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),
1215 There should be more documentation, but there isn't (yet). Yell if you need it.
1219 <para> You can't have an implicit parameter in the context of a class or instance
1220 declaration. For example, both these declarations are illegal:
1222 class (?x::Int) => C a where ...
1223 instance (?x::a) => Foo [a] where ...
1225 Reason: exactly which implicit parameter you pick up depends on exactly where
1226 you invoke a function. But the ``invocation'' of instance declarations is done
1227 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1228 Easiest thing is to outlaw the offending types.</para>
1235 <sect1 id="linear-implicit-parameters">
1236 <title>Linear implicit parameters
1239 Linear implicit parameters are an idea developed by Koen Claessen,
1240 Mark Shields, and Simon PJ. They address the long-standing
1241 problem that monads seem over-kill for certain sorts of problem, notably:
1244 <listitem> <para> distributing a supply of unique names </para> </listitem>
1245 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1246 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1250 Linear implicit parameters are just like ordinary implicit parameters,
1251 except that they are "linear" -- that is, they cannot be copied, and
1252 must be explicitly "split" instead. Linear implicit parameters are
1253 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1254 (The '/' in the '%' suggests the split!)
1259 data NameSupply = ...
1261 splitNS :: NameSupply -> (NameSupply, NameSupply)
1262 newName :: NameSupply -> Name
1264 instance PrelSplit.Splittable NameSupply where
1268 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1269 f env (Lam x e) = Lam x' (f env e)
1272 env' = extend env x x'
1273 ...more equations for f...
1275 Notice that the implicit parameter %ns is consumed
1277 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1278 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1282 So the translation done by the type checker makes
1283 the parameter explicit:
1285 f :: NameSupply -> Env -> Expr -> Expr
1286 f ns env (Lam x e) = Lam x' (f ns1 env e)
1288 (ns1,ns2) = splitNS ns
1290 env = extend env x x'
1292 Notice the call to 'split' introduced by the type checker.
1293 How did it know to use 'splitNS'? Because what it really did
1294 was to introduce a call to the overloaded function 'split',
1297 class Splittable a where
1300 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1301 split for name supplies. But we can simply write
1307 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1309 The <literal>Splittable</literal> class is built into GHC. It's defined in <literal>PrelSplit</literal>,
1310 and exported by <literal>GlaExts</literal>.
1315 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1316 are entirely distinct implicit parameters: you
1317 can use them together and they won't intefere with each other. </para>
1320 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1322 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1323 in the context of a class or instance declaration. </para></listitem>
1327 <sect2><title>Warnings</title>
1330 The monomorphism restriction is even more important than usual.
1331 Consider the example above:
1333 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1334 f env (Lam x e) = Lam x' (f env e)
1337 env' = extend env x x'
1339 If we replaced the two occurrences of x' by (newName %ns), which is
1340 usually a harmless thing to do, we get:
1342 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1343 f env (Lam x e) = Lam (newName %ns) (f env e)
1345 env' = extend env x (newName %ns)
1347 But now the name supply is consumed in <emphasis>three</emphasis> places
1348 (the two calls to newName,and the recursive call to f), so
1349 the result is utterly different. Urk! We don't even have
1353 Well, this is an experimental change. With implicit
1354 parameters we have already lost beta reduction anyway, and
1355 (as John Launchbury puts it) we can't sensibly reason about
1356 Haskell programs without knowing their typing.
1363 <sect1 id="functional-dependencies">
1364 <title>Functional dependencies
1367 <para> Functional dependencies are implemented as described by Mark Jones
1368 in "Type Classes with Functional Dependencies", Mark P. Jones,
1369 In Proceedings of the 9th European Symposium on Programming,
1370 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1374 There should be more documentation, but there isn't (yet). Yell if you need it.
1379 <sect1 id="universal-quantification">
1380 <title>Explicit universal quantification
1384 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1385 allows us to say exactly what this means. For example:
1393 g :: forall b. (b -> b)
1395 The two are treated identically.
1399 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1400 explicit universal quantification in
1402 For example, all the following types are legal:
1404 f1 :: forall a b. a -> b -> a
1405 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1407 f2 :: (forall a. a->a) -> Int -> Int
1408 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1410 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1412 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1413 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1414 The <literal>forall</literal> makes explicit the universal quantification that
1415 is implicitly added by Haskell.
1418 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1419 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1420 shows, the polymorphic type on the left of the function arrow can be overloaded.
1423 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1424 they have rank-2 types on the left of a function arrow.
1427 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1428 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1429 that restriction has now been lifted.)
1430 In particular, a forall-type (also called a "type scheme"),
1431 including an operational type class context, is legal:
1433 <listitem> <para> On the left of a function arrow </para> </listitem>
1434 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1435 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1436 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1437 field type signatures.</para> </listitem>
1438 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1439 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1441 There is one place you cannot put a <literal>forall</literal>:
1442 you cannot instantiate a type variable with a forall-type. So you cannot
1443 make a forall-type the argument of a type constructor. So these types are illegal:
1445 x1 :: [forall a. a->a]
1446 x2 :: (forall a. a->a, Int)
1447 x3 :: Maybe (forall a. a->a)
1449 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1450 a type variable any more!
1459 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1460 the types of the constructor arguments. Here are several examples:
1466 data T a = T1 (forall b. b -> b -> b) a
1468 data MonadT m = MkMonad { return :: forall a. a -> m a,
1469 bind :: forall a b. m a -> (a -> m b) -> m b
1472 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1478 The constructors have rank-2 types:
1484 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1485 MkMonad :: forall m. (forall a. a -> m a)
1486 -> (forall a b. m a -> (a -> m b) -> m b)
1488 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1494 Notice that you don't need to use a <literal>forall</literal> if there's an
1495 explicit context. For example in the first argument of the
1496 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1497 prefixed to the argument type. The implicit <literal>forall</literal>
1498 quantifies all type variables that are not already in scope, and are
1499 mentioned in the type quantified over.
1503 As for type signatures, implicit quantification happens for non-overloaded
1504 types too. So if you write this:
1507 data T a = MkT (Either a b) (b -> b)
1510 it's just as if you had written this:
1513 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1516 That is, since the type variable <literal>b</literal> isn't in scope, it's
1517 implicitly universally quantified. (Arguably, it would be better
1518 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1519 where that is what is wanted. Feedback welcomed.)
1523 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1524 the constructor to suitable values, just as usual. For example,
1535 a3 = MkSwizzle reverse
1538 a4 = let r x = Just x
1545 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1546 mkTs f x y = [T1 f x, T1 f y]
1552 The type of the argument can, as usual, be more general than the type
1553 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1554 does not need the <literal>Ord</literal> constraint.)
1558 When you use pattern matching, the bound variables may now have
1559 polymorphic types. For example:
1565 f :: T a -> a -> (a, Char)
1566 f (T1 w k) x = (w k x, w 'c' 'd')
1568 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1569 g (MkSwizzle s) xs f = s (map f (s xs))
1571 h :: MonadT m -> [m a] -> m [a]
1572 h m [] = return m []
1573 h m (x:xs) = bind m x $ \y ->
1574 bind m (h m xs) $ \ys ->
1581 In the function <function>h</function> we use the record selectors <literal>return</literal>
1582 and <literal>bind</literal> to extract the polymorphic bind and return functions
1583 from the <literal>MonadT</literal> data structure, rather than using pattern
1589 <title>Type inference</title>
1592 In general, type inference for arbitrary-rank types is undecideable.
1593 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1594 to get a decidable algorithm by requiring some help from the programmer.
1595 We do not yet have a formal specification of "some help" but the rule is this:
1598 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1599 provides an explicit polymorphic type for x, or GHC's type inference will assume
1600 that x's type has no foralls in it</emphasis>.
1603 What does it mean to "provide" an explicit type for x? You can do that by
1604 giving a type signature for x directly, using a pattern type signature
1605 (<xref linkend="scoped-type-variables">), thus:
1607 \ f :: (forall a. a->a) -> (f True, f 'c')
1609 Alternatively, you can give a type signature to the enclosing
1610 context, which GHC can "push down" to find the type for the variable:
1612 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1614 Here the type signature on the expression can be pushed inwards
1615 to give a type signature for f. Similarly, and more commonly,
1616 one can give a type signature for the function itself:
1618 h :: (forall a. a->a) -> (Bool,Char)
1619 h f = (f True, f 'c')
1621 You don't need to give a type signature if the lambda bound variable
1622 is a constructor argument. Here is an example we saw earlier:
1624 f :: T a -> a -> (a, Char)
1625 f (T1 w k) x = (w k x, w 'c' 'd')
1627 Here we do not need to give a type signature to <literal>w</literal>, because
1628 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1636 <title>Type synonyms and hoisting
1640 GHC also allows you to write a <literal>forall</literal> in a type synonym, thus:
1642 type Discard a = forall b. a -> b -> a
1647 However, it is often convenient to use these sort of synonyms at the right hand
1648 end of an arrow, thus:
1650 type Discard a = forall b. a -> b -> a
1652 g :: Int -> Discard Int
1655 Simply expanding the type synonym would give
1657 g :: Int -> (forall b. Int -> b -> Int)
1659 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1661 g :: forall b. Int -> Int -> b -> Int
1663 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1664 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1665 performs the transformation:</emphasis>
1667 <emphasis>type1</emphasis> -> forall a. <emphasis>type2</emphasis>
1669 forall a. <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1671 (In fact, GHC tries to retain as much synonym information as possible for use in
1672 error messages, but that is a usability issue.) This rule applies, of course, whether
1673 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1674 valid way to write <literal>g</literal>'s type signature:
1676 g :: Int -> Int -> forall b. b -> Int
1683 <sect1 id="existential-quantification">
1684 <title>Existentially quantified data constructors
1688 The idea of using existential quantification in data type declarations
1689 was suggested by Laufer (I believe, thought doubtless someone will
1690 correct me), and implemented in Hope+. It's been in Lennart
1691 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1692 proved very useful. Here's the idea. Consider the declaration:
1698 data Foo = forall a. MkFoo a (a -> Bool)
1705 The data type <literal>Foo</literal> has two constructors with types:
1711 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1718 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1719 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1720 For example, the following expression is fine:
1726 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1732 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1733 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1734 isUpper</function> packages a character with a compatible function. These
1735 two things are each of type <literal>Foo</literal> and can be put in a list.
1739 What can we do with a value of type <literal>Foo</literal>?. In particular,
1740 what happens when we pattern-match on <function>MkFoo</function>?
1746 f (MkFoo val fn) = ???
1752 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1753 are compatible, the only (useful) thing we can do with them is to
1754 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1761 f (MkFoo val fn) = fn val
1767 What this allows us to do is to package heterogenous values
1768 together with a bunch of functions that manipulate them, and then treat
1769 that collection of packages in a uniform manner. You can express
1770 quite a bit of object-oriented-like programming this way.
1773 <sect2 id="existential">
1774 <title>Why existential?
1778 What has this to do with <emphasis>existential</emphasis> quantification?
1779 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1785 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1791 But Haskell programmers can safely think of the ordinary
1792 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1793 adding a new existential quantification construct.
1799 <title>Type classes</title>
1802 An easy extension (implemented in <Command>hbc</Command>) is to allow
1803 arbitrary contexts before the constructor. For example:
1809 data Baz = forall a. Eq a => Baz1 a a
1810 | forall b. Show b => Baz2 b (b -> b)
1816 The two constructors have the types you'd expect:
1822 Baz1 :: forall a. Eq a => a -> a -> Baz
1823 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1829 But when pattern matching on <function>Baz1</function> the matched values can be compared
1830 for equality, and when pattern matching on <function>Baz2</function> the first matched
1831 value can be converted to a string (as well as applying the function to it).
1832 So this program is legal:
1839 f (Baz1 p q) | p == q = "Yes"
1841 f (Baz1 v fn) = show (fn v)
1847 Operationally, in a dictionary-passing implementation, the
1848 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1849 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1850 extract it on pattern matching.
1854 Notice the way that the syntax fits smoothly with that used for
1855 universal quantification earlier.
1861 <title>Restrictions</title>
1864 There are several restrictions on the ways in which existentially-quantified
1865 constructors can be use.
1874 When pattern matching, each pattern match introduces a new,
1875 distinct, type for each existential type variable. These types cannot
1876 be unified with any other type, nor can they escape from the scope of
1877 the pattern match. For example, these fragments are incorrect:
1885 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1886 is the result of <function>f1</function>. One way to see why this is wrong is to
1887 ask what type <function>f1</function> has:
1891 f1 :: Foo -> a -- Weird!
1895 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1900 f1 :: forall a. Foo -> a -- Wrong!
1904 The original program is just plain wrong. Here's another sort of error
1908 f2 (Baz1 a b) (Baz1 p q) = a==q
1912 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1913 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1914 from the two <function>Baz1</function> constructors.
1922 You can't pattern-match on an existentially quantified
1923 constructor in a <literal>let</literal> or <literal>where</literal> group of
1924 bindings. So this is illegal:
1928 f3 x = a==b where { Baz1 a b = x }
1932 You can only pattern-match
1933 on an existentially-quantified constructor in a <literal>case</literal> expression or
1934 in the patterns of a function definition.
1936 The reason for this restriction is really an implementation one.
1937 Type-checking binding groups is already a nightmare without
1938 existentials complicating the picture. Also an existential pattern
1939 binding at the top level of a module doesn't make sense, because it's
1940 not clear how to prevent the existentially-quantified type "escaping".
1941 So for now, there's a simple-to-state restriction. We'll see how
1949 You can't use existential quantification for <literal>newtype</literal>
1950 declarations. So this is illegal:
1954 newtype T = forall a. Ord a => MkT a
1958 Reason: a value of type <literal>T</literal> must be represented as a pair
1959 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1960 That contradicts the idea that <literal>newtype</literal> should have no
1961 concrete representation. You can get just the same efficiency and effect
1962 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1963 overloading involved, then there is more of a case for allowing
1964 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1965 because the <literal>data</literal> version does carry an implementation cost,
1966 but single-field existentially quantified constructors aren't much
1967 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1968 stands, unless there are convincing reasons to change it.
1976 You can't use <literal>deriving</literal> to define instances of a
1977 data type with existentially quantified data constructors.
1979 Reason: in most cases it would not make sense. For example:#
1982 data T = forall a. MkT [a] deriving( Eq )
1985 To derive <literal>Eq</literal> in the standard way we would need to have equality
1986 between the single component of two <function>MkT</function> constructors:
1990 (MkT a) == (MkT b) = ???
1993 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1994 It's just about possible to imagine examples in which the derived instance
1995 would make sense, but it seems altogether simpler simply to prohibit such
1996 declarations. Define your own instances!
2008 <sect1 id="sec-assertions">
2010 <indexterm><primary>Assertions</primary></indexterm>
2014 If you want to make use of assertions in your standard Haskell code, you
2015 could define a function like the following:
2021 assert :: Bool -> a -> a
2022 assert False x = error "assertion failed!"
2029 which works, but gives you back a less than useful error message --
2030 an assertion failed, but which and where?
2034 One way out is to define an extended <function>assert</function> function which also
2035 takes a descriptive string to include in the error message and
2036 perhaps combine this with the use of a pre-processor which inserts
2037 the source location where <function>assert</function> was used.
2041 Ghc offers a helping hand here, doing all of this for you. For every
2042 use of <function>assert</function> in the user's source:
2048 kelvinToC :: Double -> Double
2049 kelvinToC k = assert (k >= 0.0) (k+273.15)
2055 Ghc will rewrite this to also include the source location where the
2062 assert pred val ==> assertError "Main.hs|15" pred val
2068 The rewrite is only performed by the compiler when it spots
2069 applications of <function>Exception.assert</function>, so you can still define and
2070 use your own versions of <function>assert</function>, should you so wish. If not,
2071 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2075 To have the compiler ignore uses of assert, use the compiler option
2076 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2077 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2081 Assertion failures can be caught, see the documentation for the
2082 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2088 <sect1 id="scoped-type-variables">
2089 <title>Scoped Type Variables
2093 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2094 variable</emphasis>. For example
2100 f (xs::[a]) = ys ++ ys
2109 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2110 This brings the type variable <literal>a</literal> into scope; it scopes over
2111 all the patterns and right hand sides for this equation for <function>f</function>.
2112 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2116 Pattern type signatures are completely orthogonal to ordinary, separate
2117 type signatures. The two can be used independently or together.
2118 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2119 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2120 implicitly universally quantified. (If there are no type variables in
2121 scope, all type variables mentioned in the signature are universally
2122 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2123 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2124 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2125 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2126 it becomes possible to do so.
2130 Scoped type variables are implemented in both GHC and Hugs. Where the
2131 implementations differ from the specification below, those differences
2136 So much for the basic idea. Here are the details.
2140 <title>What a pattern type signature means</title>
2142 A type variable brought into scope by a pattern type signature is simply
2143 the name for a type. The restriction they express is that all occurrences
2144 of the same name mean the same type. For example:
2146 f :: [Int] -> Int -> Int
2147 f (xs::[a]) (y::a) = (head xs + y) :: a
2149 The pattern type signatures on the left hand side of
2150 <literal>f</literal> express the fact that <literal>xs</literal>
2151 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2152 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2153 specifies that this expression must have the same type <literal>a</literal>.
2154 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2155 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2156 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2157 rules, which specified that a pattern-bound type variable should be universally quantified.)
2158 For example, all of these are legal:</para>
2161 t (x::a) (y::a) = x+y*2
2163 f (x::a) (y::b) = [x,y] -- a unifies with b
2165 g (x::a) = x + 1::Int -- a unifies with Int
2167 h x = let k (y::a) = [x,y] -- a is free in the
2168 in k x -- environment
2170 k (x::a) True = ... -- a unifies with Int
2171 k (x::Int) False = ...
2174 w (x::a) = x -- a unifies with [b]
2180 <title>Scope and implicit quantification</title>
2188 All the type variables mentioned in a pattern,
2189 that are not already in scope,
2190 are brought into scope by the pattern. We describe this set as
2191 the <emphasis>type variables bound by the pattern</emphasis>.
2194 f (x::a) = let g (y::(a,b)) = fst y
2198 The pattern <literal>(x::a)</literal> brings the type variable
2199 <literal>a</literal> into scope, as well as the term
2200 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2201 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2202 and brings into scope the type variable <literal>b</literal>.
2208 The type variable(s) bound by the pattern have the same scope
2209 as the term variable(s) bound by the pattern. For example:
2212 f (x::a) = <...rhs of f...>
2213 (p::b, q::b) = (1,2)
2214 in <...body of let...>
2216 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2217 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2218 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2219 just like <literal>p</literal> and <literal>q</literal> do.
2220 Indeed, the newly bound type variables also scope over any ordinary, separate
2221 type signatures in the <literal>let</literal> group.
2228 The type variables bound by the pattern may be
2229 mentioned in ordinary type signatures or pattern
2230 type signatures anywhere within their scope.
2237 In ordinary type signatures, any type variable mentioned in the
2238 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2246 Ordinary type signatures do not bring any new type variables
2247 into scope (except in the type signature itself!). So this is illegal:
2254 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2255 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2256 and that is an incorrect typing.
2263 The pattern type signature is a monotype:
2268 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2272 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2273 not to type schemes.
2277 There is no implicit universal quantification on pattern type signatures (in contrast to
2278 ordinary type signatures).
2288 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2289 scope over the methods defined in the <literal>where</literal> part. For example:
2303 (Not implemented in Hugs yet, Dec 98).
2314 <title>Result type signatures</title>
2322 The result type of a function can be given a signature,
2327 f (x::a) :: [a] = [x,x,x]
2331 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2332 result type. Sometimes this is the only way of naming the type variable
2337 f :: Int -> [a] -> [a]
2338 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2339 in \xs -> map g (reverse xs `zip` xs)
2351 Result type signatures are not yet implemented in Hugs.
2357 <title>Where a pattern type signature can occur</title>
2360 A pattern type signature can occur in any pattern. For example:
2365 A pattern type signature can be on an arbitrary sub-pattern, not
2370 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2379 Pattern type signatures, including the result part, can be used
2380 in lambda abstractions:
2383 (\ (x::a, y) :: a -> x)
2390 Pattern type signatures, including the result part, can be used
2391 in <literal>case</literal> expressions:
2395 case e of { (x::a, y) :: a -> x }
2403 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2404 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2405 token or a parenthesised type of some sort). To see why,
2406 consider how one would parse this:
2420 Pattern type signatures can bind existential type variables.
2425 data T = forall a. MkT [a]
2428 f (MkT [t::a]) = MkT t3
2441 Pattern type signatures
2442 can be used in pattern bindings:
2445 f x = let (y, z::a) = x in ...
2446 f1 x = let (y, z::Int) = x in ...
2447 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2448 f3 :: (b->b) = \x -> x
2451 In all such cases, the binding is not generalised over the pattern-bound
2452 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2453 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2454 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2455 In contrast, the binding
2460 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2461 in <literal>f4</literal>'s scope.
2473 <sect1 id="pragmas">
2474 <title>Pragmas</title>
2476 <indexterm><primary>pragma</primary></indexterm>
2478 <para>GHC supports several pragmas, or instructions to the
2479 compiler placed in the source code. Pragmas don't normally affect
2480 the meaning of the program, but they might affect the efficiency
2481 of the generated code.</para>
2483 <para>Pragmas all take the form
2485 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2487 where <replaceable>word</replaceable> indicates the type of
2488 pragma, and is followed optionally by information specific to that
2489 type of pragma. Case is ignored in
2490 <replaceable>word</replaceable>. The various values for
2491 <replaceable>word</replaceable> that GHC understands are described
2492 in the following sections; any pragma encountered with an
2493 unrecognised <replaceable>word</replaceable> is (silently)
2496 <sect2 id="inline-pragma">
2497 <title>INLINE pragma
2499 <indexterm><primary>INLINE pragma</primary></indexterm>
2500 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2503 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2504 functions/values that are “small enough,” thus avoiding the call
2505 overhead and possibly exposing other more-wonderful optimisations.
2509 You will probably see these unfoldings (in Core syntax) in your
2514 Normally, if GHC decides a function is “too expensive” to inline, it
2515 will not do so, nor will it export that unfolding for other modules to
2520 The sledgehammer you can bring to bear is the
2521 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2524 key_function :: Int -> String -> (Bool, Double)
2526 #ifdef __GLASGOW_HASKELL__
2527 {-# INLINE key_function #-}
2531 (You don't need to do the C pre-processor carry-on unless you're going
2532 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2536 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2537 “cost” to be very low. The normal unfolding machinery will then be
2538 very keen to inline it.
2542 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2543 signature could be put.
2547 <literal>INLINE</literal> pragmas are a particularly good idea for the
2548 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2549 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2552 #ifdef __GLASGOW_HASKELL__
2553 {-# INLINE thenUs #-}
2554 {-# INLINE returnUs #-}
2562 <sect2 id="noinline-pragma">
2563 <title>NOINLINE pragma
2566 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2567 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2568 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2569 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2572 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2573 it stops the named function from being inlined by the compiler. You
2574 shouldn't ever need to do this, unless you're very cautious about code
2578 <para><literal>NOTINLINE</literal> is a synonym for
2579 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2580 by Haskell 98 as the standard way to disable inlining, so it should be
2581 used if you want your code to be portable).</para>
2585 <sect2 id="specialize-pragma">
2586 <title>SPECIALIZE pragma</title>
2588 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2589 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2590 <indexterm><primary>overloading, death to</primary></indexterm>
2592 <para>(UK spelling also accepted.) For key overloaded
2593 functions, you can create extra versions (NB: more code space)
2594 specialised to particular types. Thus, if you have an
2595 overloaded function:</para>
2598 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2601 <para>If it is heavily used on lists with
2602 <literal>Widget</literal> keys, you could specialise it as
2606 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2609 <para>To get very fancy, you can also specify a named function
2610 to use for the specialised value, as in:</para>
2613 {-# RULES hammeredLookup = blah #-}
2616 <para>where <literal>blah</literal> is an implementation of
2617 <literal>hammerdLookup</literal> written specialy for
2618 <literal>Widget</literal> lookups. It's <emphasis>Your
2619 Responsibility</emphasis> to make sure that
2620 <function>blah</function> really behaves as a specialised
2621 version of <function>hammeredLookup</function>!!!</para>
2623 <para>Note we use the <literal>RULE</literal> pragma here to
2624 indicate that <literal>hammeredLookup</literal> applied at a
2625 certain type should be replaced by <literal>blah</literal>. See
2626 <xref linkend="rules"> for more information on
2627 <literal>RULES</literal>.</para>
2629 <para>An example in which using <literal>RULES</literal> for
2630 specialisation will Win Big:
2633 toDouble :: Real a => a -> Double
2634 toDouble = fromRational . toRational
2636 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2637 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2640 The <function>i2d</function> function is virtually one machine
2641 instruction; the default conversion—via an intermediate
2642 <literal>Rational</literal>—is obscenely expensive by
2645 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2646 be put anywhere its type signature could be put.</para>
2650 <sect2 id="specialize-instance-pragma">
2651 <title>SPECIALIZE instance pragma
2655 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2656 <indexterm><primary>overloading, death to</primary></indexterm>
2657 Same idea, except for instance declarations. For example:
2660 instance (Eq a) => Eq (Foo a) where {
2661 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2665 The pragma must occur inside the <literal>where</literal> part
2666 of the instance declaration.
2669 Compatible with HBC, by the way, except perhaps in the placement
2675 <sect2 id="line-pragma">
2680 <indexterm><primary>LINE pragma</primary></indexterm>
2681 <indexterm><primary>pragma, LINE</primary></indexterm>
2685 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2686 automatically generated Haskell code. It lets you specify the line
2687 number and filename of the original code; for example
2693 {-# LINE 42 "Foo.vhs" #-}
2699 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2700 and this line corresponds to line 42 in the original. GHC will adjust
2701 its error messages to refer to the line/file named in the <literal>LINE</literal>
2708 <title>RULES pragma</title>
2711 The RULES pragma lets you specify rewrite rules. It is described in
2712 <xref LinkEnd="rewrite-rules">.
2717 <sect2 id="deprecated-pragma">
2718 <title>DEPRECATED pragma</title>
2721 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2722 There are two forms.
2726 You can deprecate an entire module thus:</para>
2728 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2732 When you compile any module that import <literal>Wibble</literal>, GHC will print
2733 the specified message.</para>
2738 You can deprecate a function, class, or type, with the following top-level declaration:
2741 {-# DEPRECATED f, C, T "Don't use these" #-}
2744 When you compile any module that imports and uses any of the specifed entities,
2745 GHC will print the specified message.
2749 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2755 <sect1 id="rewrite-rules">
2756 <title>Rewrite rules
2758 <indexterm><primary>RULES pagma</primary></indexterm>
2759 <indexterm><primary>pragma, RULES</primary></indexterm>
2760 <indexterm><primary>rewrite rules</primary></indexterm></title>
2763 The programmer can specify rewrite rules as part of the source program
2764 (in a pragma). GHC applies these rewrite rules wherever it can.
2772 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
2779 <title>Syntax</title>
2782 From a syntactic point of view:
2788 Each rule has a name, enclosed in double quotes. The name itself has
2789 no significance at all. It is only used when reporting how many times the rule fired.
2795 There may be zero or more rules in a <literal>RULES</literal> pragma.
2801 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
2802 is set, so you must lay out your rules starting in the same column as the
2803 enclosing definitions.
2809 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
2810 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
2811 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
2812 by spaces, just like in a type <literal>forall</literal>.
2818 A pattern variable may optionally have a type signature.
2819 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
2820 For example, here is the <literal>foldr/build</literal> rule:
2823 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
2824 foldr k z (build g) = g k z
2827 Since <function>g</function> has a polymorphic type, it must have a type signature.
2834 The left hand side of a rule must consist of a top-level variable applied
2835 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
2838 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
2839 "wrong2" forall f. f True = True
2842 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
2849 A rule does not need to be in the same module as (any of) the
2850 variables it mentions, though of course they need to be in scope.
2856 Rules are automatically exported from a module, just as instance declarations are.
2867 <title>Semantics</title>
2870 From a semantic point of view:
2876 Rules are only applied if you use the <option>-O</option> flag.
2882 Rules are regarded as left-to-right rewrite rules.
2883 When GHC finds an expression that is a substitution instance of the LHS
2884 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
2885 By "a substitution instance" we mean that the LHS can be made equal to the
2886 expression by substituting for the pattern variables.
2893 The LHS and RHS of a rule are typechecked, and must have the
2901 GHC makes absolutely no attempt to verify that the LHS and RHS
2902 of a rule have the same meaning. That is undecideable in general, and
2903 infeasible in most interesting cases. The responsibility is entirely the programmer's!
2910 GHC makes no attempt to make sure that the rules are confluent or
2911 terminating. For example:
2914 "loop" forall x,y. f x y = f y x
2917 This rule will cause the compiler to go into an infinite loop.
2924 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
2930 GHC currently uses a very simple, syntactic, matching algorithm
2931 for matching a rule LHS with an expression. It seeks a substitution
2932 which makes the LHS and expression syntactically equal modulo alpha
2933 conversion. The pattern (rule), but not the expression, is eta-expanded if
2934 necessary. (Eta-expanding the epression can lead to laziness bugs.)
2935 But not beta conversion (that's called higher-order matching).
2939 Matching is carried out on GHC's intermediate language, which includes
2940 type abstractions and applications. So a rule only matches if the
2941 types match too. See <xref LinkEnd="rule-spec"> below.
2947 GHC keeps trying to apply the rules as it optimises the program.
2948 For example, consider:
2957 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
2958 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
2959 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
2960 not be substituted, and the rule would not fire.
2967 In the earlier phases of compilation, GHC inlines <emphasis>nothing
2968 that appears on the LHS of a rule</emphasis>, because once you have substituted
2969 for something you can't match against it (given the simple minded
2970 matching). So if you write the rule
2973 "map/map" forall f,g. map f . map g = map (f.g)
2976 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
2977 It will only match something written with explicit use of ".".
2978 Well, not quite. It <emphasis>will</emphasis> match the expression
2984 where <function>wibble</function> is defined:
2987 wibble f g = map f . map g
2990 because <function>wibble</function> will be inlined (it's small).
2992 Later on in compilation, GHC starts inlining even things on the
2993 LHS of rules, but still leaves the rules enabled. This inlining
2994 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3001 All rules are implicitly exported from the module, and are therefore
3002 in force in any module that imports the module that defined the rule, directly
3003 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3004 in force when compiling A.) The situation is very similar to that for instance
3016 <title>List fusion</title>
3019 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3020 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3021 intermediate list should be eliminated entirely.
3025 The following are good producers:
3037 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3043 Explicit lists (e.g. <literal>[True, False]</literal>)
3049 The cons constructor (e.g <literal>3:4:[]</literal>)
3055 <function>++</function>
3061 <function>map</function>
3067 <function>filter</function>
3073 <function>iterate</function>, <function>repeat</function>
3079 <function>zip</function>, <function>zipWith</function>
3088 The following are good consumers:
3100 <function>array</function> (on its second argument)
3106 <function>length</function>
3112 <function>++</function> (on its first argument)
3118 <function>foldr</function>
3124 <function>map</function>
3130 <function>filter</function>
3136 <function>concat</function>
3142 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3148 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3149 will fuse with one but not the other)
3155 <function>partition</function>
3161 <function>head</function>
3167 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3173 <function>sequence_</function>
3179 <function>msum</function>
3185 <function>sortBy</function>
3194 So, for example, the following should generate no intermediate lists:
3197 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3203 This list could readily be extended; if there are Prelude functions that you use
3204 a lot which are not included, please tell us.
3208 If you want to write your own good consumers or producers, look at the
3209 Prelude definitions of the above functions to see how to do so.
3214 <sect2 id="rule-spec">
3215 <title>Specialisation
3219 Rewrite rules can be used to get the same effect as a feature
3220 present in earlier version of GHC:
3223 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3226 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3227 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3228 specialising the original definition of <function>fromIntegral</function> the programmer is
3229 promising that it is safe to use <function>int8ToInt16</function> instead.
3233 This feature is no longer in GHC. But rewrite rules let you do the
3238 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3242 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3243 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3244 GHC adds the type and dictionary applications to get the typed rule
3247 forall (d1::Integral Int8) (d2::Num Int16) .
3248 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3252 this rule does not need to be in the same file as fromIntegral,
3253 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3254 have an original definition available to specialise).
3260 <title>Controlling what's going on</title>
3268 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3274 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3275 If you add <option>-dppr-debug</option> you get a more detailed listing.
3281 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3284 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3285 {-# INLINE build #-}
3289 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3290 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3291 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3292 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3299 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3300 see how to write rules that will do fusion and yet give an efficient
3301 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3313 <sect1 id="generic-classes">
3314 <title>Generic classes</title>
3316 <para>(Note: support for generic classes is currently broken in
3320 The ideas behind this extension are described in detail in "Derivable type classes",
3321 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3322 An example will give the idea:
3330 fromBin :: [Int] -> (a, [Int])
3332 toBin {| Unit |} Unit = []
3333 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3334 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3335 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3337 fromBin {| Unit |} bs = (Unit, bs)
3338 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3339 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3340 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3341 (y,bs'') = fromBin bs'
3344 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3345 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3346 which are defined thus in the library module <literal>Generics</literal>:
3350 data a :+: b = Inl a | Inr b
3351 data a :*: b = a :*: b
3354 Now you can make a data type into an instance of Bin like this:
3356 instance (Bin a, Bin b) => Bin (a,b)
3357 instance Bin a => Bin [a]
3359 That is, just leave off the "where" clasuse. Of course, you can put in the
3360 where clause and over-ride whichever methods you please.
3364 <title> Using generics </title>
3365 <para>To use generics you need to</para>
3368 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3369 <option>-fgenerics</option> (to generate extra per-data-type code),
3370 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3374 <para>Import the module <literal>Generics</literal> from the
3375 <literal>lang</literal> package. This import brings into
3376 scope the data types <literal>Unit</literal>,
3377 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3378 don't need this import if you don't mention these types
3379 explicitly; for example, if you are simply giving instance
3380 declarations.)</para>
3385 <sect2> <title> Changes wrt the paper </title>
3387 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3388 can be written infix (indeed, you can now use
3389 any operator starting in a colon as an infix type constructor). Also note that
3390 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3391 Finally, note that the syntax of the type patterns in the class declaration
3392 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3393 alone would ambiguous when they appear on right hand sides (an extension we
3394 anticipate wanting).
3398 <sect2> <title>Terminology and restrictions</title>
3400 Terminology. A "generic default method" in a class declaration
3401 is one that is defined using type patterns as above.
3402 A "polymorphic default method" is a default method defined as in Haskell 98.
3403 A "generic class declaration" is a class declaration with at least one
3404 generic default method.
3412 Alas, we do not yet implement the stuff about constructor names and
3419 A generic class can have only one parameter; you can't have a generic
3420 multi-parameter class.
3426 A default method must be defined entirely using type patterns, or entirely
3427 without. So this is illegal:
3430 op :: a -> (a, Bool)
3431 op {| Unit |} Unit = (Unit, True)
3434 However it is perfectly OK for some methods of a generic class to have
3435 generic default methods and others to have polymorphic default methods.
3441 The type variable(s) in the type pattern for a generic method declaration
3442 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:
3446 op {| p :*: q |} (x :*: y) = op (x :: p)
3454 The type patterns in a generic default method must take one of the forms:
3460 where "a" and "b" are type variables. Furthermore, all the type patterns for
3461 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3462 must use the same type variables. So this is illegal:
3466 op {| a :+: b |} (Inl x) = True
3467 op {| p :+: q |} (Inr y) = False
3469 The type patterns must be identical, even in equations for different methods of the class.
3470 So this too is illegal:
3474 op1 {| a :*: b |} (x :*: y) = True
3477 op2 {| p :*: q |} (x :*: y) = False
3479 (The reason for this restriction is that we gather all the equations for a particular type consructor
3480 into a single generic instance declaration.)
3486 A generic method declaration must give a case for each of the three type constructors.
3492 The type for a generic method can be built only from:
3494 <listitem> <para> Function arrows </para> </listitem>
3495 <listitem> <para> Type variables </para> </listitem>
3496 <listitem> <para> Tuples </para> </listitem>
3497 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3499 Here are some example type signatures for generic methods:
3502 op2 :: Bool -> (a,Bool)
3503 op3 :: [Int] -> a -> a
3506 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3510 This restriction is an implementation restriction: we just havn't got around to
3511 implementing the necessary bidirectional maps over arbitrary type constructors.
3512 It would be relatively easy to add specific type constructors, such as Maybe and list,
3513 to the ones that are allowed.</para>
3518 In an instance declaration for a generic class, the idea is that the compiler
3519 will fill in the methods for you, based on the generic templates. However it can only
3524 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3529 No constructor of the instance type has unboxed fields.
3533 (Of course, these things can only arise if you are already using GHC extensions.)
3534 However, you can still give an instance declarations for types which break these rules,
3535 provided you give explicit code to override any generic default methods.
3543 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3544 what the compiler does with generic declarations.
3549 <sect2> <title> Another example </title>
3551 Just to finish with, here's another example I rather like:
3555 nCons {| Unit |} _ = 1
3556 nCons {| a :*: b |} _ = 1
3557 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3560 tag {| Unit |} _ = 1
3561 tag {| a :*: b |} _ = 1
3562 tag {| a :+: b |} (Inl x) = tag x
3563 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3569 <sect1 id="newtype-deriving">
3570 <title>Generalised derived instances for newtypes</title>
3573 When you define an abstract type using <literal>newtype</literal>, you may want
3574 the new type to inherit some instances from its representation. In
3575 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3576 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3577 other classes you have to write an explicit instance declaration. For
3578 example, if you define
3581 newtype Dollars = Dollars Int
3584 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3585 explicitly define an instance of <literal>Num</literal>:
3588 instance Num Dollars where
3589 Dollars a + Dollars b = Dollars (a+b)
3592 All the instance does is apply and remove the <literal>newtype</literal>
3593 constructor. It is particularly galling that, since the constructor
3594 doesn't appear at run-time, this instance declaration defines a
3595 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3596 dictionary, only slower!
3599 <sect2> <title> Generalising the deriving clause </title>
3601 GHC now permits such instances to be derived instead, so one can write
3603 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3606 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3607 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3608 derives an instance declaration of the form
3611 instance Num Int => Num Dollars
3614 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3618 We can also derive instances of constructor classes in a similar
3619 way. For example, suppose we have implemented state and failure monad
3620 transformers, such that
3623 instance Monad m => Monad (State s m)
3624 instance Monad m => Monad (Failure m)
3626 In Haskell 98, we can define a parsing monad by
3628 type Parser tok m a = State [tok] (Failure m) a
3631 which is automatically a monad thanks to the instance declarations
3632 above. With the extension, we can make the parser type abstract,
3633 without needing to write an instance of class <literal>Monad</literal>, via
3636 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3639 In this case the derived instance declaration is of the form
3641 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3644 Notice that, since <literal>Monad</literal> is a constructor class, the
3645 instance is a <emphasis>partial application</emphasis> of the new type, not the
3646 entire left hand side. We can imagine that the type declaration is
3647 ``eta-converted'' to generate the context of the instance
3652 We can even derive instances of multi-parameter classes, provided the
3653 newtype is the last class parameter. In this case, a ``partial
3654 application'' of the class appears in the <literal>deriving</literal>
3655 clause. For example, given the class
3658 class StateMonad s m | m -> s where ...
3659 instance Monad m => StateMonad s (State s m) where ...
3661 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3663 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3664 deriving (Monad, StateMonad [tok])
3667 The derived instance is obtained by completing the application of the
3668 class to the new type:
3671 instance StateMonad [tok] (State [tok] (Failure m)) =>
3672 StateMonad [tok] (Parser tok m)
3677 As a result of this extension, all derived instances in newtype
3678 declarations are treated uniformly (and implemented just by reusing
3679 the dictionary for the representation type), <emphasis>except</emphasis>
3680 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3681 the newtype and its representation.
3685 <sect2> <title> A more precise specification </title>
3687 Derived instance declarations are constructed as follows. Consider the
3688 declaration (after expansion of any type synonyms)
3691 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3694 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3696 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3697 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3698 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3699 declarations are, for each <literal>ci</literal>,
3702 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3704 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3705 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3709 As an example which does <emphasis>not</emphasis> work, consider
3711 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3713 Here we cannot derive the instance
3715 instance Monad (State s m) => Monad (NonMonad m)
3718 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3719 and so cannot be "eta-converted" away. It is a good thing that this
3720 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3721 not, in fact, a monad --- for the same reason. Try defining
3722 <literal>>>=</literal> with the correct type: you won't be able to.
3726 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3727 important, since we can only derive instances for the last one. If the
3728 <literal>StateMonad</literal> class above were instead defined as
3731 class StateMonad m s | m -> s where ...
3734 then we would not have been able to derive an instance for the
3735 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3736 classes usually have one "main" parameter for which deriving new
3737 instances is most interesting.
3745 ;;; Local Variables: ***
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