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>Class method types:</term>
44 <para><xref LinkEnd="classs-method-types"></para>
49 <term>Multi-parameter type classes:</term>
51 <para><xref LinkEnd="multi-param-type-classes"></para>
56 <term>Functional dependencies:</term>
58 <para><xref LinkEnd="functional-dependencies"></para>
63 <term>Implicit parameters:</term>
65 <para><xref LinkEnd="implicit-parameters"></para>
70 <term>Linear implicit parameters:</term>
72 <para><xref LinkEnd="linear-implicit-parameters"></para>
77 <term>Local universal quantification:</term>
79 <para><xref LinkEnd="universal-quantification"></para>
84 <term>Extistentially quantification in data types:</term>
86 <para><xref LinkEnd="existential-quantification"></para>
91 <term>Scoped type variables:</term>
93 <para>Scoped type variables enable the programmer to
94 supply type signatures for some nested declarations,
95 where this would not be legal in Haskell 98. Details in
96 <xref LinkEnd="scoped-type-variables">.</para>
104 <term>Pattern guards</term>
106 <para>Instead of being a boolean expression, a guard is a list
107 of qualifiers, exactly as in a list comprehension. See <xref
108 LinkEnd="pattern-guards">.</para>
113 <term>Data types with no constructors</term>
115 <para>See <xref LinkEnd="nullary-types">.</para>
120 <term>Parallel list comprehensions</term>
122 <para>An extension to the list comprehension syntax to support
123 <literal>zipWith</literal>-like functionality. See <xref
124 linkend="parallel-list-comprehensions">.</para>
129 <term>Foreign calling:</term>
131 <para>Just what it sounds like. We provide
132 <emphasis>lots</emphasis> of rope that you can dangle around
133 your neck. Please see <xref LinkEnd="ffi">.</para>
140 <para>Pragmas are special instructions to the compiler placed
141 in the source file. The pragmas GHC supports are described in
142 <xref LinkEnd="pragmas">.</para>
147 <term>Rewrite rules:</term>
149 <para>The programmer can specify rewrite rules as part of the
150 source program (in a pragma). GHC applies these rewrite rules
151 wherever it can. Details in <xref
152 LinkEnd="rewrite-rules">.</para>
157 <term>Generic classes:</term>
159 <para>(Note: support for generic classes is currently broken
162 <para>Generic class declarations allow you to define a class
163 whose methods say how to work over an arbitrary data type.
164 Then it's really easy to make any new type into an instance of
165 the class. This generalises the rather ad-hoc "deriving"
166 feature of Haskell 98. Details in <xref
167 LinkEnd="generic-classes">.</para>
173 Before you get too carried away working at the lowest level (e.g.,
174 sloshing <literal>MutableByteArray#</literal>s around your
175 program), you may wish to check if there are libraries that provide a
176 “Haskellised veneer” over the features you want. See
177 <xref linkend="book-hslibs">.
180 <sect1 id="options-language">
181 <title>Language options</title>
183 <indexterm><primary>language</primary><secondary>option</secondary>
185 <indexterm><primary>options</primary><secondary>language</secondary>
187 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
190 <para> These flags control what variation of the language are
191 permitted. Leaving out all of them gives you standard Haskell
197 <term><option>-fglasgow-exts</option>:</term>
198 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
200 <para>This simultaneously enables all of the extensions to
201 Haskell 98 described in <xref
202 linkend="ghc-language-features">, except where otherwise
208 <term><option>-fno-monomorphism-restriction</option>:</term>
209 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
211 <para> Switch off the Haskell 98 monomorphism restriction.
212 Independent of the <option>-fglasgow-exts</option>
218 <term><option>-fallow-overlapping-instances</option></term>
219 <term><option>-fallow-undecidable-instances</option></term>
220 <term><option>-fallow-incoherent-instances</option></term>
221 <term><option>-fcontext-stack</option></term>
222 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
223 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
224 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
226 <para> See <xref LinkEnd="instance-decls">. Only relevant
227 if you also use <option>-fglasgow-exts</option>.</para>
232 <term><option>-finline-phase</option></term>
233 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
235 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
236 you also use <option>-fglasgow-exts</option>.</para>
241 <term><option>-fgenerics</option></term>
242 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
244 <para>See <xref LinkEnd="generic-classes">. Independent of
245 <option>-fglasgow-exts</option>.</para>
250 <term><option>-fno-implicit-prelude</option></term>
252 <para><indexterm><primary>-fno-implicit-prelude
253 option</primary></indexterm> GHC normally imports
254 <filename>Prelude.hi</filename> files for you. If you'd
255 rather it didn't, then give it a
256 <option>-fno-implicit-prelude</option> option. The idea
257 is that you can then import a Prelude of your own. (But
258 don't call it <literal>Prelude</literal>; the Haskell
259 module namespace is flat, and you must not conflict with
260 any Prelude module.)</para>
262 <para>Even though you have not imported the Prelude, all
263 the built-in syntax still refers to the built-in Haskell
264 Prelude types and values, as specified by the Haskell
265 Report. For example, the type <literal>[Int]</literal>
266 still means <literal>Prelude.[] Int</literal>; tuples
267 continue to refer to the standard Prelude tuples; the
268 translation for list comprehensions continues to use
269 <literal>Prelude.map</literal> etc.</para>
271 <para> With one group of exceptions! You may want to
272 define your own numeric class hierarchy. It completely
273 defeats that purpose if the literal "1" means
274 "<literal>Prelude.fromInteger 1</literal>", which is what
275 the Haskell Report specifies. So the
276 <option>-fno-implicit-prelude</option> flag causes the
277 following pieces of built-in syntax to refer to <emphasis>whatever
278 is in scope</emphasis>, not the Prelude versions:</para>
282 <para>Integer and fractional literals mean
283 "<literal>fromInteger 1</literal>" and
284 "<literal>fromRational 3.2</literal>", not the
285 Prelude-qualified versions; both in expressions and in
290 <para>Negation (e.g. "<literal>- (f x)</literal>")
291 means "<literal>negate (f x)</literal>" (not
292 <literal>Prelude.negate</literal>).</para>
296 <para>In an n+k pattern, the standard Prelude
297 <literal>Ord</literal> class is still used for comparison,
298 but the necessary subtraction uses whatever
299 "<literal>(-)</literal>" is in scope (not
300 "<literal>Prelude.(-)</literal>").</para>
304 <para>Note: Negative literals, such as <literal>-3</literal>, are
305 specified by (a careful reading of) the Haskell Report as
306 meaning <literal>Prelude.negate (Prelude.fromInteger 3)</literal>.
307 However, GHC deviates from this slightly, and treats them as meaning
308 <literal>fromInteger (-3)</literal>. One particular effect of this
309 slightly-non-standard reading is that there is no difficulty with
310 the literal <literal>-2147483648</literal> at type <literal>Int</literal>;
311 it means <literal>fromInteger (-2147483648)</literal>. The strict interpretation
312 would be <literal>negate (fromInteger 2147483648)</literal>,
313 and the call to <literal>fromInteger</literal> would overflow
314 (at type <literal>Int</literal>, remember).
323 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
326 <sect1 id="glasgow-ST-monad">
327 <title>Primitive state-transformer monad</title>
330 <indexterm><primary>state transformers (Glasgow extensions)</primary></indexterm>
331 <indexterm><primary>ST monad (Glasgow extension)</primary></indexterm>
335 This monad underlies our implementation of arrays, mutable and
336 immutable, and our implementation of I/O, including “C calls”.
340 The <literal>ST</literal> library, which provides access to the
341 <function>ST</function> monad, is described in <xref
347 <sect1 id="glasgow-prim-arrays">
348 <title>Primitive arrays, mutable and otherwise
352 <indexterm><primary>primitive arrays (Glasgow extension)</primary></indexterm>
353 <indexterm><primary>arrays, primitive (Glasgow extension)</primary></indexterm>
357 GHC knows about quite a few flavours of Large Swathes of Bytes.
361 First, GHC distinguishes between primitive arrays of (boxed) Haskell
362 objects (type <literal>Array# obj</literal>) and primitive arrays of bytes (type
363 <literal>ByteArray#</literal>).
367 Second, it distinguishes between…
371 <term>Immutable:</term>
374 Arrays that do not change (as with “standard” Haskell arrays); you
375 can only read from them. Obviously, they do not need the care and
376 attention of the state-transformer monad.
381 <term>Mutable:</term>
384 Arrays that may be changed or “mutated.” All the operations on them
385 live within the state-transformer monad and the updates happen
386 <emphasis>in-place</emphasis>.
391 <term>“Static” (in C land):</term>
394 A C routine may pass an <literal>Addr#</literal> pointer back into Haskell land. There
395 are then primitive operations with which you may merrily grab values
396 over in C land, by indexing off the “static” pointer.
401 <term>“Stable” pointers:</term>
404 If, for some reason, you wish to hand a Haskell pointer (i.e.,
405 <emphasis>not</emphasis> an unboxed value) to a C routine, you first make the
406 pointer “stable,” so that the garbage collector won't forget that it
407 exists. That is, GHC provides a safe way to pass Haskell pointers to
412 Please see <xref LinkEnd="sec-stable-pointers"> for more details.
417 <term>“Foreign objects”:</term>
420 A “foreign object” is a safe way to pass an external object (a
421 C-allocated pointer, say) to Haskell and have Haskell do the Right
422 Thing when it no longer references the object. So, for example, C
423 could pass a large bitmap over to Haskell and say “please free this
424 memory when you're done with it.”
428 Please see <xref LinkEnd="sec-ForeignObj"> for more details.
436 The libraries documentatation gives more details on all these
437 “primitive array” types and the operations on them.
443 <sect1 id="nullary-types">
444 <title>Data types with no constructors</title>
446 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
447 a data type with no constructors. For example:</para>
450 data T a -- T :: * -> *
452 <para>Syntactically, the declaration lacks the "= constrs" part. The
453 type can be parameterised, but only over ordinary types, of kind *; since
454 Haskell does not have kind signatures, you cannot parameterise over higher-kinded
457 <para>Such data types have only one value, namely bottom.
458 Nevertheless, they can be useful when defining "phantom types".</para>
461 <sect1 id="pattern-guards">
462 <title>Pattern guards</title>
465 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
466 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.)
470 Suppose we have an abstract data type of finite maps, with a
474 lookup :: FiniteMap -> Int -> Maybe Int
477 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
478 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
482 clunky env var1 var2 | ok1 && ok2 = val1 + val2
483 | otherwise = var1 + var2
494 The auxiliary functions are
498 maybeToBool :: Maybe a -> Bool
499 maybeToBool (Just x) = True
500 maybeToBool Nothing = False
502 expectJust :: Maybe a -> a
503 expectJust (Just x) = x
504 expectJust Nothing = error "Unexpected Nothing"
508 What is <function>clunky</function> doing? The guard <literal>ok1 &&
509 ok2</literal> checks that both lookups succeed, using
510 <function>maybeToBool</function> to convert the <function>Maybe</function>
511 types to booleans. The (lazily evaluated) <function>expectJust</function>
512 calls extract the values from the results of the lookups, and binds the
513 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
514 respectively. If either lookup fails, then clunky takes the
515 <literal>otherwise</literal> case and returns the sum of its arguments.
519 This is certainly legal Haskell, but it is a tremendously verbose and
520 un-obvious way to achieve the desired effect. Arguably, a more direct way
521 to write clunky would be to use case expressions:
525 clunky env var1 var1 = case lookup env var1 of
527 Just val1 -> case lookup env var2 of
529 Just val2 -> val1 + val2
535 This is a bit shorter, but hardly better. Of course, we can rewrite any set
536 of pattern-matching, guarded equations as case expressions; that is
537 precisely what the compiler does when compiling equations! The reason that
538 Haskell provides guarded equations is because they allow us to write down
539 the cases we want to consider, one at a time, independently of each other.
540 This structure is hidden in the case version. Two of the right-hand sides
541 are really the same (<function>fail</function>), and the whole expression
542 tends to become more and more indented.
546 Here is how I would write clunky:
551 | Just val1 <- lookup env var1
552 , Just val2 <- lookup env var2
554 ...other equations for clunky...
558 The semantics should be clear enough. The qualifers are matched in order.
559 For a <literal><-</literal> qualifier, which I call a pattern guard, the
560 right hand side is evaluated and matched against the pattern on the left.
561 If the match fails then the whole guard fails and the next equation is
562 tried. If it succeeds, then the appropriate binding takes place, and the
563 next qualifier is matched, in the augmented environment. Unlike list
564 comprehensions, however, the type of the expression to the right of the
565 <literal><-</literal> is the same as the type of the pattern to its
566 left. The bindings introduced by pattern guards scope over all the
567 remaining guard qualifiers, and over the right hand side of the equation.
571 Just as with list comprehensions, boolean expressions can be freely mixed
572 with among the pattern guards. For example:
583 Haskell's current guards therefore emerge as a special case, in which the
584 qualifier list has just one element, a boolean expression.
588 <sect1 id="parallel-list-comprehensions">
589 <title>Parallel List Comprehensions</title>
590 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
592 <indexterm><primary>parallel list comprehensions</primary>
595 <para>Parallel list comprehensions are a natural extension to list
596 comprehensions. List comprehensions can be thought of as a nice
597 syntax for writing maps and filters. Parallel comprehensions
598 extend this to include the zipWith family.</para>
600 <para>A parallel list comprehension has multiple independent
601 branches of qualifier lists, each separated by a `|' symbol. For
602 example, the following zips together two lists:</para>
605 [ (x, y) | x <- xs | y <- ys ]
608 <para>The behavior of parallel list comprehensions follows that of
609 zip, in that the resulting list will have the same length as the
610 shortest branch.</para>
612 <para>We can define parallel list comprehensions by translation to
613 regular comprehensions. Here's the basic idea:</para>
615 <para>Given a parallel comprehension of the form: </para>
618 [ e | p1 <- e11, p2 <- e12, ...
619 | q1 <- e21, q2 <- e22, ...
624 <para>This will be translated to: </para>
627 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
628 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
633 <para>where `zipN' is the appropriate zip for the given number of
638 <sect1 id="class-method-types">
639 <title>Class method types
642 Haskell 98 prohibits class method types to mention constraints on the
643 class type variable, thus:
646 fromList :: [a] -> s a
647 elem :: Eq a => a -> s a -> Bool
649 The type of <literal>elem</literal> is illegal in Haskell 98, because it
650 contains the constraint <literal>Eq a</literal>, constrains only the
651 class type variable (in this case <literal>a</literal>).
654 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
659 <sect1 id="multi-param-type-classes">
660 <title>Multi-parameter type classes
664 This section documents GHC's implementation of multi-parameter type
665 classes. There's lots of background in the paper <ULink
666 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
667 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
672 I'd like to thank people who reported shorcomings in the GHC 3.02
673 implementation. Our default decisions were all conservative ones, and
674 the experience of these heroic pioneers has given useful concrete
675 examples to support several generalisations. (These appear below as
676 design choices not implemented in 3.02.)
680 I've discussed these notes with Mark Jones, and I believe that Hugs
681 will migrate towards the same design choices as I outline here.
682 Thanks to him, and to many others who have offered very useful
690 There are the following restrictions on the form of a qualified
697 forall tv1..tvn (c1, ...,cn) => type
703 (Here, I write the "foralls" explicitly, although the Haskell source
704 language omits them; in Haskell 1.4, all the free type variables of an
705 explicit source-language type signature are universally quantified,
706 except for the class type variables in a class declaration. However,
707 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
716 <emphasis>Each universally quantified type variable
717 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
719 The reason for this is that a value with a type that does not obey
720 this restriction could not be used without introducing
721 ambiguity. Here, for example, is an illegal type:
725 forall a. Eq a => Int
729 When a value with this type was used, the constraint <literal>Eq tv</literal>
730 would be introduced where <literal>tv</literal> is a fresh type variable, and
731 (in the dictionary-translation implementation) the value would be
732 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
733 can never know which instance of <literal>Eq</literal> to use because we never
734 get any more information about <literal>tv</literal>.
741 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
742 universally quantified type variables <literal>tvi</literal></emphasis>.
744 For example, this type is OK because <literal>C a b</literal> mentions the
745 universally quantified type variable <literal>b</literal>:
749 forall a. C a b => burble
753 The next type is illegal because the constraint <literal>Eq b</literal> does not
754 mention <literal>a</literal>:
758 forall a. Eq b => burble
762 The reason for this restriction is milder than the other one. The
763 excluded types are never useful or necessary (because the offending
764 context doesn't need to be witnessed at this point; it can be floated
765 out). Furthermore, floating them out increases sharing. Lastly,
766 excluding them is a conservative choice; it leaves a patch of
767 territory free in case we need it later.
777 These restrictions apply to all types, whether declared in a type signature
782 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
783 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
790 f :: Eq (m a) => [m a] -> [m a]
797 This choice recovers principal types, a property that Haskell 1.4 does not have.
803 <title>Class declarations</title>
811 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
815 class Collection c a where
816 union :: c a -> c a -> c a
827 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
828 of "acyclic" involves only the superclass relationships. For example,
834 op :: D b => a -> b -> b
837 class C a => D a where { ... }
841 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
842 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
843 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
850 <emphasis>There are no restrictions on the context in a class declaration
851 (which introduces superclasses), except that the class hierarchy must
852 be acyclic</emphasis>. So these class declarations are OK:
856 class Functor (m k) => FiniteMap m k where
859 class (Monad m, Monad (t m)) => Transform t m where
860 lift :: m a -> (t m) a
869 <emphasis>In the signature of a class operation, every constraint
870 must mention at least one type variable that is not a class type
877 class Collection c a where
878 mapC :: Collection c b => (a->b) -> c a -> c b
882 is OK because the constraint <literal>(Collection a b)</literal> mentions
883 <literal>b</literal>, even though it also mentions the class variable
884 <literal>a</literal>. On the other hand:
889 op :: Eq a => (a,b) -> (a,b)
893 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
894 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
895 example is easily fixed by moving the offending context up to the
900 class Eq a => C a where
905 A yet more relaxed rule would allow the context of a class-op signature
906 to mention only class type variables. However, that conflicts with
907 Rule 1(b) for types above.
914 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
915 the class type variables</emphasis>. For example:
921 insert :: s -> a -> s
925 is not OK, because the type of <literal>empty</literal> doesn't mention
926 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
927 types, and has the same motivation.
929 Sometimes, offending class declarations exhibit misunderstandings. For
930 example, <literal>Coll</literal> might be rewritten
936 insert :: s a -> a -> s a
940 which makes the connection between the type of a collection of
941 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
942 Occasionally this really doesn't work, in which case you can split the
950 class CollE s => Coll s a where
951 insert :: s -> a -> s
964 <sect2 id="instance-decls">
965 <title>Instance declarations</title>
973 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
978 instance context1 => C type1 where ...
979 instance context2 => C type2 where ...
983 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
985 However, if you give the command line option
986 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
987 option</primary></indexterm> then overlapping instance declarations are permitted.
988 However, GHC arranges never to commit to using an instance declaration
989 if another instance declaration also applies, either now or later.
995 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1001 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1002 (but not identical to <literal>type1</literal>), or vice versa.
1006 Notice that these rules
1011 make it clear which instance decl to use
1012 (pick the most specific one that matches)
1019 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1020 Reason: you can pick which instance decl
1021 "matches" based on the type.
1026 However the rules are over-conservative. Two instance declarations can overlap,
1027 but it can still be clear in particular situations which to use. For example:
1029 instance C (Int,a) where ...
1030 instance C (a,Bool) where ...
1032 These are rejected by GHC's rules, but it is clear what to do when trying
1033 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1034 cannot apply. Yell if this restriction bites you.
1037 GHC is also conservative about committing to an overlapping instance. For example:
1039 class C a where { op :: a -> a }
1040 instance C [Int] where ...
1041 instance C a => C [a] where ...
1043 f :: C b => [b] -> [b]
1046 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1047 GHC does not commit to the second instance declaration, because in a paricular
1048 call of f, b might be instantiate to Int, so the first instance declaration
1049 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1050 GHC will instead silently pick the second instance, without complaining about
1051 the problem of subsequent instantiations.
1054 Regrettably, GHC doesn't guarantee to detect overlapping instance
1055 declarations if they appear in different modules. GHC can "see" the
1056 instance declarations in the transitive closure of all the modules
1057 imported by the one being compiled, so it can "see" all instance decls
1058 when it is compiling <literal>Main</literal>. However, it currently chooses not
1059 to look at ones that can't possibly be of use in the module currently
1060 being compiled, in the interests of efficiency. (Perhaps we should
1061 change that decision, at least for <literal>Main</literal>.)
1068 <emphasis>There are no restrictions on the type in an instance
1069 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1070 The instance "head" is the bit after the "=>" in an instance decl. For
1071 example, these are OK:
1075 instance C Int a where ...
1077 instance D (Int, Int) where ...
1079 instance E [[a]] where ...
1083 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1084 For example, this is OK:
1088 instance Stateful (ST s) (MutVar s) where ...
1092 The "at least one not a type variable" restriction is to ensure that
1093 context reduction terminates: each reduction step removes one type
1094 constructor. For example, the following would make the type checker
1095 loop if it wasn't excluded:
1099 instance C a => C a where ...
1103 There are two situations in which the rule is a bit of a pain. First,
1104 if one allows overlapping instance declarations then it's quite
1105 convenient to have a "default instance" declaration that applies if
1106 something more specific does not:
1115 Second, sometimes you might want to use the following to get the
1116 effect of a "class synonym":
1120 class (C1 a, C2 a, C3 a) => C a where { }
1122 instance (C1 a, C2 a, C3 a) => C a where { }
1126 This allows you to write shorter signatures:
1138 f :: (C1 a, C2 a, C3 a) => ...
1142 I'm on the lookout for a simple rule that preserves decidability while
1143 allowing these idioms. The experimental flag
1144 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1145 option</primary></indexterm> lifts this restriction, allowing all the types in an
1146 instance head to be type variables.
1153 <emphasis>Unlike Haskell 1.4, instance heads may use type
1154 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1155 writing the RHS of the type synonym definition. For example:
1159 type Point = (Int,Int)
1160 instance C Point where ...
1161 instance C [Point] where ...
1165 is legal. However, if you added
1169 instance C (Int,Int) where ...
1173 as well, then the compiler will complain about the overlapping
1174 (actually, identical) instance declarations. As always, type synonyms
1175 must be fully applied. You cannot, for example, write:
1180 instance Monad P where ...
1184 This design decision is independent of all the others, and easily
1185 reversed, but it makes sense to me.
1192 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1193 be type variables</emphasis>. Thus
1197 instance C a b => Eq (a,b) where ...
1205 instance C Int b => Foo b where ...
1209 is not OK. Again, the intent here is to make sure that context
1210 reduction terminates.
1212 Voluminous correspondence on the Haskell mailing list has convinced me
1213 that it's worth experimenting with a more liberal rule. If you use
1214 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1215 types in an instance context. Termination is ensured by having a
1216 fixed-depth recursion stack. If you exceed the stack depth you get a
1217 sort of backtrace, and the opportunity to increase the stack depth
1218 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1231 <sect1 id="implicit-parameters">
1232 <title>Implicit parameters
1235 <para> Implicit paramters are implemented as described in
1236 "Implicit parameters: dynamic scoping with static types",
1237 J Lewis, MB Shields, E Meijer, J Launchbury,
1238 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1241 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1243 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1244 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1245 context. In Haskell, all variables are statically bound. Dynamic
1246 binding of variables is a notion that goes back to Lisp, but was later
1247 discarded in more modern incarnations, such as Scheme. Dynamic binding
1248 can be very confusing in an untyped language, and unfortunately, typed
1249 languages, in particular Hindley-Milner typed languages like Haskell,
1250 only support static scoping of variables.
1253 However, by a simple extension to the type class system of Haskell, we
1254 can support dynamic binding. Basically, we express the use of a
1255 dynamically bound variable as a constraint on the type. These
1256 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1257 function uses a dynamically-bound variable <literal>?x</literal>
1258 of type <literal>t'</literal>". For
1259 example, the following expresses the type of a sort function,
1260 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1262 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1264 The dynamic binding constraints are just a new form of predicate in the type class system.
1267 An implicit parameter is introduced by the special form <literal>?x</literal>,
1268 where <literal>x</literal> is
1269 any valid identifier. Use if this construct also introduces new
1270 dynamic binding constraints. For example, the following definition
1271 shows how we can define an implicitly parameterized sort function in
1272 terms of an explicitly parameterized <literal>sortBy</literal> function:
1274 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1276 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1279 Dynamic binding constraints behave just like other type class
1280 constraints in that they are automatically propagated. Thus, when a
1281 function is used, its implicit parameters are inherited by the
1282 function that called it. For example, our <literal>sort</literal> function might be used
1283 to pick out the least value in a list:
1285 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1286 least xs = fst (sort xs)
1288 Without lifting a finger, the <literal>?cmp</literal> parameter is
1289 propagated to become a parameter of <literal>least</literal> as well. With explicit
1290 parameters, the default is that parameters must always be explicit
1291 propagated. With implicit parameters, the default is to always
1295 An implicit parameter differs from other type class constraints in the
1296 following way: All uses of a particular implicit parameter must have
1297 the same type. This means that the type of <literal>(?x, ?x)</literal>
1298 is <literal>(?x::a) => (a,a)</literal>, and not
1299 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1303 An implicit parameter is bound using an expression of the form
1304 <emphasis>expr</emphasis> <literal>with</literal> <emphasis>binds</emphasis>,
1305 where <literal>with</literal> is a new keyword. This form binds the implicit
1306 parameters arising in the body, not the free variables as a <literal>let</literal> or
1307 <literal>where</literal> would do. For example, we define the <literal>min</literal> function by binding
1308 <literal>cmp</literal>.
1311 min = least with ?cmp = (<=)
1313 Syntactically, the <emphasis>binds</emphasis> part of a <literal>with</literal> construct must be a
1314 collection of simple bindings to variables (no function-style
1315 bindings, and no type signatures); these bindings are neither
1316 polymorphic or recursive.
1319 Note the following additional constraints:
1322 <para> You can't have an implicit parameter in the context of a class or instance
1323 declaration. For example, both these declarations are illegal:
1325 class (?x::Int) => C a where ...
1326 instance (?x::a) => Foo [a] where ...
1328 Reason: exactly which implicit parameter you pick up depends on exactly where
1329 you invoke a function. But the ``invocation'' of instance declarations is done
1330 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1331 Easiest thing is to outlaw the offending types.</para>
1338 <sect1 id="linear-implicit-parameters">
1339 <title>Linear implicit parameters
1342 Linear implicit parameters are an idea developed by Koen Claessen,
1343 Mark Shields, and Simon PJ. They address the long-standing
1344 problem that monads seem over-kill for certain sorts of problem, notably:
1347 <listitem> <para> distributing a supply of unique names </para> </listitem>
1348 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1349 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1353 Linear implicit parameters are just like ordinary implicit parameters,
1354 except that they are "linear" -- that is, they cannot be copied, and
1355 must be explicitly "split" instead. Linear implicit parameters are
1356 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1357 (The '/' in the '%' suggests the split!)
1362 data NameSupply = ...
1364 splitNS :: NameSupply -> (NameSupply, NameSupply)
1365 newName :: NameSupply -> Name
1367 instance PrelSplit.Splittable NameSupply where
1371 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1372 f env (Lam x e) = Lam x' (f env e)
1375 env' = extend env x x'
1376 ...more equations for f...
1378 Notice that the implicit parameter %ns is consumed
1380 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1381 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1385 So the translation done by the type checker makes
1386 the parameter explicit:
1388 f :: NameSupply -> Env -> Expr -> Expr
1389 f ns env (Lam x e) = Lam x' (f ns1 env e)
1391 (ns1,ns2) = splitNS ns
1393 env = extend env x x'
1395 Notice the call to 'split' introduced by the type checker.
1396 How did it know to use 'splitNS'? Because what it really did
1397 was to introduce a call to the overloaded function 'split',
1400 class Splittable a where
1403 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1404 split for name supplies. But we can simply write
1410 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1412 The <literal>Splittable</literal> class is built into GHC. It's defined in <literal>PrelSplit</literal>,
1413 and exported by <literal>GlaExts</literal>.
1418 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1419 are entirely distinct implicit parameters: you
1420 can use them together and they won't intefere with each other. </para>
1423 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1425 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1426 in the context of a class or instance declaration. </para></listitem>
1430 <sect2><title>Warnings</title>
1433 The monomorphism restriction is even more important than usual.
1434 Consider the example above:
1436 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1437 f env (Lam x e) = Lam x' (f env e)
1440 env' = extend env x x'
1442 If we replaced the two occurrences of x' by (newName %ns), which is
1443 usually a harmless thing to do, we get:
1445 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1446 f env (Lam x e) = Lam (newName %ns) (f env e)
1448 env' = extend env x (newName %ns)
1450 But now the name supply is consumed in <emphasis>three</emphasis> places
1451 (the two calls to newName,and the recursive call to f), so
1452 the result is utterly different. Urk! We don't even have
1456 Well, this is an experimental change. With implicit
1457 parameters we have already lost beta reduction anyway, and
1458 (as John Launchbury puts it) we can't sensibly reason about
1459 Haskell programs without knowing their typing.
1466 <sect1 id="functional-dependencies">
1467 <title>Functional dependencies
1470 <para> Functional dependencies are implemented as described by Mark Jones
1471 in "Type Classes with Functional Dependencies", Mark P. Jones,
1472 In Proceedings of the 9th European Symposium on Programming,
1473 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782.
1477 There should be more documentation, but there isn't (yet). Yell if you need it.
1482 <sect1 id="universal-quantification">
1483 <title>Explicit universal quantification
1487 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1488 allows us to say exactly what this means. For example:
1496 g :: forall b. (b -> b)
1498 The two are treated identically.
1502 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1503 explicit universal quantification in
1505 For example, all the following types are legal:
1507 f1 :: forall a b. a -> b -> a
1508 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1510 f2 :: (forall a. a->a) -> Int -> Int
1511 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1513 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1515 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1516 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1517 The <literal>forall</literal> makes explicit the universal quantification that
1518 is implicitly added by Haskell.
1521 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1522 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1523 shows, the polymorphic type on the left of the function arrow can be overloaded.
1526 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1527 they have rank-2 types on the left of a function arrow.
1530 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1531 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1532 that restriction has now been lifted.)
1533 In particular, a forall-type (also called a "type scheme"),
1534 including an operational type class context, is legal:
1536 <listitem> <para> On the left of a function arrow </para> </listitem>
1537 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1538 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1539 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1540 field type signatures.</para> </listitem>
1541 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1542 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1544 There is one place you cannot put a <literal>forall</literal>:
1545 you cannot instantiate a type variable with a forall-type. So you cannot
1546 make a forall-type the argument of a type constructor. So these types are illegal:
1548 x1 :: [forall a. a->a]
1549 x2 :: (forall a. a->a, Int)
1550 x3 :: Maybe (forall a. a->a)
1552 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1553 a type variable any more!
1562 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1563 the types of the constructor arguments. Here are several examples:
1569 data T a = T1 (forall b. b -> b -> b) a
1571 data MonadT m = MkMonad { return :: forall a. a -> m a,
1572 bind :: forall a b. m a -> (a -> m b) -> m b
1575 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1581 The constructors have rank-2 types:
1587 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1588 MkMonad :: forall m. (forall a. a -> m a)
1589 -> (forall a b. m a -> (a -> m b) -> m b)
1591 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1597 Notice that you don't need to use a <literal>forall</literal> if there's an
1598 explicit context. For example in the first argument of the
1599 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1600 prefixed to the argument type. The implicit <literal>forall</literal>
1601 quantifies all type variables that are not already in scope, and are
1602 mentioned in the type quantified over.
1606 As for type signatures, implicit quantification happens for non-overloaded
1607 types too. So if you write this:
1610 data T a = MkT (Either a b) (b -> b)
1613 it's just as if you had written this:
1616 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1619 That is, since the type variable <literal>b</literal> isn't in scope, it's
1620 implicitly universally quantified. (Arguably, it would be better
1621 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1622 where that is what is wanted. Feedback welcomed.)
1626 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1627 the constructor to suitable values, just as usual. For example,
1638 a3 = MkSwizzle reverse
1641 a4 = let r x = Just x
1648 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1649 mkTs f x y = [T1 f x, T1 f y]
1655 The type of the argument can, as usual, be more general than the type
1656 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1657 does not need the <literal>Ord</literal> constraint.)
1661 When you use pattern matching, the bound variables may now have
1662 polymorphic types. For example:
1668 f :: T a -> a -> (a, Char)
1669 f (T1 w k) x = (w k x, w 'c' 'd')
1671 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1672 g (MkSwizzle s) xs f = s (map f (s xs))
1674 h :: MonadT m -> [m a] -> m [a]
1675 h m [] = return m []
1676 h m (x:xs) = bind m x $ \y ->
1677 bind m (h m xs) $ \ys ->
1684 In the function <function>h</function> we use the record selectors <literal>return</literal>
1685 and <literal>bind</literal> to extract the polymorphic bind and return functions
1686 from the <literal>MonadT</literal> data structure, rather than using pattern
1692 <title>Type inference</title>
1695 In general, type inference for arbitrary-rank types is undecideable.
1696 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1697 to get a decidable algorithm by requiring some help from the programmer.
1698 We do not yet have a formal specification of "some help" but the rule is this:
1701 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1702 provides an explicit polymorphic type for x, or GHC's type inference will assume
1703 that x's type has no foralls in it</emphasis>.
1706 What does it mean to "provide" an explicit type for x? You can do that by
1707 giving a type signature for x directly, using a pattern type signature
1708 (<xref linkend="scoped-type-variables">), thus:
1710 \ f :: (forall a. a->a) -> (f True, f 'c')
1712 Alternatively, you can give a type signature to the enclosing
1713 context, which GHC can "push down" to find the type for the variable:
1715 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1717 Here the type signature on the expression can be pushed inwards
1718 to give a type signature for f. Similarly, and more commonly,
1719 one can give a type signature for the function itself:
1721 h :: (forall a. a->a) -> (Bool,Char)
1722 h f = (f True, f 'c')
1724 You don't need to give a type signature if the lambda bound variable
1725 is a constructor argument. Here is an example we saw earlier:
1727 f :: T a -> a -> (a, Char)
1728 f (T1 w k) x = (w k x, w 'c' 'd')
1730 Here we do not need to give a type signature to <literal>w</literal>, because
1731 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1738 <sect2 id="implicit-quant">
1739 <title>Implicit quantification</title>
1742 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1743 user-written types, if and only if there is no explicit <literal>forall</literal>,
1744 GHC finds all the type variables mentioned in the type that are not already
1745 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1749 f :: forall a. a -> a
1756 h :: forall b. a -> b -> b
1762 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1765 f :: (a -> a) -> Int
1767 f :: forall a. (a -> a) -> Int
1769 f :: (forall a. a -> a) -> Int
1772 g :: (Ord a => a -> a) -> Int
1773 -- MEANS the illegal type
1774 g :: forall a. (Ord a => a -> a) -> Int
1776 g :: (forall a. Ord a => a -> a) -> Int
1778 The latter produces an illegal type, which you might think is silly,
1779 but at least the rule is simple. If you want the latter type, you
1780 can write your for-alls explicitly. Indeed, doing so is strongly advised
1787 <title>Type synonyms and hoisting
1791 Type synonmys are like macros at the type level, and GHC is much more liberal
1792 about them than Haskell 98. In particular:
1794 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1795 in a type synonym, thus:
1797 type Discard a = forall b. Show b => a -> b -> (a, String)
1802 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1809 You can write an unboxed tuple in a type synonym:
1811 type Pr = (# Int, Int #)
1820 GHC does validity checking on types <emphasis>after expanding type synonyms</emphasis>
1822 this will be rejected:
1824 type Pr = (# Int, Int #)
1829 because GHC does not allow unboxed tuples on the left of a function arrow.
1833 However, it is often convenient to use these sort of generalised synonyms at the right hand
1834 end of an arrow, thus:
1836 type Discard a = forall b. a -> b -> a
1838 g :: Int -> Discard Int
1841 Simply expanding the type synonym would give
1843 g :: Int -> (forall b. Int -> b -> Int)
1845 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1847 g :: forall b. Int -> Int -> b -> Int
1849 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1850 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1851 performs the transformation:</emphasis>
1853 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1855 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1857 (In fact, GHC tries to retain as much synonym information as possible for use in
1858 error messages, but that is a usability issue.) This rule applies, of course, whether
1859 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1860 valid way to write <literal>g</literal>'s type signature:
1862 g :: Int -> Int -> forall b. b -> Int
1868 <sect1 id="existential-quantification">
1869 <title>Existentially quantified data constructors
1873 The idea of using existential quantification in data type declarations
1874 was suggested by Laufer (I believe, thought doubtless someone will
1875 correct me), and implemented in Hope+. It's been in Lennart
1876 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
1877 proved very useful. Here's the idea. Consider the declaration:
1883 data Foo = forall a. MkFoo a (a -> Bool)
1890 The data type <literal>Foo</literal> has two constructors with types:
1896 MkFoo :: forall a. a -> (a -> Bool) -> Foo
1903 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1904 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1905 For example, the following expression is fine:
1911 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1917 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1918 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1919 isUpper</function> packages a character with a compatible function. These
1920 two things are each of type <literal>Foo</literal> and can be put in a list.
1924 What can we do with a value of type <literal>Foo</literal>?. In particular,
1925 what happens when we pattern-match on <function>MkFoo</function>?
1931 f (MkFoo val fn) = ???
1937 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1938 are compatible, the only (useful) thing we can do with them is to
1939 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1946 f (MkFoo val fn) = fn val
1952 What this allows us to do is to package heterogenous values
1953 together with a bunch of functions that manipulate them, and then treat
1954 that collection of packages in a uniform manner. You can express
1955 quite a bit of object-oriented-like programming this way.
1958 <sect2 id="existential">
1959 <title>Why existential?
1963 What has this to do with <emphasis>existential</emphasis> quantification?
1964 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1970 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1976 But Haskell programmers can safely think of the ordinary
1977 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1978 adding a new existential quantification construct.
1984 <title>Type classes</title>
1987 An easy extension (implemented in <Command>hbc</Command>) is to allow
1988 arbitrary contexts before the constructor. For example:
1994 data Baz = forall a. Eq a => Baz1 a a
1995 | forall b. Show b => Baz2 b (b -> b)
2001 The two constructors have the types you'd expect:
2007 Baz1 :: forall a. Eq a => a -> a -> Baz
2008 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2014 But when pattern matching on <function>Baz1</function> the matched values can be compared
2015 for equality, and when pattern matching on <function>Baz2</function> the first matched
2016 value can be converted to a string (as well as applying the function to it).
2017 So this program is legal:
2024 f (Baz1 p q) | p == q = "Yes"
2026 f (Baz2 v fn) = show (fn v)
2032 Operationally, in a dictionary-passing implementation, the
2033 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2034 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2035 extract it on pattern matching.
2039 Notice the way that the syntax fits smoothly with that used for
2040 universal quantification earlier.
2046 <title>Restrictions</title>
2049 There are several restrictions on the ways in which existentially-quantified
2050 constructors can be use.
2059 When pattern matching, each pattern match introduces a new,
2060 distinct, type for each existential type variable. These types cannot
2061 be unified with any other type, nor can they escape from the scope of
2062 the pattern match. For example, these fragments are incorrect:
2070 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2071 is the result of <function>f1</function>. One way to see why this is wrong is to
2072 ask what type <function>f1</function> has:
2076 f1 :: Foo -> a -- Weird!
2080 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2085 f1 :: forall a. Foo -> a -- Wrong!
2089 The original program is just plain wrong. Here's another sort of error
2093 f2 (Baz1 a b) (Baz1 p q) = a==q
2097 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2098 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2099 from the two <function>Baz1</function> constructors.
2107 You can't pattern-match on an existentially quantified
2108 constructor in a <literal>let</literal> or <literal>where</literal> group of
2109 bindings. So this is illegal:
2113 f3 x = a==b where { Baz1 a b = x }
2117 You can only pattern-match
2118 on an existentially-quantified constructor in a <literal>case</literal> expression or
2119 in the patterns of a function definition.
2121 The reason for this restriction is really an implementation one.
2122 Type-checking binding groups is already a nightmare without
2123 existentials complicating the picture. Also an existential pattern
2124 binding at the top level of a module doesn't make sense, because it's
2125 not clear how to prevent the existentially-quantified type "escaping".
2126 So for now, there's a simple-to-state restriction. We'll see how
2134 You can't use existential quantification for <literal>newtype</literal>
2135 declarations. So this is illegal:
2139 newtype T = forall a. Ord a => MkT a
2143 Reason: a value of type <literal>T</literal> must be represented as a pair
2144 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2145 That contradicts the idea that <literal>newtype</literal> should have no
2146 concrete representation. You can get just the same efficiency and effect
2147 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2148 overloading involved, then there is more of a case for allowing
2149 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2150 because the <literal>data</literal> version does carry an implementation cost,
2151 but single-field existentially quantified constructors aren't much
2152 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2153 stands, unless there are convincing reasons to change it.
2161 You can't use <literal>deriving</literal> to define instances of a
2162 data type with existentially quantified data constructors.
2164 Reason: in most cases it would not make sense. For example:#
2167 data T = forall a. MkT [a] deriving( Eq )
2170 To derive <literal>Eq</literal> in the standard way we would need to have equality
2171 between the single component of two <function>MkT</function> constructors:
2175 (MkT a) == (MkT b) = ???
2178 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2179 It's just about possible to imagine examples in which the derived instance
2180 would make sense, but it seems altogether simpler simply to prohibit such
2181 declarations. Define your own instances!
2193 <sect1 id="scoped-type-variables">
2194 <title>Scoped Type Variables
2198 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2199 variable</emphasis>. For example
2205 f (xs::[a]) = ys ++ ys
2214 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2215 This brings the type variable <literal>a</literal> into scope; it scopes over
2216 all the patterns and right hand sides for this equation for <function>f</function>.
2217 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2221 Pattern type signatures are completely orthogonal to ordinary, separate
2222 type signatures. The two can be used independently or together.
2223 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2224 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2225 implicitly universally quantified. (If there are no type variables in
2226 scope, all type variables mentioned in the signature are universally
2227 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2228 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2229 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2230 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2231 it becomes possible to do so.
2235 Scoped type variables are implemented in both GHC and Hugs. Where the
2236 implementations differ from the specification below, those differences
2241 So much for the basic idea. Here are the details.
2245 <title>What a pattern type signature means</title>
2247 A type variable brought into scope by a pattern type signature is simply
2248 the name for a type. The restriction they express is that all occurrences
2249 of the same name mean the same type. For example:
2251 f :: [Int] -> Int -> Int
2252 f (xs::[a]) (y::a) = (head xs + y) :: a
2254 The pattern type signatures on the left hand side of
2255 <literal>f</literal> express the fact that <literal>xs</literal>
2256 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2257 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2258 specifies that this expression must have the same type <literal>a</literal>.
2259 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2260 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2261 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2262 rules, which specified that a pattern-bound type variable should be universally quantified.)
2263 For example, all of these are legal:</para>
2266 t (x::a) (y::a) = x+y*2
2268 f (x::a) (y::b) = [x,y] -- a unifies with b
2270 g (x::a) = x + 1::Int -- a unifies with Int
2272 h x = let k (y::a) = [x,y] -- a is free in the
2273 in k x -- environment
2275 k (x::a) True = ... -- a unifies with Int
2276 k (x::Int) False = ...
2279 w (x::a) = x -- a unifies with [b]
2285 <title>Scope and implicit quantification</title>
2293 All the type variables mentioned in a pattern,
2294 that are not already in scope,
2295 are brought into scope by the pattern. We describe this set as
2296 the <emphasis>type variables bound by the pattern</emphasis>.
2299 f (x::a) = let g (y::(a,b)) = fst y
2303 The pattern <literal>(x::a)</literal> brings the type variable
2304 <literal>a</literal> into scope, as well as the term
2305 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2306 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2307 and brings into scope the type variable <literal>b</literal>.
2313 The type variable(s) bound by the pattern have the same scope
2314 as the term variable(s) bound by the pattern. For example:
2317 f (x::a) = <...rhs of f...>
2318 (p::b, q::b) = (1,2)
2319 in <...body of let...>
2321 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2322 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2323 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2324 just like <literal>p</literal> and <literal>q</literal> do.
2325 Indeed, the newly bound type variables also scope over any ordinary, separate
2326 type signatures in the <literal>let</literal> group.
2333 The type variables bound by the pattern may be
2334 mentioned in ordinary type signatures or pattern
2335 type signatures anywhere within their scope.
2342 In ordinary type signatures, any type variable mentioned in the
2343 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2351 Ordinary type signatures do not bring any new type variables
2352 into scope (except in the type signature itself!). So this is illegal:
2359 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2360 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2361 and that is an incorrect typing.
2368 The pattern type signature is a monotype:
2373 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2377 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2378 not to type schemes.
2382 There is no implicit universal quantification on pattern type signatures (in contrast to
2383 ordinary type signatures).
2393 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2394 scope over the methods defined in the <literal>where</literal> part. For example:
2408 (Not implemented in Hugs yet, Dec 98).
2419 <title>Result type signatures</title>
2427 The result type of a function can be given a signature,
2432 f (x::a) :: [a] = [x,x,x]
2436 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2437 result type. Sometimes this is the only way of naming the type variable
2442 f :: Int -> [a] -> [a]
2443 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2444 in \xs -> map g (reverse xs `zip` xs)
2456 Result type signatures are not yet implemented in Hugs.
2462 <title>Where a pattern type signature can occur</title>
2465 A pattern type signature can occur in any pattern. For example:
2470 A pattern type signature can be on an arbitrary sub-pattern, not
2475 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2484 Pattern type signatures, including the result part, can be used
2485 in lambda abstractions:
2488 (\ (x::a, y) :: a -> x)
2495 Pattern type signatures, including the result part, can be used
2496 in <literal>case</literal> expressions:
2500 case e of { (x::a, y) :: a -> x }
2508 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2509 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2510 token or a parenthesised type of some sort). To see why,
2511 consider how one would parse this:
2525 Pattern type signatures can bind existential type variables.
2530 data T = forall a. MkT [a]
2533 f (MkT [t::a]) = MkT t3
2546 Pattern type signatures
2547 can be used in pattern bindings:
2550 f x = let (y, z::a) = x in ...
2551 f1 x = let (y, z::Int) = x in ...
2552 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2553 f3 :: (b->b) = \x -> x
2556 In all such cases, the binding is not generalised over the pattern-bound
2557 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2558 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2559 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2560 In contrast, the binding
2565 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2566 in <literal>f4</literal>'s scope.
2576 <sect1 id="sec-kinding">
2577 <title>Explicitly-kinded quantification</title>
2580 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2581 to give the kind explicitly as (machine-checked) documentation,
2582 just as it is nice to give a type signature for a function. On some occasions,
2583 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2584 John Hughes had to define the data type:
2586 data Set cxt a = Set [a]
2587 | Unused (cxt a -> ())
2589 The only use for the <literal>Unused</literal> constructor was to force the correct
2590 kind for the type variable <literal>cxt</literal>.
2593 GHC now instead allows you to specify the kind of a type variable directly, wherever
2594 a type variable is explicitly bound. Namely:
2596 <listitem><para><literal>data</literal> declarations:
2598 data Set (cxt :: * -> *) a = Set [a]
2599 </Screen></para></listitem>
2600 <listitem><para><literal>type</literal> declarations:
2602 type T (f :: * -> *) = f Int
2603 </Screen></para></listitem>
2604 <listitem><para><literal>class</literal> declarations:
2606 class (Eq a) => C (f :: * -> *) a where ...
2607 </Screen></para></listitem>
2608 <listitem><para><literal>forall</literal>'s in type signatures:
2610 f :: forall (cxt :: * -> *). Set cxt Int
2611 </Screen></para></listitem>
2616 The parentheses are required. Some of the spaces are required too, to
2617 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2618 will get a parse error, because "<literal>::*->*</literal>" is a
2619 single lexeme in Haskell.
2623 As part of the same extension, you can put kind annotations in types
2626 f :: (Int :: *) -> Int
2627 g :: forall a. a -> (a :: *)
2631 atype ::= '(' ctype '::' kind ')
2633 The parentheses are required.
2637 <sect1 id="sec-assertions">
2639 <indexterm><primary>Assertions</primary></indexterm>
2643 If you want to make use of assertions in your standard Haskell code, you
2644 could define a function like the following:
2650 assert :: Bool -> a -> a
2651 assert False x = error "assertion failed!"
2658 which works, but gives you back a less than useful error message --
2659 an assertion failed, but which and where?
2663 One way out is to define an extended <function>assert</function> function which also
2664 takes a descriptive string to include in the error message and
2665 perhaps combine this with the use of a pre-processor which inserts
2666 the source location where <function>assert</function> was used.
2670 Ghc offers a helping hand here, doing all of this for you. For every
2671 use of <function>assert</function> in the user's source:
2677 kelvinToC :: Double -> Double
2678 kelvinToC k = assert (k >= 0.0) (k+273.15)
2684 Ghc will rewrite this to also include the source location where the
2691 assert pred val ==> assertError "Main.hs|15" pred val
2697 The rewrite is only performed by the compiler when it spots
2698 applications of <function>Exception.assert</function>, so you can still define and
2699 use your own versions of <function>assert</function>, should you so wish. If not,
2700 import <literal>Exception</literal> to make use <function>assert</function> in your code.
2704 To have the compiler ignore uses of assert, use the compiler option
2705 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts option</primary></indexterm> That is,
2706 expressions of the form <literal>assert pred e</literal> will be rewritten to <literal>e</literal>.
2710 Assertion failures can be caught, see the documentation for the
2711 <literal>Exception</literal> library (<xref linkend="sec-Exception">)
2717 <sect1 id="pragmas">
2718 <title>Pragmas</title>
2720 <indexterm><primary>pragma</primary></indexterm>
2722 <para>GHC supports several pragmas, or instructions to the
2723 compiler placed in the source code. Pragmas don't normally affect
2724 the meaning of the program, but they might affect the efficiency
2725 of the generated code.</para>
2727 <para>Pragmas all take the form
2729 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
2731 where <replaceable>word</replaceable> indicates the type of
2732 pragma, and is followed optionally by information specific to that
2733 type of pragma. Case is ignored in
2734 <replaceable>word</replaceable>. The various values for
2735 <replaceable>word</replaceable> that GHC understands are described
2736 in the following sections; any pragma encountered with an
2737 unrecognised <replaceable>word</replaceable> is (silently)
2740 <sect2 id="inline-pragma">
2741 <title>INLINE pragma
2743 <indexterm><primary>INLINE pragma</primary></indexterm>
2744 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
2747 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
2748 functions/values that are “small enough,” thus avoiding the call
2749 overhead and possibly exposing other more-wonderful optimisations.
2753 You will probably see these unfoldings (in Core syntax) in your
2758 Normally, if GHC decides a function is “too expensive” to inline, it
2759 will not do so, nor will it export that unfolding for other modules to
2764 The sledgehammer you can bring to bear is the
2765 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
2768 key_function :: Int -> String -> (Bool, Double)
2770 #ifdef __GLASGOW_HASKELL__
2771 {-# INLINE key_function #-}
2775 (You don't need to do the C pre-processor carry-on unless you're going
2776 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
2780 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
2781 “cost” to be very low. The normal unfolding machinery will then be
2782 very keen to inline it.
2786 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
2787 signature could be put.
2791 <literal>INLINE</literal> pragmas are a particularly good idea for the
2792 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
2793 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
2796 #ifdef __GLASGOW_HASKELL__
2797 {-# INLINE thenUs #-}
2798 {-# INLINE returnUs #-}
2806 <sect2 id="noinline-pragma">
2807 <title>NOINLINE pragma
2810 <indexterm><primary>NOINLINE pragma</primary></indexterm>
2811 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
2812 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
2813 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
2816 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
2817 it stops the named function from being inlined by the compiler. You
2818 shouldn't ever need to do this, unless you're very cautious about code
2822 <para><literal>NOTINLINE</literal> is a synonym for
2823 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
2824 by Haskell 98 as the standard way to disable inlining, so it should be
2825 used if you want your code to be portable).</para>
2829 <sect2 id="specialize-pragma">
2830 <title>SPECIALIZE pragma</title>
2832 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2833 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
2834 <indexterm><primary>overloading, death to</primary></indexterm>
2836 <para>(UK spelling also accepted.) For key overloaded
2837 functions, you can create extra versions (NB: more code space)
2838 specialised to particular types. Thus, if you have an
2839 overloaded function:</para>
2842 hammeredLookup :: Ord key => [(key, value)] -> key -> value
2845 <para>If it is heavily used on lists with
2846 <literal>Widget</literal> keys, you could specialise it as
2850 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
2853 <para>To get very fancy, you can also specify a named function
2854 to use for the specialised value, as in:</para>
2857 {-# RULES hammeredLookup = blah #-}
2860 <para>where <literal>blah</literal> is an implementation of
2861 <literal>hammerdLookup</literal> written specialy for
2862 <literal>Widget</literal> lookups. It's <emphasis>Your
2863 Responsibility</emphasis> to make sure that
2864 <function>blah</function> really behaves as a specialised
2865 version of <function>hammeredLookup</function>!!!</para>
2867 <para>Note we use the <literal>RULE</literal> pragma here to
2868 indicate that <literal>hammeredLookup</literal> applied at a
2869 certain type should be replaced by <literal>blah</literal>. See
2870 <xref linkend="rules"> for more information on
2871 <literal>RULES</literal>.</para>
2873 <para>An example in which using <literal>RULES</literal> for
2874 specialisation will Win Big:
2877 toDouble :: Real a => a -> Double
2878 toDouble = fromRational . toRational
2880 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
2881 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
2884 The <function>i2d</function> function is virtually one machine
2885 instruction; the default conversion—via an intermediate
2886 <literal>Rational</literal>—is obscenely expensive by
2889 <para>A <literal>SPECIALIZE</literal> pragma for a function can
2890 be put anywhere its type signature could be put.</para>
2894 <sect2 id="specialize-instance-pragma">
2895 <title>SPECIALIZE instance pragma
2899 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
2900 <indexterm><primary>overloading, death to</primary></indexterm>
2901 Same idea, except for instance declarations. For example:
2904 instance (Eq a) => Eq (Foo a) where {
2905 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
2909 The pragma must occur inside the <literal>where</literal> part
2910 of the instance declaration.
2913 Compatible with HBC, by the way, except perhaps in the placement
2919 <sect2 id="line-pragma">
2924 <indexterm><primary>LINE pragma</primary></indexterm>
2925 <indexterm><primary>pragma, LINE</primary></indexterm>
2929 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
2930 automatically generated Haskell code. It lets you specify the line
2931 number and filename of the original code; for example
2937 {-# LINE 42 "Foo.vhs" #-}
2943 if you'd generated the current file from something called <filename>Foo.vhs</filename>
2944 and this line corresponds to line 42 in the original. GHC will adjust
2945 its error messages to refer to the line/file named in the <literal>LINE</literal>
2952 <title>RULES pragma</title>
2955 The RULES pragma lets you specify rewrite rules. It is described in
2956 <xref LinkEnd="rewrite-rules">.
2961 <sect2 id="deprecated-pragma">
2962 <title>DEPRECATED pragma</title>
2965 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
2966 There are two forms.
2970 You can deprecate an entire module thus:</para>
2972 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
2976 When you compile any module that import <literal>Wibble</literal>, GHC will print
2977 the specified message.</para>
2982 You can deprecate a function, class, or type, with the following top-level declaration:
2985 {-# DEPRECATED f, C, T "Don't use these" #-}
2988 When you compile any module that imports and uses any of the specifed entities,
2989 GHC will print the specified message.
2993 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
2999 <sect1 id="rewrite-rules">
3000 <title>Rewrite rules
3002 <indexterm><primary>RULES pagma</primary></indexterm>
3003 <indexterm><primary>pragma, RULES</primary></indexterm>
3004 <indexterm><primary>rewrite rules</primary></indexterm></title>
3007 The programmer can specify rewrite rules as part of the source program
3008 (in a pragma). GHC applies these rewrite rules wherever it can.
3016 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3023 <title>Syntax</title>
3026 From a syntactic point of view:
3032 Each rule has a name, enclosed in double quotes. The name itself has
3033 no significance at all. It is only used when reporting how many times the rule fired.
3039 There may be zero or more rules in a <literal>RULES</literal> pragma.
3045 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3046 is set, so you must lay out your rules starting in the same column as the
3047 enclosing definitions.
3053 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3054 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3055 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3056 by spaces, just like in a type <literal>forall</literal>.
3062 A pattern variable may optionally have a type signature.
3063 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3064 For example, here is the <literal>foldr/build</literal> rule:
3067 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3068 foldr k z (build g) = g k z
3071 Since <function>g</function> has a polymorphic type, it must have a type signature.
3078 The left hand side of a rule must consist of a top-level variable applied
3079 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3082 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3083 "wrong2" forall f. f True = True
3086 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3093 A rule does not need to be in the same module as (any of) the
3094 variables it mentions, though of course they need to be in scope.
3100 Rules are automatically exported from a module, just as instance declarations are.
3111 <title>Semantics</title>
3114 From a semantic point of view:
3120 Rules are only applied if you use the <option>-O</option> flag.
3126 Rules are regarded as left-to-right rewrite rules.
3127 When GHC finds an expression that is a substitution instance of the LHS
3128 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3129 By "a substitution instance" we mean that the LHS can be made equal to the
3130 expression by substituting for the pattern variables.
3137 The LHS and RHS of a rule are typechecked, and must have the
3145 GHC makes absolutely no attempt to verify that the LHS and RHS
3146 of a rule have the same meaning. That is undecideable in general, and
3147 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3154 GHC makes no attempt to make sure that the rules are confluent or
3155 terminating. For example:
3158 "loop" forall x,y. f x y = f y x
3161 This rule will cause the compiler to go into an infinite loop.
3168 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3174 GHC currently uses a very simple, syntactic, matching algorithm
3175 for matching a rule LHS with an expression. It seeks a substitution
3176 which makes the LHS and expression syntactically equal modulo alpha
3177 conversion. The pattern (rule), but not the expression, is eta-expanded if
3178 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3179 But not beta conversion (that's called higher-order matching).
3183 Matching is carried out on GHC's intermediate language, which includes
3184 type abstractions and applications. So a rule only matches if the
3185 types match too. See <xref LinkEnd="rule-spec"> below.
3191 GHC keeps trying to apply the rules as it optimises the program.
3192 For example, consider:
3201 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3202 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3203 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3204 not be substituted, and the rule would not fire.
3211 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3212 that appears on the LHS of a rule</emphasis>, because once you have substituted
3213 for something you can't match against it (given the simple minded
3214 matching). So if you write the rule
3217 "map/map" forall f,g. map f . map g = map (f.g)
3220 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3221 It will only match something written with explicit use of ".".
3222 Well, not quite. It <emphasis>will</emphasis> match the expression
3228 where <function>wibble</function> is defined:
3231 wibble f g = map f . map g
3234 because <function>wibble</function> will be inlined (it's small).
3236 Later on in compilation, GHC starts inlining even things on the
3237 LHS of rules, but still leaves the rules enabled. This inlining
3238 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3245 All rules are implicitly exported from the module, and are therefore
3246 in force in any module that imports the module that defined the rule, directly
3247 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3248 in force when compiling A.) The situation is very similar to that for instance
3260 <title>List fusion</title>
3263 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3264 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3265 intermediate list should be eliminated entirely.
3269 The following are good producers:
3281 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3287 Explicit lists (e.g. <literal>[True, False]</literal>)
3293 The cons constructor (e.g <literal>3:4:[]</literal>)
3299 <function>++</function>
3305 <function>map</function>
3311 <function>filter</function>
3317 <function>iterate</function>, <function>repeat</function>
3323 <function>zip</function>, <function>zipWith</function>
3332 The following are good consumers:
3344 <function>array</function> (on its second argument)
3350 <function>length</function>
3356 <function>++</function> (on its first argument)
3362 <function>foldr</function>
3368 <function>map</function>
3374 <function>filter</function>
3380 <function>concat</function>
3386 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3392 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3393 will fuse with one but not the other)
3399 <function>partition</function>
3405 <function>head</function>
3411 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3417 <function>sequence_</function>
3423 <function>msum</function>
3429 <function>sortBy</function>
3438 So, for example, the following should generate no intermediate lists:
3441 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3447 This list could readily be extended; if there are Prelude functions that you use
3448 a lot which are not included, please tell us.
3452 If you want to write your own good consumers or producers, look at the
3453 Prelude definitions of the above functions to see how to do so.
3458 <sect2 id="rule-spec">
3459 <title>Specialisation
3463 Rewrite rules can be used to get the same effect as a feature
3464 present in earlier version of GHC:
3467 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3470 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3471 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3472 specialising the original definition of <function>fromIntegral</function> the programmer is
3473 promising that it is safe to use <function>int8ToInt16</function> instead.
3477 This feature is no longer in GHC. But rewrite rules let you do the
3482 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3486 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3487 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3488 GHC adds the type and dictionary applications to get the typed rule
3491 forall (d1::Integral Int8) (d2::Num Int16) .
3492 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3496 this rule does not need to be in the same file as fromIntegral,
3497 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3498 have an original definition available to specialise).
3504 <title>Controlling what's going on</title>
3512 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3518 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3519 If you add <option>-dppr-debug</option> you get a more detailed listing.
3525 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3528 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3529 {-# INLINE build #-}
3533 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3534 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3535 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3536 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3543 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3544 see how to write rules that will do fusion and yet give an efficient
3545 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3557 <sect1 id="generic-classes">
3558 <title>Generic classes</title>
3560 <para>(Note: support for generic classes is currently broken in
3564 The ideas behind this extension are described in detail in "Derivable type classes",
3565 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3566 An example will give the idea:
3574 fromBin :: [Int] -> (a, [Int])
3576 toBin {| Unit |} Unit = []
3577 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3578 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3579 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3581 fromBin {| Unit |} bs = (Unit, bs)
3582 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3583 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3584 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3585 (y,bs'') = fromBin bs'
3588 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3589 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3590 which are defined thus in the library module <literal>Generics</literal>:
3594 data a :+: b = Inl a | Inr b
3595 data a :*: b = a :*: b
3598 Now you can make a data type into an instance of Bin like this:
3600 instance (Bin a, Bin b) => Bin (a,b)
3601 instance Bin a => Bin [a]
3603 That is, just leave off the "where" clasuse. Of course, you can put in the
3604 where clause and over-ride whichever methods you please.
3608 <title> Using generics </title>
3609 <para>To use generics you need to</para>
3612 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
3613 <option>-fgenerics</option> (to generate extra per-data-type code),
3614 and <option>-package lang</option> (to make the <literal>Generics</literal> library
3618 <para>Import the module <literal>Generics</literal> from the
3619 <literal>lang</literal> package. This import brings into
3620 scope the data types <literal>Unit</literal>,
3621 <literal>:*:</literal>, and <literal>:+:</literal>. (You
3622 don't need this import if you don't mention these types
3623 explicitly; for example, if you are simply giving instance
3624 declarations.)</para>
3629 <sect2> <title> Changes wrt the paper </title>
3631 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
3632 can be written infix (indeed, you can now use
3633 any operator starting in a colon as an infix type constructor). Also note that
3634 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
3635 Finally, note that the syntax of the type patterns in the class declaration
3636 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
3637 alone would ambiguous when they appear on right hand sides (an extension we
3638 anticipate wanting).
3642 <sect2> <title>Terminology and restrictions</title>
3644 Terminology. A "generic default method" in a class declaration
3645 is one that is defined using type patterns as above.
3646 A "polymorphic default method" is a default method defined as in Haskell 98.
3647 A "generic class declaration" is a class declaration with at least one
3648 generic default method.
3656 Alas, we do not yet implement the stuff about constructor names and
3663 A generic class can have only one parameter; you can't have a generic
3664 multi-parameter class.
3670 A default method must be defined entirely using type patterns, or entirely
3671 without. So this is illegal:
3674 op :: a -> (a, Bool)
3675 op {| Unit |} Unit = (Unit, True)
3678 However it is perfectly OK for some methods of a generic class to have
3679 generic default methods and others to have polymorphic default methods.
3685 The type variable(s) in the type pattern for a generic method declaration
3686 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:
3690 op {| p :*: q |} (x :*: y) = op (x :: p)
3698 The type patterns in a generic default method must take one of the forms:
3704 where "a" and "b" are type variables. Furthermore, all the type patterns for
3705 a single type constructor (<literal>:*:</literal>, say) must be identical; they
3706 must use the same type variables. So this is illegal:
3710 op {| a :+: b |} (Inl x) = True
3711 op {| p :+: q |} (Inr y) = False
3713 The type patterns must be identical, even in equations for different methods of the class.
3714 So this too is illegal:
3718 op1 {| a :*: b |} (x :*: y) = True
3721 op2 {| p :*: q |} (x :*: y) = False
3723 (The reason for this restriction is that we gather all the equations for a particular type consructor
3724 into a single generic instance declaration.)
3730 A generic method declaration must give a case for each of the three type constructors.
3736 The type for a generic method can be built only from:
3738 <listitem> <para> Function arrows </para> </listitem>
3739 <listitem> <para> Type variables </para> </listitem>
3740 <listitem> <para> Tuples </para> </listitem>
3741 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
3743 Here are some example type signatures for generic methods:
3746 op2 :: Bool -> (a,Bool)
3747 op3 :: [Int] -> a -> a
3750 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
3754 This restriction is an implementation restriction: we just havn't got around to
3755 implementing the necessary bidirectional maps over arbitrary type constructors.
3756 It would be relatively easy to add specific type constructors, such as Maybe and list,
3757 to the ones that are allowed.</para>
3762 In an instance declaration for a generic class, the idea is that the compiler
3763 will fill in the methods for you, based on the generic templates. However it can only
3768 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
3773 No constructor of the instance type has unboxed fields.
3777 (Of course, these things can only arise if you are already using GHC extensions.)
3778 However, you can still give an instance declarations for types which break these rules,
3779 provided you give explicit code to override any generic default methods.
3787 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
3788 what the compiler does with generic declarations.
3793 <sect2> <title> Another example </title>
3795 Just to finish with, here's another example I rather like:
3799 nCons {| Unit |} _ = 1
3800 nCons {| a :*: b |} _ = 1
3801 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
3804 tag {| Unit |} _ = 1
3805 tag {| a :*: b |} _ = 1
3806 tag {| a :+: b |} (Inl x) = tag x
3807 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
3813 <sect1 id="newtype-deriving">
3814 <title>Generalised derived instances for newtypes</title>
3817 When you define an abstract type using <literal>newtype</literal>, you may want
3818 the new type to inherit some instances from its representation. In
3819 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3820 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3821 other classes you have to write an explicit instance declaration. For
3822 example, if you define
3825 newtype Dollars = Dollars Int
3828 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3829 explicitly define an instance of <literal>Num</literal>:
3832 instance Num Dollars where
3833 Dollars a + Dollars b = Dollars (a+b)
3836 All the instance does is apply and remove the <literal>newtype</literal>
3837 constructor. It is particularly galling that, since the constructor
3838 doesn't appear at run-time, this instance declaration defines a
3839 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3840 dictionary, only slower!
3843 <sect2> <title> Generalising the deriving clause </title>
3845 GHC now permits such instances to be derived instead, so one can write
3847 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3850 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3851 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3852 derives an instance declaration of the form
3855 instance Num Int => Num Dollars
3858 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3862 We can also derive instances of constructor classes in a similar
3863 way. For example, suppose we have implemented state and failure monad
3864 transformers, such that
3867 instance Monad m => Monad (State s m)
3868 instance Monad m => Monad (Failure m)
3870 In Haskell 98, we can define a parsing monad by
3872 type Parser tok m a = State [tok] (Failure m) a
3875 which is automatically a monad thanks to the instance declarations
3876 above. With the extension, we can make the parser type abstract,
3877 without needing to write an instance of class <literal>Monad</literal>, via
3880 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3883 In this case the derived instance declaration is of the form
3885 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3888 Notice that, since <literal>Monad</literal> is a constructor class, the
3889 instance is a <emphasis>partial application</emphasis> of the new type, not the
3890 entire left hand side. We can imagine that the type declaration is
3891 ``eta-converted'' to generate the context of the instance
3896 We can even derive instances of multi-parameter classes, provided the
3897 newtype is the last class parameter. In this case, a ``partial
3898 application'' of the class appears in the <literal>deriving</literal>
3899 clause. For example, given the class
3902 class StateMonad s m | m -> s where ...
3903 instance Monad m => StateMonad s (State s m) where ...
3905 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3907 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3908 deriving (Monad, StateMonad [tok])
3911 The derived instance is obtained by completing the application of the
3912 class to the new type:
3915 instance StateMonad [tok] (State [tok] (Failure m)) =>
3916 StateMonad [tok] (Parser tok m)
3921 As a result of this extension, all derived instances in newtype
3922 declarations are treated uniformly (and implemented just by reusing
3923 the dictionary for the representation type), <emphasis>except</emphasis>
3924 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3925 the newtype and its representation.
3929 <sect2> <title> A more precise specification </title>
3931 Derived instance declarations are constructed as follows. Consider the
3932 declaration (after expansion of any type synonyms)
3935 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3938 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3940 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3941 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3942 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3943 declarations are, for each <literal>ci</literal>,
3946 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3948 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3949 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3953 As an example which does <emphasis>not</emphasis> work, consider
3955 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3957 Here we cannot derive the instance
3959 instance Monad (State s m) => Monad (NonMonad m)
3962 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3963 and so cannot be "eta-converted" away. It is a good thing that this
3964 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3965 not, in fact, a monad --- for the same reason. Try defining
3966 <literal>>>=</literal> with the correct type: you won't be able to.
3970 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3971 important, since we can only derive instances for the last one. If the
3972 <literal>StateMonad</literal> class above were instead defined as
3975 class StateMonad m s | m -> s where ...
3978 then we would not have been able to derive an instance for the
3979 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3980 classes usually have one "main" parameter for which deriving new
3981 instances is most interesting.
3989 ;;; Local Variables: ***
3991 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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