2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
6 <indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-fgenerics</option></term>
114 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
116 <para>See <xref LinkEnd="generic-classes">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fno-implicit-prelude</option></term>
124 <para><indexterm><primary>-fno-implicit-prelude
125 option</primary></indexterm> GHC normally imports
126 <filename>Prelude.hi</filename> files for you. If you'd
127 rather it didn't, then give it a
128 <option>-fno-implicit-prelude</option> option. The idea
129 is that you can then import a Prelude of your own. (But
130 don't call it <literal>Prelude</literal>; the Haskell
131 module namespace is flat, and you must not conflict with
132 any Prelude module.)</para>
134 <para>Even though you have not imported the Prelude, most of
135 the built-in syntax still refers to the built-in Haskell
136 Prelude types and values, as specified by the Haskell
137 Report. For example, the type <literal>[Int]</literal>
138 still means <literal>Prelude.[] Int</literal>; tuples
139 continue to refer to the standard Prelude tuples; the
140 translation for list comprehensions continues to use
141 <literal>Prelude.map</literal> etc.</para>
143 <para>However, <option>-fno-implicit-prelude</option> does
144 change the handling of certain built-in syntax: see
145 <xref LinkEnd="rebindable-syntax">.</para>
153 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
154 <!-- included from primitives.sgml -->
157 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
159 <sect1 id="syntax-extns">
160 <title>Syntactic extensions</title>
162 <!-- ====================== HIERARCHICAL MODULES ======================= -->
164 <sect2 id="hierarchical-modules">
165 <title>Hierarchical Modules</title>
167 <para>GHC supports a small extension to the syntax of module
168 names: a module name is allowed to contain a dot
169 <literal>‘.’</literal>. This is also known as the
170 “hierarchical module namespace” extension, because
171 it extends the normally flat Haskell module namespace into a
172 more flexible hierarchy of modules.</para>
174 <para>This extension has very little impact on the language
175 itself; modules names are <emphasis>always</emphasis> fully
176 qualified, so you can just think of the fully qualified module
177 name as <quote>the module name</quote>. In particular, this
178 means that the full module name must be given after the
179 <literal>module</literal> keyword at the beginning of the
180 module; for example, the module <literal>A.B.C</literal> must
183 <programlisting>module A.B.C</programlisting>
186 <para>It is a common strategy to use the <literal>as</literal>
187 keyword to save some typing when using qualified names with
188 hierarchical modules. For example:</para>
191 import qualified Control.Monad.ST.Strict as ST
194 <para>Hierarchical modules have an impact on the way that GHC
195 searches for files. For a description, see <xref
196 linkend="finding-hierarchical-modules">.</para>
198 <para>GHC comes with a large collection of libraries arranged
199 hierarchically; see the accompanying library documentation.
200 There is an ongoing project to create and maintain a stable set
201 of <quote>core</quote> libraries used by several Haskell
202 compilers, and the libraries that GHC comes with represent the
203 current status of that project. For more details, see <ulink
204 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
205 Libraries</ulink>.</para>
209 <!-- ====================== PATTERN GUARDS ======================= -->
211 <sect2 id="pattern-guards">
212 <title>Pattern guards</title>
215 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
216 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ULink URL="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ULink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
220 Suppose we have an abstract data type of finite maps, with a
224 lookup :: FiniteMap -> Int -> Maybe Int
227 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
228 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
232 clunky env var1 var2 | ok1 && ok2 = val1 + val2
233 | otherwise = var1 + var2
244 The auxiliary functions are
248 maybeToBool :: Maybe a -> Bool
249 maybeToBool (Just x) = True
250 maybeToBool Nothing = False
252 expectJust :: Maybe a -> a
253 expectJust (Just x) = x
254 expectJust Nothing = error "Unexpected Nothing"
258 What is <function>clunky</function> doing? The guard <literal>ok1 &&
259 ok2</literal> checks that both lookups succeed, using
260 <function>maybeToBool</function> to convert the <function>Maybe</function>
261 types to booleans. The (lazily evaluated) <function>expectJust</function>
262 calls extract the values from the results of the lookups, and binds the
263 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
264 respectively. If either lookup fails, then clunky takes the
265 <literal>otherwise</literal> case and returns the sum of its arguments.
269 This is certainly legal Haskell, but it is a tremendously verbose and
270 un-obvious way to achieve the desired effect. Arguably, a more direct way
271 to write clunky would be to use case expressions:
275 clunky env var1 var1 = case lookup env var1 of
277 Just val1 -> case lookup env var2 of
279 Just val2 -> val1 + val2
285 This is a bit shorter, but hardly better. Of course, we can rewrite any set
286 of pattern-matching, guarded equations as case expressions; that is
287 precisely what the compiler does when compiling equations! The reason that
288 Haskell provides guarded equations is because they allow us to write down
289 the cases we want to consider, one at a time, independently of each other.
290 This structure is hidden in the case version. Two of the right-hand sides
291 are really the same (<function>fail</function>), and the whole expression
292 tends to become more and more indented.
296 Here is how I would write clunky:
301 | Just val1 <- lookup env var1
302 , Just val2 <- lookup env var2
304 ...other equations for clunky...
308 The semantics should be clear enough. The qualifers are matched in order.
309 For a <literal><-</literal> qualifier, which I call a pattern guard, the
310 right hand side is evaluated and matched against the pattern on the left.
311 If the match fails then the whole guard fails and the next equation is
312 tried. If it succeeds, then the appropriate binding takes place, and the
313 next qualifier is matched, in the augmented environment. Unlike list
314 comprehensions, however, the type of the expression to the right of the
315 <literal><-</literal> is the same as the type of the pattern to its
316 left. The bindings introduced by pattern guards scope over all the
317 remaining guard qualifiers, and over the right hand side of the equation.
321 Just as with list comprehensions, boolean expressions can be freely mixed
322 with among the pattern guards. For example:
333 Haskell's current guards therefore emerge as a special case, in which the
334 qualifier list has just one element, a boolean expression.
338 <!-- ===================== Recursive do-notation =================== -->
340 <sect2 id="mdo-notation">
341 <title>The recursive do-notation
344 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
345 "A recursive do for Haskell",
346 Levent Erkok, John Launchbury",
347 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
350 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
351 that is, the variables bound in a do-expression are visible only in the textually following
352 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
353 group. It turns out that several applications can benefit from recursive bindings in
354 the do-notation, and this extension provides the necessary syntactic support.
357 Here is a simple (yet contrived) example:
360 justOnes = mdo xs <- Just (1:xs)
364 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
368 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
371 class Monad m => MonadFix m where
372 mfix :: (a -> m a) -> m a
375 The function <literal>mfix</literal>
376 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
377 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
378 For details, see the above mentioned reference.
381 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO, and
382 state monads (both lazy and strict).
385 There are three important points in using the recursive-do notation:
388 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
389 than <literal>do</literal>).
393 If you want to declare an instance of the <literal>MonadFix</literal> class for one of
394 your own monads, or you need to refer to the class name <literal>MonadFix</literal> in any other way (for
395 instance when writing a type constraint), then your program should
396 <literal>import Control.Monad.MonadFix</literal>.
397 Otherwise, you don't need to import any special libraries to use the mdo-notation. That is,
398 as long as you only use the predefined instances mentioned above, the mdo-notation will
399 be automatically available.
400 To be on the safe side, of course, you can simply import it in all cases.
404 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
410 Historical note: The old implementation of the mdo-notation (and most
411 of the existing documents) used the name
412 <literal>MonadRec</literal> for the class and the corresponding library.
413 This name is no longer supported.
417 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
418 contains up to date information on recursive monadic bindings.
424 <sect2> <title> Infix type constructors </title>
426 <para>GHC supports infix type constructors, much as it supports infix data constructors. For example:
430 data a :+: b = Inl a | Inr b
432 f :: a `Either` b -> a :+: b
437 syntax of an infix type constructor is just like that of an infix data constructor: either
438 it's an operator beginning with ":", or it is an ordinary (alphabetic) type constructor enclosed in
442 When you give a fixity declaration, the fixity applies to both the data constructor and the
443 type constructor with the specified name. You cannot give different fixities to the type constructor T
444 and the data constructor T.
450 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
452 <sect2 id="parallel-list-comprehensions">
453 <title>Parallel List Comprehensions</title>
454 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
456 <indexterm><primary>parallel list comprehensions</primary>
459 <para>Parallel list comprehensions are a natural extension to list
460 comprehensions. List comprehensions can be thought of as a nice
461 syntax for writing maps and filters. Parallel comprehensions
462 extend this to include the zipWith family.</para>
464 <para>A parallel list comprehension has multiple independent
465 branches of qualifier lists, each separated by a `|' symbol. For
466 example, the following zips together two lists:</para>
469 [ (x, y) | x <- xs | y <- ys ]
472 <para>The behavior of parallel list comprehensions follows that of
473 zip, in that the resulting list will have the same length as the
474 shortest branch.</para>
476 <para>We can define parallel list comprehensions by translation to
477 regular comprehensions. Here's the basic idea:</para>
479 <para>Given a parallel comprehension of the form: </para>
482 [ e | p1 <- e11, p2 <- e12, ...
483 | q1 <- e21, q2 <- e22, ...
488 <para>This will be translated to: </para>
491 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
492 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
497 <para>where `zipN' is the appropriate zip for the given number of
502 <sect2 id="rebindable-syntax">
503 <title>Rebindable syntax</title>
506 <para>GHC allows most kinds of built-in syntax to be rebound by
507 the user, to facilitate replacing the <literal>Prelude</literal>
508 with a home-grown version, for example.</para>
510 <para>You may want to define your own numeric class
511 hierarchy. It completely defeats that purpose if the
512 literal "1" means "<literal>Prelude.fromInteger
513 1</literal>", which is what the Haskell Report specifies.
514 So the <option>-fno-implicit-prelude</option> flag causes
515 the following pieces of built-in syntax to refer to
516 <emphasis>whatever is in scope</emphasis>, not the Prelude
521 <para>Integer and fractional literals mean
522 "<literal>fromInteger 1</literal>" and
523 "<literal>fromRational 3.2</literal>", not the
524 Prelude-qualified versions; both in expressions and in
526 <para>However, the standard Prelude <literal>Eq</literal> class
527 is still used for the equality test necessary for literal patterns.</para>
531 <para>Negation (e.g. "<literal>- (f x)</literal>")
532 means "<literal>negate (f x)</literal>" (not
533 <literal>Prelude.negate</literal>).</para>
537 <para>In an n+k pattern, the standard Prelude
538 <literal>Ord</literal> class is still used for comparison,
539 but the necessary subtraction uses whatever
540 "<literal>(-)</literal>" is in scope (not
541 "<literal>Prelude.(-)</literal>").</para>
545 <para>"Do" notation is translated using whatever
546 functions <literal>(>>=)</literal>,
547 <literal>(>>)</literal>, <literal>fail</literal>, and
548 <literal>return</literal>, are in scope (not the Prelude
549 versions). List comprehensions, and parallel array
550 comprehensions, are unaffected. </para></listitem>
553 <para>Be warned: this is an experimental facility, with fewer checks than
554 usual. In particular, it is essential that the functions GHC finds in scope
555 must have the appropriate types, namely:
557 fromInteger :: forall a. (...) => Integer -> a
558 fromRational :: forall a. (...) => Rational -> a
559 negate :: forall a. (...) => a -> a
560 (-) :: forall a. (...) => a -> a -> a
561 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
562 (>>) :: forall m a. (...) => m a -> m b -> m b
563 return :: forall m a. (...) => a -> m a
564 fail :: forall m a. (...) => String -> m a
566 (The (...) part can be any context including the empty context; that part
568 If the functions don't have the right type, very peculiar things may
569 happen. Use <literal>-dcore-lint</literal> to
570 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
576 <!-- TYPE SYSTEM EXTENSIONS -->
577 <sect1 id="type-extensions">
578 <title>Type system extensions</title>
580 <sect2 id="nullary-types">
581 <title>Data types with no constructors</title>
583 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
584 a data type with no constructors. For example:</para>
588 data T a -- T :: * -> *
591 <para>Syntactically, the declaration lacks the "= constrs" part. The
592 type can be parameterised over types of any kind, but if the kind is
593 not <literal>*</literal> then an explicit kind annotation must be used
594 (see <xref linkend="sec-kinding">).</para>
596 <para>Such data types have only one value, namely bottom.
597 Nevertheless, they can be useful when defining "phantom types".</para>
600 <sect2 id="infix-tycons">
601 <title>Infix type constructors</title>
604 GHC allows type constructors to be operators, and to be written infix, very much
605 like expressions. More specifically:
608 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
609 The lexical syntax is the same as that for data constructors.
612 Types can be written infix. For example <literal>Int :*: Bool</literal>.
616 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
617 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
620 Fixities may be declared for type constructors just as for data constructors. However,
621 one cannot distinguish between the two in a fixity declaration; a fixity declaration
622 sets the fixity for a data constructor and the corresponding type constructor. For example:
626 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
627 and similarly for <literal>:*:</literal>.
628 <literal>Int `a` Bool</literal>.
631 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
634 Data type and type-synonym declarations can be written infix. E.g.
636 data a :*: b = Foo a b
637 type a :+: b = Either a b
641 The only thing that differs between operators in types and operators in expressions is that
642 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
643 are not allowed in types. Reason: the uniform thing to do would be to make them type
644 variables, but that's not very useful. A less uniform but more useful thing would be to
645 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
646 lists. So for now we just exclude them.
653 <sect2 id="sec-kinding">
654 <title>Explicitly-kinded quantification</title>
657 Haskell infers the kind of each type variable. Sometimes it is nice to be able
658 to give the kind explicitly as (machine-checked) documentation,
659 just as it is nice to give a type signature for a function. On some occasions,
660 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
661 John Hughes had to define the data type:
663 data Set cxt a = Set [a]
664 | Unused (cxt a -> ())
666 The only use for the <literal>Unused</literal> constructor was to force the correct
667 kind for the type variable <literal>cxt</literal>.
670 GHC now instead allows you to specify the kind of a type variable directly, wherever
671 a type variable is explicitly bound. Namely:
673 <listitem><para><literal>data</literal> declarations:
675 data Set (cxt :: * -> *) a = Set [a]
676 </Screen></para></listitem>
677 <listitem><para><literal>type</literal> declarations:
679 type T (f :: * -> *) = f Int
680 </Screen></para></listitem>
681 <listitem><para><literal>class</literal> declarations:
683 class (Eq a) => C (f :: * -> *) a where ...
684 </Screen></para></listitem>
685 <listitem><para><literal>forall</literal>'s in type signatures:
687 f :: forall (cxt :: * -> *). Set cxt Int
688 </Screen></para></listitem>
693 The parentheses are required. Some of the spaces are required too, to
694 separate the lexemes. If you write <literal>(f::*->*)</literal> you
695 will get a parse error, because "<literal>::*->*</literal>" is a
696 single lexeme in Haskell.
700 As part of the same extension, you can put kind annotations in types
703 f :: (Int :: *) -> Int
704 g :: forall a. a -> (a :: *)
708 atype ::= '(' ctype '::' kind ')
710 The parentheses are required.
715 <sect2 id="class-method-types">
716 <title>Class method types
719 Haskell 98 prohibits class method types to mention constraints on the
720 class type variable, thus:
723 fromList :: [a] -> s a
724 elem :: Eq a => a -> s a -> Bool
726 The type of <literal>elem</literal> is illegal in Haskell 98, because it
727 contains the constraint <literal>Eq a</literal>, constrains only the
728 class type variable (in this case <literal>a</literal>).
731 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
736 <sect2 id="multi-param-type-classes">
737 <title>Multi-parameter type classes
741 This section documents GHC's implementation of multi-parameter type
742 classes. There's lots of background in the paper <ULink
743 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
744 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
749 I'd like to thank people who reported shorcomings in the GHC 3.02
750 implementation. Our default decisions were all conservative ones, and
751 the experience of these heroic pioneers has given useful concrete
752 examples to support several generalisations. (These appear below as
753 design choices not implemented in 3.02.)
757 I've discussed these notes with Mark Jones, and I believe that Hugs
758 will migrate towards the same design choices as I outline here.
759 Thanks to him, and to many others who have offered very useful
767 There are the following restrictions on the form of a qualified
774 forall tv1..tvn (c1, ...,cn) => type
780 (Here, I write the "foralls" explicitly, although the Haskell source
781 language omits them; in Haskell 1.4, all the free type variables of an
782 explicit source-language type signature are universally quantified,
783 except for the class type variables in a class declaration. However,
784 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
793 <emphasis>Each universally quantified type variable
794 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
796 The reason for this is that a value with a type that does not obey
797 this restriction could not be used without introducing
798 ambiguity. Here, for example, is an illegal type:
802 forall a. Eq a => Int
806 When a value with this type was used, the constraint <literal>Eq tv</literal>
807 would be introduced where <literal>tv</literal> is a fresh type variable, and
808 (in the dictionary-translation implementation) the value would be
809 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
810 can never know which instance of <literal>Eq</literal> to use because we never
811 get any more information about <literal>tv</literal>.
818 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
819 universally quantified type variables <literal>tvi</literal></emphasis>.
821 For example, this type is OK because <literal>C a b</literal> mentions the
822 universally quantified type variable <literal>b</literal>:
826 forall a. C a b => burble
830 The next type is illegal because the constraint <literal>Eq b</literal> does not
831 mention <literal>a</literal>:
835 forall a. Eq b => burble
839 The reason for this restriction is milder than the other one. The
840 excluded types are never useful or necessary (because the offending
841 context doesn't need to be witnessed at this point; it can be floated
842 out). Furthermore, floating them out increases sharing. Lastly,
843 excluding them is a conservative choice; it leaves a patch of
844 territory free in case we need it later.
854 These restrictions apply to all types, whether declared in a type signature
859 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
860 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
867 f :: Eq (m a) => [m a] -> [m a]
874 This choice recovers principal types, a property that Haskell 1.4 does not have.
880 <title>Class declarations</title>
888 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
892 class Collection c a where
893 union :: c a -> c a -> c a
904 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
905 of "acyclic" involves only the superclass relationships. For example,
911 op :: D b => a -> b -> b
914 class C a => D a where { ... }
918 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
919 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
920 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
927 <emphasis>There are no restrictions on the context in a class declaration
928 (which introduces superclasses), except that the class hierarchy must
929 be acyclic</emphasis>. So these class declarations are OK:
933 class Functor (m k) => FiniteMap m k where
936 class (Monad m, Monad (t m)) => Transform t m where
937 lift :: m a -> (t m) a
946 <emphasis>In the signature of a class operation, every constraint
947 must mention at least one type variable that is not a class type
954 class Collection c a where
955 mapC :: Collection c b => (a->b) -> c a -> c b
959 is OK because the constraint <literal>(Collection a b)</literal> mentions
960 <literal>b</literal>, even though it also mentions the class variable
961 <literal>a</literal>. On the other hand:
966 op :: Eq a => (a,b) -> (a,b)
970 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
971 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
972 example is easily fixed by moving the offending context up to the
977 class Eq a => C a where
982 A yet more relaxed rule would allow the context of a class-op signature
983 to mention only class type variables. However, that conflicts with
984 Rule 1(b) for types above.
991 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
992 the class type variables</emphasis>. For example:
998 insert :: s -> a -> s
1002 is not OK, because the type of <literal>empty</literal> doesn't mention
1003 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1004 types, and has the same motivation.
1006 Sometimes, offending class declarations exhibit misunderstandings. For
1007 example, <literal>Coll</literal> might be rewritten
1011 class Coll s a where
1013 insert :: s a -> a -> s a
1017 which makes the connection between the type of a collection of
1018 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1019 Occasionally this really doesn't work, in which case you can split the
1027 class CollE s => Coll s a where
1028 insert :: s -> a -> s
1041 <sect3 id="instance-decls">
1042 <title>Instance declarations</title>
1050 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1055 instance context1 => C type1 where ...
1056 instance context2 => C type2 where ...
1060 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1062 However, if you give the command line option
1063 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1064 option</primary></indexterm> then overlapping instance declarations are permitted.
1065 However, GHC arranges never to commit to using an instance declaration
1066 if another instance declaration also applies, either now or later.
1072 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1078 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1079 (but not identical to <literal>type1</literal>), or vice versa.
1083 Notice that these rules
1088 make it clear which instance decl to use
1089 (pick the most specific one that matches)
1096 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1097 Reason: you can pick which instance decl
1098 "matches" based on the type.
1103 However the rules are over-conservative. Two instance declarations can overlap,
1104 but it can still be clear in particular situations which to use. For example:
1106 instance C (Int,a) where ...
1107 instance C (a,Bool) where ...
1109 These are rejected by GHC's rules, but it is clear what to do when trying
1110 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1111 cannot apply. Yell if this restriction bites you.
1114 GHC is also conservative about committing to an overlapping instance. For example:
1116 class C a where { op :: a -> a }
1117 instance C [Int] where ...
1118 instance C a => C [a] where ...
1120 f :: C b => [b] -> [b]
1123 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1124 GHC does not commit to the second instance declaration, because in a paricular
1125 call of f, b might be instantiate to Int, so the first instance declaration
1126 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1127 GHC will instead silently pick the second instance, without complaining about
1128 the problem of subsequent instantiations.
1131 Regrettably, GHC doesn't guarantee to detect overlapping instance
1132 declarations if they appear in different modules. GHC can "see" the
1133 instance declarations in the transitive closure of all the modules
1134 imported by the one being compiled, so it can "see" all instance decls
1135 when it is compiling <literal>Main</literal>. However, it currently chooses not
1136 to look at ones that can't possibly be of use in the module currently
1137 being compiled, in the interests of efficiency. (Perhaps we should
1138 change that decision, at least for <literal>Main</literal>.)
1145 <emphasis>There are no restrictions on the type in an instance
1146 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1147 The instance "head" is the bit after the "=>" in an instance decl. For
1148 example, these are OK:
1152 instance C Int a where ...
1154 instance D (Int, Int) where ...
1156 instance E [[a]] where ...
1160 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1161 For example, this is OK:
1165 instance Stateful (ST s) (MutVar s) where ...
1169 The "at least one not a type variable" restriction is to ensure that
1170 context reduction terminates: each reduction step removes one type
1171 constructor. For example, the following would make the type checker
1172 loop if it wasn't excluded:
1176 instance C a => C a where ...
1180 There are two situations in which the rule is a bit of a pain. First,
1181 if one allows overlapping instance declarations then it's quite
1182 convenient to have a "default instance" declaration that applies if
1183 something more specific does not:
1192 Second, sometimes you might want to use the following to get the
1193 effect of a "class synonym":
1197 class (C1 a, C2 a, C3 a) => C a where { }
1199 instance (C1 a, C2 a, C3 a) => C a where { }
1203 This allows you to write shorter signatures:
1215 f :: (C1 a, C2 a, C3 a) => ...
1219 I'm on the lookout for a simple rule that preserves decidability while
1220 allowing these idioms. The experimental flag
1221 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1222 option</primary></indexterm> lifts this restriction, allowing all the types in an
1223 instance head to be type variables.
1230 <emphasis>Unlike Haskell 1.4, instance heads may use type
1231 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1232 writing the RHS of the type synonym definition. For example:
1236 type Point = (Int,Int)
1237 instance C Point where ...
1238 instance C [Point] where ...
1242 is legal. However, if you added
1246 instance C (Int,Int) where ...
1250 as well, then the compiler will complain about the overlapping
1251 (actually, identical) instance declarations. As always, type synonyms
1252 must be fully applied. You cannot, for example, write:
1257 instance Monad P where ...
1261 This design decision is independent of all the others, and easily
1262 reversed, but it makes sense to me.
1269 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1270 be type variables</emphasis>. Thus
1274 instance C a b => Eq (a,b) where ...
1282 instance C Int b => Foo b where ...
1286 is not OK. Again, the intent here is to make sure that context
1287 reduction terminates.
1289 Voluminous correspondence on the Haskell mailing list has convinced me
1290 that it's worth experimenting with a more liberal rule. If you use
1291 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1292 types in an instance context. Termination is ensured by having a
1293 fixed-depth recursion stack. If you exceed the stack depth you get a
1294 sort of backtrace, and the opportunity to increase the stack depth
1295 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1308 <sect2 id="implicit-parameters">
1309 <title>Implicit parameters
1312 <para> Implicit paramters are implemented as described in
1313 "Implicit parameters: dynamic scoping with static types",
1314 J Lewis, MB Shields, E Meijer, J Launchbury,
1315 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1318 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1320 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1321 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1322 context. In Haskell, all variables are statically bound. Dynamic
1323 binding of variables is a notion that goes back to Lisp, but was later
1324 discarded in more modern incarnations, such as Scheme. Dynamic binding
1325 can be very confusing in an untyped language, and unfortunately, typed
1326 languages, in particular Hindley-Milner typed languages like Haskell,
1327 only support static scoping of variables.
1330 However, by a simple extension to the type class system of Haskell, we
1331 can support dynamic binding. Basically, we express the use of a
1332 dynamically bound variable as a constraint on the type. These
1333 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1334 function uses a dynamically-bound variable <literal>?x</literal>
1335 of type <literal>t'</literal>". For
1336 example, the following expresses the type of a sort function,
1337 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1339 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1341 The dynamic binding constraints are just a new form of predicate in the type class system.
1344 An implicit parameter is introduced by the special form <literal>?x</literal>,
1345 where <literal>x</literal> is
1346 any valid identifier. Use if this construct also introduces new
1347 dynamic binding constraints. For example, the following definition
1348 shows how we can define an implicitly parameterized sort function in
1349 terms of an explicitly parameterized <literal>sortBy</literal> function:
1351 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1353 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1356 Dynamic binding constraints behave just like other type class
1357 constraints in that they are automatically propagated. Thus, when a
1358 function is used, its implicit parameters are inherited by the
1359 function that called it. For example, our <literal>sort</literal> function might be used
1360 to pick out the least value in a list:
1362 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1363 least xs = fst (sort xs)
1365 Without lifting a finger, the <literal>?cmp</literal> parameter is
1366 propagated to become a parameter of <literal>least</literal> as well. With explicit
1367 parameters, the default is that parameters must always be explicit
1368 propagated. With implicit parameters, the default is to always
1372 An implicit parameter differs from other type class constraints in the
1373 following way: All uses of a particular implicit parameter must have
1374 the same type. This means that the type of <literal>(?x, ?x)</literal>
1375 is <literal>(?x::a) => (a,a)</literal>, and not
1376 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1380 An implicit parameter is bound using the standard
1381 <literal>let</literal> binding form, where the bindings must be a
1382 collection of simple bindings to implicit-style variables (no
1383 function-style bindings, and no type signatures); these bindings are
1384 neither polymorphic or recursive. This form binds the implicit
1385 parameters arising in the body, not the free variables as a
1386 <literal>let</literal> or <literal>where</literal> would do. For
1387 example, we define the <literal>min</literal> function by binding
1388 <literal>cmp</literal>.</para>
1391 min = let ?cmp = (<=) in least
1394 Note the following points:
1397 You may not mix implicit-parameter bindings with ordinary bindings in a
1398 single <literal>let</literal>
1399 expression; use two nested <literal>let</literal>s instead.
1403 You may put multiple implicit-parameter bindings in a
1404 single <literal>let</literal> expression; they are <emphasis>not</emphasis> treated
1405 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1406 Instead they are treated as a non-recursive group, each scoping over the bindings that
1407 follow. For example, consider:
1409 f y = let { ?x = y; ?x = ?x+1 } in ?x
1411 This function adds one to its argument.
1415 You may not have an implicit-parameter binding in a <literal>where</literal> clause,
1416 only in a <literal>let</literal> binding.
1420 <para> You can't have an implicit parameter in the context of a class or instance
1421 declaration. For example, both these declarations are illegal:
1423 class (?x::Int) => C a where ...
1424 instance (?x::a) => Foo [a] where ...
1426 Reason: exactly which implicit parameter you pick up depends on exactly where
1427 you invoke a function. But the ``invocation'' of instance declarations is done
1428 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1429 Easiest thing is to outlaw the offending types.</para>
1436 <sect2 id="linear-implicit-parameters">
1437 <title>Linear implicit parameters
1440 Linear implicit parameters are an idea developed by Koen Claessen,
1441 Mark Shields, and Simon PJ. They address the long-standing
1442 problem that monads seem over-kill for certain sorts of problem, notably:
1445 <listitem> <para> distributing a supply of unique names </para> </listitem>
1446 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1447 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1451 Linear implicit parameters are just like ordinary implicit parameters,
1452 except that they are "linear" -- that is, they cannot be copied, and
1453 must be explicitly "split" instead. Linear implicit parameters are
1454 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1455 (The '/' in the '%' suggests the split!)
1460 import GHC.Exts( Splittable )
1462 data NameSupply = ...
1464 splitNS :: NameSupply -> (NameSupply, NameSupply)
1465 newName :: NameSupply -> Name
1467 instance Splittable NameSupply where
1471 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1472 f env (Lam x e) = Lam x' (f env e)
1475 env' = extend env x x'
1476 ...more equations for f...
1478 Notice that the implicit parameter %ns is consumed
1480 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1481 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1485 So the translation done by the type checker makes
1486 the parameter explicit:
1488 f :: NameSupply -> Env -> Expr -> Expr
1489 f ns env (Lam x e) = Lam x' (f ns1 env e)
1491 (ns1,ns2) = splitNS ns
1493 env = extend env x x'
1495 Notice the call to 'split' introduced by the type checker.
1496 How did it know to use 'splitNS'? Because what it really did
1497 was to introduce a call to the overloaded function 'split',
1498 defined by the class <literal>Splittable</literal>:
1500 class Splittable a where
1503 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1504 split for name supplies. But we can simply write
1510 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1512 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1513 <literal>GHC.Exts</literal>.
1518 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1519 are entirely distinct implicit parameters: you
1520 can use them together and they won't intefere with each other. </para>
1523 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1525 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1526 in the context of a class or instance declaration. </para></listitem>
1530 <sect3><title>Warnings</title>
1533 The monomorphism restriction is even more important than usual.
1534 Consider the example above:
1536 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1537 f env (Lam x e) = Lam x' (f env e)
1540 env' = extend env x x'
1542 If we replaced the two occurrences of x' by (newName %ns), which is
1543 usually a harmless thing to do, we get:
1545 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1546 f env (Lam x e) = Lam (newName %ns) (f env e)
1548 env' = extend env x (newName %ns)
1550 But now the name supply is consumed in <emphasis>three</emphasis> places
1551 (the two calls to newName,and the recursive call to f), so
1552 the result is utterly different. Urk! We don't even have
1556 Well, this is an experimental change. With implicit
1557 parameters we have already lost beta reduction anyway, and
1558 (as John Launchbury puts it) we can't sensibly reason about
1559 Haskell programs without knowing their typing.
1564 <sect3><title>Recursive functions</title>
1565 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1568 foo :: %x::T => Int -> [Int]
1570 foo n = %x : foo (n-1)
1572 where T is some type in class Splittable.</para>
1574 Do you get a list of all the same T's or all different T's
1575 (assuming that split gives two distinct T's back)?
1577 If you supply the type signature, taking advantage of polymorphic
1578 recursion, you get what you'd probably expect. Here's the
1579 translated term, where the implicit param is made explicit:
1582 foo x n = let (x1,x2) = split x
1583 in x1 : foo x2 (n-1)
1585 But if you don't supply a type signature, GHC uses the Hindley
1586 Milner trick of using a single monomorphic instance of the function
1587 for the recursive calls. That is what makes Hindley Milner type inference
1588 work. So the translation becomes
1592 foom n = x : foom (n-1)
1596 Result: 'x' is not split, and you get a list of identical T's. So the
1597 semantics of the program depends on whether or not foo has a type signature.
1600 You may say that this is a good reason to dislike linear implicit parameters
1601 and you'd be right. That is why they are an experimental feature.
1607 <sect2 id="functional-dependencies">
1608 <title>Functional dependencies
1611 <para> Functional dependencies are implemented as described by Mark Jones
1612 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1613 In Proceedings of the 9th European Symposium on Programming,
1614 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1619 There should be more documentation, but there isn't (yet). Yell if you need it.
1624 <sect2 id="universal-quantification">
1625 <title>Arbitrary-rank polymorphism
1629 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1630 allows us to say exactly what this means. For example:
1638 g :: forall b. (b -> b)
1640 The two are treated identically.
1644 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1645 explicit universal quantification in
1647 For example, all the following types are legal:
1649 f1 :: forall a b. a -> b -> a
1650 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1652 f2 :: (forall a. a->a) -> Int -> Int
1653 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1655 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1657 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1658 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1659 The <literal>forall</literal> makes explicit the universal quantification that
1660 is implicitly added by Haskell.
1663 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1664 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1665 shows, the polymorphic type on the left of the function arrow can be overloaded.
1668 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1669 they have rank-2 types on the left of a function arrow.
1672 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1673 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1674 that restriction has now been lifted.)
1675 In particular, a forall-type (also called a "type scheme"),
1676 including an operational type class context, is legal:
1678 <listitem> <para> On the left of a function arrow </para> </listitem>
1679 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1680 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1681 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1682 field type signatures.</para> </listitem>
1683 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1684 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1686 There is one place you cannot put a <literal>forall</literal>:
1687 you cannot instantiate a type variable with a forall-type. So you cannot
1688 make a forall-type the argument of a type constructor. So these types are illegal:
1690 x1 :: [forall a. a->a]
1691 x2 :: (forall a. a->a, Int)
1692 x3 :: Maybe (forall a. a->a)
1694 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1695 a type variable any more!
1704 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1705 the types of the constructor arguments. Here are several examples:
1711 data T a = T1 (forall b. b -> b -> b) a
1713 data MonadT m = MkMonad { return :: forall a. a -> m a,
1714 bind :: forall a b. m a -> (a -> m b) -> m b
1717 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1723 The constructors have rank-2 types:
1729 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1730 MkMonad :: forall m. (forall a. a -> m a)
1731 -> (forall a b. m a -> (a -> m b) -> m b)
1733 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1739 Notice that you don't need to use a <literal>forall</literal> if there's an
1740 explicit context. For example in the first argument of the
1741 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1742 prefixed to the argument type. The implicit <literal>forall</literal>
1743 quantifies all type variables that are not already in scope, and are
1744 mentioned in the type quantified over.
1748 As for type signatures, implicit quantification happens for non-overloaded
1749 types too. So if you write this:
1752 data T a = MkT (Either a b) (b -> b)
1755 it's just as if you had written this:
1758 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1761 That is, since the type variable <literal>b</literal> isn't in scope, it's
1762 implicitly universally quantified. (Arguably, it would be better
1763 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1764 where that is what is wanted. Feedback welcomed.)
1768 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1769 the constructor to suitable values, just as usual. For example,
1780 a3 = MkSwizzle reverse
1783 a4 = let r x = Just x
1790 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1791 mkTs f x y = [T1 f x, T1 f y]
1797 The type of the argument can, as usual, be more general than the type
1798 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1799 does not need the <literal>Ord</literal> constraint.)
1803 When you use pattern matching, the bound variables may now have
1804 polymorphic types. For example:
1810 f :: T a -> a -> (a, Char)
1811 f (T1 w k) x = (w k x, w 'c' 'd')
1813 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1814 g (MkSwizzle s) xs f = s (map f (s xs))
1816 h :: MonadT m -> [m a] -> m [a]
1817 h m [] = return m []
1818 h m (x:xs) = bind m x $ \y ->
1819 bind m (h m xs) $ \ys ->
1826 In the function <function>h</function> we use the record selectors <literal>return</literal>
1827 and <literal>bind</literal> to extract the polymorphic bind and return functions
1828 from the <literal>MonadT</literal> data structure, rather than using pattern
1834 <title>Type inference</title>
1837 In general, type inference for arbitrary-rank types is undecideable.
1838 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
1839 to get a decidable algorithm by requiring some help from the programmer.
1840 We do not yet have a formal specification of "some help" but the rule is this:
1843 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
1844 provides an explicit polymorphic type for x, or GHC's type inference will assume
1845 that x's type has no foralls in it</emphasis>.
1848 What does it mean to "provide" an explicit type for x? You can do that by
1849 giving a type signature for x directly, using a pattern type signature
1850 (<xref linkend="scoped-type-variables">), thus:
1852 \ f :: (forall a. a->a) -> (f True, f 'c')
1854 Alternatively, you can give a type signature to the enclosing
1855 context, which GHC can "push down" to find the type for the variable:
1857 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
1859 Here the type signature on the expression can be pushed inwards
1860 to give a type signature for f. Similarly, and more commonly,
1861 one can give a type signature for the function itself:
1863 h :: (forall a. a->a) -> (Bool,Char)
1864 h f = (f True, f 'c')
1866 You don't need to give a type signature if the lambda bound variable
1867 is a constructor argument. Here is an example we saw earlier:
1869 f :: T a -> a -> (a, Char)
1870 f (T1 w k) x = (w k x, w 'c' 'd')
1872 Here we do not need to give a type signature to <literal>w</literal>, because
1873 it is an argument of constructor <literal>T1</literal> and that tells GHC all
1880 <sect3 id="implicit-quant">
1881 <title>Implicit quantification</title>
1884 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
1885 user-written types, if and only if there is no explicit <literal>forall</literal>,
1886 GHC finds all the type variables mentioned in the type that are not already
1887 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
1891 f :: forall a. a -> a
1898 h :: forall b. a -> b -> b
1904 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
1907 f :: (a -> a) -> Int
1909 f :: forall a. (a -> a) -> Int
1911 f :: (forall a. a -> a) -> Int
1914 g :: (Ord a => a -> a) -> Int
1915 -- MEANS the illegal type
1916 g :: forall a. (Ord a => a -> a) -> Int
1918 g :: (forall a. Ord a => a -> a) -> Int
1920 The latter produces an illegal type, which you might think is silly,
1921 but at least the rule is simple. If you want the latter type, you
1922 can write your for-alls explicitly. Indeed, doing so is strongly advised
1928 <sect2 id="type-synonyms">
1929 <title>Liberalised type synonyms
1933 Type synonmys are like macros at the type level, and
1934 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
1935 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
1937 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
1938 in a type synonym, thus:
1940 type Discard a = forall b. Show b => a -> b -> (a, String)
1945 g :: Discard Int -> (Int,Bool) -- A rank-2 type
1952 You can write an unboxed tuple in a type synonym:
1954 type Pr = (# Int, Int #)
1962 You can apply a type synonym to a forall type:
1964 type Foo a = a -> a -> Bool
1966 f :: Foo (forall b. b->b)
1968 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
1970 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
1975 You can apply a type synonym to a partially applied type synonym:
1977 type Generic i o = forall x. i x -> o x
1980 foo :: Generic Id []
1982 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
1984 foo :: forall x. x -> [x]
1992 GHC currently does kind checking before expanding synonyms (though even that
1996 After expanding type synonyms, GHC does validity checking on types, looking for
1997 the following mal-formedness which isn't detected simply by kind checking:
2000 Type constructor applied to a type involving for-alls.
2003 Unboxed tuple on left of an arrow.
2006 Partially-applied type synonym.
2010 this will be rejected:
2012 type Pr = (# Int, Int #)
2017 because GHC does not allow unboxed tuples on the left of a function arrow.
2022 <title>For-all hoisting</title>
2024 It is often convenient to use generalised type synonyms at the right hand
2025 end of an arrow, thus:
2027 type Discard a = forall b. a -> b -> a
2029 g :: Int -> Discard Int
2032 Simply expanding the type synonym would give
2034 g :: Int -> (forall b. Int -> b -> Int)
2036 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2038 g :: forall b. Int -> Int -> b -> Int
2040 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2041 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2042 performs the transformation:</emphasis>
2044 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2046 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2048 (In fact, GHC tries to retain as much synonym information as possible for use in
2049 error messages, but that is a usability issue.) This rule applies, of course, whether
2050 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2051 valid way to write <literal>g</literal>'s type signature:
2053 g :: Int -> Int -> forall b. b -> Int
2057 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2060 type Foo a = (?x::Int) => Bool -> a
2065 g :: (?x::Int) => Bool -> Bool -> Int
2071 <sect2 id="existential-quantification">
2072 <title>Existentially quantified data constructors
2076 The idea of using existential quantification in data type declarations
2077 was suggested by Laufer (I believe, thought doubtless someone will
2078 correct me), and implemented in Hope+. It's been in Lennart
2079 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2080 proved very useful. Here's the idea. Consider the declaration:
2086 data Foo = forall a. MkFoo a (a -> Bool)
2093 The data type <literal>Foo</literal> has two constructors with types:
2099 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2106 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2107 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2108 For example, the following expression is fine:
2114 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2120 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2121 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2122 isUpper</function> packages a character with a compatible function. These
2123 two things are each of type <literal>Foo</literal> and can be put in a list.
2127 What can we do with a value of type <literal>Foo</literal>?. In particular,
2128 what happens when we pattern-match on <function>MkFoo</function>?
2134 f (MkFoo val fn) = ???
2140 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2141 are compatible, the only (useful) thing we can do with them is to
2142 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2149 f (MkFoo val fn) = fn val
2155 What this allows us to do is to package heterogenous values
2156 together with a bunch of functions that manipulate them, and then treat
2157 that collection of packages in a uniform manner. You can express
2158 quite a bit of object-oriented-like programming this way.
2161 <sect3 id="existential">
2162 <title>Why existential?
2166 What has this to do with <emphasis>existential</emphasis> quantification?
2167 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2173 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2179 But Haskell programmers can safely think of the ordinary
2180 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2181 adding a new existential quantification construct.
2187 <title>Type classes</title>
2190 An easy extension (implemented in <Command>hbc</Command>) is to allow
2191 arbitrary contexts before the constructor. For example:
2197 data Baz = forall a. Eq a => Baz1 a a
2198 | forall b. Show b => Baz2 b (b -> b)
2204 The two constructors have the types you'd expect:
2210 Baz1 :: forall a. Eq a => a -> a -> Baz
2211 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2217 But when pattern matching on <function>Baz1</function> the matched values can be compared
2218 for equality, and when pattern matching on <function>Baz2</function> the first matched
2219 value can be converted to a string (as well as applying the function to it).
2220 So this program is legal:
2227 f (Baz1 p q) | p == q = "Yes"
2229 f (Baz2 v fn) = show (fn v)
2235 Operationally, in a dictionary-passing implementation, the
2236 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2237 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2238 extract it on pattern matching.
2242 Notice the way that the syntax fits smoothly with that used for
2243 universal quantification earlier.
2249 <title>Restrictions</title>
2252 There are several restrictions on the ways in which existentially-quantified
2253 constructors can be use.
2262 When pattern matching, each pattern match introduces a new,
2263 distinct, type for each existential type variable. These types cannot
2264 be unified with any other type, nor can they escape from the scope of
2265 the pattern match. For example, these fragments are incorrect:
2273 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2274 is the result of <function>f1</function>. One way to see why this is wrong is to
2275 ask what type <function>f1</function> has:
2279 f1 :: Foo -> a -- Weird!
2283 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2288 f1 :: forall a. Foo -> a -- Wrong!
2292 The original program is just plain wrong. Here's another sort of error
2296 f2 (Baz1 a b) (Baz1 p q) = a==q
2300 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2301 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2302 from the two <function>Baz1</function> constructors.
2310 You can't pattern-match on an existentially quantified
2311 constructor in a <literal>let</literal> or <literal>where</literal> group of
2312 bindings. So this is illegal:
2316 f3 x = a==b where { Baz1 a b = x }
2319 Instead, use a <literal>case</literal> expression:
2322 f3 x = case x of Baz1 a b -> a==b
2325 In general, you can only pattern-match
2326 on an existentially-quantified constructor in a <literal>case</literal> expression or
2327 in the patterns of a function definition.
2329 The reason for this restriction is really an implementation one.
2330 Type-checking binding groups is already a nightmare without
2331 existentials complicating the picture. Also an existential pattern
2332 binding at the top level of a module doesn't make sense, because it's
2333 not clear how to prevent the existentially-quantified type "escaping".
2334 So for now, there's a simple-to-state restriction. We'll see how
2342 You can't use existential quantification for <literal>newtype</literal>
2343 declarations. So this is illegal:
2347 newtype T = forall a. Ord a => MkT a
2351 Reason: a value of type <literal>T</literal> must be represented as a pair
2352 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2353 That contradicts the idea that <literal>newtype</literal> should have no
2354 concrete representation. You can get just the same efficiency and effect
2355 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2356 overloading involved, then there is more of a case for allowing
2357 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2358 because the <literal>data</literal> version does carry an implementation cost,
2359 but single-field existentially quantified constructors aren't much
2360 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2361 stands, unless there are convincing reasons to change it.
2369 You can't use <literal>deriving</literal> to define instances of a
2370 data type with existentially quantified data constructors.
2372 Reason: in most cases it would not make sense. For example:#
2375 data T = forall a. MkT [a] deriving( Eq )
2378 To derive <literal>Eq</literal> in the standard way we would need to have equality
2379 between the single component of two <function>MkT</function> constructors:
2383 (MkT a) == (MkT b) = ???
2386 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2387 It's just about possible to imagine examples in which the derived instance
2388 would make sense, but it seems altogether simpler simply to prohibit such
2389 declarations. Define your own instances!
2401 <sect2 id="scoped-type-variables">
2402 <title>Scoped type variables
2406 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2407 variable</emphasis>. For example
2413 f (xs::[a]) = ys ++ ys
2422 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2423 This brings the type variable <literal>a</literal> into scope; it scopes over
2424 all the patterns and right hand sides for this equation for <function>f</function>.
2425 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2429 Pattern type signatures are completely orthogonal to ordinary, separate
2430 type signatures. The two can be used independently or together.
2431 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2432 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2433 implicitly universally quantified. (If there are no type variables in
2434 scope, all type variables mentioned in the signature are universally
2435 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2436 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2437 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2438 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2439 it becomes possible to do so.
2443 Scoped type variables are implemented in both GHC and Hugs. Where the
2444 implementations differ from the specification below, those differences
2449 So much for the basic idea. Here are the details.
2453 <title>What a pattern type signature means</title>
2455 A type variable brought into scope by a pattern type signature is simply
2456 the name for a type. The restriction they express is that all occurrences
2457 of the same name mean the same type. For example:
2459 f :: [Int] -> Int -> Int
2460 f (xs::[a]) (y::a) = (head xs + y) :: a
2462 The pattern type signatures on the left hand side of
2463 <literal>f</literal> express the fact that <literal>xs</literal>
2464 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2465 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2466 specifies that this expression must have the same type <literal>a</literal>.
2467 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2468 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2469 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2470 rules, which specified that a pattern-bound type variable should be universally quantified.)
2471 For example, all of these are legal:</para>
2474 t (x::a) (y::a) = x+y*2
2476 f (x::a) (y::b) = [x,y] -- a unifies with b
2478 g (x::a) = x + 1::Int -- a unifies with Int
2480 h x = let k (y::a) = [x,y] -- a is free in the
2481 in k x -- environment
2483 k (x::a) True = ... -- a unifies with Int
2484 k (x::Int) False = ...
2487 w (x::a) = x -- a unifies with [b]
2493 <title>Scope and implicit quantification</title>
2501 All the type variables mentioned in a pattern,
2502 that are not already in scope,
2503 are brought into scope by the pattern. We describe this set as
2504 the <emphasis>type variables bound by the pattern</emphasis>.
2507 f (x::a) = let g (y::(a,b)) = fst y
2511 The pattern <literal>(x::a)</literal> brings the type variable
2512 <literal>a</literal> into scope, as well as the term
2513 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2514 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2515 and brings into scope the type variable <literal>b</literal>.
2521 The type variable(s) bound by the pattern have the same scope
2522 as the term variable(s) bound by the pattern. For example:
2525 f (x::a) = <...rhs of f...>
2526 (p::b, q::b) = (1,2)
2527 in <...body of let...>
2529 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2530 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2531 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2532 just like <literal>p</literal> and <literal>q</literal> do.
2533 Indeed, the newly bound type variables also scope over any ordinary, separate
2534 type signatures in the <literal>let</literal> group.
2541 The type variables bound by the pattern may be
2542 mentioned in ordinary type signatures or pattern
2543 type signatures anywhere within their scope.
2550 In ordinary type signatures, any type variable mentioned in the
2551 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2559 Ordinary type signatures do not bring any new type variables
2560 into scope (except in the type signature itself!). So this is illegal:
2567 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2568 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2569 and that is an incorrect typing.
2576 The pattern type signature is a monotype:
2581 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2585 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2586 not to type schemes.
2590 There is no implicit universal quantification on pattern type signatures (in contrast to
2591 ordinary type signatures).
2601 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2602 scope over the methods defined in the <literal>where</literal> part. For example:
2616 (Not implemented in Hugs yet, Dec 98).
2627 <title>Result type signatures</title>
2635 The result type of a function can be given a signature,
2640 f (x::a) :: [a] = [x,x,x]
2644 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2645 result type. Sometimes this is the only way of naming the type variable
2650 f :: Int -> [a] -> [a]
2651 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2652 in \xs -> map g (reverse xs `zip` xs)
2664 Result type signatures are not yet implemented in Hugs.
2670 <title>Where a pattern type signature can occur</title>
2673 A pattern type signature can occur in any pattern. For example:
2678 A pattern type signature can be on an arbitrary sub-pattern, not
2683 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2692 Pattern type signatures, including the result part, can be used
2693 in lambda abstractions:
2696 (\ (x::a, y) :: a -> x)
2703 Pattern type signatures, including the result part, can be used
2704 in <literal>case</literal> expressions:
2708 case e of { (x::a, y) :: a -> x }
2716 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2717 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2718 token or a parenthesised type of some sort). To see why,
2719 consider how one would parse this:
2733 Pattern type signatures can bind existential type variables.
2738 data T = forall a. MkT [a]
2741 f (MkT [t::a]) = MkT t3
2754 Pattern type signatures
2755 can be used in pattern bindings:
2758 f x = let (y, z::a) = x in ...
2759 f1 x = let (y, z::Int) = x in ...
2760 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2761 f3 :: (b->b) = \x -> x
2764 In all such cases, the binding is not generalised over the pattern-bound
2765 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2766 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2767 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2768 In contrast, the binding
2773 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2774 in <literal>f4</literal>'s scope.
2784 <sect2 id="newtype-deriving">
2785 <title>Generalised derived instances for newtypes</title>
2788 When you define an abstract type using <literal>newtype</literal>, you may want
2789 the new type to inherit some instances from its representation. In
2790 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2791 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2792 other classes you have to write an explicit instance declaration. For
2793 example, if you define
2796 newtype Dollars = Dollars Int
2799 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2800 explicitly define an instance of <literal>Num</literal>:
2803 instance Num Dollars where
2804 Dollars a + Dollars b = Dollars (a+b)
2807 All the instance does is apply and remove the <literal>newtype</literal>
2808 constructor. It is particularly galling that, since the constructor
2809 doesn't appear at run-time, this instance declaration defines a
2810 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
2811 dictionary, only slower!
2815 <sect3> <title> Generalising the deriving clause </title>
2817 GHC now permits such instances to be derived instead, so one can write
2819 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
2822 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
2823 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
2824 derives an instance declaration of the form
2827 instance Num Int => Num Dollars
2830 which just adds or removes the <literal>newtype</literal> constructor according to the type.
2834 We can also derive instances of constructor classes in a similar
2835 way. For example, suppose we have implemented state and failure monad
2836 transformers, such that
2839 instance Monad m => Monad (State s m)
2840 instance Monad m => Monad (Failure m)
2842 In Haskell 98, we can define a parsing monad by
2844 type Parser tok m a = State [tok] (Failure m) a
2847 which is automatically a monad thanks to the instance declarations
2848 above. With the extension, we can make the parser type abstract,
2849 without needing to write an instance of class <literal>Monad</literal>, via
2852 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2855 In this case the derived instance declaration is of the form
2857 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
2860 Notice that, since <literal>Monad</literal> is a constructor class, the
2861 instance is a <emphasis>partial application</emphasis> of the new type, not the
2862 entire left hand side. We can imagine that the type declaration is
2863 ``eta-converted'' to generate the context of the instance
2868 We can even derive instances of multi-parameter classes, provided the
2869 newtype is the last class parameter. In this case, a ``partial
2870 application'' of the class appears in the <literal>deriving</literal>
2871 clause. For example, given the class
2874 class StateMonad s m | m -> s where ...
2875 instance Monad m => StateMonad s (State s m) where ...
2877 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
2879 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
2880 deriving (Monad, StateMonad [tok])
2883 The derived instance is obtained by completing the application of the
2884 class to the new type:
2887 instance StateMonad [tok] (State [tok] (Failure m)) =>
2888 StateMonad [tok] (Parser tok m)
2893 As a result of this extension, all derived instances in newtype
2894 declarations are treated uniformly (and implemented just by reusing
2895 the dictionary for the representation type), <emphasis>except</emphasis>
2896 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
2897 the newtype and its representation.
2901 <sect3> <title> A more precise specification </title>
2903 Derived instance declarations are constructed as follows. Consider the
2904 declaration (after expansion of any type synonyms)
2907 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
2910 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
2912 <literal>vk+1...vn</literal> are type variables which do not occur in any of
2913 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
2914 classes of the form <literal>C t1'...tj'</literal>. The derived instance
2915 declarations are, for each <literal>ci</literal>,
2918 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
2920 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
2921 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
2925 As an example which does <emphasis>not</emphasis> work, consider
2927 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
2929 Here we cannot derive the instance
2931 instance Monad (State s m) => Monad (NonMonad m)
2934 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
2935 and so cannot be "eta-converted" away. It is a good thing that this
2936 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
2937 not, in fact, a monad --- for the same reason. Try defining
2938 <literal>>>=</literal> with the correct type: you won't be able to.
2942 Notice also that the <emphasis>order</emphasis> of class parameters becomes
2943 important, since we can only derive instances for the last one. If the
2944 <literal>StateMonad</literal> class above were instead defined as
2947 class StateMonad m s | m -> s where ...
2950 then we would not have been able to derive an instance for the
2951 <literal>Parser</literal> type above. We hypothesise that multi-parameter
2952 classes usually have one "main" parameter for which deriving new
2953 instances is most interesting.
2961 <!-- ==================== End of type system extensions ================= -->
2963 <!-- ====================== TEMPLATE HASKELL ======================= -->
2965 <sect1 id="template-haskell">
2966 <title>Template Haskell</title>
2968 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
2969 the main technical innovations are discussed in "<ulink
2970 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
2971 Template Meta-programming for Haskell</ulink>", in
2972 Proc Haskell Workshop 2002.
2976 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
2977 Tim Sheard is going to expand it.)
2980 <sect2> <title> Syntax </title>
2982 Template Haskell has the following new syntactic constructions. You need to use the flag
2983 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
2987 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
2988 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
2989 There must be no space between the "$" and the identifier or parenthesis. This use
2990 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
2991 of "." as an infix operator. If you want the infix operator, put spaces around it.
2993 <para> A splice can occur in place of
2995 <listitem><para> an expression;</para></listitem>
2996 <listitem><para> a list of top-level declarations;</para></listitem>
2997 <listitem><para> a pattern;</para></listitem>
2998 <listitem><para> a type;</para></listitem>
3004 A expression quotation is written in Oxford brackets, thus:
3006 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;</para></listitem>
3007 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;</para></listitem>
3008 <listitem><para> <literal>[p| ... |]</literal>, where the "..." is a pattern;</para></listitem>
3009 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;</para></listitem>
3010 </itemizedlist></para></listitem>
3013 Reification is written thus:
3015 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3016 has type <literal>Dec</literal>. </para></listitem>
3017 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3018 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3019 <listitem><para> Still to come: fixities </para></listitem>
3021 </itemizedlist></para>
3029 <sect2> <title> Using Template Haskell </title>
3033 The data types and monadic constructor functions for Template Haskell are in the library
3034 <literal>Language.Haskell.THSyntax</literal>.
3038 If the module contains any top-level splices that must be run, you must use GHC with
3039 <literal>--make</literal> or <literal>--interactive</literal> flags. (Reason: that
3040 means it walks the dependency tree and knows what modules must be linked etc.)
3044 You can only run a function at compile time if it is imported from another module. That is,
3045 you can't define a function in a module, and call it from within a splice in the same module.
3046 (It would make sense to do so, but it's hard to implement.)
3050 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3058 <!-- ==================== ASSERTIONS ================= -->
3060 <sect1 id="sec-assertions">
3062 <indexterm><primary>Assertions</primary></indexterm>
3066 If you want to make use of assertions in your standard Haskell code, you
3067 could define a function like the following:
3073 assert :: Bool -> a -> a
3074 assert False x = error "assertion failed!"
3081 which works, but gives you back a less than useful error message --
3082 an assertion failed, but which and where?
3086 One way out is to define an extended <function>assert</function> function which also
3087 takes a descriptive string to include in the error message and
3088 perhaps combine this with the use of a pre-processor which inserts
3089 the source location where <function>assert</function> was used.
3093 Ghc offers a helping hand here, doing all of this for you. For every
3094 use of <function>assert</function> in the user's source:
3100 kelvinToC :: Double -> Double
3101 kelvinToC k = assert (k >= 0.0) (k+273.15)
3107 Ghc will rewrite this to also include the source location where the
3114 assert pred val ==> assertError "Main.hs|15" pred val
3120 The rewrite is only performed by the compiler when it spots
3121 applications of <function>Control.Exception.assert</function>, so you
3122 can still define and use your own versions of
3123 <function>assert</function>, should you so wish. If not, import
3124 <literal>Control.Exception</literal> to make use
3125 <function>assert</function> in your code.
3129 To have the compiler ignore uses of assert, use the compiler option
3130 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3131 option</primary></indexterm> That is, expressions of the form
3132 <literal>assert pred e</literal> will be rewritten to
3133 <literal>e</literal>.
3137 Assertion failures can be caught, see the documentation for the
3138 <literal>Control.Exception</literal> library for the details.
3144 <!-- =============================== PRAGMAS =========================== -->
3146 <sect1 id="pragmas">
3147 <title>Pragmas</title>
3149 <indexterm><primary>pragma</primary></indexterm>
3151 <para>GHC supports several pragmas, or instructions to the
3152 compiler placed in the source code. Pragmas don't normally affect
3153 the meaning of the program, but they might affect the efficiency
3154 of the generated code.</para>
3156 <para>Pragmas all take the form
3158 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3160 where <replaceable>word</replaceable> indicates the type of
3161 pragma, and is followed optionally by information specific to that
3162 type of pragma. Case is ignored in
3163 <replaceable>word</replaceable>. The various values for
3164 <replaceable>word</replaceable> that GHC understands are described
3165 in the following sections; any pragma encountered with an
3166 unrecognised <replaceable>word</replaceable> is (silently)
3169 <sect2 id="inline-pragma">
3170 <title>INLINE pragma
3172 <indexterm><primary>INLINE pragma</primary></indexterm>
3173 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
3176 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
3177 functions/values that are “small enough,” thus avoiding the call
3178 overhead and possibly exposing other more-wonderful optimisations.
3182 You will probably see these unfoldings (in Core syntax) in your
3187 Normally, if GHC decides a function is “too expensive” to inline, it
3188 will not do so, nor will it export that unfolding for other modules to
3193 The sledgehammer you can bring to bear is the
3194 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
3197 key_function :: Int -> String -> (Bool, Double)
3199 #ifdef __GLASGOW_HASKELL__
3200 {-# INLINE key_function #-}
3204 (You don't need to do the C pre-processor carry-on unless you're going
3205 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
3209 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
3210 “cost” to be very low. The normal unfolding machinery will then be
3211 very keen to inline it.
3215 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
3216 signature could be put.
3220 <literal>INLINE</literal> pragmas are a particularly good idea for the
3221 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
3222 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
3225 #ifdef __GLASGOW_HASKELL__
3226 {-# INLINE thenUs #-}
3227 {-# INLINE returnUs #-}
3235 <sect2 id="noinline-pragma">
3236 <title>NOINLINE pragma
3239 <indexterm><primary>NOINLINE pragma</primary></indexterm>
3240 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
3241 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
3242 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
3245 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
3246 it stops the named function from being inlined by the compiler. You
3247 shouldn't ever need to do this, unless you're very cautious about code
3251 <para><literal>NOTINLINE</literal> is a synonym for
3252 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
3253 by Haskell 98 as the standard way to disable inlining, so it should be
3254 used if you want your code to be portable).</para>
3258 <sect2 id="specialize-pragma">
3259 <title>SPECIALIZE pragma</title>
3261 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3262 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
3263 <indexterm><primary>overloading, death to</primary></indexterm>
3265 <para>(UK spelling also accepted.) For key overloaded
3266 functions, you can create extra versions (NB: more code space)
3267 specialised to particular types. Thus, if you have an
3268 overloaded function:</para>
3271 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3274 <para>If it is heavily used on lists with
3275 <literal>Widget</literal> keys, you could specialise it as
3279 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3282 <para>To get very fancy, you can also specify a named function
3283 to use for the specialised value, as in:</para>
3286 {-# RULES hammeredLookup = blah #-}
3289 <para>where <literal>blah</literal> is an implementation of
3290 <literal>hammerdLookup</literal> written specialy for
3291 <literal>Widget</literal> lookups. It's <emphasis>Your
3292 Responsibility</emphasis> to make sure that
3293 <function>blah</function> really behaves as a specialised
3294 version of <function>hammeredLookup</function>!!!</para>
3296 <para>Note we use the <literal>RULE</literal> pragma here to
3297 indicate that <literal>hammeredLookup</literal> applied at a
3298 certain type should be replaced by <literal>blah</literal>. See
3299 <xref linkend="rules"> for more information on
3300 <literal>RULES</literal>.</para>
3302 <para>An example in which using <literal>RULES</literal> for
3303 specialisation will Win Big:
3306 toDouble :: Real a => a -> Double
3307 toDouble = fromRational . toRational
3309 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
3310 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3313 The <function>i2d</function> function is virtually one machine
3314 instruction; the default conversion—via an intermediate
3315 <literal>Rational</literal>—is obscenely expensive by
3318 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3319 be put anywhere its type signature could be put.</para>
3323 <sect2 id="specialize-instance-pragma">
3324 <title>SPECIALIZE instance pragma
3328 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3329 <indexterm><primary>overloading, death to</primary></indexterm>
3330 Same idea, except for instance declarations. For example:
3333 instance (Eq a) => Eq (Foo a) where {
3334 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3338 The pragma must occur inside the <literal>where</literal> part
3339 of the instance declaration.
3342 Compatible with HBC, by the way, except perhaps in the placement
3348 <sect2 id="line-pragma">
3353 <indexterm><primary>LINE pragma</primary></indexterm>
3354 <indexterm><primary>pragma, LINE</primary></indexterm>
3358 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
3359 automatically generated Haskell code. It lets you specify the line
3360 number and filename of the original code; for example
3366 {-# LINE 42 "Foo.vhs" #-}
3372 if you'd generated the current file from something called <filename>Foo.vhs</filename>
3373 and this line corresponds to line 42 in the original. GHC will adjust
3374 its error messages to refer to the line/file named in the <literal>LINE</literal>
3381 <title>RULES pragma</title>
3384 The RULES pragma lets you specify rewrite rules. It is described in
3385 <xref LinkEnd="rewrite-rules">.
3390 <sect2 id="deprecated-pragma">
3391 <title>DEPRECATED pragma</title>
3394 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
3395 There are two forms.
3399 You can deprecate an entire module thus:</para>
3401 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3405 When you compile any module that import <literal>Wibble</literal>, GHC will print
3406 the specified message.</para>
3411 You can deprecate a function, class, or type, with the following top-level declaration:
3414 {-# DEPRECATED f, C, T "Don't use these" #-}
3417 When you compile any module that imports and uses any of the specifed entities,
3418 GHC will print the specified message.
3422 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
3428 <!-- ======================= REWRITE RULES ======================== -->
3430 <sect1 id="rewrite-rules">
3431 <title>Rewrite rules
3433 <indexterm><primary>RULES pagma</primary></indexterm>
3434 <indexterm><primary>pragma, RULES</primary></indexterm>
3435 <indexterm><primary>rewrite rules</primary></indexterm></title>
3438 The programmer can specify rewrite rules as part of the source program
3439 (in a pragma). GHC applies these rewrite rules wherever it can.
3447 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3454 <title>Syntax</title>
3457 From a syntactic point of view:
3463 Each rule has a name, enclosed in double quotes. The name itself has
3464 no significance at all. It is only used when reporting how many times the rule fired.
3470 There may be zero or more rules in a <literal>RULES</literal> pragma.
3476 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3477 is set, so you must lay out your rules starting in the same column as the
3478 enclosing definitions.
3484 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3485 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3486 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3487 by spaces, just like in a type <literal>forall</literal>.
3493 A pattern variable may optionally have a type signature.
3494 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3495 For example, here is the <literal>foldr/build</literal> rule:
3498 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3499 foldr k z (build g) = g k z
3502 Since <function>g</function> has a polymorphic type, it must have a type signature.
3509 The left hand side of a rule must consist of a top-level variable applied
3510 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3513 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3514 "wrong2" forall f. f True = True
3517 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3524 A rule does not need to be in the same module as (any of) the
3525 variables it mentions, though of course they need to be in scope.
3531 Rules are automatically exported from a module, just as instance declarations are.
3542 <title>Semantics</title>
3545 From a semantic point of view:
3551 Rules are only applied if you use the <option>-O</option> flag.
3557 Rules are regarded as left-to-right rewrite rules.
3558 When GHC finds an expression that is a substitution instance of the LHS
3559 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3560 By "a substitution instance" we mean that the LHS can be made equal to the
3561 expression by substituting for the pattern variables.
3568 The LHS and RHS of a rule are typechecked, and must have the
3576 GHC makes absolutely no attempt to verify that the LHS and RHS
3577 of a rule have the same meaning. That is undecideable in general, and
3578 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3585 GHC makes no attempt to make sure that the rules are confluent or
3586 terminating. For example:
3589 "loop" forall x,y. f x y = f y x
3592 This rule will cause the compiler to go into an infinite loop.
3599 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3605 GHC currently uses a very simple, syntactic, matching algorithm
3606 for matching a rule LHS with an expression. It seeks a substitution
3607 which makes the LHS and expression syntactically equal modulo alpha
3608 conversion. The pattern (rule), but not the expression, is eta-expanded if
3609 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3610 But not beta conversion (that's called higher-order matching).
3614 Matching is carried out on GHC's intermediate language, which includes
3615 type abstractions and applications. So a rule only matches if the
3616 types match too. See <xref LinkEnd="rule-spec"> below.
3622 GHC keeps trying to apply the rules as it optimises the program.
3623 For example, consider:
3632 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3633 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3634 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3635 not be substituted, and the rule would not fire.
3642 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3643 that appears on the LHS of a rule</emphasis>, because once you have substituted
3644 for something you can't match against it (given the simple minded
3645 matching). So if you write the rule
3648 "map/map" forall f,g. map f . map g = map (f.g)
3651 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3652 It will only match something written with explicit use of ".".
3653 Well, not quite. It <emphasis>will</emphasis> match the expression
3659 where <function>wibble</function> is defined:
3662 wibble f g = map f . map g
3665 because <function>wibble</function> will be inlined (it's small).
3667 Later on in compilation, GHC starts inlining even things on the
3668 LHS of rules, but still leaves the rules enabled. This inlining
3669 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3676 All rules are implicitly exported from the module, and are therefore
3677 in force in any module that imports the module that defined the rule, directly
3678 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3679 in force when compiling A.) The situation is very similar to that for instance
3691 <title>List fusion</title>
3694 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3695 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3696 intermediate list should be eliminated entirely.
3700 The following are good producers:
3712 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3718 Explicit lists (e.g. <literal>[True, False]</literal>)
3724 The cons constructor (e.g <literal>3:4:[]</literal>)
3730 <function>++</function>
3736 <function>map</function>
3742 <function>filter</function>
3748 <function>iterate</function>, <function>repeat</function>
3754 <function>zip</function>, <function>zipWith</function>
3763 The following are good consumers:
3775 <function>array</function> (on its second argument)
3781 <function>length</function>
3787 <function>++</function> (on its first argument)
3793 <function>foldr</function>
3799 <function>map</function>
3805 <function>filter</function>
3811 <function>concat</function>
3817 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
3823 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
3824 will fuse with one but not the other)
3830 <function>partition</function>
3836 <function>head</function>
3842 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
3848 <function>sequence_</function>
3854 <function>msum</function>
3860 <function>sortBy</function>
3869 So, for example, the following should generate no intermediate lists:
3872 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
3878 This list could readily be extended; if there are Prelude functions that you use
3879 a lot which are not included, please tell us.
3883 If you want to write your own good consumers or producers, look at the
3884 Prelude definitions of the above functions to see how to do so.
3889 <sect2 id="rule-spec">
3890 <title>Specialisation
3894 Rewrite rules can be used to get the same effect as a feature
3895 present in earlier version of GHC:
3898 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
3901 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
3902 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
3903 specialising the original definition of <function>fromIntegral</function> the programmer is
3904 promising that it is safe to use <function>int8ToInt16</function> instead.
3908 This feature is no longer in GHC. But rewrite rules let you do the
3913 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
3917 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
3918 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
3919 GHC adds the type and dictionary applications to get the typed rule
3922 forall (d1::Integral Int8) (d2::Num Int16) .
3923 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
3927 this rule does not need to be in the same file as fromIntegral,
3928 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
3929 have an original definition available to specialise).
3935 <title>Controlling what's going on</title>
3943 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
3949 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
3950 If you add <option>-dppr-debug</option> you get a more detailed listing.
3956 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
3959 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
3960 {-# INLINE build #-}
3964 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
3965 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
3966 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
3967 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
3974 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
3975 see how to write rules that will do fusion and yet give an efficient
3976 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
3988 <sect1 id="generic-classes">
3989 <title>Generic classes</title>
3991 <para>(Note: support for generic classes is currently broken in
3995 The ideas behind this extension are described in detail in "Derivable type classes",
3996 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
3997 An example will give the idea:
4005 fromBin :: [Int] -> (a, [Int])
4007 toBin {| Unit |} Unit = []
4008 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4009 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4010 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4012 fromBin {| Unit |} bs = (Unit, bs)
4013 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4014 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4015 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4016 (y,bs'') = fromBin bs'
4019 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4020 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4021 which are defined thus in the library module <literal>Generics</literal>:
4025 data a :+: b = Inl a | Inr b
4026 data a :*: b = a :*: b
4029 Now you can make a data type into an instance of Bin like this:
4031 instance (Bin a, Bin b) => Bin (a,b)
4032 instance Bin a => Bin [a]
4034 That is, just leave off the "where" clasuse. Of course, you can put in the
4035 where clause and over-ride whichever methods you please.
4039 <title> Using generics </title>
4040 <para>To use generics you need to</para>
4043 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4044 <option>-fgenerics</option> (to generate extra per-data-type code),
4045 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4049 <para>Import the module <literal>Generics</literal> from the
4050 <literal>lang</literal> package. This import brings into
4051 scope the data types <literal>Unit</literal>,
4052 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4053 don't need this import if you don't mention these types
4054 explicitly; for example, if you are simply giving instance
4055 declarations.)</para>
4060 <sect2> <title> Changes wrt the paper </title>
4062 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4063 can be written infix (indeed, you can now use
4064 any operator starting in a colon as an infix type constructor). Also note that
4065 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4066 Finally, note that the syntax of the type patterns in the class declaration
4067 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4068 alone would ambiguous when they appear on right hand sides (an extension we
4069 anticipate wanting).
4073 <sect2> <title>Terminology and restrictions</title>
4075 Terminology. A "generic default method" in a class declaration
4076 is one that is defined using type patterns as above.
4077 A "polymorphic default method" is a default method defined as in Haskell 98.
4078 A "generic class declaration" is a class declaration with at least one
4079 generic default method.
4087 Alas, we do not yet implement the stuff about constructor names and
4094 A generic class can have only one parameter; you can't have a generic
4095 multi-parameter class.
4101 A default method must be defined entirely using type patterns, or entirely
4102 without. So this is illegal:
4105 op :: a -> (a, Bool)
4106 op {| Unit |} Unit = (Unit, True)
4109 However it is perfectly OK for some methods of a generic class to have
4110 generic default methods and others to have polymorphic default methods.
4116 The type variable(s) in the type pattern for a generic method declaration
4117 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:
4121 op {| p :*: q |} (x :*: y) = op (x :: p)
4129 The type patterns in a generic default method must take one of the forms:
4135 where "a" and "b" are type variables. Furthermore, all the type patterns for
4136 a single type constructor (<literal>:*:</literal>, say) must be identical; they
4137 must use the same type variables. So this is illegal:
4141 op {| a :+: b |} (Inl x) = True
4142 op {| p :+: q |} (Inr y) = False
4144 The type patterns must be identical, even in equations for different methods of the class.
4145 So this too is illegal:
4149 op1 {| a :*: b |} (x :*: y) = True
4152 op2 {| p :*: q |} (x :*: y) = False
4154 (The reason for this restriction is that we gather all the equations for a particular type consructor
4155 into a single generic instance declaration.)
4161 A generic method declaration must give a case for each of the three type constructors.
4167 The type for a generic method can be built only from:
4169 <listitem> <para> Function arrows </para> </listitem>
4170 <listitem> <para> Type variables </para> </listitem>
4171 <listitem> <para> Tuples </para> </listitem>
4172 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
4174 Here are some example type signatures for generic methods:
4177 op2 :: Bool -> (a,Bool)
4178 op3 :: [Int] -> a -> a
4181 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
4185 This restriction is an implementation restriction: we just havn't got around to
4186 implementing the necessary bidirectional maps over arbitrary type constructors.
4187 It would be relatively easy to add specific type constructors, such as Maybe and list,
4188 to the ones that are allowed.</para>
4193 In an instance declaration for a generic class, the idea is that the compiler
4194 will fill in the methods for you, based on the generic templates. However it can only
4199 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4204 No constructor of the instance type has unboxed fields.
4208 (Of course, these things can only arise if you are already using GHC extensions.)
4209 However, you can still give an instance declarations for types which break these rules,
4210 provided you give explicit code to override any generic default methods.
4218 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
4219 what the compiler does with generic declarations.
4224 <sect2> <title> Another example </title>
4226 Just to finish with, here's another example I rather like:
4230 nCons {| Unit |} _ = 1
4231 nCons {| a :*: b |} _ = 1
4232 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4235 tag {| Unit |} _ = 1
4236 tag {| a :*: b |} _ = 1
4237 tag {| a :+: b |} (Inl x) = tag x
4238 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4247 ;;; Local Variables: ***
4249 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
projects / ghc-hetmet.git / blob