two overlapping instance declarations are permitted
973 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
979 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
980 (but not identical to <literal>type1</literal>)
993 Notice that these rules
1000 make it clear which instance decl to use
1001 (pick the most specific one that matches)
1008 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1009 Reason: you can pick which instance decl
1010 "matches" based on the type.
1017 Regrettably, GHC doesn't guarantee to detect overlapping instance
1018 declarations if they appear in different modules. GHC can "see" the
1019 instance declarations in the transitive closure of all the modules
1020 imported by the one being compiled, so it can "see" all instance decls
1021 when it is compiling <literal>Main</literal>. However, it currently chooses not
1022 to look at ones that can't possibly be of use in the module currently
1023 being compiled, in the interests of efficiency. (Perhaps we should
1024 change that decision, at least for <literal>Main</literal>.)
1031 <emphasis>There are no restrictions on the type in an instance
1032 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1033 The instance "head" is the bit after the "=>" in an instance decl. For
1034 example, these are OK:
1038 instance C Int a where ...
1040 instance D (Int, Int) where ...
1042 instance E [[a]] where ...
1046 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1047 For example, this is OK:
1051 instance Stateful (ST s) (MutVar s) where ...
1055 The "at least one not a type variable" restriction is to ensure that
1056 context reduction terminates: each reduction step removes one type
1057 constructor. For example, the following would make the type checker
1058 loop if it wasn't excluded:
1062 instance C a => C a where ...
1066 There are two situations in which the rule is a bit of a pain. First,
1067 if one allows overlapping instance declarations then it's quite
1068 convenient to have a "default instance" declaration that applies if
1069 something more specific does not:
1078 Second, sometimes you might want to use the following to get the
1079 effect of a "class synonym":
1083 class (C1 a, C2 a, C3 a) => C a where { }
1085 instance (C1 a, C2 a, C3 a) => C a where { }
1089 This allows you to write shorter signatures:
1101 f :: (C1 a, C2 a, C3 a) => ...
1105 I'm on the lookout for a simple rule that preserves decidability while
1106 allowing these idioms. The experimental flag
1107 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1108 option</primary></indexterm> lifts this restriction, allowing all the types in an
1109 instance head to be type variables.
1116 <emphasis>Unlike Haskell 1.4, instance heads may use type
1117 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1118 writing the RHS of the type synonym definition. For example:
1122 type Point = (Int,Int)
1123 instance C Point where ...
1124 instance C [Point] where ...
1128 is legal. However, if you added
1132 instance C (Int,Int) where ...
1136 as well, then the compiler will complain about the overlapping
1137 (actually, identical) instance declarations. As always, type synonyms
1138 must be fully applied. You cannot, for example, write:
1143 instance Monad P where ...
1147 This design decision is independent of all the others, and easily
1148 reversed, but it makes sense to me.
1155 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1156 be type variables</emphasis>. Thus
1160 instance C a b => Eq (a,b) where ...
1168 instance C Int b => Foo b where ...
1172 is not OK. Again, the intent here is to make sure that context
1173 reduction terminates.
1175 Voluminous correspondence on the Haskell mailing list has convinced me
1176 that it's worth experimenting with a more liberal rule. If you use
1177 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1178 types in an instance context. Termination is ensured by having a
1179 fixed-depth recursion stack. If you exceed the stack depth you get a
1180 sort of backtrace, and the opportunity to increase the stack depth
1181 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1194 <sect1 id="implicit-parameters">
1195 <title>Implicit parameters
1198 <para> Implicit paramters are implemented as described in
1199 "Implicit parameters: dynamic scoping with static types",
1200 J Lewis, MB Shields, E Meijer, J Launchbury,
1201 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1206 There should be more documentation, but there isn't (yet). Yell if you need it.
1210 <para> You can't have an implicit parameter in the context of a class or instance
1211 declaration. For example, both these declarations are illegal:
1213 class (?x::Int) => C a where ...
1214 instance (?x::a) => Foo [a] where ...
1216 Reason: exactly which implicit parameter you pick up depends on exactly where
1217 you invoke a function. But the ``invocation'' of instance declarations is done
1218 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1219 Easiest thing is to outlaw the offending types.</para>
1227 <sect1 id="functional-dependencies">
1228 <title>Functional dependencies
1231 <para> Functional dependencies are implemented as described by Mark Jones
1232 in "Type Classes with Functional Dependencies", Mark P. Jones,
1233 In Proceedings of the 9th European Symposium on Programming,
1234 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1238 There should be more documentation, but there isn't (yet). Yell if you need it.
1243 <sect1 id="universal-quantification">
1244 <title>Explicit universal quantification
1248 GHC's type system supports explicit universal quantification in
1249 constructor fields and function arguments. This is useful for things
1250 like defining <literal>runST</literal> from the state-thread world.
1251 GHC's syntax for this now agrees with Hugs's, namely:
1257 forall a b. (Ord a, Eq b) => a -> b -> a
1263 The context is, of course, optional. You can't use <literal>forall</literal> as
1264 a type variable any more!
1268 Haskell type signatures are implicitly quantified. The <literal>forall</literal>
1269 allows us to say exactly what this means. For example:
1287 g :: forall b. (b -> b)
1293 The two are treated identically.
1297 <title>Universally-quantified data type fields
1301 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1302 the types of the constructor arguments. Here are several examples:
1308 data T a = T1 (forall b. b -> b -> b) a
1310 data MonadT m = MkMonad { return :: forall a. a -> m a,
1311 bind :: forall a b. m a -> (a -> m b) -> m b
1314 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1320 The constructors now have so-called <emphasis>rank 2</emphasis> polymorphic
1321 types, in which there is a for-all in the argument types.:
1327 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1328 MkMonad :: forall m. (forall a. a -> m a)
1329 -> (forall a b. m a -> (a -> m b) -> m b)
1331 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1337 Notice that you don't need to use a <literal>forall</literal> if there's an
1338 explicit context. For example in the first argument of the
1339 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1340 prefixed to the argument type. The implicit <literal>forall</literal>
1341 quantifies all type variables that are not already in scope, and are
1342 mentioned in the type quantified over.
1346 As for type signatures, implicit quantification happens for non-overloaded
1347 types too. So if you write this:
1350 data T a = MkT (Either a b) (b -> b)
1353 it's just as if you had written this:
1356 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1359 That is, since the type variable <literal>b</literal> isn't in scope, it's
1360 implicitly universally quantified. (Arguably, it would be better
1361 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1362 where that is what is wanted. Feedback welcomed.)
1368 <title>Construction </title>
1371 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1372 the constructor to suitable values, just as usual. For example,
1378 (T1 (\xy->x) 3) :: T Int
1380 (MkSwizzle sort) :: Swizzle
1381 (MkSwizzle reverse) :: Swizzle
1388 MkMonad r b) :: MonadT Maybe
1394 The type of the argument can, as usual, be more general than the type
1395 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1396 does not need the <literal>Ord</literal> constraint.)
1402 <title>Pattern matching</title>
1405 When you use pattern matching, the bound variables may now have
1406 polymorphic types. For example:
1412 f :: T a -> a -> (a, Char)
1413 f (T1 f k) x = (f k x, f 'c' 'd')
1415 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1416 g (MkSwizzle s) xs f = s (map f (s xs))
1418 h :: MonadT m -> [m a] -> m [a]
1419 h m [] = return m []
1420 h m (x:xs) = bind m x $ \y ->
1421 bind m (h m xs) $ \ys ->
1428 In the function <function>h</function> we use the record selectors <literal>return</literal>
1429 and <literal>bind</literal> to extract the polymorphic bind and return functions
1430 from the <literal>MonadT</literal> data structure, rather than using pattern
1435 You cannot pattern-match against an argument that is polymorphic.
1439 newtype TIM s a = TIM (ST s (Maybe a))
1441 runTIM :: (forall s. TIM s a) -> Maybe a
1442 runTIM (TIM m) = runST m
1448 Here the pattern-match fails, because you can't pattern-match against
1449 an argument of type <literal>(forall s. TIM s a)</literal>. Instead you
1450 must bind the variable and pattern match in the right hand side:
1453 runTIM :: (forall s. TIM s a) -> Maybe a
1454 runTIM tm = case tm of { TIM m -> runST m }
1457 The <literal>tm</literal> on the right hand side is (invisibly) instantiated, like
1458 any polymorphic value at its occurrence site, and now you can pattern-match
1465 <title>The partial-application restriction</title>
1468 There is really only one way in which data structures with polymorphic
1469 components might surprise you: you must not partially apply them.
1470 For example, this is illegal:
1476 map MkSwizzle [sort, reverse]
1482 The restriction is this: <emphasis>every subexpression of the program must
1483 have a type that has no for-alls, except that in a function
1484 application (f e1…en) the partial applications are not subject to
1485 this rule</emphasis>. The restriction makes type inference feasible.
1489 In the illegal example, the sub-expression <literal>MkSwizzle</literal> has the
1490 polymorphic type <literal>(Ord b => [b] -> [b]) -> Swizzle</literal> and is not
1491 a sub-expression of an enclosing application. On the other hand, this
1498 map (T1 (\a b -> a)) [1,2,3]
1504 even though it involves a partial application of <function>T1</function>, because
1505 the sub-expression <literal>T1 (\a b -> a)</literal> has type <literal>Int -> T
1512 <title>Type signatures
1516 Once you have data constructors with universally-quantified fields, or
1517 constants such as <Constant>runST</Constant> that have rank-2 types, it isn't long
1518 before you discover that you need more! Consider:
1524 mkTs f x y = [T1 f x, T1 f y]
1530 <function>mkTs</function> is a fuction that constructs some values of type
1531 <literal>T</literal>, using some pieces passed to it. The trouble is that since
1532 <literal>f</literal> is a function argument, Haskell assumes that it is
1533 monomorphic, so we'll get a type error when applying <function>T1</function> to
1534 it. This is a rather silly example, but the problem really bites in
1535 practice. Lots of people trip over the fact that you can't make
1536 "wrappers functions" for <Constant>runST</Constant> for exactly the same reason.
1537 In short, it is impossible to build abstractions around functions with
1542 The solution is fairly clear. We provide the ability to give a rank-2
1543 type signature for <emphasis>ordinary</emphasis> functions (not only data
1544 constructors), thus:
1550 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1551 mkTs f x y = [T1 f x, T1 f y]
1557 This type signature tells the compiler to attribute <literal>f</literal> with
1558 the polymorphic type <literal>(forall b. b -> b -> b)</literal> when type
1559 checking the body of <function>mkTs</function>, so now the application of
1560 <function>T1</function> is fine.
1564 There are two restrictions:
1573 You can only define a rank 2 type, specified by the following
1578 rank2type ::= [forall tyvars .] [context =>] funty
1579 funty ::= ([forall tyvars .] [context =>] ty) -> funty
1581 ty ::= ...current Haskell monotype syntax...
1585 Informally, the universal quantification must all be right at the beginning,
1586 or at the top level of a function argument.
1593 There is a restriction on the definition of a function whose
1594 type signature is a rank-2 type: the polymorphic arguments must be
1595 matched on the left hand side of the "<literal>=</literal>" sign. You can't
1596 define <function>mkTs</function> like this:
1600 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1601 mkTs = \ f x y -> [T1 f x, T1 f y]
1606 The same partial-application rule applies to ordinary functions with
1607 rank-2 types as applied to data constructors.
1620 <title>Type synonyms and hoisting
1624 GHC also allows you to write a <literal>forall</literal> in a type synonym, thus:
1626 type Discard a = forall b. a -> b -> a
1631 However, it is often convenient to use these sort of synonyms at the right hand
1632 end of an arrow, thus:
1634 type Discard a = forall b. a -> b -> a
1636 g :: Int -> Discard Int
1639 Simply expanding the type synonym would give
1641 g :: Int -> (forall b. Int -> b -> Int)
1643 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1645 g :: forall b. Int -> Int -> b -> Int
1647 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1648 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1649 performs the transformation:</emphasis>
1651 <emphasis>type1</emphasis> -> forall a. <emphasis>type2</emphasis>
1653 forall a. <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1655 (In fact, GHC tries to retain as much synonym information as possible for use in
1656 error messages, but that is a usability issue.) This rule applies, of course, whether
1657 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1658 valid way to write <literal>g</literal>'s type signature:
1660 g :: Int -> Int -> forall b. b -> Int
1667 <sect1 id="existential-quantification">
1668 <title>Existentially quantified data constructors
1672 The idea of using existential quantification in data type declarations
1673 was suggested by Laufer (I believe, thought doubtless someone will
1674 correct me), and implemented in Hope+. It's been in Lennart
1675 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1676 proved very useful. Here's the idea. Consider the declaration:
1682 data Foo = forall a. MkFoo a (a -> Bool)
1689 The data type <literal>Foo</literal> has two constructors with types:
1695 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1702 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1703 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1704 For example, the following expression is fine:
1710 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1716 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1717 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1718 isUpper</function> packages a character with a compatible function. These
1719 two things are each of type <literal>Foo</literal> and can be put in a list.
1723 What can we do with a value of type <literal>Foo</literal>?. In particular,
1724 what happens when we pattern-match on <function>MkFoo</function>?
1730 f (MkFoo val fn) = ???
1736 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1737 are compatible, the only (useful) thing we can do with them is to
1738 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1745 f (MkFoo val fn) = fn val
1751 What this allows us to do is to package heterogenous values
1752 together with a bunch of functions that manipulate them, and then treat
1753 that collection of packages in a uniform manner. You can express
1754 quite a bit of object-oriented-like programming this way.
1757 <sect2 id="existential">
1758 <title>Why existential?
1762 What has this to do with <emphasis>existential</emphasis> quantification?
1763 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1769 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1775 But Haskell programmers can safely think of the ordinary
1776 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1777 adding a new existential quantification construct.
1783 <title>Type classes</title>
1786 An easy extension (implemented in <Command>hbc</Command>) is to allow
1787 arbitrary contexts before the constructor. For example:
1793 data Baz = forall a. Eq a => Baz1 a a
1794 | forall b. Show b => Baz2 b (b -> b)
1800 The two constructors have the types you'd expect:
1806 Baz1 :: forall a. Eq a => a -> a -> Baz
1807 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1813 But when pattern matching on <function>Baz1</function> the matched values can be compared
1814 for equality, and when pattern matching on <function>Baz2</function> the first matched
1815 value can be converted to a string (as well as applying the function to it).
1816 So this program is legal:
1823 f (Baz1 p q) | p == q = "Yes"
1825 f (Baz1 v fn) = show (fn v)
1831 Operationally, in a dictionary-passing implementation, the
1832 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1833 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1834 extract it on pattern matching.
1838 Notice the way that the syntax fits smoothly with that used for
1839 universal quantification earlier.
1845 <title>Restrictions</title>
1848 There are several restrictions on the ways in which existentially-quantified
1849 constructors can be use.
1858 When pattern matching, each pattern match introduces a new,
1859 distinct, type for each existential type variable. These types cannot
1860 be unified with any other type, nor can they escape from the scope of
1861 the pattern match. For example, these fragments are incorrect:
1869 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1870 is the result of <function>f1</function>. One way to see why this is wrong is to
1871 ask what type <function>f1</function> has:
1875 f1 :: Foo -> a -- Weird!
1879 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1884 f1 :: forall a. Foo -> a -- Wrong!
1888 The original program is just plain wrong. Here's another sort of error
1892 f2 (Baz1 a b) (Baz1 p q) = a==q
1896 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1897 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1898 from the two <function>Baz1</function> constructors.
1906 You can't pattern-match on an existentially quantified
1907 constructor in a <literal>let</literal> or <literal>where</literal> group of
1908 bindings. So this is illegal:
1912 f3 x = a==b where { Baz1 a b = x }
1916 You can only pattern-match
1917 on an existentially-quantified constructor in a <literal>case</literal> expression or
1918 in the patterns of a function definition.
1920 The reason for this restriction is really an implementation one.
1921 Type-checking binding groups is already a nightmare without
1922 existentials complicating the picture. Also an existential pattern
1923 binding at the top level of a module doesn't make sense, because it's
1924 not clear how to prevent the existentially-quantified type "escaping".
1925 So for now, there's a simple-to-state restriction. We'll see how
1933 You can't use existential quantification for <literal>newtype</literal>
1934 declarations. So this is illegal:
1938 newtype T = forall a. Ord a => MkT a
1942 Reason: a value of type <literal>T</literal> must be represented as a pair
1943 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1944 That contradicts the idea that <literal>newtype</literal> should have no
1945 concrete representation. You can get just the same efficiency and effect
1946 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1947 overloading involved, then there is more of a case for allowing
1948 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1949 because the <literal>data</literal> version does carry an implementation cost,
1950 but single-field existentially quantified constructors aren't much
1951 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1952 stands, unless there are convincing reasons to change it.
1960 You can't use <literal>deriving</literal> to define instances of a
1961 data type with existentially quantified data constructors.
1963 Reason: in most cases it would not make sense. For example:#
1966 data T = forall a. MkT [a] deriving( Eq )
1969 To derive <literal>Eq</literal> in the standard way we would need to have equality
1970 between the single component of two <function>MkT</function> constructors:
1974 (MkT a) == (MkT b) = ???
1977 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1978 It's just about possible to imagine examples in which the derived instance
1979 would make sense, but it seems altogether simpler simply to prohibit such
1980 declarations. Define your own instances!
1992 <sect1 id="sec-assertions">
1994 <indexterm><primary>Assertions</primary></indexterm>
1998 If you want to make use of assertions in your standard Haskell code, you
1999 could define a function like the following:
2005 assert :: Bool -> a -> a
2006 assert False x = error "assertion failed!"
2013 which works, but gives you back a less than useful error message --
2014 an assertion failed, but which and where?
2018 One way out is to define an extended <function>assert</function> function which also
2019 takes a descriptive string to include in the error message and
2020 perhaps combine this with the use of a pre-processor which inserts
2021 the source location where <function>assert</function> was used.
2025 Ghc offers a helping hand here, doing all of this for you. For every
2026 use of <function>assert</function> in the user's source:
2032 kelvinToC :: Double -> Double
2033 kelvinToC k = assert (k >= 0.0) (k+273.15)
2039 Ghc will rewrite this to also include the source location where the
2046 assert pred val ==> assertError "Main.hs|15" pred val
2052 The rewrite is only performed by the compiler when it spots
2053 applications of <function>Exception.assert</function>, so you can still define and
2054 use your own versions of <function>assert</function>, should you so wish. If not,
2055 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2059 To have the compiler ignore uses of assert, use the compiler option
2060 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2061 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2065 Assertion failures can be caught, see the documentation for the
2066 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2072 <sect1 id="scoped-type-variables">
2073 <title>Scoped Type Variables
2077 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2078 variable</emphasis>. For example
2084 f (xs::[a]) = ys ++ ys
2093 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2094 This brings the type variable <literal>a</literal> into scope; it scopes over
2095 all the patterns and right hand sides for this equation for <function>f</function>.
2096 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2100 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2101 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2102 implicitly universally quantified. (If there are no type variables in
2103 scope, all type variables mentioned in the signature are universally
2104 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2105 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2106 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2107 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2108 it becomes possible to do so.
2112 Scoped type variables are implemented in both GHC and Hugs. Where the
2113 implementations differ from the specification below, those differences
2118 So much for the basic idea. Here are the details.
2122 <title>Scope and implicit quantification</title>
2130 All the type variables mentioned in the patterns for a single
2131 function definition equation, that are not already in scope,
2132 are brought into scope by the patterns. We describe this set as
2133 the <emphasis>type variables bound by the equation</emphasis>.
2140 The type variables thus brought into scope may be mentioned
2141 in ordinary type signatures or pattern type signatures anywhere within
2149 In ordinary type signatures, any type variable mentioned in the
2150 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2157 Ordinary type signatures do not bring any new type variables
2158 into scope (except in the type signature itself!). So this is illegal:
2167 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2168 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2169 and that is an incorrect typing.
2176 There is no implicit universal quantification on pattern type
2177 signatures, nor may one write an explicit <literal>forall</literal> type in a pattern
2178 type signature. The pattern type signature is a monotype.
2186 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2187 scope over the methods defined in the <literal>where</literal> part. For example:
2201 (Not implemented in Hugs yet, Dec 98).
2212 <title>Polymorphism</title>
2220 Pattern type signatures are completely orthogonal to ordinary, separate
2221 type signatures. The two can be used independently or together. There is
2222 no scoping associated with the names of the type variables in a separate type signature.
2227 f (xs::[b]) = reverse xs
2236 The function must be polymorphic in the type variables
2237 bound by all its equations. Operationally, the type variables bound
2238 by one equation must not:
2245 Be unified with a type (such as <literal>Int</literal>, or <literal>[a]</literal>).
2251 Be unified with a type variable free in the environment.
2257 Be unified with each other. (They may unify with the type variables
2258 bound by another equation for the same function, of course.)
2265 For example, the following all fail to type check:
2269 f (x::a) (y::b) = [x,y] -- a unifies with b
2271 g (x::a) = x + 1::Int -- a unifies with Int
2273 h x = let k (y::a) = [x,y] -- a is free in the
2274 in k x -- environment
2276 k (x::a) True = ... -- a unifies with Int
2277 k (x::Int) False = ...
2280 w (x::a) = x -- a unifies with [b]
2289 The pattern-bound type variable may, however, be constrained
2290 by the context of the principal type, thus:
2294 f (x::a) (y::a) = x+y*2
2298 gets the inferred type: <literal>forall a. Num a => a -> a -> a</literal>.
2309 <title>Result type signatures</title>
2317 The result type of a function can be given a signature,
2322 f (x::a) :: [a] = [x,x,x]
2326 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2327 result type. Sometimes this is the only way of naming the type variable
2332 f :: Int -> [a] -> [a]
2333 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2334 in \xs -> map g (reverse xs `zip` xs)
2346 Result type signatures are not yet implemented in Hugs.
2352 <title>Pattern signatures on other constructs</title>
2360 A pattern type signature can be on an arbitrary sub-pattern, not
2365 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2374 Pattern type signatures, including the result part, can be used
2375 in lambda abstractions:
2379 (\ (x::a, y) :: a -> x)
2383 Type variables bound by these patterns must be polymorphic in
2384 the sense defined above.
2389 f1 (x::c) = f1 x -- ok
2390 f2 = \(x::c) -> f2 x -- not ok
2394 Here, <function>f1</function> is OK, but <function>f2</function> is not, because <VarName>c</VarName> gets unified
2395 with a type variable free in the environment, in this
2396 case, the type of <function>f2</function>, which is in the environment when
2397 the lambda abstraction is checked.
2404 Pattern type signatures, including the result part, can be used
2405 in <literal>case</literal> expressions:
2409 case e of { (x::a, y) :: a -> x }
2413 The pattern-bound type variables must, as usual,
2414 be polymorphic in the following sense: each case alternative,
2415 considered as a lambda abstraction, must be polymorphic.
2420 case (True,False) of { (x::a, y) -> x }
2424 Even though the context is that of a pair of booleans,
2425 the alternative itself is polymorphic. Of course, it is
2430 case (True,False) of { (x::Bool, y) -> x }
2439 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2440 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2441 token or a parenthesised type of some sort). To see why,
2442 consider how one would parse this:
2455 Pattern type signatures that bind new type variables
2456 may not be used in pattern bindings at all.
2461 f x = let (y, z::a) = x in ...
2465 But these are OK, because they do not bind fresh type variables:
2469 f1 x = let (y, z::Int) = x in ...
2470 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2474 However a single variable is considered a degenerate function binding,
2475 rather than a degerate pattern binding, so this is permitted, even
2476 though it binds a type variable:
2480 f :: (b->b) = \(x::b) -> x
2489 Such degnerate function bindings do not fall under the monomorphism
2496 g :: a -> a -> Bool = \x y. x==y
2502 Here <function>g</function> has type <literal>forall a. Eq a => a -> a -> Bool</literal>, just as if
2503 <function>g</function> had a separate type signature. Lacking a type signature, <function>g</function>
2504 would get a monomorphic type.
2510 <title>Existentials</title>
2518 Pattern type signatures can bind existential type variables.
2523 data T = forall a. MkT [a]
2526 f (MkT [t::a]) = MkT t3
2543 <sect1 id="pragmas">
2548 GHC supports several pragmas, or instructions to the compiler placed
2549 in the source code. Pragmas don't affect the meaning of the program,
2550 but they might affect the efficiency of the generated code.
2553 <sect2 id="inline-pragma">
2554 <title>INLINE pragma
2556 <indexterm><primary>INLINE pragma</primary></indexterm>
2557 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2560 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2561 functions/values that are “small enough,” thus avoiding the call
2562 overhead and possibly exposing other more-wonderful optimisations.
2566 You will probably see these unfoldings (in Core syntax) in your
2571 Normally, if GHC decides a function is “too expensive” to inline, it
2572 will not do so, nor will it export that unfolding for other modules to
2577 The sledgehammer you can bring to bear is the
2578 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2581 key_function :: Int -> String -> (Bool, Double)
2583 #ifdef __GLASGOW_HASKELL__
2584 {-# INLINE key_function #-}
2588 (You don't need to do the C pre-processor carry-on unless you're going
2589 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2593 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2594 “cost” to be very low. The normal unfolding machinery will then be
2595 very keen to inline it.
2599 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2600 signature could be put.
2604 <literal>INLINE</literal> pragmas are a particularly good idea for the
2605 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2606 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2609 #ifdef __GLASGOW_HASKELL__
2610 {-# INLINE thenUs #-}
2611 {-# INLINE returnUs #-}
2619 <sect2 id="noinline-pragma">
2620 <title>NOINLINE pragma
2624 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2625 <indexterm><primary>pragma, NOINLINE</primary></indexterm>
2629 The <literal>NOINLINE</literal> pragma does exactly what you'd expect: it stops the
2630 named function from being inlined by the compiler. You shouldn't ever
2631 need to do this, unless you're very cautious about code size.
2636 <sect2 id="specialize-pragma">
2637 <title>SPECIALIZE pragma</title>
2639 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2640 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2641 <indexterm><primary>overloading, death to</primary></indexterm>
2643 <para>(UK spelling also accepted.) For key overloaded
2644 functions, you can create extra versions (NB: more code space)
2645 specialised to particular types. Thus, if you have an
2646 overloaded function:</para>
2649 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2652 <para>If it is heavily used on lists with
2653 <literal>Widget</literal> keys, you could specialise it as
2657 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2660 <para>To get very fancy, you can also specify a named function
2661 to use for the specialised value, as in:</para>
2664 {-# RULES hammeredLookup = blah #-}
2667 <para>where <literal>blah</literal> is an implementation of
2668 <literal>hammerdLookup</literal> written specialy for
2669 <literal>Widget</literal> lookups. It's <emphasis>Your
2670 Responsibility</emphasis> to make sure that
2671 <function>blah</function> really behaves as a specialised
2672 version of <function>hammeredLookup</function>!!!</para>
2674 <para>Note we use the <literal>RULE</literal> pragma here to
2675 indicate that <literal>hammeredLookup</literal> applied at a
2676 certain type should be replaced by <literal>blah</literal>. See
2677 <xref linkend="rules"> for more information on
2678 <literal>RULES</literal>.</para>
2680 <para>An example in which using <literal>RULES</literal> for
2681 specialisation will Win Big:
2684 toDouble :: Real a => a -> Double
2685 toDouble = fromRational . toRational
2687 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2688 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2691 The <function>i2d</function> function is virtually one machine
2692 instruction; the default conversion—via an intermediate
2693 <literal>Rational</literal>—is obscenely expensive by
2696 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2697 be put anywhere its type signature could be put.</para>
2701 <sect2 id="specialize-instance-pragma">
2702 <title>SPECIALIZE instance pragma
2706 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2707 <indexterm><primary>overloading, death to</primary></indexterm>
2708 Same idea, except for instance declarations. For example:
2711 instance (Eq a) => Eq (Foo a) where { ... usual stuff ... }
2713 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)] #-}
2716 Compatible with HBC, by the way.
2721 <sect2 id="line-pragma">
2726 <indexterm><primary>LINE pragma</primary></indexterm>
2727 <indexterm><primary>pragma, LINE</primary></indexterm>
2731 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2732 automatically generated Haskell code. It lets you specify the line
2733 number and filename of the original code; for example
2739 {-# LINE 42 "Foo.vhs" #-}
2745 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2746 and this line corresponds to line 42 in the original. GHC will adjust
2747 its error messages to refer to the line/file named in the <literal>LINE</literal>
2754 <title>RULES pragma</title>
2757 The RULES pragma lets you specify rewrite rules. It is described in
2758 <xref LinkEnd="rewrite-rules">.
2765 <sect1 id="rewrite-rules">
2766 <title>Rewrite rules
2768 <indexterm><primary>RULES pagma</primary></indexterm>
2769 <indexterm><primary>pragma, RULES</primary></indexterm>
2770 <indexterm><primary>rewrite rules</primary></indexterm></title>
2773 The programmer can specify rewrite rules as part of the source program
2774 (in a pragma). GHC applies these rewrite rules wherever it can.
2782 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2789 <title>Syntax</title>
2792 From a syntactic point of view:
2798 Each rule has a name, enclosed in double quotes. The name itself has
2799 no significance at all. It is only used when reporting how many times the rule fired.
2805 There may be zero or more rules in a <literal>RULES</literal> pragma.
2811 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2812 is set, so you must lay out your rules starting in the same column as the
2813 enclosing definitions.
2819 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2820 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2821 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2822 by spaces, just like in a type <literal>forall</literal>.
2828 A pattern variable may optionally have a type signature.
2829 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2830 For example, here is the <literal>foldr/build</literal> rule:
2833 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2834 foldr k z (build g) = g k z
2837 Since <function>g</function> has a polymorphic type, it must have a type signature.
2844 The left hand side of a rule must consist of a top-level variable applied
2845 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2848 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2849 "wrong2" forall f. f True = True
2852 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2859 A rule does not need to be in the same module as (any of) the
2860 variables it mentions, though of course they need to be in scope.
2866 Rules are automatically exported from a module, just as instance declarations are.
2877 <title>Semantics</title>
2880 From a semantic point of view:
2886 Rules are only applied if you use the <option>-O</option> flag.
2892 Rules are regarded as left-to-right rewrite rules.
2893 When GHC finds an expression that is a substitution instance of the LHS
2894 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
2895 By "a substitution instance" we mean that the LHS can be made equal to the
2896 expression by substituting for the pattern variables.
2903 The LHS and RHS of a rule are typechecked, and must have the
2911 GHC makes absolutely no attempt to verify that the LHS and RHS
2912 of a rule have the same meaning. That is undecideable in general, and
2913 infeasible in most interesting cases. The responsibility is entirely the programmer's!
2920 GHC makes no attempt to make sure that the rules are confluent or
2921 terminating. For example:
2924 "loop" forall x,y. f x y = f y x
2927 This rule will cause the compiler to go into an infinite loop.
2934 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
2940 GHC currently uses a very simple, syntactic, matching algorithm
2941 for matching a rule LHS with an expression. It seeks a substitution
2942 which makes the LHS and expression syntactically equal modulo alpha
2943 conversion. The pattern (rule), but not the expression, is eta-expanded if
2944 necessary. (Eta-expanding the epression can lead to laziness bugs.)
2945 But not beta conversion (that's called higher-order matching).
2949 Matching is carried out on GHC's intermediate language, which includes
2950 type abstractions and applications. So a rule only matches if the
2951 types match too. See <xref LinkEnd="rule-spec"> below.
2957 GHC keeps trying to apply the rules as it optimises the program.
2958 For example, consider:
2967 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
2968 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
2969 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
2970 not be substituted, and the rule would not fire.
2977 In the earlier phases of compilation, GHC inlines <emphasis>nothing
2978 that appears on the LHS of a rule</emphasis>, because once you have substituted
2979 for something you can't match against it (given the simple minded
2980 matching). So if you write the rule
2983 "map/map" forall f,g. map f . map g = map (f.g)
2986 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
2987 It will only match something written with explicit use of ".".
2988 Well, not quite. It <emphasis>will</emphasis> match the expression
2994 where <function>wibble</function> is defined:
2997 wibble f g = map f . map g
3000 because <function>wibble</function> will be inlined (it's small).
3002 Later on in compilation, GHC starts inlining even things on the
3003 LHS of rules, but still leaves the rules enabled. This inlining
3004 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3011 All rules are implicitly exported from the module, and are therefore
3012 in force in any module that imports the module that defined the rule, directly
3013 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3014 in force when compiling A.) The situation is very similar to that for instance
3026 <title>List fusion</title>
3029 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3030 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3031 intermediate list should be eliminated entirely.
3035 The following are good producers:
3047 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3053 Explicit lists (e.g. <literal>[True, False]</literal>)
3059 The cons constructor (e.g <literal>3:4:[]</literal>)
3065 <function>++</function>
3071 <function>map</function>
3077 <function>filter</function>
3083 <function>iterate</function>, <function>repeat</function>
3089 <function>zip</function>, <function>zipWith</function>
3098 The following are good consumers:
3110 <function>array</function> (on its second argument)
3116 <function>length</function>
3122 <function>++</function> (on its first argument)
3128 <function>map</function>
3134 <function>filter</function>
3140 <function>concat</function>
3146 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3152 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3153 will fuse with one but not the other)
3159 <function>partition</function>
3165 <function>head</function>
3171 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3177 <function>sequence_</function>
3183 <function>msum</function>
3189 <function>sortBy</function>
3198 So, for example, the following should generate no intermediate lists:
3201 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3207 This list could readily be extended; if there are Prelude functions that you use
3208 a lot which are not included, please tell us.
3212 If you want to write your own good consumers or producers, look at the
3213 Prelude definitions of the above functions to see how to do so.
3218 <sect2 id="rule-spec">
3219 <title>Specialisation
3223 Rewrite rules can be used to get the same effect as a feature
3224 present in earlier version of GHC:
3227 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3230 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3231 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3232 specialising the original definition of <function>fromIntegral</function> the programmer is
3233 promising that it is safe to use <function>int8ToInt16</function> instead.
3237 This feature is no longer in GHC. But rewrite rules let you do the
3242 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3246 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3247 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3248 GHC adds the type and dictionary applications to get the typed rule
3251 forall (d1::Integral Int8) (d2::Num Int16) .
3252 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3256 this rule does not need to be in the same file as fromIntegral,
3257 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3258 have an original definition available to specialise).
3264 <title>Controlling what's going on</title>
3272 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3278 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3279 If you add <option>-dppr-debug</option> you get a more detailed listing.
3285 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3288 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3289 {-# INLINE build #-}
3293 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3294 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3295 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3296 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3303 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3304 see how to write rules that will do fusion and yet give an efficient
3305 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3317 <sect1 id="generic-classes">
3318 <title>Generic classes</title>
3321 The ideas behind this extension are described in detail in "Derivable type classes",
3322 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3323 An example will give the idea:
3331 fromBin :: [Int] -> (a, [Int])
3333 toBin {| Unit |} Unit = []
3334 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3335 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3336 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3338 fromBin {| Unit |} bs = (Unit, bs)
3339 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3340 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3341 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3342 (y,bs'') = fromBin bs'
3345 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3346 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3347 which are defined thus in the library module <literal>Generics</literal>:
3351 data a :+: b = Inl a | Inr b
3352 data a :*: b = a :*: b
3355 Now you can make a data type into an instance of Bin like this:
3357 instance (Bin a, Bin b) => Bin (a,b)
3358 instance Bin a => Bin [a]
3360 That is, just leave off the "where" clasuse. Of course, you can put in the
3361 where clause and over-ride whichever methods you please.
3365 <title> Using generics </title>
3366 <para>To use generics you need to</para>
3369 <para>Use the <option>-fgenerics</option> flag.</para>
3372 <para>Import the module <literal>Generics</literal> from the
3373 <literal>lang</literal> package. This import brings into
3374 scope the data types <literal>Unit</literal>,
3375 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3376 don't need this import if you don't mention these types
3377 explicitly; for example, if you are simply giving instance
3378 declarations.)</para>
3383 <sect2> <title> Changes wrt the paper </title>
3385 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3386 can be written infix (indeed, you can now use
3387 any operator starting in a colon as an infix type constructor). Also note that
3388 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3389 Finally, note that the syntax of the type patterns in the class declaration
3390 uses "<literal>{|</literal>" and "<literal>{|</literal>" brackets; curly braces
3391 alone would ambiguous when they appear on right hand sides (an extension we
3392 anticipate wanting).
3396 <sect2> <title>Terminology and restrictions</title>
3398 Terminology. A "generic default method" in a class declaration
3399 is one that is defined using type patterns as above.
3400 A "polymorphic default method" is a default method defined as in Haskell 98.
3401 A "generic class declaration" is a class declaration with at least one
3402 generic default method.
3410 Alas, we do not yet implement the stuff about constructor names and
3417 A generic class can have only one parameter; you can't have a generic
3418 multi-parameter class.
3424 A default method must be defined entirely using type patterns, or entirely
3425 without. So this is illegal:
3428 op :: a -> (a, Bool)
3429 op {| Unit |} Unit = (Unit, True)
3432 However it is perfectly OK for some methods of a generic class to have
3433 generic default methods and others to have polymorphic default methods.
3439 The type variable(s) in the type pattern for a generic method declaration
3440 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:
3444 op {| p :*: q |} (x :*: y) = op (x :: p)
3452 The type patterns in a generic default method must take one of the forms:
3458 where "a" and "b" are type variables. Furthermore, all the type patterns for
3459 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3460 must use the same type variables. So this is illegal:
3464 op {| a :+: b |} (Inl x) = True
3465 op {| p :+: q |} (Inr y) = False
3467 The type patterns must be identical, even in equations for different methods of the class.
3468 So this too is illegal:
3472 op {| a :*: b |} (Inl x) = True
3475 op {| p :*: q |} (Inr y) = False
3477 (The reason for this restriction is that we gather all the equations for a particular type consructor
3478 into a single generic instance declaration.)
3484 A generic method declaration must give a case for each of the three type constructors.
3490 The type for a generic method can be built only from:
3492 <listitem> <para> Function arrows </para> </listitem>
3493 <listitem> <para> Type variables </para> </listitem>
3494 <listitem> <para> Tuples </para> </listitem>
3495 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3497 Here are some example type signatures for generic methods:
3500 op2 :: Bool -> (a,Bool)
3501 op3 :: [Int] -> a -> a
3504 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3508 This restriction is an implementation restriction: we just havn't got around to
3509 implementing the necessary bidirectional maps over arbitrary type constructors.
3510 It would be relatively easy to add specific type constructors, such as Maybe and list,
3511 to the ones that are allowed.</para>
3516 In an instance declaration for a generic class, the idea is that the compiler
3517 will fill in the methods for you, based on the generic templates. However it can only
3522 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3527 No constructor of the instance type has unboxed fields.
3531 (Of course, these things can only arise if you are already using GHC extensions.)
3532 However, you can still give an instance declarations for types which break these rules,
3533 provided you give explicit code to override any generic default methods.
3541 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3542 what the compiler does with generic declarations.
3547 <sect2> <title> Another example </title>
3549 Just to finish with, here's another example I rather like:
3553 nCons {| Unit |} _ = 1
3554 nCons {| a :*: b |} _ = 1
3555 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3558 tag {| Unit |} _ = 1
3559 tag {| a :*: b |} _ = 1
3560 tag {| a :+: b |} (Inl x) = tag x
3561 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3568 ;;; Local Variables: ***
3570 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
projects / ghc-hetmet.git / blob