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 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-fgenerics</option></term>
114 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
116 <para>See <xref LinkEnd="generic-classes">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fno-implicit-prelude</option></term>
124 <para><indexterm><primary>-fno-implicit-prelude
125 option</primary></indexterm> GHC normally imports
126 <filename>Prelude.hi</filename> files for you. If you'd
127 rather it didn't, then give it a
128 <option>-fno-implicit-prelude</option> option. The idea
129 is that you can then import a Prelude of your own. (But
130 don't call it <literal>Prelude</literal>; the Haskell
131 module namespace is flat, and you must not conflict with
132 any Prelude module.)</para>
134 <para>Even though you have not imported the Prelude, most of
135 the built-in syntax still refers to the built-in Haskell
136 Prelude types and values, as specified by the Haskell
137 Report. For example, the type <literal>[Int]</literal>
138 still means <literal>Prelude.[] Int</literal>; tuples
139 continue to refer to the standard Prelude tuples; the
140 translation for list comprehensions continues to use
141 <literal>Prelude.map</literal> etc.</para>
143 <para>However, <option>-fno-implicit-prelude</option> does
144 change the handling of certain built-in syntax: see
145 <xref LinkEnd="rebindable-syntax">.</para>
153 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
154 <!-- included from primitives.sgml -->
157 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
159 <sect1 id="syntax-extns">
160 <title>Syntactic extensions</title>
162 <!-- ====================== HIERARCHICAL MODULES ======================= -->
164 <sect2 id="hierarchical-modules">
165 <title>Hierarchical Modules</title>
167 <para>GHC supports a small extension to the syntax of module
168 names: a module name is allowed to contain a dot
169 <literal>‘.’</literal>. This is also known as the
170 “hierarchical module namespace” extension, because
171 it extends the normally flat Haskell module namespace into a
172 more flexible hierarchy of modules.</para>
174 <para>This extension has very little impact on the language
175 itself; modules names are <emphasis>always</emphasis> fully
176 qualified, so you can just think of the fully qualified module
177 name as <quote>the module name</quote>. In particular, this
178 means that the full module name must be given after the
179 <literal>module</literal> keyword at the beginning of the
180 module; for example, the module <literal>A.B.C</literal> must
183 <programlisting>module A.B.C</programlisting>
186 <para>It is a common strategy to use the <literal>as</literal>
187 keyword to save some typing when using qualified names with
188 hierarchical modules. For example:</para>
191 import qualified Control.Monad.ST.Strict as ST
194 <para>Hierarchical modules have an impact on the way that GHC
195 searches for files. For a description, see <xref
196 linkend="finding-hierarchical-modules">.</para>
198 <para>GHC comes with a large collection of libraries arranged
199 hierarchically; see the accompanying library documentation.
200 There is an ongoing project to create and maintain a stable set
201 of <quote>core</quote> libraries used by several Haskell
202 compilers, and the libraries that GHC comes with represent the
203 current status of that project. For more details, see <ulink
204 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
205 Libraries</ulink>.</para>
209 <!-- ====================== PATTERN GUARDS ======================= -->
211 <sect2 id="pattern-guards">
212 <title>Pattern guards</title>
215 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
216 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.)
220 Suppose we have an abstract data type of finite maps, with a
224 lookup :: FiniteMap -> Int -> Maybe Int
227 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
228 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
232 clunky env var1 var2 | ok1 && ok2 = val1 + val2
233 | otherwise = var1 + var2
244 The auxiliary functions are
248 maybeToBool :: Maybe a -> Bool
249 maybeToBool (Just x) = True
250 maybeToBool Nothing = False
252 expectJust :: Maybe a -> a
253 expectJust (Just x) = x
254 expectJust Nothing = error "Unexpected Nothing"
258 What is <function>clunky</function> doing? The guard <literal>ok1 &&
259 ok2</literal> checks that both lookups succeed, using
260 <function>maybeToBool</function> to convert the <function>Maybe</function>
261 types to booleans. The (lazily evaluated) <function>expectJust</function>
262 calls extract the values from the results of the lookups, and binds the
263 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
264 respectively. If either lookup fails, then clunky takes the
265 <literal>otherwise</literal> case and returns the sum of its arguments.
269 This is certainly legal Haskell, but it is a tremendously verbose and
270 un-obvious way to achieve the desired effect. Arguably, a more direct way
271 to write clunky would be to use case expressions:
275 clunky env var1 var1 = case lookup env var1 of
277 Just val1 -> case lookup env var2 of
279 Just val2 -> val1 + val2
285 This is a bit shorter, but hardly better. Of course, we can rewrite any set
286 of pattern-matching, guarded equations as case expressions; that is
287 precisely what the compiler does when compiling equations! The reason that
288 Haskell provides guarded equations is because they allow us to write down
289 the cases we want to consider, one at a time, independently of each other.
290 This structure is hidden in the case version. Two of the right-hand sides
291 are really the same (<function>fail</function>), and the whole expression
292 tends to become more and more indented.
296 Here is how I would write clunky:
301 | Just val1 <- lookup env var1
302 , Just val2 <- lookup env var2
304 ...other equations for clunky...
308 The semantics should be clear enough. The qualifers are matched in order.
309 For a <literal><-</literal> qualifier, which I call a pattern guard, the
310 right hand side is evaluated and matched against the pattern on the left.
311 If the match fails then the whole guard fails and the next equation is
312 tried. If it succeeds, then the appropriate binding takes place, and the
313 next qualifier is matched, in the augmented environment. Unlike list
314 comprehensions, however, the type of the expression to the right of the
315 <literal><-</literal> is the same as the type of the pattern to its
316 left. The bindings introduced by pattern guards scope over all the
317 remaining guard qualifiers, and over the right hand side of the equation.
321 Just as with list comprehensions, boolean expressions can be freely mixed
322 with among the pattern guards. For example:
333 Haskell's current guards therefore emerge as a special case, in which the
334 qualifier list has just one element, a boolean expression.
338 <!-- ===================== Recursive do-notation =================== -->
340 <sect2 id="mdo-notation">
341 <title>The recursive do-notation
344 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
345 "A recursive do for Haskell",
346 Levent Erkok, John Launchbury",
347 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
350 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
351 that is, the variables bound in a do-expression are visible only in the textually following
352 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
353 group. It turns out that several applications can benefit from recursive bindings in
354 the do-notation, and this extension provides the necessary syntactic support.
357 Here is a simple (yet contrived) example:
360 justOnes = mdo xs <- Just (1:xs)
364 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
368 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
371 class Monad m => MonadFix m where
372 mfix :: (a -> m a) -> m a
375 The function <literal>mfix</literal>
376 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
377 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
378 For details, see the above mentioned reference.
381 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO, and
382 state monads (both lazy and strict).
385 There are three important points in using the recursive-do notation:
388 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
389 than <literal>do</literal>).
393 If you want to declare an instance of the <literal>MonadFix</literal> class for one of
394 your own monads, or you need to refer to the class name <literal>MonadFix</literal> in any other way (for
395 instance when writing a type constraint), then your program should
396 <literal>import Control.Monad.MonadFix</literal>.
397 Otherwise, you don't need to import any special libraries to use the mdo-notation. That is,
398 as long as you only use the predefined instances mentioned above, the mdo-notation will
399 be automatically available.
400 To be on the safe side, of course, you can simply import it in all cases.
404 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
410 Historical note: The old implementation of the mdo-notation (and most
411 of the existing documents) used the name
412 <literal>MonadRec</literal> for the class and the corresponding library.
413 This name is no longer supported.
417 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
418 contains up to date information on recursive monadic bindings.
423 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
425 <sect2 id="parallel-list-comprehensions">
426 <title>Parallel List Comprehensions</title>
427 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
429 <indexterm><primary>parallel list comprehensions</primary>
432 <para>Parallel list comprehensions are a natural extension to list
433 comprehensions. List comprehensions can be thought of as a nice
434 syntax for writing maps and filters. Parallel comprehensions
435 extend this to include the zipWith family.</para>
437 <para>A parallel list comprehension has multiple independent
438 branches of qualifier lists, each separated by a `|' symbol. For
439 example, the following zips together two lists:</para>
442 [ (x, y) | x <- xs | y <- ys ]
445 <para>The behavior of parallel list comprehensions follows that of
446 zip, in that the resulting list will have the same length as the
447 shortest branch.</para>
449 <para>We can define parallel list comprehensions by translation to
450 regular comprehensions. Here's the basic idea:</para>
452 <para>Given a parallel comprehension of the form: </para>
455 [ e | p1 <- e11, p2 <- e12, ...
456 | q1 <- e21, q2 <- e22, ...
461 <para>This will be translated to: </para>
464 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
465 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
470 <para>where `zipN' is the appropriate zip for the given number of
475 <sect2 id="rebindable-syntax">
476 <title>Rebindable syntax</title>
479 <para>GHC allows most kinds of built-in syntax to be rebound by
480 the user, to facilitate replacing the <literal>Prelude</literal>
481 with a home-grown version, for example.</para>
483 <para>You may want to define your own numeric class
484 hierarchy. It completely defeats that purpose if the
485 literal "1" means "<literal>Prelude.fromInteger
486 1</literal>", which is what the Haskell Report specifies.
487 So the <option>-fno-implicit-prelude</option> flag causes
488 the following pieces of built-in syntax to refer to
489 <emphasis>whatever is in scope</emphasis>, not the Prelude
494 <para>Integer and fractional literals mean
495 "<literal>fromInteger 1</literal>" and
496 "<literal>fromRational 3.2</literal>", not the
497 Prelude-qualified versions; both in expressions and in
499 <para>However, the standard Prelude <literal>Eq</literal> class
500 is still used for the equality test necessary for literal patterns.</para>
504 <para>Negation (e.g. "<literal>- (f x)</literal>")
505 means "<literal>negate (f x)</literal>" (not
506 <literal>Prelude.negate</literal>).</para>
510 <para>In an n+k pattern, the standard Prelude
511 <literal>Ord</literal> class is still used for comparison,
512 but the necessary subtraction uses whatever
513 "<literal>(-)</literal>" is in scope (not
514 "<literal>Prelude.(-)</literal>").</para>
518 <para>"Do" notation is translated using whatever
519 functions <literal>(>>=)</literal>,
520 <literal>(>>)</literal>, <literal>fail</literal>, and
521 <literal>return</literal>, are in scope (not the Prelude
522 versions). List comprehensions, and parallel array
523 comprehensions, are unaffected. </para></listitem>
526 <para>Be warned: this is an experimental facility, with fewer checks than
527 usual. In particular, it is essential that the functions GHC finds in scope
528 must have the appropriate types, namely:
530 fromInteger :: forall a. (...) => Integer -> a
531 fromRational :: forall a. (...) => Rational -> a
532 negate :: forall a. (...) => a -> a
533 (-) :: forall a. (...) => a -> a -> a
534 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
535 (>>) :: forall m a. (...) => m a -> m b -> m b
536 return :: forall m a. (...) => a -> m a
537 fail :: forall m a. (...) => String -> m a
539 (The (...) part can be any context including the empty context; that part
541 If the functions don't have the right type, very peculiar things may
542 happen. Use <literal>-dcore-lint</literal> to
543 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
549 <!-- TYPE SYSTEM EXTENSIONS -->
550 <sect1 id="type-extensions">
551 <title>Type system extensions</title>
553 <sect2 id="nullary-types">
554 <title>Data types with no constructors</title>
556 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
557 a data type with no constructors. For example:</para>
561 data T a -- T :: * -> *
564 <para>Syntactically, the declaration lacks the "= constrs" part. The
565 type can be parameterised over types of any kind, but if the kind is
566 not <literal>*</literal> then an explicit kind annotation must be used
567 (see <xref linkend="sec-kinding">).</para>
569 <para>Such data types have only one value, namely bottom.
570 Nevertheless, they can be useful when defining "phantom types".</para>
573 <sect2 id="infix-tycons">
574 <title>Infix type constructors</title>
577 GHC allows type constructors to be operators, and to be written infix, very much
578 like expressions. More specifically:
581 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
582 The lexical syntax is the same as that for data constructors.
585 Types can be written infix. For example <literal>Int :*: Bool</literal>.
589 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
590 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
593 Fixities may be declared for type constructors just as for data constructors. However,
594 one cannot distinguish between the two in a fixity declaration; a fixity declaration
595 sets the fixity for a data constructor and the corresponding type constructor. For example:
599 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
600 and similarly for <literal>:*:</literal>.
601 <literal>Int `a` Bool</literal>.
604 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
607 Data type and type-synonym declarations can be written infix. E.g.
609 data a :*: b = Foo a b
610 type a :+: b = Either a b
614 The only thing that differs between operators in types and operators in expressions is that
615 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
616 are not allowed in types. Reason: the uniform thing to do would be to make them type
617 variables, but that's not very useful. A less uniform but more useful thing would be to
618 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
619 lists. So for now we just exclude them.
626 <sect2 id="sec-kinding">
627 <title>Explicitly-kinded quantification</title>
630 Haskell infers the kind of each type variable. Sometimes it is nice to be able
631 to give the kind explicitly as (machine-checked) documentation,
632 just as it is nice to give a type signature for a function. On some occasions,
633 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
634 John Hughes had to define the data type:
636 data Set cxt a = Set [a]
637 | Unused (cxt a -> ())
639 The only use for the <literal>Unused</literal> constructor was to force the correct
640 kind for the type variable <literal>cxt</literal>.
643 GHC now instead allows you to specify the kind of a type variable directly, wherever
644 a type variable is explicitly bound. Namely:
646 <listitem><para><literal>data</literal> declarations:
648 data Set (cxt :: * -> *) a = Set [a]
649 </Screen></para></listitem>
650 <listitem><para><literal>type</literal> declarations:
652 type T (f :: * -> *) = f Int
653 </Screen></para></listitem>
654 <listitem><para><literal>class</literal> declarations:
656 class (Eq a) => C (f :: * -> *) a where ...
657 </Screen></para></listitem>
658 <listitem><para><literal>forall</literal>'s in type signatures:
660 f :: forall (cxt :: * -> *). Set cxt Int
661 </Screen></para></listitem>
666 The parentheses are required. Some of the spaces are required too, to
667 separate the lexemes. If you write <literal>(f::*->*)</literal> you
668 will get a parse error, because "<literal>::*->*</literal>" is a
669 single lexeme in Haskell.
673 As part of the same extension, you can put kind annotations in types
676 f :: (Int :: *) -> Int
677 g :: forall a. a -> (a :: *)
681 atype ::= '(' ctype '::' kind ')
683 The parentheses are required.
688 <sect2 id="class-method-types">
689 <title>Class method types
692 Haskell 98 prohibits class method types to mention constraints on the
693 class type variable, thus:
696 fromList :: [a] -> s a
697 elem :: Eq a => a -> s a -> Bool
699 The type of <literal>elem</literal> is illegal in Haskell 98, because it
700 contains the constraint <literal>Eq a</literal>, constrains only the
701 class type variable (in this case <literal>a</literal>).
704 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
709 <sect2 id="multi-param-type-classes">
710 <title>Multi-parameter type classes
714 This section documents GHC's implementation of multi-parameter type
715 classes. There's lots of background in the paper <ULink
716 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
717 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
722 I'd like to thank people who reported shorcomings in the GHC 3.02
723 implementation. Our default decisions were all conservative ones, and
724 the experience of these heroic pioneers has given useful concrete
725 examples to support several generalisations. (These appear below as
726 design choices not implemented in 3.02.)
730 I've discussed these notes with Mark Jones, and I believe that Hugs
731 will migrate towards the same design choices as I outline here.
732 Thanks to him, and to many others who have offered very useful
740 There are the following restrictions on the form of a qualified
747 forall tv1..tvn (c1, ...,cn) => type
753 (Here, I write the "foralls" explicitly, although the Haskell source
754 language omits them; in Haskell 1.4, all the free type variables of an
755 explicit source-language type signature are universally quantified,
756 except for the class type variables in a class declaration. However,
757 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
766 <emphasis>Each universally quantified type variable
767 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
769 The reason for this is that a value with a type that does not obey
770 this restriction could not be used without introducing
771 ambiguity. Here, for example, is an illegal type:
775 forall a. Eq a => Int
779 When a value with this type was used, the constraint <literal>Eq tv</literal>
780 would be introduced where <literal>tv</literal> is a fresh type variable, and
781 (in the dictionary-translation implementation) the value would be
782 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
783 can never know which instance of <literal>Eq</literal> to use because we never
784 get any more information about <literal>tv</literal>.
791 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
792 universally quantified type variables <literal>tvi</literal></emphasis>.
794 For example, this type is OK because <literal>C a b</literal> mentions the
795 universally quantified type variable <literal>b</literal>:
799 forall a. C a b => burble
803 The next type is illegal because the constraint <literal>Eq b</literal> does not
804 mention <literal>a</literal>:
808 forall a. Eq b => burble
812 The reason for this restriction is milder than the other one. The
813 excluded types are never useful or necessary (because the offending
814 context doesn't need to be witnessed at this point; it can be floated
815 out). Furthermore, floating them out increases sharing. Lastly,
816 excluding them is a conservative choice; it leaves a patch of
817 territory free in case we need it later.
827 These restrictions apply to all types, whether declared in a type signature
832 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
833 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
840 f :: Eq (m a) => [m a] -> [m a]
847 This choice recovers principal types, a property that Haskell 1.4 does not have.
853 <title>Class declarations</title>
861 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
865 class Collection c a where
866 union :: c a -> c a -> c a
877 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
878 of "acyclic" involves only the superclass relationships. For example,
884 op :: D b => a -> b -> b
887 class C a => D a where { ... }
891 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
892 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
893 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
900 <emphasis>There are no restrictions on the context in a class declaration
901 (which introduces superclasses), except that the class hierarchy must
902 be acyclic</emphasis>. So these class declarations are OK:
906 class Functor (m k) => FiniteMap m k where
909 class (Monad m, Monad (t m)) => Transform t m where
910 lift :: m a -> (t m) a
919 <emphasis>In the signature of a class operation, every constraint
920 must mention at least one type variable that is not a class type
927 class Collection c a where
928 mapC :: Collection c b => (a->b) -> c a -> c b
932 is OK because the constraint <literal>(Collection a b)</literal> mentions
933 <literal>b</literal>, even though it also mentions the class variable
934 <literal>a</literal>. On the other hand:
939 op :: Eq a => (a,b) -> (a,b)
943 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
944 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
945 example is easily fixed by moving the offending context up to the
950 class Eq a => C a where
955 A yet more relaxed rule would allow the context of a class-op signature
956 to mention only class type variables. However, that conflicts with
957 Rule 1(b) for types above.
964 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
965 the class type variables</emphasis>. For example:
971 insert :: s -> a -> s
975 is not OK, because the type of <literal>empty</literal> doesn't mention
976 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
977 types, and has the same motivation.
979 Sometimes, offending class declarations exhibit misunderstandings. For
980 example, <literal>Coll</literal> might be rewritten
986 insert :: s a -> a -> s a
990 which makes the connection between the type of a collection of
991 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
992 Occasionally this really doesn't work, in which case you can split the
1000 class CollE s => Coll s a where
1001 insert :: s -> a -> s
1014 <sect3 id="instance-decls">
1015 <title>Instance declarations</title>
1023 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1028 instance context1 => C type1 where ...
1029 instance context2 => C type2 where ...
1033 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1035 However, if you give the command line option
1036 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1037 option</primary></indexterm> then overlapping instance declarations are permitted.
1038 However, GHC arranges never to commit to using an instance declaration
1039 if another instance declaration also applies, either now or later.
1045 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1051 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1052 (but not identical to <literal>type1</literal>), or vice versa.
1056 Notice that these rules
1061 make it clear which instance decl to use
1062 (pick the most specific one that matches)
1069 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1070 Reason: you can pick which instance decl
1071 "matches" based on the type.
1076 However the rules are over-conservative. Two instance declarations can overlap,
1077 but it can still be clear in particular situations which to use. For example:
1079 instance C (Int,a) where ...
1080 instance C (a,Bool) where ...
1082 These are rejected by GHC's rules, but it is clear what to do when trying
1083 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1084 cannot apply. Yell if this restriction bites you.
1087 GHC is also conservative about committing to an overlapping instance. For example:
1089 class C a where { op :: a -> a }
1090 instance C [Int] where ...
1091 instance C a => C [a] where ...
1093 f :: C b => [b] -> [b]
1096 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1097 GHC does not commit to the second instance declaration, because in a paricular
1098 call of f, b might be instantiate to Int, so the first instance declaration
1099 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1100 GHC will instead silently pick the second instance, without complaining about
1101 the problem of subsequent instantiations.
1104 Regrettably, GHC doesn't guarantee to detect overlapping instance
1105 declarations if they appear in different modules. GHC can "see" the
1106 instance declarations in the transitive closure of all the modules
1107 imported by the one being compiled, so it can "see" all instance decls
1108 when it is compiling <literal>Main</literal>. However, it currently chooses not
1109 to look at ones that can't possibly be of use in the module currently
1110 being compiled, in the interests of efficiency. (Perhaps we should
1111 change that decision, at least for <literal>Main</literal>.)
1118 <emphasis>There are no restrictions on the type in an instance
1119 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1120 The instance "head" is the bit after the "=>" in an instance decl. For
1121 example, these are OK:
1125 instance C Int a where ...
1127 instance D (Int, Int) where ...
1129 instance E [[a]] where ...
1133 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1134 For example, this is OK:
1138 instance Stateful (ST s) (MutVar s) where ...
1142 The "at least one not a type variable" restriction is to ensure that
1143 context reduction terminates: each reduction step removes one type
1144 constructor. For example, the following would make the type checker
1145 loop if it wasn't excluded:
1149 instance C a => C a where ...
1153 There are two situations in which the rule is a bit of a pain. First,
1154 if one allows overlapping instance declarations then it's quite
1155 convenient to have a "default instance" declaration that applies if
1156 something more specific does not:
1165 Second, sometimes you might want to use the following to get the
1166 effect of a "class synonym":
1170 class (C1 a, C2 a, C3 a) => C a where { }
1172 instance (C1 a, C2 a, C3 a) => C a where { }
1176 This allows you to write shorter signatures:
1188 f :: (C1 a, C2 a, C3 a) => ...
1192 I'm on the lookout for a simple rule that preserves decidability while
1193 allowing these idioms. The experimental flag
1194 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1195 option</primary></indexterm> lifts this restriction, allowing all the types in an
1196 instance head to be type variables.
1203 <emphasis>Unlike Haskell 1.4, instance heads may use type
1204 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1205 writing the RHS of the type synonym definition. For example:
1209 type Point = (Int,Int)
1210 instance C Point where ...
1211 instance C [Point] where ...
1215 is legal. However, if you added
1219 instance C (Int,Int) where ...
1223 as well, then the compiler will complain about the overlapping
1224 (actually, identical) instance declarations. As always, type synonyms
1225 must be fully applied. You cannot, for example, write:
1230 instance Monad P where ...
1234 This design decision is independent of all the others, and easily
1235 reversed, but it makes sense to me.
1242 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1243 be type variables</emphasis>. Thus
1247 instance C a b => Eq (a,b) where ...
1255 instance C Int b => Foo b where ...
1259 is not OK. Again, the intent here is to make sure that context
1260 reduction terminates.
1262 Voluminous correspondence on the Haskell mailing list has convinced me
1263 that it's worth experimenting with a more liberal rule. If you use
1264 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1265 types in an instance context. Termination is ensured by having a
1266 fixed-depth recursion stack. If you exceed the stack depth you get a
1267 sort of backtrace, and the opportunity to increase the stack depth
1268 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1281 <sect2 id="implicit-parameters">
1282 <title>Implicit parameters
1285 <para> Implicit paramters are implemented as described in
1286 "Implicit parameters: dynamic scoping with static types",
1287 J Lewis, MB Shields, E Meijer, J Launchbury,
1288 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1291 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1293 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1294 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1295 context. In Haskell, all variables are statically bound. Dynamic
1296 binding of variables is a notion that goes back to Lisp, but was later
1297 discarded in more modern incarnations, such as Scheme. Dynamic binding
1298 can be very confusing in an untyped language, and unfortunately, typed
1299 languages, in particular Hindley-Milner typed languages like Haskell,
1300 only support static scoping of variables.
1303 However, by a simple extension to the type class system of Haskell, we
1304 can support dynamic binding. Basically, we express the use of a
1305 dynamically bound variable as a constraint on the type. These
1306 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1307 function uses a dynamically-bound variable <literal>?x</literal>
1308 of type <literal>t'</literal>". For
1309 example, the following expresses the type of a sort function,
1310 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1312 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1314 The dynamic binding constraints are just a new form of predicate in the type class system.
1317 An implicit parameter is introduced by the special form <literal>?x</literal>,
1318 where <literal>x</literal> is
1319 any valid identifier. Use if this construct also introduces new
1320 dynamic binding constraints. For example, the following definition
1321 shows how we can define an implicitly parameterized sort function in
1322 terms of an explicitly parameterized <literal>sortBy</literal> function:
1324 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1326 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1329 Dynamic binding constraints behave just like other type class
1330 constraints in that they are automatically propagated. Thus, when a
1331 function is used, its implicit parameters are inherited by the
1332 function that called it. For example, our <literal>sort</literal> function might be used
1333 to pick out the least value in a list:
1335 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1336 least xs = fst (sort xs)
1338 Without lifting a finger, the <literal>?cmp</literal> parameter is
1339 propagated to become a parameter of <literal>least</literal> as well. With explicit
1340 parameters, the default is that parameters must always be explicit
1341 propagated. With implicit parameters, the default is to always
1345 An implicit parameter differs from other type class constraints in the
1346 following way: All uses of a particular implicit parameter must have
1347 the same type. This means that the type of <literal>(?x, ?x)</literal>
1348 is <literal>(?x::a) => (a,a)</literal>, and not
1349 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1353 An implicit parameter is bound using the standard
1354 <literal>let</literal> binding form, where the bindings must be a
1355 collection of simple bindings to implicit-style variables (no
1356 function-style bindings, and no type signatures); these bindings are
1357 neither polymorphic or recursive. This form binds the implicit
1358 parameters arising in the body, not the free variables as a
1359 <literal>let</literal> or <literal>where</literal> would do. For
1360 example, we define the <literal>min</literal> function by binding
1361 <literal>cmp</literal>.</para>
1364 min = let ?cmp = (<=) in least
1367 Note the following points:
1370 You may not mix implicit-parameter bindings with ordinary bindings in a
1371 single <literal>let</literal>
1372 expression; use two nested <literal>let</literal>s instead.
1376 You may put multiple implicit-parameter bindings in a
1377 single <literal>let</literal> expression; they are <emphasis>not</emphasis> treated
1378 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1379 Instead they are treated as a non-recursive group, each scoping over the bindings that
1380 follow. For example, consider:
1382 f y = let { ?x = y; ?x = ?x+1 } in ?x
1384 This function adds one to its argument.
1388 You may not have an implicit-parameter binding in a <literal>where</literal> clause,
1389 only in a <literal>let</literal> binding.
1393 <para> You can't have an implicit parameter in the context of a class or instance
1394 declaration. For example, both these declarations are illegal:
1396 class (?x::Int) => C a where ...
1397 instance (?x::a) => Foo [a] where ...
1399 Reason: exactly which implicit parameter you pick up depends on exactly where
1400 you invoke a function. But the ``invocation'' of instance declarations is done
1401 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1402 Easiest thing is to outlaw the offending types.</para>
1409 <sect2 id="linear-implicit-parameters">
1410 <title>Linear implicit parameters
1413 Linear implicit parameters are an idea developed by Koen Claessen,
1414 Mark Shields, and Simon PJ. They address the long-standing
1415 problem that monads seem over-kill for certain sorts of problem, notably:
1418 <listitem> <para> distributing a supply of unique names </para> </listitem>
1419 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1420 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1424 Linear implicit parameters are just like ordinary implicit parameters,
1425 except that they are "linear" -- that is, they cannot be copied, and
1426 must be explicitly "split" instead. Linear implicit parameters are
1427 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1428 (The '/' in the '%' suggests the split!)
1433 import GHC.Exts( Splittable )
1435 data NameSupply = ...
1437 splitNS :: NameSupply -> (NameSupply, NameSupply)
1438 newName :: NameSupply -> Name
1440 instance Splittable NameSupply where
1444 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1445 f env (Lam x e) = Lam x' (f env e)
1448 env' = extend env x x'
1449 ...more equations for f...
1451 Notice that the implicit parameter %ns is consumed
1453 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1454 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1458 So the translation done by the type checker makes
1459 the parameter explicit:
1461 f :: NameSupply -> Env -> Expr -> Expr
1462 f ns env (Lam x e) = Lam x' (f ns1 env e)
1464 (ns1,ns2) = splitNS ns
1466 env = extend env x x'
1468 Notice the call to 'split' introduced by the type checker.
1469 How did it know to use 'splitNS'? Because what it really did
1470 was to introduce a call to the overloaded function 'split',
1471 defined by the class <literal>Splittable</literal>:
1473 class Splittable a where
1476 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1477 split for name supplies. But we can simply write
1483 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1485 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1486 <literal>GHC.Exts</literal>.
1491 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1492 are entirely distinct implicit parameters: you
1493 can use them together and they won't intefere with each other. </para>
1496 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1498 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1499 in the context of a class or instance declaration. </para></listitem>
1503 <sect3><title>Warnings</title>
1506 The monomorphism restriction is even more important than usual.
1507 Consider the example above:
1509 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1510 f env (Lam x e) = Lam x' (f env e)
1513 env' = extend env x x'
1515 If we replaced the two occurrences of x' by (newName %ns), which is
1516 usually a harmless thing to do, we get:
1518 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1519 f env (Lam x e) = Lam (newName %ns) (f env e)
1521 env' = extend env x (newName %ns)
1523 But now the name supply is consumed in <emphasis>three</emphasis> places
1524 (the two calls to newName,and the recursive call to f), so
1525 the result is utterly different. Urk! We don't even have
1529 Well, this is an experimental change. With implicit
1530 parameters we have already lost beta reduction anyway, and
1531 (as John Launchbury puts it) we can't sensibly reason about
1532 Haskell programs without knowing their typing.
1537 <sect3><title>Recursive functions</title>
1538 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1541 foo :: %x::T => Int -> [Int]
1543 foo n = %x : foo (n-1)
1545 where T is some type in class Splittable.</para>
1547 Do you get a list of all the same T's or all different T's
1548 (assuming that split gives two distinct T's back)?
1550 If you supply the type signature, taking advantage of polymorphic
1551 recursion, you get what you'd probably expect. Here's the
1552 translated term, where the implicit param is made explicit:
1555 foo x n = let (x1,x2) = split x
1556 in x1 : foo x2 (n-1)
1558 But if you don't supply a type signature, GHC uses the Hindley
1559 Milner trick of using a single monomorphic instance of the function
1560 for the recursive calls. That is what makes Hindley Milner type inference
1561 work. So the translation becomes
1565 foom n = x : foom (n-1)
1569 Result: 'x' is not split, and you get a list of identical T's. So the
1570 semantics of the program depends on whether or not foo has a type signature.
1573 You may say that this is a good reason to dislike linear implicit parameters
1574 and you'd be right. That is why they are an experimental feature.
1580 <sect2 id="functional-dependencies">
1581 <title>Functional dependencies
1584 <para> Functional dependencies are implemented as described by Mark Jones
1585 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1586 In Proceedings of the 9th European Symposium on Programming,
1587 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1592 There should be more documentation, but there isn't (yet). Yell if you need it.
1597 <sect2 id="universal-quantification">
1598 <title>Arbitrary-rank polymorphism
1602 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1603 allows us to say exactly what this means. For example:
1611 g :: forall b. (b -> b)
1613 The two are treated identically.
1617 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1618 explicit universal quantification in
1620 For example, all the following types are legal:
1622 f1 :: forall a b. a -> b -> a
1623 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1625 f2 :: (forall a. a->a) -> Int -> Int
1626 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1628 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1630 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1631 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1632 The <literal>forall</literal> makes explicit the universal quantification that
1633 is implicitly added by Haskell.
1636 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1637 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1638 shows, the polymorphic type on the left of the function arrow can be overloaded.
1641 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1642 they have rank-2 types on the left of a function arrow.
1645 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1646 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1647 that restriction has now been lifted.)
1648 In particular, a forall-type (also called a "type scheme"),
1649 including an operational type class context, is legal:
1651 <listitem> <para> On the left of a function arrow </para> </listitem>
1652 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1653 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1654 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1655 field type signatures.</para> </listitem>
1656 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1657 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1659 There is one place you cannot put a <literal>forall</literal>:
1660 you cannot instantiate a type variable with a forall-type. So you cannot
1661 make a forall-type the argument of a type constructor. So these types are illegal:
1663 x1 :: [forall a. a->a]
1664 x2 :: (forall a. a->a, Int)
1665 x3 :: Maybe (forall a. a->a)
1667 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1668 a type variable any more!
1677 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1678 the types of the constructor arguments. Here are several examples:
1684 data T a = T1 (forall b. b -> b -> b) a
1686 data MonadT m = MkMonad { return :: forall a. a -> m a,
1687 bind :: forall a b. m a -> (a -> m b) -> m b
1690 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1696 The constructors have rank-2 types:
1702 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1703 MkMonad :: forall m. (forall a. a -> m a)
1704 -> (forall a b. m a -> (a -> m b) -> m b)
1706 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1712 Notice that you don't need to use a <literal>forall</literal> if there's an
1713 explicit context. For example in the first argument of the
1714 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1715 prefixed to the argument type. The implicit <literal>forall</literal>
1716 quantifies all type variables that are not already in scope, and are
1717 mentioned in the type quantified over.
1721 As for type signatures, implicit quantification happens for non-overloaded
1722 types too. So if you write this:
1725 data T a = MkT (Either a b) (b -> b)
1728 it's just as if you had written this:
1731 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1734 That is, since the type variable <literal>b</literal> isn't in scope, it's
1735 implicitly universally quantified. (Arguably, it would be better
1736 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1737 where that is what is wanted. Feedback welcomed.)
1741 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1742 the constructor to suitable values, just as usual. For example,
1753 a3 = MkSwizzle reverse
1756 a4 = let r x = Just x
1763 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1764 mkTs f x y = [T1 f x, T1 f y]
1770 The type of the argument can, as usual, be more general than the type
1771 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1772 does not need the <literal>Ord</literal> constraint.)
1776 When you use pattern matching, the bound variables may now have
1777 polymorphic types. For example:
1783 f :: T a -> a -> (a, Char)
1784 f (T1 w k) x = (w k x, w 'c' 'd')
1786 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1787 g (MkSwizzle s) xs f = s (map f (s xs))
1789 h :: MonadT m -> [m a] -> m [a]
1790 h m [] = return m []
1791 h m (x:xs) = bind m x $ \y ->
1792 bind m (h m xs) $ \ys ->
1799 In the function <function>h</function> we use the record selectors <literal>return</literal>
1800 and <literal>bind</literal> to extract the polymorphic bind and return functions
1801 from the <literal>MonadT</literal> data structure, rather than using pattern
1807 <title>Type inference</title>
1810 In general, type inference for arbitrary-rank types is undecideable.
1811 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1812 to get a decidable algorithm by requiring some help from the programmer.
1813 We do not yet have a formal specification of "some help" but the rule is this:
1816 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1817 provides an explicit polymorphic type for x, or GHC's type inference will assume
1818 that x's type has no foralls in it</emphasis>.
1821 What does it mean to "provide" an explicit type for x? You can do that by
1822 giving a type signature for x directly, using a pattern type signature
1823 (<xref linkend="scoped-type-variables">), thus:
1825 \ f :: (forall a. a->a) -> (f True, f 'c')
1827 Alternatively, you can give a type signature to the enclosing
1828 context, which GHC can "push down" to find the type for the variable:
1830 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1832 Here the type signature on the expression can be pushed inwards
1833 to give a type signature for f. Similarly, and more commonly,
1834 one can give a type signature for the function itself:
1836 h :: (forall a. a->a) -> (Bool,Char)
1837 h f = (f True, f 'c')
1839 You don't need to give a type signature if the lambda bound variable
1840 is a constructor argument. Here is an example we saw earlier:
1842 f :: T a -> a -> (a, Char)
1843 f (T1 w k) x = (w k x, w 'c' 'd')
1845 Here we do not need to give a type signature to <literal>w</literal>, because
1846 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1853 <sect3 id="implicit-quant">
1854 <title>Implicit quantification</title>
1857 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1858 user-written types, if and only if there is no explicit <literal>forall</literal>,
1859 GHC finds all the type variables mentioned in the type that are not already
1860 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1864 f :: forall a. a -> a
1871 h :: forall b. a -> b -> b
1877 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1880 f :: (a -> a) -> Int
1882 f :: forall a. (a -> a) -> Int
1884 f :: (forall a. a -> a) -> Int
1887 g :: (Ord a => a -> a) -> Int
1888 -- MEANS the illegal type
1889 g :: forall a. (Ord a => a -> a) -> Int
1891 g :: (forall a. Ord a => a -> a) -> Int
1893 The latter produces an illegal type, which you might think is silly,
1894 but at least the rule is simple. If you want the latter type, you
1895 can write your for-alls explicitly. Indeed, doing so is strongly advised
1901 <sect2 id="type-synonyms">
1902 <title>Liberalised type synonyms
1906 Type synonmys are like macros at the type level, and
1907 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1908 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1910 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1911 in a type synonym, thus:
1913 type Discard a = forall b. Show b => a -> b -> (a, String)
1918 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1925 You can write an unboxed tuple in a type synonym:
1927 type Pr = (# Int, Int #)
1935 You can apply a type synonym to a forall type:
1937 type Foo a = a -> a -> Bool
1939 f :: Foo (forall b. b->b)
1941 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1943 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1948 You can apply a type synonym to a partially applied type synonym:
1950 type Generic i o = forall x. i x -> o x
1953 foo :: Generic Id []
1955 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1957 foo :: forall x. x -> [x]
1965 GHC currently does kind checking before expanding synonyms (though even that
1969 After expanding type synonyms, GHC does validity checking on types, looking for
1970 the following mal-formedness which isn't detected simply by kind checking:
1973 Type constructor applied to a type involving for-alls.
1976 Unboxed tuple on left of an arrow.
1979 Partially-applied type synonym.
1983 this will be rejected:
1985 type Pr = (# Int, Int #)
1990 because GHC does not allow unboxed tuples on the left of a function arrow.
1995 <title>For-all hoisting</title>
1997 It is often convenient to use generalised type synonyms at the right hand
1998 end of an arrow, thus:
2000 type Discard a = forall b. a -> b -> a
2002 g :: Int -> Discard Int
2005 Simply expanding the type synonym would give
2007 g :: Int -> (forall b. Int -> b -> Int)
2009 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2011 g :: forall b. Int -> Int -> b -> Int
2013 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2014 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2015 performs the transformation:</emphasis>
2017 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2019 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2021 (In fact, GHC tries to retain as much synonym information as possible for use in
2022 error messages, but that is a usability issue.) This rule applies, of course, whether
2023 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2024 valid way to write <literal>g</literal>'s type signature:
2026 g :: Int -> Int -> forall b. b -> Int
2030 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2033 type Foo a = (?x::Int) => Bool -> a
2038 g :: (?x::Int) => Bool -> Bool -> Int
2044 <sect2 id="existential-quantification">
2045 <title>Existentially quantified data constructors
2049 The idea of using existential quantification in data type declarations
2050 was suggested by Laufer (I believe, thought doubtless someone will
2051 correct me), and implemented in Hope+. It's been in Lennart
2052 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2053 proved very useful. Here's the idea. Consider the declaration:
2059 data Foo = forall a. MkFoo a (a -> Bool)
2066 The data type <literal>Foo</literal> has two constructors with types:
2072 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2079 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2080 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2081 For example, the following expression is fine:
2087 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2093 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2094 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2095 isUpper</function> packages a character with a compatible function. These
2096 two things are each of type <literal>Foo</literal> and can be put in a list.
2100 What can we do with a value of type <literal>Foo</literal>?. In particular,
2101 what happens when we pattern-match on <function>MkFoo</function>?
2107 f (MkFoo val fn) = ???
2113 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2114 are compatible, the only (useful) thing we can do with them is to
2115 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2122 f (MkFoo val fn) = fn val
2128 What this allows us to do is to package heterogenous values
2129 together with a bunch of functions that manipulate them, and then treat
2130 that collection of packages in a uniform manner. You can express
2131 quite a bit of object-oriented-like programming this way.
2134 <sect3 id="existential">
2135 <title>Why existential?
2139 What has this to do with <emphasis>existential</emphasis> quantification?
2140 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2146 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2152 But Haskell programmers can safely think of the ordinary
2153 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2154 adding a new existential quantification construct.
2160 <title>Type classes</title>
2163 An easy extension (implemented in <Command>hbc</Command>) is to allow
2164 arbitrary contexts before the constructor. For example:
2170 data Baz = forall a. Eq a => Baz1 a a
2171 | forall b. Show b => Baz2 b (b -> b)
2177 The two constructors have the types you'd expect:
2183 Baz1 :: forall a. Eq a => a -> a -> Baz
2184 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2190 But when pattern matching on <function>Baz1</function> the matched values can be compared
2191 for equality, and when pattern matching on <function>Baz2</function> the first matched
2192 value can be converted to a string (as well as applying the function to it).
2193 So this program is legal:
2200 f (Baz1 p q) | p == q = "Yes"
2202 f (Baz2 v fn) = show (fn v)
2208 Operationally, in a dictionary-passing implementation, the
2209 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2210 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2211 extract it on pattern matching.
2215 Notice the way that the syntax fits smoothly with that used for
2216 universal quantification earlier.
2222 <title>Restrictions</title>
2225 There are several restrictions on the ways in which existentially-quantified
2226 constructors can be use.
2235 When pattern matching, each pattern match introduces a new,
2236 distinct, type for each existential type variable. These types cannot
2237 be unified with any other type, nor can they escape from the scope of
2238 the pattern match. For example, these fragments are incorrect:
2246 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2247 is the result of <function>f1</function>. One way to see why this is wrong is to
2248 ask what type <function>f1</function> has:
2252 f1 :: Foo -> a -- Weird!
2256 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2261 f1 :: forall a. Foo -> a -- Wrong!
2265 The original program is just plain wrong. Here's another sort of error
2269 f2 (Baz1 a b) (Baz1 p q) = a==q
2273 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2274 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2275 from the two <function>Baz1</function> constructors.
2283 You can't pattern-match on an existentially quantified
2284 constructor in a <literal>let</literal> or <literal>where</literal> group of
2285 bindings. So this is illegal:
2289 f3 x = a==b where { Baz1 a b = x }
2292 Instead, use a <literal>case</literal> expression:
2295 f3 x = case x of Baz1 a b -> a==b
2298 In general, you can only pattern-match
2299 on an existentially-quantified constructor in a <literal>case</literal> expression or
2300 in the patterns of a function definition.
2302 The reason for this restriction is really an implementation one.
2303 Type-checking binding groups is already a nightmare without
2304 existentials complicating the picture. Also an existential pattern
2305 binding at the top level of a module doesn't make sense, because it's
2306 not clear how to prevent the existentially-quantified type "escaping".
2307 So for now, there's a simple-to-state restriction. We'll see how
2315 You can't use existential quantification for <literal>newtype</literal>
2316 declarations. So this is illegal:
2320 newtype T = forall a. Ord a => MkT a
2324 Reason: a value of type <literal>T</literal> must be represented as a pair
2325 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2326 That contradicts the idea that <literal>newtype</literal> should have no
2327 concrete representation. You can get just the same efficiency and effect
2328 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2329 overloading involved, then there is more of a case for allowing
2330 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2331 because the <literal>data</literal> version does carry an implementation cost,
2332 but single-field existentially quantified constructors aren't much
2333 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2334 stands, unless there are convincing reasons to change it.
2342 You can't use <literal>deriving</literal> to define instances of a
2343 data type with existentially quantified data constructors.
2345 Reason: in most cases it would not make sense. For example:#
2348 data T = forall a. MkT [a] deriving( Eq )
2351 To derive <literal>Eq</literal> in the standard way we would need to have equality
2352 between the single component of two <function>MkT</function> constructors:
2356 (MkT a) == (MkT b) = ???
2359 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2360 It's just about possible to imagine examples in which the derived instance
2361 would make sense, but it seems altogether simpler simply to prohibit such
2362 declarations. Define your own instances!
2374 <sect2 id="scoped-type-variables">
2375 <title>Scoped type variables
2379 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2380 variable</emphasis>. For example
2386 f (xs::[a]) = ys ++ ys
2395 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2396 This brings the type variable <literal>a</literal> into scope; it scopes over
2397 all the patterns and right hand sides for this equation for <function>f</function>.
2398 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2402 Pattern type signatures are completely orthogonal to ordinary, separate
2403 type signatures. The two can be used independently or together.
2404 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2405 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2406 implicitly universally quantified. (If there are no type variables in
2407 scope, all type variables mentioned in the signature are universally
2408 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2409 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2410 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2411 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2412 it becomes possible to do so.
2416 Scoped type variables are implemented in both GHC and Hugs. Where the
2417 implementations differ from the specification below, those differences
2422 So much for the basic idea. Here are the details.
2426 <title>What a pattern type signature means</title>
2428 A type variable brought into scope by a pattern type signature is simply
2429 the name for a type. The restriction they express is that all occurrences
2430 of the same name mean the same type. For example:
2432 f :: [Int] -> Int -> Int
2433 f (xs::[a]) (y::a) = (head xs + y) :: a
2435 The pattern type signatures on the left hand side of
2436 <literal>f</literal> express the fact that <literal>xs</literal>
2437 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2438 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2439 specifies that this expression must have the same type <literal>a</literal>.
2440 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2441 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2442 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2443 rules, which specified that a pattern-bound type variable should be universally quantified.)
2444 For example, all of these are legal:</para>
2447 t (x::a) (y::a) = x+y*2
2449 f (x::a) (y::b) = [x,y] -- a unifies with b
2451 g (x::a) = x + 1::Int -- a unifies with Int
2453 h x = let k (y::a) = [x,y] -- a is free in the
2454 in k x -- environment
2456 k (x::a) True = ... -- a unifies with Int
2457 k (x::Int) False = ...
2460 w (x::a) = x -- a unifies with [b]
2466 <title>Scope and implicit quantification</title>
2474 All the type variables mentioned in a pattern,
2475 that are not already in scope,
2476 are brought into scope by the pattern. We describe this set as
2477 the <emphasis>type variables bound by the pattern</emphasis>.
2480 f (x::a) = let g (y::(a,b)) = fst y
2484 The pattern <literal>(x::a)</literal> brings the type variable
2485 <literal>a</literal> into scope, as well as the term
2486 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2487 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2488 and brings into scope the type variable <literal>b</literal>.
2494 The type variable(s) bound by the pattern have the same scope
2495 as the term variable(s) bound by the pattern. For example:
2498 f (x::a) = <...rhs of f...>
2499 (p::b, q::b) = (1,2)
2500 in <...body of let...>
2502 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2503 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2504 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2505 just like <literal>p</literal> and <literal>q</literal> do.
2506 Indeed, the newly bound type variables also scope over any ordinary, separate
2507 type signatures in the <literal>let</literal> group.
2514 The type variables bound by the pattern may be
2515 mentioned in ordinary type signatures or pattern
2516 type signatures anywhere within their scope.
2523 In ordinary type signatures, any type variable mentioned in the
2524 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2532 Ordinary type signatures do not bring any new type variables
2533 into scope (except in the type signature itself!). So this is illegal:
2540 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2541 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2542 and that is an incorrect typing.
2549 The pattern type signature is a monotype:
2554 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2558 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2559 not to type schemes.
2563 There is no implicit universal quantification on pattern type signatures (in contrast to
2564 ordinary type signatures).
2574 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2575 scope over the methods defined in the <literal>where</literal> part. For example:
2589 (Not implemented in Hugs yet, Dec 98).
2600 <title>Result type signatures</title>
2608 The result type of a function can be given a signature,
2613 f (x::a) :: [a] = [x,x,x]
2617 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2618 result type. Sometimes this is the only way of naming the type variable
2623 f :: Int -> [a] -> [a]
2624 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2625 in \xs -> map g (reverse xs `zip` xs)
2637 Result type signatures are not yet implemented in Hugs.
2643 <title>Where a pattern type signature can occur</title>
2646 A pattern type signature can occur in any pattern. For example:
2651 A pattern type signature can be on an arbitrary sub-pattern, not
2656 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2665 Pattern type signatures, including the result part, can be used
2666 in lambda abstractions:
2669 (\ (x::a, y) :: a -> x)
2676 Pattern type signatures, including the result part, can be used
2677 in <literal>case</literal> expressions:
2681 case e of { (x::a, y) :: a -> x }
2689 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2690 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2691 token or a parenthesised type of some sort). To see why,
2692 consider how one would parse this:
2706 Pattern type signatures can bind existential type variables.
2711 data T = forall a. MkT [a]
2714 f (MkT [t::a]) = MkT t3
2727 Pattern type signatures
2728 can be used in pattern bindings:
2731 f x = let (y, z::a) = x in ...
2732 f1 x = let (y, z::Int) = x in ...
2733 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2734 f3 :: (b->b) = \x -> x
2737 In all such cases, the binding is not generalised over the pattern-bound
2738 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2739 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2740 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2741 In contrast, the binding
2746 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2747 in <literal>f4</literal>'s scope.
2757 <sect2 id="newtype-deriving">
2758 <title>Generalised derived instances for newtypes</title>
2761 When you define an abstract type using <literal>newtype</literal>, you may want
2762 the new type to inherit some instances from its representation. In
2763 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2764 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2765 other classes you have to write an explicit instance declaration. For
2766 example, if you define
2769 newtype Dollars = Dollars Int
2772 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2773 explicitly define an instance of <literal>Num</literal>:
2776 instance Num Dollars where
2777 Dollars a + Dollars b = Dollars (a+b)
2780 All the instance does is apply and remove the <literal>newtype</literal>
2781 constructor. It is particularly galling that, since the constructor
2782 doesn't appear at run-time, this instance declaration defines a
2783 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2784 dictionary, only slower!
2788 <sect3> <title> Generalising the deriving clause </title>
2790 GHC now permits such instances to be derived instead, so one can write
2792 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2795 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2796 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2797 derives an instance declaration of the form
2800 instance Num Int => Num Dollars
2803 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2807 We can also derive instances of constructor classes in a similar
2808 way. For example, suppose we have implemented state and failure monad
2809 transformers, such that
2812 instance Monad m => Monad (State s m)
2813 instance Monad m => Monad (Failure m)
2815 In Haskell 98, we can define a parsing monad by
2817 type Parser tok m a = State [tok] (Failure m) a
2820 which is automatically a monad thanks to the instance declarations
2821 above. With the extension, we can make the parser type abstract,
2822 without needing to write an instance of class <literal>Monad</literal>, via
2825 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2828 In this case the derived instance declaration is of the form
2830 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2833 Notice that, since <literal>Monad</literal> is a constructor class, the
2834 instance is a <emphasis>partial application</emphasis> of the new type, not the
2835 entire left hand side. We can imagine that the type declaration is
2836 ``eta-converted'' to generate the context of the instance
2841 We can even derive instances of multi-parameter classes, provided the
2842 newtype is the last class parameter. In this case, a ``partial
2843 application'' of the class appears in the <literal>deriving</literal>
2844 clause. For example, given the class
2847 class StateMonad s m | m -> s where ...
2848 instance Monad m => StateMonad s (State s m) where ...
2850 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2852 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2853 deriving (Monad, StateMonad [tok])
2856 The derived instance is obtained by completing the application of the
2857 class to the new type:
2860 instance StateMonad [tok] (State [tok] (Failure m)) =>
2861 StateMonad [tok] (Parser tok m)
2866 As a result of this extension, all derived instances in newtype
2867 declarations are treated uniformly (and implemented just by reusing
2868 the dictionary for the representation type), <emphasis>except</emphasis>
2869 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2870 the newtype and its representation.
2874 <sect3> <title> A more precise specification </title>
2876 Derived instance declarations are constructed as follows. Consider the
2877 declaration (after expansion of any type synonyms)
2880 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
2883 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
2885 <literal>vk+1...vn</literal> are type variables which do not occur in any of
2886 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
2887 classes of the form <literal>C t1'...tj'</literal>. The derived instance
2888 declarations are, for each <literal>ci</literal>,
2891 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
2893 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
2894 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
2898 As an example which does <emphasis>not</emphasis> work, consider
2900 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2902 Here we cannot derive the instance
2904 instance Monad (State s m) => Monad (NonMonad m)
2907 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2908 and so cannot be "eta-converted" away. It is a good thing that this
2909 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2910 not, in fact, a monad --- for the same reason. Try defining
2911 <literal>>>=</literal> with the correct type: you won't be able to.
2915 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2916 important, since we can only derive instances for the last one. If the
2917 <literal>StateMonad</literal> class above were instead defined as
2920 class StateMonad m s | m -> s where ...
2923 then we would not have been able to derive an instance for the
2924 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2925 classes usually have one "main" parameter for which deriving new
2926 instances is most interesting.
2934 <!-- ==================== End of type system extensions ================= -->
2936 <!-- ====================== TEMPLATE HASKELL ======================= -->
2938 <sect1 id="template-haskell">
2939 <title>Template Haskell</title>
2941 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
2942 the main technical innovations are discussed in "<ulink
2943 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
2944 Template Meta-programming for Haskell</ulink>", in
2945 Proc Haskell Workshop 2002.
2949 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
2950 Tim Sheard is going to expand it.)
2953 <sect2> <title> Syntax </title>
2955 Template Haskell has the following new syntactic constructions. You need to use the flag
2956 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
2960 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
2961 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
2962 There must be no space between the "$" and the identifier or parenthesis. This use
2963 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
2964 of "." as an infix operator. If you want the infix operator, put spaces around it.
2966 <para> A splice can occur in place of
2968 <listitem><para> an expression;</para></listitem>
2969 <listitem><para> a list of top-level declarations;</para></listitem>
2970 <listitem><para> a pattern;</para></listitem>
2971 <listitem><para> a type;</para></listitem>
2977 A expression quotation is written in Oxford brackets, thus:
2979 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;</para></listitem>
2980 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;</para></listitem>
2981 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;</para></listitem>
2982 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;</para></listitem>
2983 </itemizedlist></para></listitem>
2986 Reification is written thus:
2988 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
2989 has type <literal>Dec</literal>. </para></listitem>
2990 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
2991 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
2992 <listitem><para> Still to come: fixities </para></listitem>
2994 </itemizedlist></para>
3002 <sect2> <title> Using Template Haskell </title>
3006 The data types and monadic constructor functions for Template Haskell are in the library
3007 <literal>Language.Haskell.THSyntax</literal>.
3011 If the module contains any top-level splices that must be run, you must use GHC with
3012 <literal>--make</literal> or <literal>--interactive</literal> flags. (Reason: that
3013 means it walks the dependency tree and knows what modules must be linked etc.)
3017 You can only run a function at compile time if it is imported from another module. That is,
3018 you can't define a function in a module, and call it from within a splice in the same module.
3019 (It would make sense to do so, but it's hard to implement.)
3023 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3031 <!-- ==================== ASSERTIONS ================= -->
3033 <sect1 id="sec-assertions">
3035 <indexterm><primary>Assertions</primary></indexterm>
3039 If you want to make use of assertions in your standard Haskell code, you
3040 could define a function like the following:
3046 assert :: Bool -> a -> a
3047 assert False x = error "assertion failed!"
3054 which works, but gives you back a less than useful error message --
3055 an assertion failed, but which and where?
3059 One way out is to define an extended <function>assert</function> function which also
3060 takes a descriptive string to include in the error message and
3061 perhaps combine this with the use of a pre-processor which inserts
3062 the source location where <function>assert</function> was used.
3066 Ghc offers a helping hand here, doing all of this for you. For every
3067 use of <function>assert</function> in the user's source:
3073 kelvinToC :: Double -> Double
3074 kelvinToC k = assert (k >= 0.0) (k+273.15)
3080 Ghc will rewrite this to also include the source location where the
3087 assert pred val ==> assertError "Main.hs|15" pred val
3093 The rewrite is only performed by the compiler when it spots
3094 applications of <function>Control.Exception.assert</function>, so you
3095 can still define and use your own versions of
3096 <function>assert</function>, should you so wish. If not, import
3097 <literal>Control.Exception</literal> to make use
3098 <function>assert</function> in your code.
3102 To have the compiler ignore uses of assert, use the compiler option
3103 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3104 option</primary></indexterm> That is, expressions of the form
3105 <literal>assert pred e</literal> will be rewritten to
3106 <literal>e</literal>.
3110 Assertion failures can be caught, see the documentation for the
3111 <literal>Control.Exception</literal> library for the details.
3117 <!-- =============================== PRAGMAS =========================== -->
3119 <sect1 id="pragmas">
3120 <title>Pragmas</title>
3122 <indexterm><primary>pragma</primary></indexterm>
3124 <para>GHC supports several pragmas, or instructions to the
3125 compiler placed in the source code. Pragmas don't normally affect
3126 the meaning of the program, but they might affect the efficiency
3127 of the generated code.</para>
3129 <para>Pragmas all take the form
3131 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3133 where <replaceable>word</replaceable> indicates the type of
3134 pragma, and is followed optionally by information specific to that
3135 type of pragma. Case is ignored in
3136 <replaceable>word</replaceable>. The various values for
3137 <replaceable>word</replaceable> that GHC understands are described
3138 in the following sections; any pragma encountered with an
3139 unrecognised <replaceable>word</replaceable> is (silently)
3142 <sect2 id="inline-pragma">
3143 <title>INLINE pragma
3145 <indexterm><primary>INLINE pragma</primary></indexterm>
3146 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
3149 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
3150 functions/values that are “small enough,” thus avoiding the call
3151 overhead and possibly exposing other more-wonderful optimisations.
3155 You will probably see these unfoldings (in Core syntax) in your
3160 Normally, if GHC decides a function is “too expensive” to inline, it
3161 will not do so, nor will it export that unfolding for other modules to
3166 The sledgehammer you can bring to bear is the
3167 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
3170 key_function :: Int -> String -> (Bool, Double)
3172 #ifdef __GLASGOW_HASKELL__
3173 {-# INLINE key_function #-}
3177 (You don't need to do the C pre-processor carry-on unless you're going
3178 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
3182 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
3183 “cost” to be very low. The normal unfolding machinery will then be
3184 very keen to inline it.
3188 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
3189 signature could be put.
3193 <literal>INLINE</literal> pragmas are a particularly good idea for the
3194 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
3195 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
3198 #ifdef __GLASGOW_HASKELL__
3199 {-# INLINE thenUs #-}
3200 {-# INLINE returnUs #-}
3208 <sect2 id="noinline-pragma">
3209 <title>NOINLINE pragma
3212 <indexterm><primary>NOINLINE pragma</primary></indexterm>
3213 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
3214 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
3215 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
3218 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
3219 it stops the named function from being inlined by the compiler. You
3220 shouldn't ever need to do this, unless you're very cautious about code
3224 <para><literal>NOTINLINE</literal> is a synonym for
3225 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
3226 by Haskell 98 as the standard way to disable inlining, so it should be
3227 used if you want your code to be portable).</para>
3231 <sect2 id="specialize-pragma">
3232 <title>SPECIALIZE pragma</title>
3234 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3235 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
3236 <indexterm><primary>overloading, death to</primary></indexterm>
3238 <para>(UK spelling also accepted.) For key overloaded
3239 functions, you can create extra versions (NB: more code space)
3240 specialised to particular types. Thus, if you have an
3241 overloaded function:</para>
3244 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3247 <para>If it is heavily used on lists with
3248 <literal>Widget</literal> keys, you could specialise it as
3252 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3255 <para>To get very fancy, you can also specify a named function
3256 to use for the specialised value, as in:</para>
3259 {-# RULES hammeredLookup = blah #-}
3262 <para>where <literal>blah</literal> is an implementation of
3263 <literal>hammerdLookup</literal> written specialy for
3264 <literal>Widget</literal> lookups. It's <emphasis>Your
3265 Responsibility</emphasis> to make sure that
3266 <function>blah</function> really behaves as a specialised
3267 version of <function>hammeredLookup</function>!!!</para>
3269 <para>Note we use the <literal>RULE</literal> pragma here to
3270 indicate that <literal>hammeredLookup</literal> applied at a
3271 certain type should be replaced by <literal>blah</literal>. See
3272 <xref linkend="rules"> for more information on
3273 <literal>RULES</literal>.</para>
3275 <para>An example in which using <literal>RULES</literal> for
3276 specialisation will Win Big:
3279 toDouble :: Real a => a -> Double
3280 toDouble = fromRational . toRational
3282 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
3283 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3286 The <function>i2d</function> function is virtually one machine
3287 instruction; the default conversion—via an intermediate
3288 <literal>Rational</literal>—is obscenely expensive by
3291 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3292 be put anywhere its type signature could be put.</para>
3296 <sect2 id="specialize-instance-pragma">
3297 <title>SPECIALIZE instance pragma
3301 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3302 <indexterm><primary>overloading, death to</primary></indexterm>
3303 Same idea, except for instance declarations. For example:
3306 instance (Eq a) => Eq (Foo a) where {
3307 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3311 The pragma must occur inside the <literal>where</literal> part
3312 of the instance declaration.
3315 Compatible with HBC, by the way, except perhaps in the placement
3321 <sect2 id="line-pragma">
3326 <indexterm><primary>LINE pragma</primary></indexterm>
3327 <indexterm><primary>pragma, LINE</primary></indexterm>
3331 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
3332 automatically generated Haskell code. It lets you specify the line
3333 number and filename of the original code; for example
3339 {-# LINE 42 "Foo.vhs" #-}
3345 if you'd generated the current file from something called <filename>Foo.vhs</filename>
3346 and this line corresponds to line 42 in the original. GHC will adjust
3347 its error messages to refer to the line/file named in the <literal>LINE</literal>
3354 <title>RULES pragma</title>
3357 The RULES pragma lets you specify rewrite rules. It is described in
3358 <xref LinkEnd="rewrite-rules">.
3363 <sect2 id="deprecated-pragma">
3364 <title>DEPRECATED pragma</title>
3367 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
3368 There are two forms.
3372 You can deprecate an entire module thus:</para>
3374 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3378 When you compile any module that import <literal>Wibble</literal>, GHC will print
3379 the specified message.</para>
3384 You can deprecate a function, class, or type, with the following top-level declaration:
3387 {-# DEPRECATED f, C, T "Don't use these" #-}
3390 When you compile any module that imports and uses any of the specifed entities,
3391 GHC will print the specified message.
3395 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
3401 <!-- ======================= REWRITE RULES ======================== -->
3403 <sect1 id="rewrite-rules">
3404 <title>Rewrite rules
3406 <indexterm><primary>RULES pagma</primary></indexterm>
3407 <indexterm><primary>pragma, RULES</primary></indexterm>
3408 <indexterm><primary>rewrite rules</primary></indexterm></title>
3411 The programmer can specify rewrite rules as part of the source program
3412 (in a pragma). GHC applies these rewrite rules wherever it can.
3420 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3427 <title>Syntax</title>
3430 From a syntactic point of view:
3436 Each rule has a name, enclosed in double quotes. The name itself has
3437 no significance at all. It is only used when reporting how many times the rule fired.
3443 There may be zero or more rules in a <literal>RULES</literal> pragma.
3449 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3450 is set, so you must lay out your rules starting in the same column as the
3451 enclosing definitions.
3457 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3458 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3459 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3460 by spaces, just like in a type <literal>forall</literal>.
3466 A pattern variable may optionally have a type signature.
3467 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3468 For example, here is the <literal>foldr/build</literal> rule:
3471 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3472 foldr k z (build g) = g k z
3475 Since <function>g</function> has a polymorphic type, it must have a type signature.
3482 The left hand side of a rule must consist of a top-level variable applied
3483 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3486 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3487 "wrong2" forall f. f True = True
3490 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3497 A rule does not need to be in the same module as (any of) the
3498 variables it mentions, though of course they need to be in scope.
3504 Rules are automatically exported from a module, just as instance declarations are.
3515 <title>Semantics</title>
3518 From a semantic point of view:
3524 Rules are only applied if you use the <option>-O</option> flag.
3530 Rules are regarded as left-to-right rewrite rules.
3531 When GHC finds an expression that is a substitution instance of the LHS
3532 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3533 By "a substitution instance" we mean that the LHS can be made equal to the
3534 expression by substituting for the pattern variables.
3541 The LHS and RHS of a rule are typechecked, and must have the
3549 GHC makes absolutely no attempt to verify that the LHS and RHS
3550 of a rule have the same meaning. That is undecideable in general, and
3551 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3558 GHC makes no attempt to make sure that the rules are confluent or
3559 terminating. For example:
3562 "loop" forall x,y. f x y = f y x
3565 This rule will cause the compiler to go into an infinite loop.
3572 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3578 GHC currently uses a very simple, syntactic, matching algorithm
3579 for matching a rule LHS with an expression. It seeks a substitution
3580 which makes the LHS and expression syntactically equal modulo alpha
3581 conversion. The pattern (rule), but not the expression, is eta-expanded if
3582 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3583 But not beta conversion (that's called higher-order matching).
3587 Matching is carried out on GHC's intermediate language, which includes
3588 type abstractions and applications. So a rule only matches if the
3589 types match too. See <xref LinkEnd="rule-spec"> below.
3595 GHC keeps trying to apply the rules as it optimises the program.
3596 For example, consider:
3605 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3606 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3607 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3608 not be substituted, and the rule would not fire.
3615 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3616 that appears on the LHS of a rule</emphasis>, because once you have substituted
3617 for something you can't match against it (given the simple minded
3618 matching). So if you write the rule
3621 "map/map" forall f,g. map f . map g = map (f.g)
3624 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3625 It will only match something written with explicit use of ".".
3626 Well, not quite. It <emphasis>will</emphasis> match the expression
3632 where <function>wibble</function> is defined:
3635 wibble f g = map f . map g
3638 because <function>wibble</function> will be inlined (it's small).
3640 Later on in compilation, GHC starts inlining even things on the
3641 LHS of rules, but still leaves the rules enabled. This inlining
3642 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3649 All rules are implicitly exported from the module, and are therefore
3650 in force in any module that imports the module that defined the rule, directly
3651 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3652 in force when compiling A.) The situation is very similar to that for instance
3664 <title>List fusion</title>
3667 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3668 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3669 intermediate list should be eliminated entirely.
3673 The following are good producers:
3685 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3691 Explicit lists (e.g. <literal>[True, False]</literal>)
3697 The cons constructor (e.g <literal>3:4:[]</literal>)
3703 <function>++</function>
3709 <function>map</function>
3715 <function>filter</function>
3721 <function>iterate</function>, <function>repeat</function>
3727 <function>zip</function>, <function>zipWith</function>
3736 The following are good consumers:
3748 <function>array</function> (on its second argument)
3754 <function>length</function>
3760 <function>++</function> (on its first argument)
3766 <function>foldr</function>
3772 <function>map</function>
3778 <function>filter</function>
3784 <function>concat</function>
3790 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3796 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3797 will fuse with one but not the other)
3803 <function>partition</function>
3809 <function>head</function>
3815 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3821 <function>sequence_</function>
3827 <function>msum</function>
3833 <function>sortBy</function>
3842 So, for example, the following should generate no intermediate lists:
3845 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3851 This list could readily be extended; if there are Prelude functions that you use
3852 a lot which are not included, please tell us.
3856 If you want to write your own good consumers or producers, look at the
3857 Prelude definitions of the above functions to see how to do so.
3862 <sect2 id="rule-spec">
3863 <title>Specialisation
3867 Rewrite rules can be used to get the same effect as a feature
3868 present in earlier version of GHC:
3871 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3874 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3875 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3876 specialising the original definition of <function>fromIntegral</function> the programmer is
3877 promising that it is safe to use <function>int8ToInt16</function> instead.
3881 This feature is no longer in GHC. But rewrite rules let you do the
3886 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3890 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3891 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3892 GHC adds the type and dictionary applications to get the typed rule
3895 forall (d1::Integral Int8) (d2::Num Int16) .
3896 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3900 this rule does not need to be in the same file as fromIntegral,
3901 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3902 have an original definition available to specialise).
3908 <title>Controlling what's going on</title>
3916 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3922 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3923 If you add <option>-dppr-debug</option> you get a more detailed listing.
3929 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3932 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3933 {-# INLINE build #-}
3937 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3938 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3939 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3940 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3947 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3948 see how to write rules that will do fusion and yet give an efficient
3949 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3961 <sect1 id="generic-classes">
3962 <title>Generic classes</title>
3964 <para>(Note: support for generic classes is currently broken in
3968 The ideas behind this extension are described in detail in "Derivable type classes",
3969 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3970 An example will give the idea:
3978 fromBin :: [Int] -> (a, [Int])
3980 toBin {| Unit |} Unit = []
3981 toBin {| a :+: b |} (Inl x) = 0 : toBin x
3982 toBin {| a :+: b |} (Inr y) = 1 : toBin y
3983 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
3985 fromBin {| Unit |} bs = (Unit, bs)
3986 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
3987 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
3988 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
3989 (y,bs'') = fromBin bs'
3992 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
3993 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
3994 which are defined thus in the library module <literal>Generics</literal>:
3998 data a :+: b = Inl a | Inr b
3999 data a :*: b = a :*: b
4002 Now you can make a data type into an instance of Bin like this:
4004 instance (Bin a, Bin b) => Bin (a,b)
4005 instance Bin a => Bin [a]
4007 That is, just leave off the "where" clasuse. Of course, you can put in the
4008 where clause and over-ride whichever methods you please.
4012 <title> Using generics </title>
4013 <para>To use generics you need to</para>
4016 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4017 <option>-fgenerics</option> (to generate extra per-data-type code),
4018 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4022 <para>Import the module <literal>Generics</literal> from the
4023 <literal>lang</literal> package. This import brings into
4024 scope the data types <literal>Unit</literal>,
4025 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4026 don't need this import if you don't mention these types
4027 explicitly; for example, if you are simply giving instance
4028 declarations.)</para>
4033 <sect2> <title> Changes wrt the paper </title>
4035 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4036 can be written infix (indeed, you can now use
4037 any operator starting in a colon as an infix type constructor). Also note that
4038 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4039 Finally, note that the syntax of the type patterns in the class declaration
4040 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4041 alone would ambiguous when they appear on right hand sides (an extension we
4042 anticipate wanting).
4046 <sect2> <title>Terminology and restrictions</title>
4048 Terminology. A "generic default method" in a class declaration
4049 is one that is defined using type patterns as above.
4050 A "polymorphic default method" is a default method defined as in Haskell 98.
4051 A "generic class declaration" is a class declaration with at least one
4052 generic default method.
4060 Alas, we do not yet implement the stuff about constructor names and
4067 A generic class can have only one parameter; you can't have a generic
4068 multi-parameter class.
4074 A default method must be defined entirely using type patterns, or entirely
4075 without. So this is illegal:
4078 op :: a -> (a, Bool)
4079 op {| Unit |} Unit = (Unit, True)
4082 However it is perfectly OK for some methods of a generic class to have
4083 generic default methods and others to have polymorphic default methods.
4089 The type variable(s) in the type pattern for a generic method declaration
4090 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:
4094 op {| p :*: q |} (x :*: y) = op (x :: p)
4102 The type patterns in a generic default method must take one of the forms:
4108 where "a" and "b" are type variables. Furthermore, all the type patterns for
4109 a single type constructor (<literal>:*:</literal>, say) must be identical; they
4110 must use the same type variables. So this is illegal:
4114 op {| a :+: b |} (Inl x) = True
4115 op {| p :+: q |} (Inr y) = False
4117 The type patterns must be identical, even in equations for different methods of the class.
4118 So this too is illegal:
4122 op1 {| a :*: b |} (x :*: y) = True
4125 op2 {| p :*: q |} (x :*: y) = False
4127 (The reason for this restriction is that we gather all the equations for a particular type consructor
4128 into a single generic instance declaration.)
4134 A generic method declaration must give a case for each of the three type constructors.
4140 The type for a generic method can be built only from:
4142 <listitem> <para> Function arrows </para> </listitem>
4143 <listitem> <para> Type variables </para> </listitem>
4144 <listitem> <para> Tuples </para> </listitem>
4145 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
4147 Here are some example type signatures for generic methods:
4150 op2 :: Bool -> (a,Bool)
4151 op3 :: [Int] -> a -> a
4154 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
4158 This restriction is an implementation restriction: we just havn't got around to
4159 implementing the necessary bidirectional maps over arbitrary type constructors.
4160 It would be relatively easy to add specific type constructors, such as Maybe and list,
4161 to the ones that are allowed.</para>
4166 In an instance declaration for a generic class, the idea is that the compiler
4167 will fill in the methods for you, based on the generic templates. However it can only
4172 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4177 No constructor of the instance type has unboxed fields.
4181 (Of course, these things can only arise if you are already using GHC extensions.)
4182 However, you can still give an instance declarations for types which break these rules,
4183 provided you give explicit code to override any generic default methods.
4191 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
4192 what the compiler does with generic declarations.
4197 <sect2> <title> Another example </title>
4199 Just to finish with, here's another example I rather like:
4203 nCons {| Unit |} _ = 1
4204 nCons {| a :*: b |} _ = 1
4205 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4208 tag {| Unit |} _ = 1
4209 tag {| a :*: b |} _ = 1
4210 tag {| a :+: b |} (Inl x) = tag x
4211 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4220 ;;; Local Variables: ***
4222 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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