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>Linear implicit parameters:</term>
65 <para><xref LinkEnd="linear-implicit-parameters"></para>
70 <term>Local universal quantification:</term>
72 <para><xref LinkEnd="universal-quantification"></para>
77 <term>Extistentially quantification in data types:</term>
79 <para><xref LinkEnd="existential-quantification"></para>
84 <term>Scoped type variables:</term>
86 <para>Scoped type variables enable the programmer to
87 supply type signatures for some nested declarations,
88 where this would not be legal in Haskell 98. Details in
89 <xref LinkEnd="scoped-type-variables">.</para>
97 <term>Pattern guards</term>
99 <para>Instead of being a boolean expression, a guard is a list
100 of qualifiers, exactly as in a list comprehension. See <xref
101 LinkEnd="pattern-guards">.</para>
106 <term>Data types with no constructors</term>
108 <para>See <xref LinkEnd="nullary-types">.</para>
113 <term>Parallel list comprehensions</term>
115 <para>An extension to the list comprehension syntax to support
116 <literal>zipWith</literal>-like functionality. See <xref
117 linkend="parallel-list-comprehensions">.</para>
122 <term>Foreign calling:</term>
124 <para>Just what it sounds like. We provide
125 <emphasis>lots</emphasis> of rope that you can dangle around
126 your neck. Please see <xref LinkEnd="ffi">.</para>
133 <para>Pragmas are special instructions to the compiler placed
134 in the source file. The pragmas GHC supports are described in
135 <xref LinkEnd="pragmas">.</para>
140 <term>Rewrite rules:</term>
142 <para>The programmer can specify rewrite rules as part of the
143 source program (in a pragma). GHC applies these rewrite rules
144 wherever it can. Details in <xref
145 LinkEnd="rewrite-rules">.</para>
150 <term>Generic classes:</term>
152 <para>(Note: support for generic classes is currently broken
155 <para>Generic class declarations allow you to define a class
156 whose methods say how to work over an arbitrary data type.
157 Then it's really easy to make any new type into an instance of
158 the class. This generalises the rather ad-hoc "deriving"
159 feature of Haskell 98. Details in <xref
160 LinkEnd="generic-classes">.</para>
166 Before you get too carried away working at the lowest level (e.g.,
167 sloshing <literal>MutableByteArray#</literal>s around your
168 program), you may wish to check if there are libraries that provide a
169 “Haskellised veneer” over the features you want. See
170 <xref linkend="book-hslibs">.
173 <sect1 id="options-language">
174 <title>Language options</title>
176 <indexterm><primary>language</primary><secondary>option</secondary>
178 <indexterm><primary>options</primary><secondary>language</secondary>
180 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
183 <para> These flags control what variation of the language are
184 permitted. Leaving out all of them gives you standard Haskell
190 <term><option>-fglasgow-exts</option>:</term>
191 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
193 <para>This simultaneously enables all of the extensions to
194 Haskell 98 described in <xref
195 linkend="ghc-language-features">, except where otherwise
201 <term><option>-fno-monomorphism-restriction</option>:</term>
202 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
204 <para> Switch off the Haskell 98 monomorphism restriction.
205 Independent of the <option>-fglasgow-exts</option>
211 <term><option>-fallow-overlapping-instances</option></term>
212 <term><option>-fallow-undecidable-instances</option></term>
213 <term><option>-fallow-incoherent-instances</option></term>
214 <term><option>-fcontext-stack</option></term>
215 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
216 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
217 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
219 <para> See <xref LinkEnd="instance-decls">. Only relevant
220 if you also use <option>-fglasgow-exts</option>.</para>
225 <term><option>-finline-phase</option></term>
226 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
228 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
229 you also use <option>-fglasgow-exts</option>.</para>
234 <term><option>-fgenerics</option></term>
235 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
237 <para>See <xref LinkEnd="generic-classes">. Independent of
238 <option>-fglasgow-exts</option>.</para>
243 <term><option>-fno-implicit-prelude</option></term>
245 <para><indexterm><primary>-fno-implicit-prelude
246 option</primary></indexterm> GHC normally imports
247 <filename>Prelude.hi</filename> files for you. If you'd
248 rather it didn't, then give it a
249 <option>-fno-implicit-prelude</option> option. The idea
250 is that you can then import a Prelude of your own. (But
251 don't call it <literal>Prelude</literal>; the Haskell
252 module namespace is flat, and you must not conflict with
253 any Prelude module.)</para>
255 <para>Even though you have not imported the Prelude, all
256 the built-in syntax still refers to the built-in Haskell
257 Prelude types and values, as specified by the Haskell
258 Report. For example, the type <literal>[Int]</literal>
259 still means <literal>Prelude.[] Int</literal>; tuples
260 continue to refer to the standard Prelude tuples; the
261 translation for list comprehensions continues to use
262 <literal>Prelude.map</literal> etc.</para>
264 <para> With one group of exceptions! You may want to
265 define your own numeric class hierarchy. It completely
266 defeats that purpose if the literal "1" means
267 "<literal>Prelude.fromInteger 1</literal>", which is what
268 the Haskell Report specifies. So the
269 <option>-fno-implicit-prelude</option> flag causes the
270 following pieces of built-in syntax to refer to <emphasis>whatever
271 is in scope</emphasis>, not the Prelude versions:</para>
275 <para>Integer and fractional literals mean
276 "<literal>fromInteger 1</literal>" and
277 "<literal>fromRational 3.2</literal>", not the
278 Prelude-qualified versions; both in expressions and in
283 <para>Negation (e.g. "<literal>- (f x)</literal>")
284 means "<literal>negate (f x)</literal>" (not
285 <literal>Prelude.negate</literal>).</para>
289 <para>In an n+k pattern, the standard Prelude
290 <literal>Ord</literal> class is still used for comparison,
291 but the necessary subtraction uses whatever
292 "<literal>(-)</literal>" is in scope (not
293 "<literal>Prelude.(-)</literal>").</para>
297 <para>Note: Negative literals, such as <literal>-3</literal>, are
298 specified by (a careful reading of) the Haskell Report as
299 meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
300 However, GHC deviates from this slightly, and treats them as meaning
301 <literal>fromInteger (-3)</literal>. One particular effect of this
302 slightly-non-standard reading is that there is no difficulty with
303 the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
304 it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
305 would be <literal>negate (fromInteger 2147483648)</literal>,
306 and the call to <literal>fromInteger</literal> would overflow
307 (at type <literal>Int</literal>, remember).
316 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
319 <sect1 id="glasgow-ST-monad">
320 <title>Primitive state-transformer monad</title>
323 <indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
324 <indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
328 This monad underlies our implementation of arrays, mutable and
329 immutable, and our implementation of I/O, including “C calls”.
333 The <literal>ST</literal> library, which provides access to the
334 <function>ST</function> monad, is described in <xref
340 <sect1 id="glasgow-prim-arrays">
341 <title>Primitive arrays, mutable and otherwise
345 <indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
346 <indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
350 GHC knows about quite a few flavours of Large Swathes of Bytes.
354 First, GHC distinguishes between primitive arrays of (boxed) Haskell
355 objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
356 <literal>ByteArray#</literal>).
360 Second, it distinguishes between…
364 <term>Immutable:</term>
367 Arrays that do not change (as with “standard” Haskell arrays); you
368 can only read from them. Obviously, they do not need the care and
369 attention of the state-transformer monad.
374 <term>Mutable:</term>
377 Arrays that may be changed or “mutated.” All the operations on them
378 live within the state-transformer monad and the updates happen
379 <emphasis>in-place</emphasis>.
384 <term>“Static” (in C land):</term>
387 A C routine may pass an <literal>Addr#</literal> pointer back into Haskell land. There
388 are then primitive operations with which you may merrily grab values
389 over in C land, by indexing off the “static” pointer.
394 <term>“Stable” pointers:</term>
397 If, for some reason, you wish to hand a Haskell pointer (i.e.,
398 <emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
399 pointer “stable,” so that the garbage collector won't forget that it
400 exists. That is, GHC provides a safe way to pass Haskell pointers to
405 Please see <xref LinkEnd="sec-stable-pointers"> for more details.
410 <term>“Foreign objects”:</term>
413 A “foreign object” is a safe way to pass an external object (a
414 C-allocated pointer, say) to Haskell and have Haskell do the Right
415 Thing when it no longer references the object. So, for example, C
416 could pass a large bitmap over to Haskell and say “please free this
417 memory when you're done with it.”
421 Please see <xref LinkEnd="sec-ForeignObj"> for more details.
429 The libraries documentatation gives more details on all these
430 “primitive array” types and the operations on them.
436 <sect1 id="nullary-types">
437 <title>Data types with no constructors</title>
439 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
440 a data type with no constructors. For example:</para>
443 data T a -- T :: * -> *
445 <para>Syntactically, the declaration lacks the "= constrs" part. The
446 type can be parameterised, but only over ordinary types, of kind *; since
447 Haskell does not have kind signatures, you cannot parameterise over higher-kinded
450 <para>Such data types have only one value, namely bottom.
451 Nevertheless, they can be useful when defining "phantom types".</para>
454 <sect1 id="pattern-guards">
455 <title>Pattern guards</title>
458 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
459 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.)
463 Suppose we have an abstract data type of finite maps, with a
467 lookup :: FiniteMap -> Int -> Maybe Int
470 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
471 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
475 clunky env var1 var2 | ok1 && ok2 = val1 + val2
476 | otherwise = var1 + var2
487 The auxiliary functions are
491 maybeToBool :: Maybe a -> Bool
492 maybeToBool (Just x) = True
493 maybeToBool Nothing = False
495 expectJust :: Maybe a -> a
496 expectJust (Just x) = x
497 expectJust Nothing = error "Unexpected Nothing"
501 What is <function>clunky</function> doing? The guard <literal>ok1 &&
502 ok2</literal> checks that both lookups succeed, using
503 <function>maybeToBool</function> to convert the <function>Maybe</function>
504 types to booleans. The (lazily evaluated) <function>expectJust</function>
505 calls extract the values from the results of the lookups, and binds the
506 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
507 respectively. If either lookup fails, then clunky takes the
508 <literal>otherwise</literal> case and returns the sum of its arguments.
512 This is certainly legal Haskell, but it is a tremendously verbose and
513 un-obvious way to achieve the desired effect. Arguably, a more direct way
514 to write clunky would be to use case expressions:
518 clunky env var1 var1 = case lookup env var1 of
520 Just val1 -> case lookup env var2 of
522 Just val2 -> val1 + val2
528 This is a bit shorter, but hardly better. Of course, we can rewrite any set
529 of pattern-matching, guarded equations as case expressions; that is
530 precisely what the compiler does when compiling equations! The reason that
531 Haskell provides guarded equations is because they allow us to write down
532 the cases we want to consider, one at a time, independently of each other.
533 This structure is hidden in the case version. Two of the right-hand sides
534 are really the same (<function>fail</function>), and the whole expression
535 tends to become more and more indented.
539 Here is how I would write clunky:
544 | Just val1 <- lookup env var1
545 , Just val2 <- lookup env var2
547 ...other equations for clunky...
551 The semantics should be clear enough. The qualifers are matched in order.
552 For a <literal><-</literal> qualifier, which I call a pattern guard, the
553 right hand side is evaluated and matched against the pattern on the left.
554 If the match fails then the whole guard fails and the next equation is
555 tried. If it succeeds, then the appropriate binding takes place, and the
556 next qualifier is matched, in the augmented environment. Unlike list
557 comprehensions, however, the type of the expression to the right of the
558 <literal><-</literal> is the same as the type of the pattern to its
559 left. The bindings introduced by pattern guards scope over all the
560 remaining guard qualifiers, and over the right hand side of the equation.
564 Just as with list comprehensions, boolean expressions can be freely mixed
565 with among the pattern guards. For example:
576 Haskell's current guards therefore emerge as a special case, in which the
577 qualifier list has just one element, a boolean expression.
581 <sect1 id="parallel-list-comprehensions">
582 <title>Parallel List Comprehensions</title>
583 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
585 <indexterm><primary>parallel list comprehensions</primary>
588 <para>Parallel list comprehensions are a natural extension to list
589 comprehensions. List comprehensions can be thought of as a nice
590 syntax for writing maps and filters. Parallel comprehensions
591 extend this to include the zipWith family.</para>
593 <para>A parallel list comprehension has multiple independent
594 branches of qualifier lists, each separated by a `|' symbol. For
595 example, the following zips together two lists:</para>
598 [ (x, y) | x <- xs | y <- ys ]
601 <para>The behavior of parallel list comprehensions follows that of
602 zip, in that the resulting list will have the same length as the
603 shortest branch.</para>
605 <para>We can define parallel list comprehensions by translation to
606 regular comprehensions. Here's the basic idea:</para>
608 <para>Given a parallel comprehension of the form: </para>
611 [ e | p1 <- e11, p2 <- e12, ...
612 | q1 <- e21, q2 <- e22, ...
617 <para>This will be translated to: </para>
620 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
621 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
626 <para>where `zipN' is the appropriate zip for the given number of
631 <sect1 id="multi-param-type-classes">
632 <title>Multi-parameter type classes
636 This section documents GHC's implementation of multi-parameter type
637 classes. There's lots of background in the paper <ULink
638 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
639 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
644 I'd like to thank people who reported shorcomings in the GHC 3.02
645 implementation. Our default decisions were all conservative ones, and
646 the experience of these heroic pioneers has given useful concrete
647 examples to support several generalisations. (These appear below as
648 design choices not implemented in 3.02.)
652 I've discussed these notes with Mark Jones, and I believe that Hugs
653 will migrate towards the same design choices as I outline here.
654 Thanks to him, and to many others who have offered very useful
662 There are the following restrictions on the form of a qualified
669 forall tv1..tvn (c1, ...,cn) => type
675 (Here, I write the "foralls" explicitly, although the Haskell source
676 language omits them; in Haskell 1.4, all the free type variables of an
677 explicit source-language type signature are universally quantified,
678 except for the class type variables in a class declaration. However,
679 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
688 <emphasis>Each universally quantified type variable
689 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
691 The reason for this is that a value with a type that does not obey
692 this restriction could not be used without introducing
693 ambiguity. Here, for example, is an illegal type:
697 forall a. Eq a => Int
701 When a value with this type was used, the constraint <literal>Eq tv</literal>
702 would be introduced where <literal>tv</literal> is a fresh type variable, and
703 (in the dictionary-translation implementation) the value would be
704 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
705 can never know which instance of <literal>Eq</literal> to use because we never
706 get any more information about <literal>tv</literal>.
713 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
714 universally quantified type variables <literal>tvi</literal></emphasis>.
716 For example, this type is OK because <literal>C a b</literal> mentions the
717 universally quantified type variable <literal>b</literal>:
721 forall a. C a b => burble
725 The next type is illegal because the constraint <literal>Eq b</literal> does not
726 mention <literal>a</literal>:
730 forall a. Eq b => burble
734 The reason for this restriction is milder than the other one. The
735 excluded types are never useful or necessary (because the offending
736 context doesn't need to be witnessed at this point; it can be floated
737 out). Furthermore, floating them out increases sharing. Lastly,
738 excluding them is a conservative choice; it leaves a patch of
739 territory free in case we need it later.
749 These restrictions apply to all types, whether declared in a type signature
754 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
755 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
762 f :: Eq (m a) => [m a] -> [m a]
769 This choice recovers principal types, a property that Haskell 1.4 does not have.
775 <title>Class declarations</title>
783 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
787 class Collection c a where
788 union :: c a -> c a -> c a
799 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
800 of "acyclic" involves only the superclass relationships. For example,
806 op :: D b => a -> b -> b
809 class C a => D a where { ... }
813 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
814 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
815 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
822 <emphasis>There are no restrictions on the context in a class declaration
823 (which introduces superclasses), except that the class hierarchy must
824 be acyclic</emphasis>. So these class declarations are OK:
828 class Functor (m k) => FiniteMap m k where
831 class (Monad m, Monad (t m)) => Transform t m where
832 lift :: m a -> (t m) a
841 <emphasis>In the signature of a class operation, every constraint
842 must mention at least one type variable that is not a class type
849 class Collection c a where
850 mapC :: Collection c b => (a->b) -> c a -> c b
854 is OK because the constraint <literal>(Collection a b)</literal> mentions
855 <literal>b</literal>, even though it also mentions the class variable
856 <literal>a</literal>. On the other hand:
861 op :: Eq a => (a,b) -> (a,b)
865 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
866 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
867 example is easily fixed by moving the offending context up to the
872 class Eq a => C a where
877 A yet more relaxed rule would allow the context of a class-op signature
878 to mention only class type variables. However, that conflicts with
879 Rule 1(b) for types above.
886 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
887 the class type variables</emphasis>. For example:
893 insert :: s -> a -> s
897 is not OK, because the type of <literal>empty</literal> doesn't mention
898 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
899 types, and has the same motivation.
901 Sometimes, offending class declarations exhibit misunderstandings. For
902 example, <literal>Coll</literal> might be rewritten
908 insert :: s a -> a -> s a
912 which makes the connection between the type of a collection of
913 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
914 Occasionally this really doesn't work, in which case you can split the
922 class CollE s => Coll s a where
923 insert :: s -> a -> s
936 <sect2 id="instance-decls">
937 <title>Instance declarations</title>
945 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
950 instance context1 => C type1 where ...
951 instance context2 => C type2 where ...
955 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
957 However, if you give the command line option
958 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
959 option</primary></indexterm> then overlapping instance declarations are permitted.
960 However, GHC arranges never to commit to using an instance declaration
961 if another instance declaration also applies, either now or later.
967 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
973 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
974 (but not identical to <literal>type1</literal>), or vice versa.
978 Notice that these rules
983 make it clear which instance decl to use
984 (pick the most specific one that matches)
991 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
992 Reason: you can pick which instance decl
993 "matches" based on the type.
998 However the rules are over-conservative. Two instance declarations can overlap,
999 but it can still be clear in particular situations which to use. For example:
1001 instance C (Int,a) where ...
1002 instance C (a,Bool) where ...
1004 These are rejected by GHC's rules, but it is clear what to do when trying
1005 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1006 cannot apply. Yell if this restriction bites you.
1009 GHC is also conservative about committing to an overlapping instance. For example:
1011 class C a where { op :: a -> a }
1012 instance C [Int] where ...
1013 instance C a => C [a] where ...
1015 f :: C b => [b] -> [b]
1018 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1019 GHC does not commit to the second instance declaration, because in a paricular
1020 call of f, b might be instantiate to Int, so the first instance declaration
1021 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1022 GHC will instead silently pick the second instance, without complaining about
1023 the problem of subsequent instantiations.
1026 Regrettably, GHC doesn't guarantee to detect overlapping instance
1027 declarations if they appear in different modules. GHC can "see" the
1028 instance declarations in the transitive closure of all the modules
1029 imported by the one being compiled, so it can "see" all instance decls
1030 when it is compiling <literal>Main</literal>. However, it currently chooses not
1031 to look at ones that can't possibly be of use in the module currently
1032 being compiled, in the interests of efficiency. (Perhaps we should
1033 change that decision, at least for <literal>Main</literal>.)
1040 <emphasis>There are no restrictions on the type in an instance
1041 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1042 The instance "head" is the bit after the "=>" in an instance decl. For
1043 example, these are OK:
1047 instance C Int a where ...
1049 instance D (Int, Int) where ...
1051 instance E [[a]] where ...
1055 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1056 For example, this is OK:
1060 instance Stateful (ST s) (MutVar s) where ...
1064 The "at least one not a type variable" restriction is to ensure that
1065 context reduction terminates: each reduction step removes one type
1066 constructor. For example, the following would make the type checker
1067 loop if it wasn't excluded:
1071 instance C a => C a where ...
1075 There are two situations in which the rule is a bit of a pain. First,
1076 if one allows overlapping instance declarations then it's quite
1077 convenient to have a "default instance" declaration that applies if
1078 something more specific does not:
1087 Second, sometimes you might want to use the following to get the
1088 effect of a "class synonym":
1092 class (C1 a, C2 a, C3 a) => C a where { }
1094 instance (C1 a, C2 a, C3 a) => C a where { }
1098 This allows you to write shorter signatures:
1110 f :: (C1 a, C2 a, C3 a) => ...
1114 I'm on the lookout for a simple rule that preserves decidability while
1115 allowing these idioms. The experimental flag
1116 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1117 option</primary></indexterm> lifts this restriction, allowing all the types in an
1118 instance head to be type variables.
1125 <emphasis>Unlike Haskell 1.4, instance heads may use type
1126 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1127 writing the RHS of the type synonym definition. For example:
1131 type Point = (Int,Int)
1132 instance C Point where ...
1133 instance C [Point] where ...
1137 is legal. However, if you added
1141 instance C (Int,Int) where ...
1145 as well, then the compiler will complain about the overlapping
1146 (actually, identical) instance declarations. As always, type synonyms
1147 must be fully applied. You cannot, for example, write:
1152 instance Monad P where ...
1156 This design decision is independent of all the others, and easily
1157 reversed, but it makes sense to me.
1164 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1165 be type variables</emphasis>. Thus
1169 instance C a b => Eq (a,b) where ...
1177 instance C Int b => Foo b where ...
1181 is not OK. Again, the intent here is to make sure that context
1182 reduction terminates.
1184 Voluminous correspondence on the Haskell mailing list has convinced me
1185 that it's worth experimenting with a more liberal rule. If you use
1186 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1187 types in an instance context. Termination is ensured by having a
1188 fixed-depth recursion stack. If you exceed the stack depth you get a
1189 sort of backtrace, and the opportunity to increase the stack depth
1190 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1203 <sect1 id="implicit-parameters">
1204 <title>Implicit parameters
1207 <para> Implicit paramters are implemented as described in
1208 "Implicit parameters: dynamic scoping with static types",
1209 J Lewis, MB Shields, E Meijer, J Launchbury,
1210 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1213 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1215 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1216 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1217 context. In Haskell, all variables are statically bound. Dynamic
1218 binding of variables is a notion that goes back to Lisp, but was later
1219 discarded in more modern incarnations, such as Scheme. Dynamic binding
1220 can be very confusing in an untyped language, and unfortunately, typed
1221 languages, in particular Hindley-Milner typed languages like Haskell,
1222 only support static scoping of variables.
1225 However, by a simple extension to the type class system of Haskell, we
1226 can support dynamic binding. Basically, we express the use of a
1227 dynamically bound variable as a constraint on the type. These
1228 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1229 function uses a dynamically-bound variable <literal>?x</literal>
1230 of type <literal>t'</literal>". For
1231 example, the following expresses the type of a sort function,
1232 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1234 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1236 The dynamic binding constraints are just a new form of predicate in the type class system.
1239 An implicit parameter is introduced by the special form <literal>?x</literal>,
1240 where <literal>x</literal> is
1241 any valid identifier. Use if this construct also introduces new
1242 dynamic binding constraints. For example, the following definition
1243 shows how we can define an implicitly parameterized sort function in
1244 terms of an explicitly parameterized <literal>sortBy</literal> function:
1246 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1248 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1251 Dynamic binding constraints behave just like other type class
1252 constraints in that they are automatically propagated. Thus, when a
1253 function is used, its implicit parameters are inherited by the
1254 function that called it. For example, our <literal>sort</literal> function might be used
1255 to pick out the least value in a list:
1257 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1258 least xs = fst (sort xs)
1260 Without lifting a finger, the <literal>?cmp</literal> parameter is
1261 propagated to become a parameter of <literal>least</literal> as well. With explicit
1262 parameters, the default is that parameters must always be explicit
1263 propagated. With implicit parameters, the default is to always
1267 An implicit parameter differs from other type class constraints in the
1268 following way: All uses of a particular implicit parameter must have
1269 the same type. This means that the type of <literal>(?x, ?x)</literal>
1270 is <literal>(?x::a) => (a,a)</literal>, and not
1271 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1275 An implicit parameter is bound using an expression of the form
1276 <emphasis>expr</emphasis> <literal>with</literal> <emphasis>binds</emphasis>,
1277 where <literal>with</literal> is a new keyword. This form binds the implicit
1278 parameters arising in the body, not the free variables as a <literal>let</literal> or
1279 <literal>where</literal> would do. For example, we define the <literal>min</literal> function by binding
1280 <literal>cmp</literal>.
1283 min = least with ?cmp = (<=)
1285 Syntactically, the <emphasis>binds</emphasis> part of a <literal>with</literal> construct must be a
1286 collection of simple bindings to variables (no function-style
1287 bindings, and no type signatures); these bindings are neither
1288 polymorphic or recursive.
1291 Note the following additional constraints:
1294 <para> You can't have an implicit parameter in the context of a class or instance
1295 declaration. For example, both these declarations are illegal:
1297 class (?x::Int) => C a where ...
1298 instance (?x::a) => Foo [a] where ...
1300 Reason: exactly which implicit parameter you pick up depends on exactly where
1301 you invoke a function. But the ``invocation'' of instance declarations is done
1302 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1303 Easiest thing is to outlaw the offending types.</para>
1310 <sect1 id="linear-implicit-parameters">
1311 <title>Linear implicit parameters
1314 Linear implicit parameters are an idea developed by Koen Claessen,
1315 Mark Shields, and Simon PJ. They address the long-standing
1316 problem that monads seem over-kill for certain sorts of problem, notably:
1319 <listitem> <para> distributing a supply of unique names </para> </listitem>
1320 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1321 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1325 Linear implicit parameters are just like ordinary implicit parameters,
1326 except that they are "linear" -- that is, they cannot be copied, and
1327 must be explicitly "split" instead. Linear implicit parameters are
1328 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1329 (The '/' in the '%' suggests the split!)
1334 data NameSupply = ...
1336 splitNS :: NameSupply -> (NameSupply, NameSupply)
1337 newName :: NameSupply -> Name
1339 instance PrelSplit.Splittable NameSupply where
1343 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1344 f env (Lam x e) = Lam x' (f env e)
1347 env' = extend env x x'
1348 ...more equations for f...
1350 Notice that the implicit parameter %ns is consumed
1352 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1353 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1357 So the translation done by the type checker makes
1358 the parameter explicit:
1360 f :: NameSupply -> Env -> Expr -> Expr
1361 f ns env (Lam x e) = Lam x' (f ns1 env e)
1363 (ns1,ns2) = splitNS ns
1365 env = extend env x x'
1367 Notice the call to 'split' introduced by the type checker.
1368 How did it know to use 'splitNS'? Because what it really did
1369 was to introduce a call to the overloaded function 'split',
1372 class Splittable a where
1375 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1376 split for name supplies. But we can simply write
1382 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1384 The <literal>Splittable</literal> class is built into GHC. It's defined in <literal>PrelSplit</literal>,
1385 and exported by <literal>GlaExts</literal>.
1390 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1391 are entirely distinct implicit parameters: you
1392 can use them together and they won't intefere with each other. </para>
1395 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1397 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1398 in the context of a class or instance declaration. </para></listitem>
1402 <sect2><title>Warnings</title>
1405 The monomorphism restriction is even more important than usual.
1406 Consider the example above:
1408 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1409 f env (Lam x e) = Lam x' (f env e)
1412 env' = extend env x x'
1414 If we replaced the two occurrences of x' by (newName %ns), which is
1415 usually a harmless thing to do, we get:
1417 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1418 f env (Lam x e) = Lam (newName %ns) (f env e)
1420 env' = extend env x (newName %ns)
1422 But now the name supply is consumed in <emphasis>three</emphasis> places
1423 (the two calls to newName,and the recursive call to f), so
1424 the result is utterly different. Urk! We don't even have
1428 Well, this is an experimental change. With implicit
1429 parameters we have already lost beta reduction anyway, and
1430 (as John Launchbury puts it) we can't sensibly reason about
1431 Haskell programs without knowing their typing.
1438 <sect1 id="functional-dependencies">
1439 <title>Functional dependencies
1442 <para> Functional dependencies are implemented as described by Mark Jones
1443 in "Type Classes with Functional Dependencies", Mark P. Jones,
1444 In Proceedings of the 9th European Symposium on Programming,
1445 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1449 There should be more documentation, but there isn't (yet). Yell if you need it.
1454 <sect1 id="universal-quantification">
1455 <title>Explicit universal quantification
1459 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1460 allows us to say exactly what this means. For example:
1468 g :: forall b. (b -> b)
1470 The two are treated identically.
1474 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1475 explicit universal quantification in
1477 For example, all the following types are legal:
1479 f1 :: forall a b. a -> b -> a
1480 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1482 f2 :: (forall a. a->a) -> Int -> Int
1483 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1485 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1487 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1488 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1489 The <literal>forall</literal> makes explicit the universal quantification that
1490 is implicitly added by Haskell.
1493 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1494 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1495 shows, the polymorphic type on the left of the function arrow can be overloaded.
1498 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1499 they have rank-2 types on the left of a function arrow.
1502 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1503 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1504 that restriction has now been lifted.)
1505 In particular, a forall-type (also called a "type scheme"),
1506 including an operational type class context, is legal:
1508 <listitem> <para> On the left of a function arrow </para> </listitem>
1509 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1510 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1511 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1512 field type signatures.</para> </listitem>
1513 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1514 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1516 There is one place you cannot put a <literal>forall</literal>:
1517 you cannot instantiate a type variable with a forall-type. So you cannot
1518 make a forall-type the argument of a type constructor. So these types are illegal:
1520 x1 :: [forall a. a->a]
1521 x2 :: (forall a. a->a, Int)
1522 x3 :: Maybe (forall a. a->a)
1524 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1525 a type variable any more!
1534 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1535 the types of the constructor arguments. Here are several examples:
1541 data T a = T1 (forall b. b -> b -> b) a
1543 data MonadT m = MkMonad { return :: forall a. a -> m a,
1544 bind :: forall a b. m a -> (a -> m b) -> m b
1547 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1553 The constructors have rank-2 types:
1559 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1560 MkMonad :: forall m. (forall a. a -> m a)
1561 -> (forall a b. m a -> (a -> m b) -> m b)
1563 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1569 Notice that you don't need to use a <literal>forall</literal> if there's an
1570 explicit context. For example in the first argument of the
1571 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1572 prefixed to the argument type. The implicit <literal>forall</literal>
1573 quantifies all type variables that are not already in scope, and are
1574 mentioned in the type quantified over.
1578 As for type signatures, implicit quantification happens for non-overloaded
1579 types too. So if you write this:
1582 data T a = MkT (Either a b) (b -> b)
1585 it's just as if you had written this:
1588 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1591 That is, since the type variable <literal>b</literal> isn't in scope, it's
1592 implicitly universally quantified. (Arguably, it would be better
1593 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1594 where that is what is wanted. Feedback welcomed.)
1598 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1599 the constructor to suitable values, just as usual. For example,
1610 a3 = MkSwizzle reverse
1613 a4 = let r x = Just x
1620 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1621 mkTs f x y = [T1 f x, T1 f y]
1627 The type of the argument can, as usual, be more general than the type
1628 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1629 does not need the <literal>Ord</literal> constraint.)
1633 When you use pattern matching, the bound variables may now have
1634 polymorphic types. For example:
1640 f :: T a -> a -> (a, Char)
1641 f (T1 w k) x = (w k x, w 'c' 'd')
1643 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1644 g (MkSwizzle s) xs f = s (map f (s xs))
1646 h :: MonadT m -> [m a] -> m [a]
1647 h m [] = return m []
1648 h m (x:xs) = bind m x $ \y ->
1649 bind m (h m xs) $ \ys ->
1656 In the function <function>h</function> we use the record selectors <literal>return</literal>
1657 and <literal>bind</literal> to extract the polymorphic bind and return functions
1658 from the <literal>MonadT</literal> data structure, rather than using pattern
1664 <title>Type inference</title>
1667 In general, type inference for arbitrary-rank types is undecideable.
1668 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1669 to get a decidable algorithm by requiring some help from the programmer.
1670 We do not yet have a formal specification of "some help" but the rule is this:
1673 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1674 provides an explicit polymorphic type for x, or GHC's type inference will assume
1675 that x's type has no foralls in it</emphasis>.
1678 What does it mean to "provide" an explicit type for x? You can do that by
1679 giving a type signature for x directly, using a pattern type signature
1680 (<xref linkend="scoped-type-variables">), thus:
1682 \ f :: (forall a. a->a) -> (f True, f 'c')
1684 Alternatively, you can give a type signature to the enclosing
1685 context, which GHC can "push down" to find the type for the variable:
1687 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1689 Here the type signature on the expression can be pushed inwards
1690 to give a type signature for f. Similarly, and more commonly,
1691 one can give a type signature for the function itself:
1693 h :: (forall a. a->a) -> (Bool,Char)
1694 h f = (f True, f 'c')
1696 You don't need to give a type signature if the lambda bound variable
1697 is a constructor argument. Here is an example we saw earlier:
1699 f :: T a -> a -> (a, Char)
1700 f (T1 w k) x = (w k x, w 'c' 'd')
1702 Here we do not need to give a type signature to <literal>w</literal>, because
1703 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1710 <sect2 id="implicit-quant">
1711 <title>Implicit quantification</title>
1714 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1715 user-written types, if and only if there is no explicit <literal>forall</literal>,
1716 GHC finds all the type variables mentioned in the type that are not already
1717 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1721 f :: forall a. a -> a
1728 h :: forall b. a -> b -> b
1734 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1737 f :: (a -> a) -> Int
1739 f :: forall a. (a -> a) -> Int
1741 f :: (forall a. a -> a) -> Int
1744 g :: (Ord a => a -> a) -> Int
1745 -- MEANS the illegal type
1746 g :: forall a. (Ord a => a -> a) -> Int
1748 g :: (forall a. Ord a => a -> a) -> Int
1750 The latter produces an illegal type, which you might think is silly,
1751 but at least the rule is simple. If you want the latter type, you
1752 can write your for-alls explicitly. Indeed, doing so is strongly advised
1759 <title>Type synonyms and hoisting
1763 Type synonmys are like macros at the type level, and GHC is much more liberal
1764 about them than Haskell 98. In particular:
1766 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1767 in a type synonym, thus:
1769 type Discard a = forall b. Show b => a -> b -> (a, String)
1774 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1781 You can write an unboxed tuple in a type synonym:
1783 type Pr = (# Int, Int #)
1792 GHC does validity checking on types <emphasis>after expanding type synonyms</emphasis>
1794 this will be rejected:
1796 type Pr = (# Int, Int #)
1801 because GHC does not allow unboxed tuples on the left of a function arrow.
1805 However, it is often convenient to use these sort of generalised synonyms at the right hand
1806 end of an arrow, thus:
1808 type Discard a = forall b. a -> b -> a
1810 g :: Int -> Discard Int
1813 Simply expanding the type synonym would give
1815 g :: Int -> (forall b. Int -> b -> Int)
1817 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1819 g :: forall b. Int -> Int -> b -> Int
1821 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1822 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1823 performs the transformation:</emphasis>
1825 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1827 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1829 (In fact, GHC tries to retain as much synonym information as possible for use in
1830 error messages, but that is a usability issue.) This rule applies, of course, whether
1831 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1832 valid way to write <literal>g</literal>'s type signature:
1834 g :: Int -> Int -> forall b. b -> Int
1840 <sect1 id="existential-quantification">
1841 <title>Existentially quantified data constructors
1845 The idea of using existential quantification in data type declarations
1846 was suggested by Laufer (I believe, thought doubtless someone will
1847 correct me), and implemented in Hope+. It's been in Lennart
1848 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1849 proved very useful. Here's the idea. Consider the declaration:
1855 data Foo = forall a. MkFoo a (a -> Bool)
1862 The data type <literal>Foo</literal> has two constructors with types:
1868 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1875 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1876 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1877 For example, the following expression is fine:
1883 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1889 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1890 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1891 isUpper</function> packages a character with a compatible function. These
1892 two things are each of type <literal>Foo</literal> and can be put in a list.
1896 What can we do with a value of type <literal>Foo</literal>?. In particular,
1897 what happens when we pattern-match on <function>MkFoo</function>?
1903 f (MkFoo val fn) = ???
1909 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1910 are compatible, the only (useful) thing we can do with them is to
1911 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1918 f (MkFoo val fn) = fn val
1924 What this allows us to do is to package heterogenous values
1925 together with a bunch of functions that manipulate them, and then treat
1926 that collection of packages in a uniform manner. You can express
1927 quite a bit of object-oriented-like programming this way.
1930 <sect2 id="existential">
1931 <title>Why existential?
1935 What has this to do with <emphasis>existential</emphasis> quantification?
1936 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1942 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1948 But Haskell programmers can safely think of the ordinary
1949 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1950 adding a new existential quantification construct.
1956 <title>Type classes</title>
1959 An easy extension (implemented in <Command>hbc</Command>) is to allow
1960 arbitrary contexts before the constructor. For example:
1966 data Baz = forall a. Eq a => Baz1 a a
1967 | forall b. Show b => Baz2 b (b -> b)
1973 The two constructors have the types you'd expect:
1979 Baz1 :: forall a. Eq a => a -> a -> Baz
1980 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1986 But when pattern matching on <function>Baz1</function> the matched values can be compared
1987 for equality, and when pattern matching on <function>Baz2</function> the first matched
1988 value can be converted to a string (as well as applying the function to it).
1989 So this program is legal:
1996 f (Baz1 p q) | p == q = "Yes"
1998 f (Baz2 v fn) = show (fn v)
2004 Operationally, in a dictionary-passing implementation, the
2005 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2006 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2007 extract it on pattern matching.
2011 Notice the way that the syntax fits smoothly with that used for
2012 universal quantification earlier.
2018 <title>Restrictions</title>
2021 There are several restrictions on the ways in which existentially-quantified
2022 constructors can be use.
2031 When pattern matching, each pattern match introduces a new,
2032 distinct, type for each existential type variable. These types cannot
2033 be unified with any other type, nor can they escape from the scope of
2034 the pattern match. For example, these fragments are incorrect:
2042 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2043 is the result of <function>f1</function>. One way to see why this is wrong is to
2044 ask what type <function>f1</function> has:
2048 f1 :: Foo -> a -- Weird!
2052 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2057 f1 :: forall a. Foo -> a -- Wrong!
2061 The original program is just plain wrong. Here's another sort of error
2065 f2 (Baz1 a b) (Baz1 p q) = a==q
2069 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2070 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2071 from the two <function>Baz1</function> constructors.
2079 You can't pattern-match on an existentially quantified
2080 constructor in a <literal>let</literal> or <literal>where</literal> group of
2081 bindings. So this is illegal:
2085 f3 x = a==b where { Baz1 a b = x }
2089 You can only pattern-match
2090 on an existentially-quantified constructor in a <literal>case</literal> expression or
2091 in the patterns of a function definition.
2093 The reason for this restriction is really an implementation one.
2094 Type-checking binding groups is already a nightmare without
2095 existentials complicating the picture. Also an existential pattern
2096 binding at the top level of a module doesn't make sense, because it's
2097 not clear how to prevent the existentially-quantified type "escaping".
2098 So for now, there's a simple-to-state restriction. We'll see how
2106 You can't use existential quantification for <literal>newtype</literal>
2107 declarations. So this is illegal:
2111 newtype T = forall a. Ord a => MkT a
2115 Reason: a value of type <literal>T</literal> must be represented as a pair
2116 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2117 That contradicts the idea that <literal>newtype</literal> should have no
2118 concrete representation. You can get just the same efficiency and effect
2119 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2120 overloading involved, then there is more of a case for allowing
2121 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2122 because the <literal>data</literal> version does carry an implementation cost,
2123 but single-field existentially quantified constructors aren't much
2124 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2125 stands, unless there are convincing reasons to change it.
2133 You can't use <literal>deriving</literal> to define instances of a
2134 data type with existentially quantified data constructors.
2136 Reason: in most cases it would not make sense. For example:#
2139 data T = forall a. MkT [a] deriving( Eq )
2142 To derive <literal>Eq</literal> in the standard way we would need to have equality
2143 between the single component of two <function>MkT</function> constructors:
2147 (MkT a) == (MkT b) = ???
2150 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2151 It's just about possible to imagine examples in which the derived instance
2152 would make sense, but it seems altogether simpler simply to prohibit such
2153 declarations. Define your own instances!
2165 <sect1 id="scoped-type-variables">
2166 <title>Scoped Type Variables
2170 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2171 variable</emphasis>. For example
2177 f (xs::[a]) = ys ++ ys
2186 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2187 This brings the type variable <literal>a</literal> into scope; it scopes over
2188 all the patterns and right hand sides for this equation for <function>f</function>.
2189 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2193 Pattern type signatures are completely orthogonal to ordinary, separate
2194 type signatures. The two can be used independently or together.
2195 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2196 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2197 implicitly universally quantified. (If there are no type variables in
2198 scope, all type variables mentioned in the signature are universally
2199 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2200 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2201 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2202 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2203 it becomes possible to do so.
2207 Scoped type variables are implemented in both GHC and Hugs. Where the
2208 implementations differ from the specification below, those differences
2213 So much for the basic idea. Here are the details.
2217 <title>What a pattern type signature means</title>
2219 A type variable brought into scope by a pattern type signature is simply
2220 the name for a type. The restriction they express is that all occurrences
2221 of the same name mean the same type. For example:
2223 f :: [Int] -> Int -> Int
2224 f (xs::[a]) (y::a) = (head xs + y) :: a
2226 The pattern type signatures on the left hand side of
2227 <literal>f</literal> express the fact that <literal>xs</literal>
2228 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2229 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2230 specifies that this expression must have the same type <literal>a</literal>.
2231 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2232 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2233 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2234 rules, which specified that a pattern-bound type variable should be universally quantified.)
2235 For example, all of these are legal:</para>
2238 t (x::a) (y::a) = x+y*2
2240 f (x::a) (y::b) = [x,y] -- a unifies with b
2242 g (x::a) = x + 1::Int -- a unifies with Int
2244 h x = let k (y::a) = [x,y] -- a is free in the
2245 in k x -- environment
2247 k (x::a) True = ... -- a unifies with Int
2248 k (x::Int) False = ...
2251 w (x::a) = x -- a unifies with [b]
2257 <title>Scope and implicit quantification</title>
2265 All the type variables mentioned in a pattern,
2266 that are not already in scope,
2267 are brought into scope by the pattern. We describe this set as
2268 the <emphasis>type variables bound by the pattern</emphasis>.
2271 f (x::a) = let g (y::(a,b)) = fst y
2275 The pattern <literal>(x::a)</literal> brings the type variable
2276 <literal>a</literal> into scope, as well as the term
2277 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2278 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2279 and brings into scope the type variable <literal>b</literal>.
2285 The type variable(s) bound by the pattern have the same scope
2286 as the term variable(s) bound by the pattern. For example:
2289 f (x::a) = <...rhs of f...>
2290 (p::b, q::b) = (1,2)
2291 in <...body of let...>
2293 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2294 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2295 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2296 just like <literal>p</literal> and <literal>q</literal> do.
2297 Indeed, the newly bound type variables also scope over any ordinary, separate
2298 type signatures in the <literal>let</literal> group.
2305 The type variables bound by the pattern may be
2306 mentioned in ordinary type signatures or pattern
2307 type signatures anywhere within their scope.
2314 In ordinary type signatures, any type variable mentioned in the
2315 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2323 Ordinary type signatures do not bring any new type variables
2324 into scope (except in the type signature itself!). So this is illegal:
2331 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2332 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2333 and that is an incorrect typing.
2340 The pattern type signature is a monotype:
2345 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2349 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2350 not to type schemes.
2354 There is no implicit universal quantification on pattern type signatures (in contrast to
2355 ordinary type signatures).
2365 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2366 scope over the methods defined in the <literal>where</literal> part. For example:
2380 (Not implemented in Hugs yet, Dec 98).
2391 <title>Result type signatures</title>
2399 The result type of a function can be given a signature,
2404 f (x::a) :: [a] = [x,x,x]
2408 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2409 result type. Sometimes this is the only way of naming the type variable
2414 f :: Int -> [a] -> [a]
2415 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2416 in \xs -> map g (reverse xs `zip` xs)
2428 Result type signatures are not yet implemented in Hugs.
2434 <title>Where a pattern type signature can occur</title>
2437 A pattern type signature can occur in any pattern. For example:
2442 A pattern type signature can be on an arbitrary sub-pattern, not
2447 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2456 Pattern type signatures, including the result part, can be used
2457 in lambda abstractions:
2460 (\ (x::a, y) :: a -> x)
2467 Pattern type signatures, including the result part, can be used
2468 in <literal>case</literal> expressions:
2472 case e of { (x::a, y) :: a -> x }
2480 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2481 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2482 token or a parenthesised type of some sort). To see why,
2483 consider how one would parse this:
2497 Pattern type signatures can bind existential type variables.
2502 data T = forall a. MkT [a]
2505 f (MkT [t::a]) = MkT t3
2518 Pattern type signatures
2519 can be used in pattern bindings:
2522 f x = let (y, z::a) = x in ...
2523 f1 x = let (y, z::Int) = x in ...
2524 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2525 f3 :: (b->b) = \x -> x
2528 In all such cases, the binding is not generalised over the pattern-bound
2529 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2530 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2531 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2532 In contrast, the binding
2537 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2538 in <literal>f4</literal>'s scope.
2548 <sect1 id="sec-kinding">
2549 <title>Explicitly-kinded quantification</title>
2552 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2553 to give the kind explicitly as (machine-checked) documentation,
2554 just as it is nice to give a type signature for a function. On some occasions,
2555 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2556 John Hughes had to define the data type:
2558 data Set cxt a = Set [a]
2559 | Unused (cxt a -> ())
2561 The only use for the <literal>Unused</literal> constructor was to force the correct
2562 kind for the type variable <literal>cxt</literal>.
2565 GHC now instead allows you to specify the kind of a type variable directly, wherever
2566 a type variable is explicitly bound. Namely:
2568 <listitem><para><literal>data</literal> declarations:
2570 data Set (cxt :: * -> *) a = Set [a]
2571 </Screen></para></listitem>
2572 <listitem><para><literal>type</literal> declarations:
2574 type T (f :: * -> *) = f Int
2575 </Screen></para></listitem>
2576 <listitem><para><literal>class</literal> declarations:
2578 class (Eq a) => C (f :: * -> *) a where ...
2579 </Screen></para></listitem>
2580 <listitem><para><literal>forall</literal>'s in type signatures:
2582 f :: forall (cxt :: * -> *). Set cxt Int
2583 </Screen></para></listitem>
2588 The parentheses are required. Some of the spaces are required too, to
2589 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2590 will get a parse error, because "<literal>::*->*</literal>" is a
2591 single lexeme in Haskell.
2595 As part of the same extension, you can put kind annotations in types
2598 f :: (Int :: *) -> Int
2599 g :: forall a. a -> (a :: *)
2603 atype ::= '(' ctype '::' kind ')
2605 The parentheses are required.
2609 <sect1 id="sec-assertions">
2611 <indexterm><primary>Assertions</primary></indexterm>
2615 If you want to make use of assertions in your standard Haskell code, you
2616 could define a function like the following:
2622 assert :: Bool -> a -> a
2623 assert False x = error "assertion failed!"
2630 which works, but gives you back a less than useful error message --
2631 an assertion failed, but which and where?
2635 One way out is to define an extended <function>assert</function> function which also
2636 takes a descriptive string to include in the error message and
2637 perhaps combine this with the use of a pre-processor which inserts
2638 the source location where <function>assert</function> was used.
2642 Ghc offers a helping hand here, doing all of this for you. For every
2643 use of <function>assert</function> in the user's source:
2649 kelvinToC :: Double -> Double
2650 kelvinToC k = assert (k >= 0.0) (k+273.15)
2656 Ghc will rewrite this to also include the source location where the
2663 assert pred val ==> assertError "Main.hs|15" pred val
2669 The rewrite is only performed by the compiler when it spots
2670 applications of <function>Exception.assert</function>, so you can still define and
2671 use your own versions of <function>assert</function>, should you so wish. If not,
2672 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2676 To have the compiler ignore uses of assert, use the compiler option
2677 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2678 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2682 Assertion failures can be caught, see the documentation for the
2683 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2689 <sect1 id="pragmas">
2690 <title>Pragmas</title>
2692 <indexterm><primary>pragma</primary></indexterm>
2694 <para>GHC supports several pragmas, or instructions to the
2695 compiler placed in the source code. Pragmas don't normally affect
2696 the meaning of the program, but they might affect the efficiency
2697 of the generated code.</para>
2699 <para>Pragmas all take the form
2701 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2703 where <replaceable>word</replaceable> indicates the type of
2704 pragma, and is followed optionally by information specific to that
2705 type of pragma. Case is ignored in
2706 <replaceable>word</replaceable>. The various values for
2707 <replaceable>word</replaceable> that GHC understands are described
2708 in the following sections; any pragma encountered with an
2709 unrecognised <replaceable>word</replaceable> is (silently)
2712 <sect2 id="inline-pragma">
2713 <title>INLINE pragma
2715 <indexterm><primary>INLINE pragma</primary></indexterm>
2716 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2719 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2720 functions/values that are “small enough,” thus avoiding the call
2721 overhead and possibly exposing other more-wonderful optimisations.
2725 You will probably see these unfoldings (in Core syntax) in your
2730 Normally, if GHC decides a function is “too expensive” to inline, it
2731 will not do so, nor will it export that unfolding for other modules to
2736 The sledgehammer you can bring to bear is the
2737 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2740 key_function :: Int -> String -> (Bool, Double)
2742 #ifdef __GLASGOW_HASKELL__
2743 {-# INLINE key_function #-}
2747 (You don't need to do the C pre-processor carry-on unless you're going
2748 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2752 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2753 “cost” to be very low. The normal unfolding machinery will then be
2754 very keen to inline it.
2758 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2759 signature could be put.
2763 <literal>INLINE</literal> pragmas are a particularly good idea for the
2764 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2765 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2768 #ifdef __GLASGOW_HASKELL__
2769 {-# INLINE thenUs #-}
2770 {-# INLINE returnUs #-}
2778 <sect2 id="noinline-pragma">
2779 <title>NOINLINE pragma
2782 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2783 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2784 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2785 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2788 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2789 it stops the named function from being inlined by the compiler. You
2790 shouldn't ever need to do this, unless you're very cautious about code
2794 <para><literal>NOTINLINE</literal> is a synonym for
2795 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2796 by Haskell 98 as the standard way to disable inlining, so it should be
2797 used if you want your code to be portable).</para>
2801 <sect2 id="specialize-pragma">
2802 <title>SPECIALIZE pragma</title>
2804 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2805 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2806 <indexterm><primary>overloading, death to</primary></indexterm>
2808 <para>(UK spelling also accepted.) For key overloaded
2809 functions, you can create extra versions (NB: more code space)
2810 specialised to particular types. Thus, if you have an
2811 overloaded function:</para>
2814 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2817 <para>If it is heavily used on lists with
2818 <literal>Widget</literal> keys, you could specialise it as
2822 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2825 <para>To get very fancy, you can also specify a named function
2826 to use for the specialised value, as in:</para>
2829 {-# RULES hammeredLookup = blah #-}
2832 <para>where <literal>blah</literal> is an implementation of
2833 <literal>hammerdLookup</literal> written specialy for
2834 <literal>Widget</literal> lookups. It's <emphasis>Your
2835 Responsibility</emphasis> to make sure that
2836 <function>blah</function> really behaves as a specialised
2837 version of <function>hammeredLookup</function>!!!</para>
2839 <para>Note we use the <literal>RULE</literal> pragma here to
2840 indicate that <literal>hammeredLookup</literal> applied at a
2841 certain type should be replaced by <literal>blah</literal>. See
2842 <xref linkend="rules"> for more information on
2843 <literal>RULES</literal>.</para>
2845 <para>An example in which using <literal>RULES</literal> for
2846 specialisation will Win Big:
2849 toDouble :: Real a => a -> Double
2850 toDouble = fromRational . toRational
2852 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2853 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2856 The <function>i2d</function> function is virtually one machine
2857 instruction; the default conversion—via an intermediate
2858 <literal>Rational</literal>—is obscenely expensive by
2861 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2862 be put anywhere its type signature could be put.</para>
2866 <sect2 id="specialize-instance-pragma">
2867 <title>SPECIALIZE instance pragma
2871 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2872 <indexterm><primary>overloading, death to</primary></indexterm>
2873 Same idea, except for instance declarations. For example:
2876 instance (Eq a) => Eq (Foo a) where {
2877 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2881 The pragma must occur inside the <literal>where</literal> part
2882 of the instance declaration.
2885 Compatible with HBC, by the way, except perhaps in the placement
2891 <sect2 id="line-pragma">
2896 <indexterm><primary>LINE pragma</primary></indexterm>
2897 <indexterm><primary>pragma, LINE</primary></indexterm>
2901 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2902 automatically generated Haskell code. It lets you specify the line
2903 number and filename of the original code; for example
2909 {-# LINE 42 "Foo.vhs" #-}
2915 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2916 and this line corresponds to line 42 in the original. GHC will adjust
2917 its error messages to refer to the line/file named in the <literal>LINE</literal>
2924 <title>RULES pragma</title>
2927 The RULES pragma lets you specify rewrite rules. It is described in
2928 <xref LinkEnd="rewrite-rules">.
2933 <sect2 id="deprecated-pragma">
2934 <title>DEPRECATED pragma</title>
2937 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2938 There are two forms.
2942 You can deprecate an entire module thus:</para>
2944 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2948 When you compile any module that import <literal>Wibble</literal>, GHC will print
2949 the specified message.</para>
2954 You can deprecate a function, class, or type, with the following top-level declaration:
2957 {-# DEPRECATED f, C, T "Don't use these" #-}
2960 When you compile any module that imports and uses any of the specifed entities,
2961 GHC will print the specified message.
2965 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2971 <sect1 id="rewrite-rules">
2972 <title>Rewrite rules
2974 <indexterm><primary>RULES pagma</primary></indexterm>
2975 <indexterm><primary>pragma, RULES</primary></indexterm>
2976 <indexterm><primary>rewrite rules</primary></indexterm></title>
2979 The programmer can specify rewrite rules as part of the source program
2980 (in a pragma). GHC applies these rewrite rules wherever it can.
2988 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2995 <title>Syntax</title>
2998 From a syntactic point of view:
3004 Each rule has a name, enclosed in double quotes. The name itself has
3005 no significance at all. It is only used when reporting how many times the rule fired.
3011 There may be zero or more rules in a <literal>RULES</literal> pragma.
3017 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3018 is set, so you must lay out your rules starting in the same column as the
3019 enclosing definitions.
3025 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3026 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3027 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3028 by spaces, just like in a type <literal>forall</literal>.
3034 A pattern variable may optionally have a type signature.
3035 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3036 For example, here is the <literal>foldr/build</literal> rule:
3039 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3040 foldr k z (build g) = g k z
3043 Since <function>g</function> has a polymorphic type, it must have a type signature.
3050 The left hand side of a rule must consist of a top-level variable applied
3051 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3054 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3055 "wrong2" forall f. f True = True
3058 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3065 A rule does not need to be in the same module as (any of) the
3066 variables it mentions, though of course they need to be in scope.
3072 Rules are automatically exported from a module, just as instance declarations are.
3083 <title>Semantics</title>
3086 From a semantic point of view:
3092 Rules are only applied if you use the <option>-O</option> flag.
3098 Rules are regarded as left-to-right rewrite rules.
3099 When GHC finds an expression that is a substitution instance of the LHS
3100 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3101 By "a substitution instance" we mean that the LHS can be made equal to the
3102 expression by substituting for the pattern variables.
3109 The LHS and RHS of a rule are typechecked, and must have the
3117 GHC makes absolutely no attempt to verify that the LHS and RHS
3118 of a rule have the same meaning. That is undecideable in general, and
3119 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3126 GHC makes no attempt to make sure that the rules are confluent or
3127 terminating. For example:
3130 "loop" forall x,y. f x y = f y x
3133 This rule will cause the compiler to go into an infinite loop.
3140 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3146 GHC currently uses a very simple, syntactic, matching algorithm
3147 for matching a rule LHS with an expression. It seeks a substitution
3148 which makes the LHS and expression syntactically equal modulo alpha
3149 conversion. The pattern (rule), but not the expression, is eta-expanded if
3150 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3151 But not beta conversion (that's called higher-order matching).
3155 Matching is carried out on GHC's intermediate language, which includes
3156 type abstractions and applications. So a rule only matches if the
3157 types match too. See <xref LinkEnd="rule-spec"> below.
3163 GHC keeps trying to apply the rules as it optimises the program.
3164 For example, consider:
3173 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3174 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3175 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3176 not be substituted, and the rule would not fire.
3183 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3184 that appears on the LHS of a rule</emphasis>, because once you have substituted
3185 for something you can't match against it (given the simple minded
3186 matching). So if you write the rule
3189 "map/map" forall f,g. map f . map g = map (f.g)
3192 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3193 It will only match something written with explicit use of ".".
3194 Well, not quite. It <emphasis>will</emphasis> match the expression
3200 where <function>wibble</function> is defined:
3203 wibble f g = map f . map g
3206 because <function>wibble</function> will be inlined (it's small).
3208 Later on in compilation, GHC starts inlining even things on the
3209 LHS of rules, but still leaves the rules enabled. This inlining
3210 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3217 All rules are implicitly exported from the module, and are therefore
3218 in force in any module that imports the module that defined the rule, directly
3219 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3220 in force when compiling A.) The situation is very similar to that for instance
3232 <title>List fusion</title>
3235 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3236 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3237 intermediate list should be eliminated entirely.
3241 The following are good producers:
3253 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3259 Explicit lists (e.g. <literal>[True, False]</literal>)
3265 The cons constructor (e.g <literal>3:4:[]</literal>)
3271 <function>++</function>
3277 <function>map</function>
3283 <function>filter</function>
3289 <function>iterate</function>, <function>repeat</function>
3295 <function>zip</function>, <function>zipWith</function>
3304 The following are good consumers:
3316 <function>array</function> (on its second argument)
3322 <function>length</function>
3328 <function>++</function> (on its first argument)
3334 <function>foldr</function>
3340 <function>map</function>
3346 <function>filter</function>
3352 <function>concat</function>
3358 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3364 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3365 will fuse with one but not the other)
3371 <function>partition</function>
3377 <function>head</function>
3383 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3389 <function>sequence_</function>
3395 <function>msum</function>
3401 <function>sortBy</function>
3410 So, for example, the following should generate no intermediate lists:
3413 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3419 This list could readily be extended; if there are Prelude functions that you use
3420 a lot which are not included, please tell us.
3424 If you want to write your own good consumers or producers, look at the
3425 Prelude definitions of the above functions to see how to do so.
3430 <sect2 id="rule-spec">
3431 <title>Specialisation
3435 Rewrite rules can be used to get the same effect as a feature
3436 present in earlier version of GHC:
3439 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3442 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3443 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3444 specialising the original definition of <function>fromIntegral</function> the programmer is
3445 promising that it is safe to use <function>int8ToInt16</function> instead.
3449 This feature is no longer in GHC. But rewrite rules let you do the
3454 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3458 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3459 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3460 GHC adds the type and dictionary applications to get the typed rule
3463 forall (d1::Integral Int8) (d2::Num Int16) .
3464 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3468 this rule does not need to be in the same file as fromIntegral,
3469 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3470 have an original definition available to specialise).
3476 <title>Controlling what's going on</title>
3484 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3490 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3491 If you add <option>-dppr-debug</option> you get a more detailed listing.
3497 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3500 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3501 {-# INLINE build #-}
3505 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3506 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3507 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3508 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3515 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3516 see how to write rules that will do fusion and yet give an efficient
3517 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3529 <sect1 id="generic-classes">
3530 <title>Generic classes</title>
3532 <para>(Note: support for generic classes is currently broken in
3536 The ideas behind this extension are described in detail in "Derivable type classes",
3537 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3538 An example will give the idea:
3546 fromBin :: [Int] -> (a, [Int])
3548 toBin {| Unit |} Unit = []
3549 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3550 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3551 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3553 fromBin {| Unit |} bs = (Unit, bs)
3554 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3555 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3556 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3557 (y,bs'') = fromBin bs'
3560 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3561 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3562 which are defined thus in the library module <literal>Generics</literal>:
3566 data a :+: b = Inl a | Inr b
3567 data a :*: b = a :*: b
3570 Now you can make a data type into an instance of Bin like this:
3572 instance (Bin a, Bin b) => Bin (a,b)
3573 instance Bin a => Bin [a]
3575 That is, just leave off the "where" clasuse. Of course, you can put in the
3576 where clause and over-ride whichever methods you please.
3580 <title> Using generics </title>
3581 <para>To use generics you need to</para>
3584 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3585 <option>-fgenerics</option> (to generate extra per-data-type code),
3586 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3590 <para>Import the module <literal>Generics</literal> from the
3591 <literal>lang</literal> package. This import brings into
3592 scope the data types <literal>Unit</literal>,
3593 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3594 don't need this import if you don't mention these types
3595 explicitly; for example, if you are simply giving instance
3596 declarations.)</para>
3601 <sect2> <title> Changes wrt the paper </title>
3603 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3604 can be written infix (indeed, you can now use
3605 any operator starting in a colon as an infix type constructor). Also note that
3606 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3607 Finally, note that the syntax of the type patterns in the class declaration
3608 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3609 alone would ambiguous when they appear on right hand sides (an extension we
3610 anticipate wanting).
3614 <sect2> <title>Terminology and restrictions</title>
3616 Terminology. A "generic default method" in a class declaration
3617 is one that is defined using type patterns as above.
3618 A "polymorphic default method" is a default method defined as in Haskell 98.
3619 A "generic class declaration" is a class declaration with at least one
3620 generic default method.
3628 Alas, we do not yet implement the stuff about constructor names and
3635 A generic class can have only one parameter; you can't have a generic
3636 multi-parameter class.
3642 A default method must be defined entirely using type patterns, or entirely
3643 without. So this is illegal:
3646 op :: a -> (a, Bool)
3647 op {| Unit |} Unit = (Unit, True)
3650 However it is perfectly OK for some methods of a generic class to have
3651 generic default methods and others to have polymorphic default methods.
3657 The type variable(s) in the type pattern for a generic method declaration
3658 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:
3662 op {| p :*: q |} (x :*: y) = op (x :: p)
3670 The type patterns in a generic default method must take one of the forms:
3676 where "a" and "b" are type variables. Furthermore, all the type patterns for
3677 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3678 must use the same type variables. So this is illegal:
3682 op {| a :+: b |} (Inl x) = True
3683 op {| p :+: q |} (Inr y) = False
3685 The type patterns must be identical, even in equations for different methods of the class.
3686 So this too is illegal:
3690 op1 {| a :*: b |} (x :*: y) = True
3693 op2 {| p :*: q |} (x :*: y) = False
3695 (The reason for this restriction is that we gather all the equations for a particular type consructor
3696 into a single generic instance declaration.)
3702 A generic method declaration must give a case for each of the three type constructors.
3708 The type for a generic method can be built only from:
3710 <listitem> <para> Function arrows </para> </listitem>
3711 <listitem> <para> Type variables </para> </listitem>
3712 <listitem> <para> Tuples </para> </listitem>
3713 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3715 Here are some example type signatures for generic methods:
3718 op2 :: Bool -> (a,Bool)
3719 op3 :: [Int] -> a -> a
3722 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3726 This restriction is an implementation restriction: we just havn't got around to
3727 implementing the necessary bidirectional maps over arbitrary type constructors.
3728 It would be relatively easy to add specific type constructors, such as Maybe and list,
3729 to the ones that are allowed.</para>
3734 In an instance declaration for a generic class, the idea is that the compiler
3735 will fill in the methods for you, based on the generic templates. However it can only
3740 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3745 No constructor of the instance type has unboxed fields.
3749 (Of course, these things can only arise if you are already using GHC extensions.)
3750 However, you can still give an instance declarations for types which break these rules,
3751 provided you give explicit code to override any generic default methods.
3759 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3760 what the compiler does with generic declarations.
3765 <sect2> <title> Another example </title>
3767 Just to finish with, here's another example I rather like:
3771 nCons {| Unit |} _ = 1
3772 nCons {| a :*: b |} _ = 1
3773 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3776 tag {| Unit |} _ = 1
3777 tag {| a :*: b |} _ = 1
3778 tag {| a :+: b |} (Inl x) = tag x
3779 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3785 <sect1 id="newtype-deriving">
3786 <title>Generalised derived instances for newtypes</title>
3789 When you define an abstract type using <literal>newtype</literal>, you may want
3790 the new type to inherit some instances from its representation. In
3791 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3792 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3793 other classes you have to write an explicit instance declaration. For
3794 example, if you define
3797 newtype Dollars = Dollars Int
3800 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3801 explicitly define an instance of <literal>Num</literal>:
3804 instance Num Dollars where
3805 Dollars a + Dollars b = Dollars (a+b)
3808 All the instance does is apply and remove the <literal>newtype</literal>
3809 constructor. It is particularly galling that, since the constructor
3810 doesn't appear at run-time, this instance declaration defines a
3811 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3812 dictionary, only slower!
3815 <sect2> <title> Generalising the deriving clause </title>
3817 GHC now permits such instances to be derived instead, so one can write
3819 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3822 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3823 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3824 derives an instance declaration of the form
3827 instance Num Int => Num Dollars
3830 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3834 We can also derive instances of constructor classes in a similar
3835 way. For example, suppose we have implemented state and failure monad
3836 transformers, such that
3839 instance Monad m => Monad (State s m)
3840 instance Monad m => Monad (Failure m)
3842 In Haskell 98, we can define a parsing monad by
3844 type Parser tok m a = State [tok] (Failure m) a
3847 which is automatically a monad thanks to the instance declarations
3848 above. With the extension, we can make the parser type abstract,
3849 without needing to write an instance of class <literal>Monad</literal>, via
3852 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3855 In this case the derived instance declaration is of the form
3857 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3860 Notice that, since <literal>Monad</literal> is a constructor class, the
3861 instance is a <emphasis>partial application</emphasis> of the new type, not the
3862 entire left hand side. We can imagine that the type declaration is
3863 ``eta-converted'' to generate the context of the instance
3868 We can even derive instances of multi-parameter classes, provided the
3869 newtype is the last class parameter. In this case, a ``partial
3870 application'' of the class appears in the <literal>deriving</literal>
3871 clause. For example, given the class
3874 class StateMonad s m | m -> s where ...
3875 instance Monad m => StateMonad s (State s m) where ...
3877 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3879 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3880 deriving (Monad, StateMonad [tok])
3883 The derived instance is obtained by completing the application of the
3884 class to the new type:
3887 instance StateMonad [tok] (State [tok] (Failure m)) =>
3888 StateMonad [tok] (Parser tok m)
3893 As a result of this extension, all derived instances in newtype
3894 declarations are treated uniformly (and implemented just by reusing
3895 the dictionary for the representation type), <emphasis>except</emphasis>
3896 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3897 the newtype and its representation.
3901 <sect2> <title> A more precise specification </title>
3903 Derived instance declarations are constructed as follows. Consider the
3904 declaration (after expansion of any type synonyms)
3907 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3910 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3912 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3913 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3914 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3915 declarations are, for each <literal>ci</literal>,
3918 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3920 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3921 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3925 As an example which does <emphasis>not</emphasis> work, consider
3927 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3929 Here we cannot derive the instance
3931 instance Monad (State s m) => Monad (NonMonad m)
3934 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3935 and so cannot be "eta-converted" away. It is a good thing that this
3936 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3937 not, in fact, a monad --- for the same reason. Try defining
3938 <literal>>>=</literal> with the correct type: you won't be able to.
3942 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3943 important, since we can only derive instances for the last one. If the
3944 <literal>StateMonad</literal> class above were instead defined as
3947 class StateMonad m s | m -> s where ...
3950 then we would not have been able to derive an instance for the
3951 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3952 classes usually have one "main" parameter for which deriving new
3953 instances is most interesting.
3961 ;;; Local Variables: ***
3963 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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