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 import Control.Monad.Fix
362 justOnes = mdo xs <- Just (1:xs)
366 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
370 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
373 class Monad m => MonadFix m where
374 mfix :: (a -> m a) -> m a
377 The function <literal>mfix</literal>
378 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
379 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
380 For details, see the above mentioned reference.
383 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
384 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
385 for Haskell's internal state monad (strict and lazy, respectively).
388 There are three important points in using the recursive-do notation:
391 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
392 than <literal>do</literal>).
396 You should <literal>import Control.Monad.Fix</literal>.
397 (Note: Strictly speaking, this import is required only when you need to refer to the name
398 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
399 are encouraged to always import this module when using the mdo-notation.)
403 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
409 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
410 contains up to date information on recursive monadic bindings.
414 Historical note: The old implementation of the mdo-notation (and most
415 of the existing documents) used the name
416 <literal>MonadRec</literal> for the class and the corresponding library.
417 This name is not supported by GHC.
423 <sect2> <title> Infix type constructors </title>
425 <para>GHC supports infix type constructors, much as it supports infix data constructors. For example:
429 data a :+: b = Inl a | Inr b
431 f :: a `Either` b -> a :+: b
436 syntax of an infix type constructor is just like that of an infix data constructor: either
437 it's an operator beginning with ":", or it is an ordinary (alphabetic) type constructor enclosed in
441 When you give a fixity declaration, the fixity applies to both the data constructor and the
442 type constructor with the specified name. You cannot give different fixities to the type constructor T
443 and the data constructor T.
449 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
451 <sect2 id="parallel-list-comprehensions">
452 <title>Parallel List Comprehensions</title>
453 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
455 <indexterm><primary>parallel list comprehensions</primary>
458 <para>Parallel list comprehensions are a natural extension to list
459 comprehensions. List comprehensions can be thought of as a nice
460 syntax for writing maps and filters. Parallel comprehensions
461 extend this to include the zipWith family.</para>
463 <para>A parallel list comprehension has multiple independent
464 branches of qualifier lists, each separated by a `|' symbol. For
465 example, the following zips together two lists:</para>
468 [ (x, y) | x <- xs | y <- ys ]
471 <para>The behavior of parallel list comprehensions follows that of
472 zip, in that the resulting list will have the same length as the
473 shortest branch.</para>
475 <para>We can define parallel list comprehensions by translation to
476 regular comprehensions. Here's the basic idea:</para>
478 <para>Given a parallel comprehension of the form: </para>
481 [ e | p1 <- e11, p2 <- e12, ...
482 | q1 <- e21, q2 <- e22, ...
487 <para>This will be translated to: </para>
490 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
491 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
496 <para>where `zipN' is the appropriate zip for the given number of
501 <sect2 id="rebindable-syntax">
502 <title>Rebindable syntax</title>
505 <para>GHC allows most kinds of built-in syntax to be rebound by
506 the user, to facilitate replacing the <literal>Prelude</literal>
507 with a home-grown version, for example.</para>
509 <para>You may want to define your own numeric class
510 hierarchy. It completely defeats that purpose if the
511 literal "1" means "<literal>Prelude.fromInteger
512 1</literal>", which is what the Haskell Report specifies.
513 So the <option>-fno-implicit-prelude</option> flag causes
514 the following pieces of built-in syntax to refer to
515 <emphasis>whatever is in scope</emphasis>, not the Prelude
520 <para>Integer and fractional literals mean
521 "<literal>fromInteger 1</literal>" and
522 "<literal>fromRational 3.2</literal>", not the
523 Prelude-qualified versions; both in expressions and in
525 <para>However, the standard Prelude <literal>Eq</literal> class
526 is still used for the equality test necessary for literal patterns.</para>
530 <para>Negation (e.g. "<literal>- (f x)</literal>")
531 means "<literal>negate (f x)</literal>" (not
532 <literal>Prelude.negate</literal>).</para>
536 <para>In an n+k pattern, the standard Prelude
537 <literal>Ord</literal> class is still used for comparison,
538 but the necessary subtraction uses whatever
539 "<literal>(-)</literal>" is in scope (not
540 "<literal>Prelude.(-)</literal>").</para>
544 <para>"Do" notation is translated using whatever
545 functions <literal>(>>=)</literal>,
546 <literal>(>>)</literal>, <literal>fail</literal>, and
547 <literal>return</literal>, are in scope (not the Prelude
548 versions). List comprehensions, and parallel array
549 comprehensions, are unaffected. </para></listitem>
552 <para>Be warned: this is an experimental facility, with fewer checks than
553 usual. In particular, it is essential that the functions GHC finds in scope
554 must have the appropriate types, namely:
556 fromInteger :: forall a. (...) => Integer -> a
557 fromRational :: forall a. (...) => Rational -> a
558 negate :: forall a. (...) => a -> a
559 (-) :: forall a. (...) => a -> a -> a
560 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
561 (>>) :: forall m a. (...) => m a -> m b -> m b
562 return :: forall m a. (...) => a -> m a
563 fail :: forall m a. (...) => String -> m a
565 (The (...) part can be any context including the empty context; that part
567 If the functions don't have the right type, very peculiar things may
568 happen. Use <literal>-dcore-lint</literal> to
569 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
575 <!-- TYPE SYSTEM EXTENSIONS -->
576 <sect1 id="type-extensions">
577 <title>Type system extensions</title>
579 <sect2 id="nullary-types">
580 <title>Data types with no constructors</title>
582 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
583 a data type with no constructors. For example:</para>
587 data T a -- T :: * -> *
590 <para>Syntactically, the declaration lacks the "= constrs" part. The
591 type can be parameterised over types of any kind, but if the kind is
592 not <literal>*</literal> then an explicit kind annotation must be used
593 (see <xref linkend="sec-kinding">).</para>
595 <para>Such data types have only one value, namely bottom.
596 Nevertheless, they can be useful when defining "phantom types".</para>
599 <sect2 id="infix-tycons">
600 <title>Infix type constructors</title>
603 GHC allows type constructors to be operators, and to be written infix, very much
604 like expressions. More specifically:
607 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
608 The lexical syntax is the same as that for data constructors.
611 Types can be written infix. For example <literal>Int :*: Bool</literal>.
615 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
616 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
619 Fixities may be declared for type constructors just as for data constructors. However,
620 one cannot distinguish between the two in a fixity declaration; a fixity declaration
621 sets the fixity for a data constructor and the corresponding type constructor. For example:
625 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
626 and similarly for <literal>:*:</literal>.
627 <literal>Int `a` Bool</literal>.
630 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
633 Data type and type-synonym declarations can be written infix. E.g.
635 data a :*: b = Foo a b
636 type a :+: b = Either a b
640 The only thing that differs between operators in types and operators in expressions is that
641 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
642 are not allowed in types. Reason: the uniform thing to do would be to make them type
643 variables, but that's not very useful. A less uniform but more useful thing would be to
644 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
645 lists. So for now we just exclude them.
652 <sect2 id="sec-kinding">
653 <title>Explicitly-kinded quantification</title>
656 Haskell infers the kind of each type variable. Sometimes it is nice to be able
657 to give the kind explicitly as (machine-checked) documentation,
658 just as it is nice to give a type signature for a function. On some occasions,
659 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
660 John Hughes had to define the data type:
662 data Set cxt a = Set [a]
663 | Unused (cxt a -> ())
665 The only use for the <literal>Unused</literal> constructor was to force the correct
666 kind for the type variable <literal>cxt</literal>.
669 GHC now instead allows you to specify the kind of a type variable directly, wherever
670 a type variable is explicitly bound. Namely:
672 <listitem><para><literal>data</literal> declarations:
674 data Set (cxt :: * -> *) a = Set [a]
675 </Screen></para></listitem>
676 <listitem><para><literal>type</literal> declarations:
678 type T (f :: * -> *) = f Int
679 </Screen></para></listitem>
680 <listitem><para><literal>class</literal> declarations:
682 class (Eq a) => C (f :: * -> *) a where ...
683 </Screen></para></listitem>
684 <listitem><para><literal>forall</literal>'s in type signatures:
686 f :: forall (cxt :: * -> *). Set cxt Int
687 </Screen></para></listitem>
692 The parentheses are required. Some of the spaces are required too, to
693 separate the lexemes. If you write <literal>(f::*->*)</literal> you
694 will get a parse error, because "<literal>::*->*</literal>" is a
695 single lexeme in Haskell.
699 As part of the same extension, you can put kind annotations in types
702 f :: (Int :: *) -> Int
703 g :: forall a. a -> (a :: *)
707 atype ::= '(' ctype '::' kind ')
709 The parentheses are required.
714 <sect2 id="class-method-types">
715 <title>Class method types
718 Haskell 98 prohibits class method types to mention constraints on the
719 class type variable, thus:
722 fromList :: [a] -> s a
723 elem :: Eq a => a -> s a -> Bool
725 The type of <literal>elem</literal> is illegal in Haskell 98, because it
726 contains the constraint <literal>Eq a</literal>, constrains only the
727 class type variable (in this case <literal>a</literal>).
730 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
735 <sect2 id="multi-param-type-classes">
736 <title>Multi-parameter type classes
740 This section documents GHC's implementation of multi-parameter type
741 classes. There's lots of background in the paper <ULink
742 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
743 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
748 I'd like to thank people who reported shorcomings in the GHC 3.02
749 implementation. Our default decisions were all conservative ones, and
750 the experience of these heroic pioneers has given useful concrete
751 examples to support several generalisations. (These appear below as
752 design choices not implemented in 3.02.)
756 I've discussed these notes with Mark Jones, and I believe that Hugs
757 will migrate towards the same design choices as I outline here.
758 Thanks to him, and to many others who have offered very useful
766 There are the following restrictions on the form of a qualified
773 forall tv1..tvn (c1, ...,cn) => type
779 (Here, I write the "foralls" explicitly, although the Haskell source
780 language omits them; in Haskell 1.4, all the free type variables of an
781 explicit source-language type signature are universally quantified,
782 except for the class type variables in a class declaration. However,
783 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
792 <emphasis>Each universally quantified type variable
793 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
795 The reason for this is that a value with a type that does not obey
796 this restriction could not be used without introducing
797 ambiguity. Here, for example, is an illegal type:
801 forall a. Eq a => Int
805 When a value with this type was used, the constraint <literal>Eq tv</literal>
806 would be introduced where <literal>tv</literal> is a fresh type variable, and
807 (in the dictionary-translation implementation) the value would be
808 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
809 can never know which instance of <literal>Eq</literal> to use because we never
810 get any more information about <literal>tv</literal>.
817 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
818 universally quantified type variables <literal>tvi</literal></emphasis>.
820 For example, this type is OK because <literal>C a b</literal> mentions the
821 universally quantified type variable <literal>b</literal>:
825 forall a. C a b => burble
829 The next type is illegal because the constraint <literal>Eq b</literal> does not
830 mention <literal>a</literal>:
834 forall a. Eq b => burble
838 The reason for this restriction is milder than the other one. The
839 excluded types are never useful or necessary (because the offending
840 context doesn't need to be witnessed at this point; it can be floated
841 out). Furthermore, floating them out increases sharing. Lastly,
842 excluding them is a conservative choice; it leaves a patch of
843 territory free in case we need it later.
853 These restrictions apply to all types, whether declared in a type signature
858 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
859 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
866 f :: Eq (m a) => [m a] -> [m a]
873 This choice recovers principal types, a property that Haskell 1.4 does not have.
879 <title>Class declarations</title>
887 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
891 class Collection c a where
892 union :: c a -> c a -> c a
903 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
904 of "acyclic" involves only the superclass relationships. For example,
910 op :: D b => a -> b -> b
913 class C a => D a where { ... }
917 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
918 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
919 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
926 <emphasis>There are no restrictions on the context in a class declaration
927 (which introduces superclasses), except that the class hierarchy must
928 be acyclic</emphasis>. So these class declarations are OK:
932 class Functor (m k) => FiniteMap m k where
935 class (Monad m, Monad (t m)) => Transform t m where
936 lift :: m a -> (t m) a
945 <emphasis>In the signature of a class operation, every constraint
946 must mention at least one type variable that is not a class type
953 class Collection c a where
954 mapC :: Collection c b => (a->b) -> c a -> c b
958 is OK because the constraint <literal>(Collection a b)</literal> mentions
959 <literal>b</literal>, even though it also mentions the class variable
960 <literal>a</literal>. On the other hand:
965 op :: Eq a => (a,b) -> (a,b)
969 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
970 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
971 example is easily fixed by moving the offending context up to the
976 class Eq a => C a where
981 A yet more relaxed rule would allow the context of a class-op signature
982 to mention only class type variables. However, that conflicts with
983 Rule 1(b) for types above.
990 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
991 the class type variables</emphasis>. For example:
997 insert :: s -> a -> s
1001 is not OK, because the type of <literal>empty</literal> doesn't mention
1002 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1003 types, and has the same motivation.
1005 Sometimes, offending class declarations exhibit misunderstandings. For
1006 example, <literal>Coll</literal> might be rewritten
1010 class Coll s a where
1012 insert :: s a -> a -> s a
1016 which makes the connection between the type of a collection of
1017 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1018 Occasionally this really doesn't work, in which case you can split the
1026 class CollE s => Coll s a where
1027 insert :: s -> a -> s
1040 <sect3 id="instance-decls">
1041 <title>Instance declarations</title>
1049 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1054 instance context1 => C type1 where ...
1055 instance context2 => C type2 where ...
1059 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1061 However, if you give the command line option
1062 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1063 option</primary></indexterm> then overlapping instance declarations are permitted.
1064 However, GHC arranges never to commit to using an instance declaration
1065 if another instance declaration also applies, either now or later.
1071 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1077 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1078 (but not identical to <literal>type1</literal>), or vice versa.
1082 Notice that these rules
1087 make it clear which instance decl to use
1088 (pick the most specific one that matches)
1095 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1096 Reason: you can pick which instance decl
1097 "matches" based on the type.
1102 However the rules are over-conservative. Two instance declarations can overlap,
1103 but it can still be clear in particular situations which to use. For example:
1105 instance C (Int,a) where ...
1106 instance C (a,Bool) where ...
1108 These are rejected by GHC's rules, but it is clear what to do when trying
1109 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1110 cannot apply. Yell if this restriction bites you.
1113 GHC is also conservative about committing to an overlapping instance. For example:
1115 class C a where { op :: a -> a }
1116 instance C [Int] where ...
1117 instance C a => C [a] where ...
1119 f :: C b => [b] -> [b]
1122 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1123 GHC does not commit to the second instance declaration, because in a paricular
1124 call of f, b might be instantiate to Int, so the first instance declaration
1125 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1126 GHC will instead silently pick the second instance, without complaining about
1127 the problem of subsequent instantiations.
1130 Regrettably, GHC doesn't guarantee to detect overlapping instance
1131 declarations if they appear in different modules. GHC can "see" the
1132 instance declarations in the transitive closure of all the modules
1133 imported by the one being compiled, so it can "see" all instance decls
1134 when it is compiling <literal>Main</literal>. However, it currently chooses not
1135 to look at ones that can't possibly be of use in the module currently
1136 being compiled, in the interests of efficiency. (Perhaps we should
1137 change that decision, at least for <literal>Main</literal>.)
1144 <emphasis>There are no restrictions on the type in an instance
1145 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1146 The instance "head" is the bit after the "=>" in an instance decl. For
1147 example, these are OK:
1151 instance C Int a where ...
1153 instance D (Int, Int) where ...
1155 instance E [[a]] where ...
1159 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1160 For example, this is OK:
1164 instance Stateful (ST s) (MutVar s) where ...
1168 The "at least one not a type variable" restriction is to ensure that
1169 context reduction terminates: each reduction step removes one type
1170 constructor. For example, the following would make the type checker
1171 loop if it wasn't excluded:
1175 instance C a => C a where ...
1179 There are two situations in which the rule is a bit of a pain. First,
1180 if one allows overlapping instance declarations then it's quite
1181 convenient to have a "default instance" declaration that applies if
1182 something more specific does not:
1191 Second, sometimes you might want to use the following to get the
1192 effect of a "class synonym":
1196 class (C1 a, C2 a, C3 a) => C a where { }
1198 instance (C1 a, C2 a, C3 a) => C a where { }
1202 This allows you to write shorter signatures:
1214 f :: (C1 a, C2 a, C3 a) => ...
1218 I'm on the lookout for a simple rule that preserves decidability while
1219 allowing these idioms. The experimental flag
1220 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1221 option</primary></indexterm> lifts this restriction, allowing all the types in an
1222 instance head to be type variables.
1229 <emphasis>Unlike Haskell 1.4, instance heads may use type
1230 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1231 writing the RHS of the type synonym definition. For example:
1235 type Point = (Int,Int)
1236 instance C Point where ...
1237 instance C [Point] where ...
1241 is legal. However, if you added
1245 instance C (Int,Int) where ...
1249 as well, then the compiler will complain about the overlapping
1250 (actually, identical) instance declarations. As always, type synonyms
1251 must be fully applied. You cannot, for example, write:
1256 instance Monad P where ...
1260 This design decision is independent of all the others, and easily
1261 reversed, but it makes sense to me.
1268 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1269 be type variables</emphasis>. Thus
1273 instance C a b => Eq (a,b) where ...
1281 instance C Int b => Foo b where ...
1285 is not OK. Again, the intent here is to make sure that context
1286 reduction terminates.
1288 Voluminous correspondence on the Haskell mailing list has convinced me
1289 that it's worth experimenting with a more liberal rule. If you use
1290 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1291 types in an instance context. Termination is ensured by having a
1292 fixed-depth recursion stack. If you exceed the stack depth you get a
1293 sort of backtrace, and the opportunity to increase the stack depth
1294 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1307 <sect2 id="implicit-parameters">
1308 <title>Implicit parameters
1311 <para> Implicit paramters are implemented as described in
1312 "Implicit parameters: dynamic scoping with static types",
1313 J Lewis, MB Shields, E Meijer, J Launchbury,
1314 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1317 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1319 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1320 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1321 context. In Haskell, all variables are statically bound. Dynamic
1322 binding of variables is a notion that goes back to Lisp, but was later
1323 discarded in more modern incarnations, such as Scheme. Dynamic binding
1324 can be very confusing in an untyped language, and unfortunately, typed
1325 languages, in particular Hindley-Milner typed languages like Haskell,
1326 only support static scoping of variables.
1329 However, by a simple extension to the type class system of Haskell, we
1330 can support dynamic binding. Basically, we express the use of a
1331 dynamically bound variable as a constraint on the type. These
1332 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1333 function uses a dynamically-bound variable <literal>?x</literal>
1334 of type <literal>t'</literal>". For
1335 example, the following expresses the type of a sort function,
1336 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1338 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1340 The dynamic binding constraints are just a new form of predicate in the type class system.
1343 An implicit parameter is introduced by the special form <literal>?x</literal>,
1344 where <literal>x</literal> is
1345 any valid identifier. Use if this construct also introduces new
1346 dynamic binding constraints. For example, the following definition
1347 shows how we can define an implicitly parameterized sort function in
1348 terms of an explicitly parameterized <literal>sortBy</literal> function:
1350 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1352 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1355 Dynamic binding constraints behave just like other type class
1356 constraints in that they are automatically propagated. Thus, when a
1357 function is used, its implicit parameters are inherited by the
1358 function that called it. For example, our <literal>sort</literal> function might be used
1359 to pick out the least value in a list:
1361 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1362 least xs = fst (sort xs)
1364 Without lifting a finger, the <literal>?cmp</literal> parameter is
1365 propagated to become a parameter of <literal>least</literal> as well. With explicit
1366 parameters, the default is that parameters must always be explicit
1367 propagated. With implicit parameters, the default is to always
1371 An implicit parameter differs from other type class constraints in the
1372 following way: All uses of a particular implicit parameter must have
1373 the same type. This means that the type of <literal>(?x, ?x)</literal>
1374 is <literal>(?x::a) => (a,a)</literal>, and not
1375 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1379 An implicit parameter is bound using the standard
1380 <literal>let</literal> binding form, where the bindings must be a
1381 collection of simple bindings to implicit-style variables (no
1382 function-style bindings, and no type signatures); these bindings are
1383 neither polymorphic or recursive. This form binds the implicit
1384 parameters arising in the body, not the free variables as a
1385 <literal>let</literal> or <literal>where</literal> would do. For
1386 example, we define the <literal>min</literal> function by binding
1387 <literal>cmp</literal>.</para>
1390 min = let ?cmp = (<=) in least
1393 Note the following points:
1396 You may not mix implicit-parameter bindings with ordinary bindings in a
1397 single <literal>let</literal>
1398 expression; use two nested <literal>let</literal>s instead.
1402 You may put multiple implicit-parameter bindings in a
1403 single <literal>let</literal> expression; they are <emphasis>not</emphasis> treated
1404 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1405 Instead they are treated as a non-recursive group, each scoping over the bindings that
1406 follow. For example, consider:
1408 f y = let { ?x = y; ?x = ?x+1 } in ?x
1410 This function adds one to its argument.
1414 You may not have an implicit-parameter binding in a <literal>where</literal> clause,
1415 only in a <literal>let</literal> binding.
1419 <para> You can't have an implicit parameter in the context of a class or instance
1420 declaration. For example, both these declarations are illegal:
1422 class (?x::Int) => C a where ...
1423 instance (?x::a) => Foo [a] where ...
1425 Reason: exactly which implicit parameter you pick up depends on exactly where
1426 you invoke a function. But the ``invocation'' of instance declarations is done
1427 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1428 Easiest thing is to outlaw the offending types.</para>
1435 <sect2 id="linear-implicit-parameters">
1436 <title>Linear implicit parameters
1439 Linear implicit parameters are an idea developed by Koen Claessen,
1440 Mark Shields, and Simon PJ. They address the long-standing
1441 problem that monads seem over-kill for certain sorts of problem, notably:
1444 <listitem> <para> distributing a supply of unique names </para> </listitem>
1445 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1446 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1450 Linear implicit parameters are just like ordinary implicit parameters,
1451 except that they are "linear" -- that is, they cannot be copied, and
1452 must be explicitly "split" instead. Linear implicit parameters are
1453 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1454 (The '/' in the '%' suggests the split!)
1459 import GHC.Exts( Splittable )
1461 data NameSupply = ...
1463 splitNS :: NameSupply -> (NameSupply, NameSupply)
1464 newName :: NameSupply -> Name
1466 instance Splittable NameSupply where
1470 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1471 f env (Lam x e) = Lam x' (f env e)
1474 env' = extend env x x'
1475 ...more equations for f...
1477 Notice that the implicit parameter %ns is consumed
1479 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1480 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1484 So the translation done by the type checker makes
1485 the parameter explicit:
1487 f :: NameSupply -> Env -> Expr -> Expr
1488 f ns env (Lam x e) = Lam x' (f ns1 env e)
1490 (ns1,ns2) = splitNS ns
1492 env = extend env x x'
1494 Notice the call to 'split' introduced by the type checker.
1495 How did it know to use 'splitNS'? Because what it really did
1496 was to introduce a call to the overloaded function 'split',
1497 defined by the class <literal>Splittable</literal>:
1499 class Splittable a where
1502 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1503 split for name supplies. But we can simply write
1509 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1511 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1512 <literal>GHC.Exts</literal>.
1517 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1518 are entirely distinct implicit parameters: you
1519 can use them together and they won't intefere with each other. </para>
1522 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1524 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1525 in the context of a class or instance declaration. </para></listitem>
1529 <sect3><title>Warnings</title>
1532 The monomorphism restriction is even more important than usual.
1533 Consider the example above:
1535 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1536 f env (Lam x e) = Lam x' (f env e)
1539 env' = extend env x x'
1541 If we replaced the two occurrences of x' by (newName %ns), which is
1542 usually a harmless thing to do, we get:
1544 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1545 f env (Lam x e) = Lam (newName %ns) (f env e)
1547 env' = extend env x (newName %ns)
1549 But now the name supply is consumed in <emphasis>three</emphasis> places
1550 (the two calls to newName,and the recursive call to f), so
1551 the result is utterly different. Urk! We don't even have
1555 Well, this is an experimental change. With implicit
1556 parameters we have already lost beta reduction anyway, and
1557 (as John Launchbury puts it) we can't sensibly reason about
1558 Haskell programs without knowing their typing.
1563 <sect3><title>Recursive functions</title>
1564 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1567 foo :: %x::T => Int -> [Int]
1569 foo n = %x : foo (n-1)
1571 where T is some type in class Splittable.</para>
1573 Do you get a list of all the same T's or all different T's
1574 (assuming that split gives two distinct T's back)?
1576 If you supply the type signature, taking advantage of polymorphic
1577 recursion, you get what you'd probably expect. Here's the
1578 translated term, where the implicit param is made explicit:
1581 foo x n = let (x1,x2) = split x
1582 in x1 : foo x2 (n-1)
1584 But if you don't supply a type signature, GHC uses the Hindley
1585 Milner trick of using a single monomorphic instance of the function
1586 for the recursive calls. That is what makes Hindley Milner type inference
1587 work. So the translation becomes
1591 foom n = x : foom (n-1)
1595 Result: 'x' is not split, and you get a list of identical T's. So the
1596 semantics of the program depends on whether or not foo has a type signature.
1599 You may say that this is a good reason to dislike linear implicit parameters
1600 and you'd be right. That is why they are an experimental feature.
1606 <sect2 id="functional-dependencies">
1607 <title>Functional dependencies
1610 <para> Functional dependencies are implemented as described by Mark Jones
1611 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1612 In Proceedings of the 9th European Symposium on Programming,
1613 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1618 There should be more documentation, but there isn't (yet). Yell if you need it.
1623 <sect2 id="universal-quantification">
1624 <title>Arbitrary-rank polymorphism
1628 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1629 allows us to say exactly what this means. For example:
1637 g :: forall b. (b -> b)
1639 The two are treated identically.
1643 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1644 explicit universal quantification in
1646 For example, all the following types are legal:
1648 f1 :: forall a b. a -> b -> a
1649 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1651 f2 :: (forall a. a->a) -> Int -> Int
1652 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1654 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1656 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1657 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1658 The <literal>forall</literal> makes explicit the universal quantification that
1659 is implicitly added by Haskell.
1662 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1663 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1664 shows, the polymorphic type on the left of the function arrow can be overloaded.
1667 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1668 they have rank-2 types on the left of a function arrow.
1671 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1672 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1673 that restriction has now been lifted.)
1674 In particular, a forall-type (also called a "type scheme"),
1675 including an operational type class context, is legal:
1677 <listitem> <para> On the left of a function arrow </para> </listitem>
1678 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1679 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1680 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1681 field type signatures.</para> </listitem>
1682 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1683 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1685 There is one place you cannot put a <literal>forall</literal>:
1686 you cannot instantiate a type variable with a forall-type. So you cannot
1687 make a forall-type the argument of a type constructor. So these types are illegal:
1689 x1 :: [forall a. a->a]
1690 x2 :: (forall a. a->a, Int)
1691 x3 :: Maybe (forall a. a->a)
1693 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1694 a type variable any more!
1703 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1704 the types of the constructor arguments. Here are several examples:
1710 data T a = T1 (forall b. b -> b -> b) a
1712 data MonadT m = MkMonad { return :: forall a. a -> m a,
1713 bind :: forall a b. m a -> (a -> m b) -> m b
1716 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1722 The constructors have rank-2 types:
1728 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1729 MkMonad :: forall m. (forall a. a -> m a)
1730 -> (forall a b. m a -> (a -> m b) -> m b)
1732 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1738 Notice that you don't need to use a <literal>forall</literal> if there's an
1739 explicit context. For example in the first argument of the
1740 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1741 prefixed to the argument type. The implicit <literal>forall</literal>
1742 quantifies all type variables that are not already in scope, and are
1743 mentioned in the type quantified over.
1747 As for type signatures, implicit quantification happens for non-overloaded
1748 types too. So if you write this:
1751 data T a = MkT (Either a b) (b -> b)
1754 it's just as if you had written this:
1757 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1760 That is, since the type variable <literal>b</literal> isn't in scope, it's
1761 implicitly universally quantified. (Arguably, it would be better
1762 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1763 where that is what is wanted. Feedback welcomed.)
1767 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1768 the constructor to suitable values, just as usual. For example,
1779 a3 = MkSwizzle reverse
1782 a4 = let r x = Just x
1789 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1790 mkTs f x y = [T1 f x, T1 f y]
1796 The type of the argument can, as usual, be more general than the type
1797 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1798 does not need the <literal>Ord</literal> constraint.)
1802 When you use pattern matching, the bound variables may now have
1803 polymorphic types. For example:
1809 f :: T a -> a -> (a, Char)
1810 f (T1 w k) x = (w k x, w 'c' 'd')
1812 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1813 g (MkSwizzle s) xs f = s (map f (s xs))
1815 h :: MonadT m -> [m a] -> m [a]
1816 h m [] = return m []
1817 h m (x:xs) = bind m x $ \y ->
1818 bind m (h m xs) $ \ys ->
1825 In the function <function>h</function> we use the record selectors <literal>return</literal>
1826 and <literal>bind</literal> to extract the polymorphic bind and return functions
1827 from the <literal>MonadT</literal> data structure, rather than using pattern
1833 <title>Type inference</title>
1836 In general, type inference for arbitrary-rank types is undecideable.
1837 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1838 to get a decidable algorithm by requiring some help from the programmer.
1839 We do not yet have a formal specification of "some help" but the rule is this:
1842 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1843 provides an explicit polymorphic type for x, or GHC's type inference will assume
1844 that x's type has no foralls in it</emphasis>.
1847 What does it mean to "provide" an explicit type for x? You can do that by
1848 giving a type signature for x directly, using a pattern type signature
1849 (<xref linkend="scoped-type-variables">), thus:
1851 \ f :: (forall a. a->a) -> (f True, f 'c')
1853 Alternatively, you can give a type signature to the enclosing
1854 context, which GHC can "push down" to find the type for the variable:
1856 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1858 Here the type signature on the expression can be pushed inwards
1859 to give a type signature for f. Similarly, and more commonly,
1860 one can give a type signature for the function itself:
1862 h :: (forall a. a->a) -> (Bool,Char)
1863 h f = (f True, f 'c')
1865 You don't need to give a type signature if the lambda bound variable
1866 is a constructor argument. Here is an example we saw earlier:
1868 f :: T a -> a -> (a, Char)
1869 f (T1 w k) x = (w k x, w 'c' 'd')
1871 Here we do not need to give a type signature to <literal>w</literal>, because
1872 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1879 <sect3 id="implicit-quant">
1880 <title>Implicit quantification</title>
1883 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1884 user-written types, if and only if there is no explicit <literal>forall</literal>,
1885 GHC finds all the type variables mentioned in the type that are not already
1886 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1890 f :: forall a. a -> a
1897 h :: forall b. a -> b -> b
1903 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1906 f :: (a -> a) -> Int
1908 f :: forall a. (a -> a) -> Int
1910 f :: (forall a. a -> a) -> Int
1913 g :: (Ord a => a -> a) -> Int
1914 -- MEANS the illegal type
1915 g :: forall a. (Ord a => a -> a) -> Int
1917 g :: (forall a. Ord a => a -> a) -> Int
1919 The latter produces an illegal type, which you might think is silly,
1920 but at least the rule is simple. If you want the latter type, you
1921 can write your for-alls explicitly. Indeed, doing so is strongly advised
1927 <sect2 id="type-synonyms">
1928 <title>Liberalised type synonyms
1932 Type synonmys are like macros at the type level, and
1933 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1934 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1936 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1937 in a type synonym, thus:
1939 type Discard a = forall b. Show b => a -> b -> (a, String)
1944 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1951 You can write an unboxed tuple in a type synonym:
1953 type Pr = (# Int, Int #)
1961 You can apply a type synonym to a forall type:
1963 type Foo a = a -> a -> Bool
1965 f :: Foo (forall b. b->b)
1967 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1969 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1974 You can apply a type synonym to a partially applied type synonym:
1976 type Generic i o = forall x. i x -> o x
1979 foo :: Generic Id []
1981 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1983 foo :: forall x. x -> [x]
1991 GHC currently does kind checking before expanding synonyms (though even that
1995 After expanding type synonyms, GHC does validity checking on types, looking for
1996 the following mal-formedness which isn't detected simply by kind checking:
1999 Type constructor applied to a type involving for-alls.
2002 Unboxed tuple on left of an arrow.
2005 Partially-applied type synonym.
2009 this will be rejected:
2011 type Pr = (# Int, Int #)
2016 because GHC does not allow unboxed tuples on the left of a function arrow.
2021 <title>For-all hoisting</title>
2023 It is often convenient to use generalised type synonyms at the right hand
2024 end of an arrow, thus:
2026 type Discard a = forall b. a -> b -> a
2028 g :: Int -> Discard Int
2031 Simply expanding the type synonym would give
2033 g :: Int -> (forall b. Int -> b -> Int)
2035 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2037 g :: forall b. Int -> Int -> b -> Int
2039 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2040 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2041 performs the transformation:</emphasis>
2043 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2045 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2047 (In fact, GHC tries to retain as much synonym information as possible for use in
2048 error messages, but that is a usability issue.) This rule applies, of course, whether
2049 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2050 valid way to write <literal>g</literal>'s type signature:
2052 g :: Int -> Int -> forall b. b -> Int
2056 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2059 type Foo a = (?x::Int) => Bool -> a
2064 g :: (?x::Int) => Bool -> Bool -> Int
2070 <sect2 id="existential-quantification">
2071 <title>Existentially quantified data constructors
2075 The idea of using existential quantification in data type declarations
2076 was suggested by Laufer (I believe, thought doubtless someone will
2077 correct me), and implemented in Hope+. It's been in Lennart
2078 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2079 proved very useful. Here's the idea. Consider the declaration:
2085 data Foo = forall a. MkFoo a (a -> Bool)
2092 The data type <literal>Foo</literal> has two constructors with types:
2098 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2105 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2106 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2107 For example, the following expression is fine:
2113 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2119 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2120 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2121 isUpper</function> packages a character with a compatible function. These
2122 two things are each of type <literal>Foo</literal> and can be put in a list.
2126 What can we do with a value of type <literal>Foo</literal>?. In particular,
2127 what happens when we pattern-match on <function>MkFoo</function>?
2133 f (MkFoo val fn) = ???
2139 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2140 are compatible, the only (useful) thing we can do with them is to
2141 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2148 f (MkFoo val fn) = fn val
2154 What this allows us to do is to package heterogenous values
2155 together with a bunch of functions that manipulate them, and then treat
2156 that collection of packages in a uniform manner. You can express
2157 quite a bit of object-oriented-like programming this way.
2160 <sect3 id="existential">
2161 <title>Why existential?
2165 What has this to do with <emphasis>existential</emphasis> quantification?
2166 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2172 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2178 But Haskell programmers can safely think of the ordinary
2179 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2180 adding a new existential quantification construct.
2186 <title>Type classes</title>
2189 An easy extension (implemented in <Command>hbc</Command>) is to allow
2190 arbitrary contexts before the constructor. For example:
2196 data Baz = forall a. Eq a => Baz1 a a
2197 | forall b. Show b => Baz2 b (b -> b)
2203 The two constructors have the types you'd expect:
2209 Baz1 :: forall a. Eq a => a -> a -> Baz
2210 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2216 But when pattern matching on <function>Baz1</function> the matched values can be compared
2217 for equality, and when pattern matching on <function>Baz2</function> the first matched
2218 value can be converted to a string (as well as applying the function to it).
2219 So this program is legal:
2226 f (Baz1 p q) | p == q = "Yes"
2228 f (Baz2 v fn) = show (fn v)
2234 Operationally, in a dictionary-passing implementation, the
2235 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2236 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2237 extract it on pattern matching.
2241 Notice the way that the syntax fits smoothly with that used for
2242 universal quantification earlier.
2248 <title>Restrictions</title>
2251 There are several restrictions on the ways in which existentially-quantified
2252 constructors can be use.
2261 When pattern matching, each pattern match introduces a new,
2262 distinct, type for each existential type variable. These types cannot
2263 be unified with any other type, nor can they escape from the scope of
2264 the pattern match. For example, these fragments are incorrect:
2272 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2273 is the result of <function>f1</function>. One way to see why this is wrong is to
2274 ask what type <function>f1</function> has:
2278 f1 :: Foo -> a -- Weird!
2282 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2287 f1 :: forall a. Foo -> a -- Wrong!
2291 The original program is just plain wrong. Here's another sort of error
2295 f2 (Baz1 a b) (Baz1 p q) = a==q
2299 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2300 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2301 from the two <function>Baz1</function> constructors.
2309 You can't pattern-match on an existentially quantified
2310 constructor in a <literal>let</literal> or <literal>where</literal> group of
2311 bindings. So this is illegal:
2315 f3 x = a==b where { Baz1 a b = x }
2318 Instead, use a <literal>case</literal> expression:
2321 f3 x = case x of Baz1 a b -> a==b
2324 In general, you can only pattern-match
2325 on an existentially-quantified constructor in a <literal>case</literal> expression or
2326 in the patterns of a function definition.
2328 The reason for this restriction is really an implementation one.
2329 Type-checking binding groups is already a nightmare without
2330 existentials complicating the picture. Also an existential pattern
2331 binding at the top level of a module doesn't make sense, because it's
2332 not clear how to prevent the existentially-quantified type "escaping".
2333 So for now, there's a simple-to-state restriction. We'll see how
2341 You can't use existential quantification for <literal>newtype</literal>
2342 declarations. So this is illegal:
2346 newtype T = forall a. Ord a => MkT a
2350 Reason: a value of type <literal>T</literal> must be represented as a pair
2351 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2352 That contradicts the idea that <literal>newtype</literal> should have no
2353 concrete representation. You can get just the same efficiency and effect
2354 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2355 overloading involved, then there is more of a case for allowing
2356 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2357 because the <literal>data</literal> version does carry an implementation cost,
2358 but single-field existentially quantified constructors aren't much
2359 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2360 stands, unless there are convincing reasons to change it.
2368 You can't use <literal>deriving</literal> to define instances of a
2369 data type with existentially quantified data constructors.
2371 Reason: in most cases it would not make sense. For example:#
2374 data T = forall a. MkT [a] deriving( Eq )
2377 To derive <literal>Eq</literal> in the standard way we would need to have equality
2378 between the single component of two <function>MkT</function> constructors:
2382 (MkT a) == (MkT b) = ???
2385 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2386 It's just about possible to imagine examples in which the derived instance
2387 would make sense, but it seems altogether simpler simply to prohibit such
2388 declarations. Define your own instances!
2400 <sect2 id="scoped-type-variables">
2401 <title>Scoped type variables
2405 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2406 variable</emphasis>. For example
2412 f (xs::[a]) = ys ++ ys
2421 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2422 This brings the type variable <literal>a</literal> into scope; it scopes over
2423 all the patterns and right hand sides for this equation for <function>f</function>.
2424 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2428 Pattern type signatures are completely orthogonal to ordinary, separate
2429 type signatures. The two can be used independently or together.
2430 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2431 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2432 implicitly universally quantified. (If there are no type variables in
2433 scope, all type variables mentioned in the signature are universally
2434 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2435 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2436 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2437 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2438 it becomes possible to do so.
2442 Scoped type variables are implemented in both GHC and Hugs. Where the
2443 implementations differ from the specification below, those differences
2448 So much for the basic idea. Here are the details.
2452 <title>What a pattern type signature means</title>
2454 A type variable brought into scope by a pattern type signature is simply
2455 the name for a type. The restriction they express is that all occurrences
2456 of the same name mean the same type. For example:
2458 f :: [Int] -> Int -> Int
2459 f (xs::[a]) (y::a) = (head xs + y) :: a
2461 The pattern type signatures on the left hand side of
2462 <literal>f</literal> express the fact that <literal>xs</literal>
2463 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2464 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2465 specifies that this expression must have the same type <literal>a</literal>.
2466 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2467 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2468 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2469 rules, which specified that a pattern-bound type variable should be universally quantified.)
2470 For example, all of these are legal:</para>
2473 t (x::a) (y::a) = x+y*2
2475 f (x::a) (y::b) = [x,y] -- a unifies with b
2477 g (x::a) = x + 1::Int -- a unifies with Int
2479 h x = let k (y::a) = [x,y] -- a is free in the
2480 in k x -- environment
2482 k (x::a) True = ... -- a unifies with Int
2483 k (x::Int) False = ...
2486 w (x::a) = x -- a unifies with [b]
2492 <title>Scope and implicit quantification</title>
2500 All the type variables mentioned in a pattern,
2501 that are not already in scope,
2502 are brought into scope by the pattern. We describe this set as
2503 the <emphasis>type variables bound by the pattern</emphasis>.
2506 f (x::a) = let g (y::(a,b)) = fst y
2510 The pattern <literal>(x::a)</literal> brings the type variable
2511 <literal>a</literal> into scope, as well as the term
2512 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2513 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2514 and brings into scope the type variable <literal>b</literal>.
2520 The type variable(s) bound by the pattern have the same scope
2521 as the term variable(s) bound by the pattern. For example:
2524 f (x::a) = <...rhs of f...>
2525 (p::b, q::b) = (1,2)
2526 in <...body of let...>
2528 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2529 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2530 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2531 just like <literal>p</literal> and <literal>q</literal> do.
2532 Indeed, the newly bound type variables also scope over any ordinary, separate
2533 type signatures in the <literal>let</literal> group.
2540 The type variables bound by the pattern may be
2541 mentioned in ordinary type signatures or pattern
2542 type signatures anywhere within their scope.
2549 In ordinary type signatures, any type variable mentioned in the
2550 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2558 Ordinary type signatures do not bring any new type variables
2559 into scope (except in the type signature itself!). So this is illegal:
2566 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2567 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2568 and that is an incorrect typing.
2575 The pattern type signature is a monotype:
2580 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2584 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2585 not to type schemes.
2589 There is no implicit universal quantification on pattern type signatures (in contrast to
2590 ordinary type signatures).
2600 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2601 scope over the methods defined in the <literal>where</literal> part. For example:
2615 (Not implemented in Hugs yet, Dec 98).
2626 <title>Result type signatures</title>
2634 The result type of a function can be given a signature,
2639 f (x::a) :: [a] = [x,x,x]
2643 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2644 result type. Sometimes this is the only way of naming the type variable
2649 f :: Int -> [a] -> [a]
2650 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2651 in \xs -> map g (reverse xs `zip` xs)
2663 Result type signatures are not yet implemented in Hugs.
2669 <title>Where a pattern type signature can occur</title>
2672 A pattern type signature can occur in any pattern. For example:
2677 A pattern type signature can be on an arbitrary sub-pattern, not
2682 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2691 Pattern type signatures, including the result part, can be used
2692 in lambda abstractions:
2695 (\ (x::a, y) :: a -> x)
2702 Pattern type signatures, including the result part, can be used
2703 in <literal>case</literal> expressions:
2707 case e of { (x::a, y) :: a -> x }
2715 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2716 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2717 token or a parenthesised type of some sort). To see why,
2718 consider how one would parse this:
2732 Pattern type signatures can bind existential type variables.
2737 data T = forall a. MkT [a]
2740 f (MkT [t::a]) = MkT t3
2753 Pattern type signatures
2754 can be used in pattern bindings:
2757 f x = let (y, z::a) = x in ...
2758 f1 x = let (y, z::Int) = x in ...
2759 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2760 f3 :: (b->b) = \x -> x
2763 In all such cases, the binding is not generalised over the pattern-bound
2764 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2765 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2766 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2767 In contrast, the binding
2772 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2773 in <literal>f4</literal>'s scope.
2783 <sect2 id="newtype-deriving">
2784 <title>Generalised derived instances for newtypes</title>
2787 When you define an abstract type using <literal>newtype</literal>, you may want
2788 the new type to inherit some instances from its representation. In
2789 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2790 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2791 other classes you have to write an explicit instance declaration. For
2792 example, if you define
2795 newtype Dollars = Dollars Int
2798 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2799 explicitly define an instance of <literal>Num</literal>:
2802 instance Num Dollars where
2803 Dollars a + Dollars b = Dollars (a+b)
2806 All the instance does is apply and remove the <literal>newtype</literal>
2807 constructor. It is particularly galling that, since the constructor
2808 doesn't appear at run-time, this instance declaration defines a
2809 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2810 dictionary, only slower!
2814 <sect3> <title> Generalising the deriving clause </title>
2816 GHC now permits such instances to be derived instead, so one can write
2818 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2821 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2822 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2823 derives an instance declaration of the form
2826 instance Num Int => Num Dollars
2829 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2833 We can also derive instances of constructor classes in a similar
2834 way. For example, suppose we have implemented state and failure monad
2835 transformers, such that
2838 instance Monad m => Monad (State s m)
2839 instance Monad m => Monad (Failure m)
2841 In Haskell 98, we can define a parsing monad by
2843 type Parser tok m a = State [tok] (Failure m) a
2846 which is automatically a monad thanks to the instance declarations
2847 above. With the extension, we can make the parser type abstract,
2848 without needing to write an instance of class <literal>Monad</literal>, via
2851 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2854 In this case the derived instance declaration is of the form
2856 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2859 Notice that, since <literal>Monad</literal> is a constructor class, the
2860 instance is a <emphasis>partial application</emphasis> of the new type, not the
2861 entire left hand side. We can imagine that the type declaration is
2862 ``eta-converted'' to generate the context of the instance
2867 We can even derive instances of multi-parameter classes, provided the
2868 newtype is the last class parameter. In this case, a ``partial
2869 application'' of the class appears in the <literal>deriving</literal>
2870 clause. For example, given the class
2873 class StateMonad s m | m -> s where ...
2874 instance Monad m => StateMonad s (State s m) where ...
2876 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2878 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2879 deriving (Monad, StateMonad [tok])
2882 The derived instance is obtained by completing the application of the
2883 class to the new type:
2886 instance StateMonad [tok] (State [tok] (Failure m)) =>
2887 StateMonad [tok] (Parser tok m)
2892 As a result of this extension, all derived instances in newtype
2893 declarations are treated uniformly (and implemented just by reusing
2894 the dictionary for the representation type), <emphasis>except</emphasis>
2895 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2896 the newtype and its representation.
2900 <sect3> <title> A more precise specification </title>
2902 Derived instance declarations are constructed as follows. Consider the
2903 declaration (after expansion of any type synonyms)
2906 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
2909 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
2911 <literal>vk+1...vn</literal> are type variables which do not occur in any of
2912 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
2913 classes of the form <literal>C t1'...tj'</literal>. The derived instance
2914 declarations are, for each <literal>ci</literal>,
2917 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
2919 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
2920 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
2924 As an example which does <emphasis>not</emphasis> work, consider
2926 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2928 Here we cannot derive the instance
2930 instance Monad (State s m) => Monad (NonMonad m)
2933 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2934 and so cannot be "eta-converted" away. It is a good thing that this
2935 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2936 not, in fact, a monad --- for the same reason. Try defining
2937 <literal>>>=</literal> with the correct type: you won't be able to.
2941 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2942 important, since we can only derive instances for the last one. If the
2943 <literal>StateMonad</literal> class above were instead defined as
2946 class StateMonad m s | m -> s where ...
2949 then we would not have been able to derive an instance for the
2950 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2951 classes usually have one "main" parameter for which deriving new
2952 instances is most interesting.
2960 <!-- ==================== End of type system extensions ================= -->
2962 <!-- ====================== TEMPLATE HASKELL ======================= -->
2964 <sect1 id="template-haskell">
2965 <title>Template Haskell</title>
2967 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
2968 the main technical innovations are discussed in "<ulink
2969 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
2970 Template Meta-programming for Haskell</ulink>", in
2971 Proc Haskell Workshop 2002.
2975 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
2976 Tim Sheard is going to expand it.)
2979 <sect2> <title> Syntax </title>
2981 Template Haskell has the following new syntactic constructions. You need to use the flag
2982 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
2986 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
2987 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
2988 There must be no space between the "$" and the identifier or parenthesis. This use
2989 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
2990 of "." as an infix operator. If you want the infix operator, put spaces around it.
2992 <para> A splice can occur in place of
2994 <listitem><para> an expression;</para></listitem>
2995 <listitem><para> a list of top-level declarations;</para></listitem>
2996 <listitem><para> a pattern;</para></listitem>
2997 <listitem><para> a type;</para></listitem>
3003 A expression quotation is written in Oxford brackets, thus:
3005 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;</para></listitem>
3006 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;</para></listitem>
3007 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;</para></listitem>
3008 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;</para></listitem>
3009 </itemizedlist></para></listitem>
3012 Reification is written thus:
3014 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3015 has type <literal>Dec</literal>. </para></listitem>
3016 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3017 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3018 <listitem><para> Still to come: fixities </para></listitem>
3020 </itemizedlist></para>
3028 <sect2> <title> Using Template Haskell </title>
3032 The data types and monadic constructor functions for Template Haskell are in the library
3033 <literal>Language.Haskell.THSyntax</literal>.
3037 If the module contains any top-level splices that must be run, you must use GHC with
3038 <literal>--make</literal> or <literal>--interactive</literal> flags. (Reason: that
3039 means it walks the dependency tree and knows what modules must be linked etc.)
3043 You can only run a function at compile time if it is imported from another module. That is,
3044 you can't define a function in a module, and call it from within a splice in the same module.
3045 (It would make sense to do so, but it's hard to implement.)
3049 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3057 <!-- ==================== ASSERTIONS ================= -->
3059 <sect1 id="sec-assertions">
3061 <indexterm><primary>Assertions</primary></indexterm>
3065 If you want to make use of assertions in your standard Haskell code, you
3066 could define a function like the following:
3072 assert :: Bool -> a -> a
3073 assert False x = error "assertion failed!"
3080 which works, but gives you back a less than useful error message --
3081 an assertion failed, but which and where?
3085 One way out is to define an extended <function>assert</function> function which also
3086 takes a descriptive string to include in the error message and
3087 perhaps combine this with the use of a pre-processor which inserts
3088 the source location where <function>assert</function> was used.
3092 Ghc offers a helping hand here, doing all of this for you. For every
3093 use of <function>assert</function> in the user's source:
3099 kelvinToC :: Double -> Double
3100 kelvinToC k = assert (k >= 0.0) (k+273.15)
3106 Ghc will rewrite this to also include the source location where the
3113 assert pred val ==> assertError "Main.hs|15" pred val
3119 The rewrite is only performed by the compiler when it spots
3120 applications of <function>Control.Exception.assert</function>, so you
3121 can still define and use your own versions of
3122 <function>assert</function>, should you so wish. If not, import
3123 <literal>Control.Exception</literal> to make use
3124 <function>assert</function> in your code.
3128 To have the compiler ignore uses of assert, use the compiler option
3129 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3130 option</primary></indexterm> That is, expressions of the form
3131 <literal>assert pred e</literal> will be rewritten to
3132 <literal>e</literal>.
3136 Assertion failures can be caught, see the documentation for the
3137 <literal>Control.Exception</literal> library for the details.
3143 <!-- =============================== PRAGMAS =========================== -->
3145 <sect1 id="pragmas">
3146 <title>Pragmas</title>
3148 <indexterm><primary>pragma</primary></indexterm>
3150 <para>GHC supports several pragmas, or instructions to the
3151 compiler placed in the source code. Pragmas don't normally affect
3152 the meaning of the program, but they might affect the efficiency
3153 of the generated code.</para>
3155 <para>Pragmas all take the form
3157 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3159 where <replaceable>word</replaceable> indicates the type of
3160 pragma, and is followed optionally by information specific to that
3161 type of pragma. Case is ignored in
3162 <replaceable>word</replaceable>. The various values for
3163 <replaceable>word</replaceable> that GHC understands are described
3164 in the following sections; any pragma encountered with an
3165 unrecognised <replaceable>word</replaceable> is (silently)
3168 <sect2 id="inline-pragma">
3169 <title>INLINE pragma
3171 <indexterm><primary>INLINE pragma</primary></indexterm>
3172 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
3175 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
3176 functions/values that are “small enough,” thus avoiding the call
3177 overhead and possibly exposing other more-wonderful optimisations.
3181 You will probably see these unfoldings (in Core syntax) in your
3186 Normally, if GHC decides a function is “too expensive” to inline, it
3187 will not do so, nor will it export that unfolding for other modules to
3192 The sledgehammer you can bring to bear is the
3193 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
3196 key_function :: Int -> String -> (Bool, Double)
3198 #ifdef __GLASGOW_HASKELL__
3199 {-# INLINE key_function #-}
3203 (You don't need to do the C pre-processor carry-on unless you're going
3204 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
3208 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
3209 “cost” to be very low. The normal unfolding machinery will then be
3210 very keen to inline it.
3214 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
3215 signature could be put.
3219 <literal>INLINE</literal> pragmas are a particularly good idea for the
3220 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
3221 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
3224 #ifdef __GLASGOW_HASKELL__
3225 {-# INLINE thenUs #-}
3226 {-# INLINE returnUs #-}
3234 <sect2 id="noinline-pragma">
3235 <title>NOINLINE pragma
3238 <indexterm><primary>NOINLINE pragma</primary></indexterm>
3239 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
3240 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
3241 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
3244 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
3245 it stops the named function from being inlined by the compiler. You
3246 shouldn't ever need to do this, unless you're very cautious about code
3250 <para><literal>NOTINLINE</literal> is a synonym for
3251 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
3252 by Haskell 98 as the standard way to disable inlining, so it should be
3253 used if you want your code to be portable).</para>
3257 <sect2 id="specialize-pragma">
3258 <title>SPECIALIZE pragma</title>
3260 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3261 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
3262 <indexterm><primary>overloading, death to</primary></indexterm>
3264 <para>(UK spelling also accepted.) For key overloaded
3265 functions, you can create extra versions (NB: more code space)
3266 specialised to particular types. Thus, if you have an
3267 overloaded function:</para>
3270 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3273 <para>If it is heavily used on lists with
3274 <literal>Widget</literal> keys, you could specialise it as
3278 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3281 <para>To get very fancy, you can also specify a named function
3282 to use for the specialised value, as in:</para>
3285 {-# RULES hammeredLookup = blah #-}
3288 <para>where <literal>blah</literal> is an implementation of
3289 <literal>hammerdLookup</literal> written specialy for
3290 <literal>Widget</literal> lookups. It's <emphasis>Your
3291 Responsibility</emphasis> to make sure that
3292 <function>blah</function> really behaves as a specialised
3293 version of <function>hammeredLookup</function>!!!</para>
3295 <para>Note we use the <literal>RULE</literal> pragma here to
3296 indicate that <literal>hammeredLookup</literal> applied at a
3297 certain type should be replaced by <literal>blah</literal>. See
3298 <xref linkend="rules"> for more information on
3299 <literal>RULES</literal>.</para>
3301 <para>An example in which using <literal>RULES</literal> for
3302 specialisation will Win Big:
3305 toDouble :: Real a => a -> Double
3306 toDouble = fromRational . toRational
3308 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
3309 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3312 The <function>i2d</function> function is virtually one machine
3313 instruction; the default conversion—via an intermediate
3314 <literal>Rational</literal>—is obscenely expensive by
3317 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3318 be put anywhere its type signature could be put.</para>
3322 <sect2 id="specialize-instance-pragma">
3323 <title>SPECIALIZE instance pragma
3327 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3328 <indexterm><primary>overloading, death to</primary></indexterm>
3329 Same idea, except for instance declarations. For example:
3332 instance (Eq a) => Eq (Foo a) where {
3333 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3337 The pragma must occur inside the <literal>where</literal> part
3338 of the instance declaration.
3341 Compatible with HBC, by the way, except perhaps in the placement
3347 <sect2 id="line-pragma">
3352 <indexterm><primary>LINE pragma</primary></indexterm>
3353 <indexterm><primary>pragma, LINE</primary></indexterm>
3357 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
3358 automatically generated Haskell code. It lets you specify the line
3359 number and filename of the original code; for example
3365 {-# LINE 42 "Foo.vhs" #-}
3371 if you'd generated the current file from something called <filename>Foo.vhs</filename>
3372 and this line corresponds to line 42 in the original. GHC will adjust
3373 its error messages to refer to the line/file named in the <literal>LINE</literal>
3380 <title>RULES pragma</title>
3383 The RULES pragma lets you specify rewrite rules. It is described in
3384 <xref LinkEnd="rewrite-rules">.
3389 <sect2 id="deprecated-pragma">
3390 <title>DEPRECATED pragma</title>
3393 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
3394 There are two forms.
3398 You can deprecate an entire module thus:</para>
3400 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3404 When you compile any module that import <literal>Wibble</literal>, GHC will print
3405 the specified message.</para>
3410 You can deprecate a function, class, or type, with the following top-level declaration:
3413 {-# DEPRECATED f, C, T "Don't use these" #-}
3416 When you compile any module that imports and uses any of the specifed entities,
3417 GHC will print the specified message.
3421 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
3427 <!-- ======================= REWRITE RULES ======================== -->
3429 <sect1 id="rewrite-rules">
3430 <title>Rewrite rules
3432 <indexterm><primary>RULES pagma</primary></indexterm>
3433 <indexterm><primary>pragma, RULES</primary></indexterm>
3434 <indexterm><primary>rewrite rules</primary></indexterm></title>
3437 The programmer can specify rewrite rules as part of the source program
3438 (in a pragma). GHC applies these rewrite rules wherever it can.
3446 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3453 <title>Syntax</title>
3456 From a syntactic point of view:
3462 Each rule has a name, enclosed in double quotes. The name itself has
3463 no significance at all. It is only used when reporting how many times the rule fired.
3469 There may be zero or more rules in a <literal>RULES</literal> pragma.
3475 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3476 is set, so you must lay out your rules starting in the same column as the
3477 enclosing definitions.
3483 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3484 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3485 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3486 by spaces, just like in a type <literal>forall</literal>.
3492 A pattern variable may optionally have a type signature.
3493 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3494 For example, here is the <literal>foldr/build</literal> rule:
3497 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3498 foldr k z (build g) = g k z
3501 Since <function>g</function> has a polymorphic type, it must have a type signature.
3508 The left hand side of a rule must consist of a top-level variable applied
3509 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3512 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3513 "wrong2" forall f. f True = True
3516 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3523 A rule does not need to be in the same module as (any of) the
3524 variables it mentions, though of course they need to be in scope.
3530 Rules are automatically exported from a module, just as instance declarations are.
3541 <title>Semantics</title>
3544 From a semantic point of view:
3550 Rules are only applied if you use the <option>-O</option> flag.
3556 Rules are regarded as left-to-right rewrite rules.
3557 When GHC finds an expression that is a substitution instance of the LHS
3558 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3559 By "a substitution instance" we mean that the LHS can be made equal to the
3560 expression by substituting for the pattern variables.
3567 The LHS and RHS of a rule are typechecked, and must have the
3575 GHC makes absolutely no attempt to verify that the LHS and RHS
3576 of a rule have the same meaning. That is undecideable in general, and
3577 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3584 GHC makes no attempt to make sure that the rules are confluent or
3585 terminating. For example:
3588 "loop" forall x,y. f x y = f y x
3591 This rule will cause the compiler to go into an infinite loop.
3598 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3604 GHC currently uses a very simple, syntactic, matching algorithm
3605 for matching a rule LHS with an expression. It seeks a substitution
3606 which makes the LHS and expression syntactically equal modulo alpha
3607 conversion. The pattern (rule), but not the expression, is eta-expanded if
3608 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3609 But not beta conversion (that's called higher-order matching).
3613 Matching is carried out on GHC's intermediate language, which includes
3614 type abstractions and applications. So a rule only matches if the
3615 types match too. See <xref LinkEnd="rule-spec"> below.
3621 GHC keeps trying to apply the rules as it optimises the program.
3622 For example, consider:
3631 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3632 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3633 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3634 not be substituted, and the rule would not fire.
3641 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3642 that appears on the LHS of a rule</emphasis>, because once you have substituted
3643 for something you can't match against it (given the simple minded
3644 matching). So if you write the rule
3647 "map/map" forall f,g. map f . map g = map (f.g)
3650 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3651 It will only match something written with explicit use of ".".
3652 Well, not quite. It <emphasis>will</emphasis> match the expression
3658 where <function>wibble</function> is defined:
3661 wibble f g = map f . map g
3664 because <function>wibble</function> will be inlined (it's small).
3666 Later on in compilation, GHC starts inlining even things on the
3667 LHS of rules, but still leaves the rules enabled. This inlining
3668 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3675 All rules are implicitly exported from the module, and are therefore
3676 in force in any module that imports the module that defined the rule, directly
3677 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3678 in force when compiling A.) The situation is very similar to that for instance
3690 <title>List fusion</title>
3693 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3694 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3695 intermediate list should be eliminated entirely.
3699 The following are good producers:
3711 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3717 Explicit lists (e.g. <literal>[True, False]</literal>)
3723 The cons constructor (e.g <literal>3:4:[]</literal>)
3729 <function>++</function>
3735 <function>map</function>
3741 <function>filter</function>
3747 <function>iterate</function>, <function>repeat</function>
3753 <function>zip</function>, <function>zipWith</function>
3762 The following are good consumers:
3774 <function>array</function> (on its second argument)
3780 <function>length</function>
3786 <function>++</function> (on its first argument)
3792 <function>foldr</function>
3798 <function>map</function>
3804 <function>filter</function>
3810 <function>concat</function>
3816 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3822 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3823 will fuse with one but not the other)
3829 <function>partition</function>
3835 <function>head</function>
3841 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3847 <function>sequence_</function>
3853 <function>msum</function>
3859 <function>sortBy</function>
3868 So, for example, the following should generate no intermediate lists:
3871 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3877 This list could readily be extended; if there are Prelude functions that you use
3878 a lot which are not included, please tell us.
3882 If you want to write your own good consumers or producers, look at the
3883 Prelude definitions of the above functions to see how to do so.
3888 <sect2 id="rule-spec">
3889 <title>Specialisation
3893 Rewrite rules can be used to get the same effect as a feature
3894 present in earlier version of GHC:
3897 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3900 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3901 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3902 specialising the original definition of <function>fromIntegral</function> the programmer is
3903 promising that it is safe to use <function>int8ToInt16</function> instead.
3907 This feature is no longer in GHC. But rewrite rules let you do the
3912 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3916 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3917 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3918 GHC adds the type and dictionary applications to get the typed rule
3921 forall (d1::Integral Int8) (d2::Num Int16) .
3922 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3926 this rule does not need to be in the same file as fromIntegral,
3927 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3928 have an original definition available to specialise).
3934 <title>Controlling what's going on</title>
3942 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3948 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3949 If you add <option>-dppr-debug</option> you get a more detailed listing.
3955 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3958 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3959 {-# INLINE build #-}
3963 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3964 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3965 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3966 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3973 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3974 see how to write rules that will do fusion and yet give an efficient
3975 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3987 <sect1 id="generic-classes">
3988 <title>Generic classes</title>
3990 <para>(Note: support for generic classes is currently broken in
3994 The ideas behind this extension are described in detail in "Derivable type classes",
3995 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3996 An example will give the idea:
4004 fromBin :: [Int] -> (a, [Int])
4006 toBin {| Unit |} Unit = []
4007 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4008 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4009 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4011 fromBin {| Unit |} bs = (Unit, bs)
4012 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4013 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4014 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4015 (y,bs'') = fromBin bs'
4018 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4019 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4020 which are defined thus in the library module <literal>Generics</literal>:
4024 data a :+: b = Inl a | Inr b
4025 data a :*: b = a :*: b
4028 Now you can make a data type into an instance of Bin like this:
4030 instance (Bin a, Bin b) => Bin (a,b)
4031 instance Bin a => Bin [a]
4033 That is, just leave off the "where" clasuse. Of course, you can put in the
4034 where clause and over-ride whichever methods you please.
4038 <title> Using generics </title>
4039 <para>To use generics you need to</para>
4042 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4043 <option>-fgenerics</option> (to generate extra per-data-type code),
4044 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4048 <para>Import the module <literal>Generics</literal> from the
4049 <literal>lang</literal> package. This import brings into
4050 scope the data types <literal>Unit</literal>,
4051 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4052 don't need this import if you don't mention these types
4053 explicitly; for example, if you are simply giving instance
4054 declarations.)</para>
4059 <sect2> <title> Changes wrt the paper </title>
4061 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4062 can be written infix (indeed, you can now use
4063 any operator starting in a colon as an infix type constructor). Also note that
4064 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4065 Finally, note that the syntax of the type patterns in the class declaration
4066 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4067 alone would ambiguous when they appear on right hand sides (an extension we
4068 anticipate wanting).
4072 <sect2> <title>Terminology and restrictions</title>
4074 Terminology. A "generic default method" in a class declaration
4075 is one that is defined using type patterns as above.
4076 A "polymorphic default method" is a default method defined as in Haskell 98.
4077 A "generic class declaration" is a class declaration with at least one
4078 generic default method.
4086 Alas, we do not yet implement the stuff about constructor names and
4093 A generic class can have only one parameter; you can't have a generic
4094 multi-parameter class.
4100 A default method must be defined entirely using type patterns, or entirely
4101 without. So this is illegal:
4104 op :: a -> (a, Bool)
4105 op {| Unit |} Unit = (Unit, True)
4108 However it is perfectly OK for some methods of a generic class to have
4109 generic default methods and others to have polymorphic default methods.
4115 The type variable(s) in the type pattern for a generic method declaration
4116 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:
4120 op {| p :*: q |} (x :*: y) = op (x :: p)
4128 The type patterns in a generic default method must take one of the forms:
4134 where "a" and "b" are type variables. Furthermore, all the type patterns for
4135 a single type constructor (<literal>:*:</literal>, say) must be identical; they
4136 must use the same type variables. So this is illegal:
4140 op {| a :+: b |} (Inl x) = True
4141 op {| p :+: q |} (Inr y) = False
4143 The type patterns must be identical, even in equations for different methods of the class.
4144 So this too is illegal:
4148 op1 {| a :*: b |} (x :*: y) = True
4151 op2 {| p :*: q |} (x :*: y) = False
4153 (The reason for this restriction is that we gather all the equations for a particular type consructor
4154 into a single generic instance declaration.)
4160 A generic method declaration must give a case for each of the three type constructors.
4166 The type for a generic method can be built only from:
4168 <listitem> <para> Function arrows </para> </listitem>
4169 <listitem> <para> Type variables </para> </listitem>
4170 <listitem> <para> Tuples </para> </listitem>
4171 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
4173 Here are some example type signatures for generic methods:
4176 op2 :: Bool -> (a,Bool)
4177 op3 :: [Int] -> a -> a
4180 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
4184 This restriction is an implementation restriction: we just havn't got around to
4185 implementing the necessary bidirectional maps over arbitrary type constructors.
4186 It would be relatively easy to add specific type constructors, such as Maybe and list,
4187 to the ones that are allowed.</para>
4192 In an instance declaration for a generic class, the idea is that the compiler
4193 will fill in the methods for you, based on the generic templates. However it can only
4198 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4203 No constructor of the instance type has unboxed fields.
4207 (Of course, these things can only arise if you are already using GHC extensions.)
4208 However, you can still give an instance declarations for types which break these rules,
4209 provided you give explicit code to override any generic default methods.
4217 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
4218 what the compiler does with generic declarations.
4223 <sect2> <title> Another example </title>
4225 Just to finish with, here's another example I rather like:
4229 nCons {| Unit |} _ = 1
4230 nCons {| a :*: b |} _ = 1
4231 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4234 tag {| Unit |} _ = 1
4235 tag {| a :*: b |} _ = 1
4236 tag {| a :+: b |} (Inl x) = tag x
4237 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4246 ;;; Local Variables: ***
4248 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
projects / ghc-hetmet.git / blob