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 -->
155 <!-- &primitives; -->
156 <sect1 id="primitives">
157 <title>Unboxed types and primitive operations</title>
159 <para>GHC is built on a raft of primitive data types and operations.
160 While you really can use this stuff to write fast code,
161 we generally find it a lot less painful, and more satisfying in the
162 long run, to use higher-level language features and libraries. With
163 any luck, the code you write will be optimised to the efficient
164 unboxed version in any case. And if it isn't, we'd like to know
167 <para>We do not currently have good, up-to-date documentation about the
168 primitives, perhaps because they are mainly intended for internal use.
169 There used to be a long section about them here in the User Guide, but it
170 became out of date, and wrong information is worse than none.</para>
172 <para>The Real Truth about what primitive types there are, and what operations
173 work over those types, is held in the file
174 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
175 This file is used directly to generate GHC's primitive-operation definitions, so
176 it is always correct! It is also intended for processing into text.</para>
179 the result of such processing is part of the description of the
181 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
182 Core language</ulink>.
183 So that document is a good place to look for a type-set version.
184 We would be very happy if someone wanted to volunteer to produce an SGML
185 back end to the program that processes <filename>primops.txt</filename> so that
186 we could include the results here in the User Guide.</para>
188 <para>What follows here is a brief summary of some main points.</para>
190 <sect2 id="glasgow-unboxed">
195 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
198 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
199 that values of that type are represented by a pointer to a heap
200 object. The representation of a Haskell <literal>Int</literal>, for
201 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
202 type, however, is represented by the value itself, no pointers or heap
203 allocation are involved.
207 Unboxed types correspond to the “raw machine” types you
208 would use in C: <literal>Int#</literal> (long int),
209 <literal>Double#</literal> (double), <literal>Addr#</literal>
210 (void *), etc. The <emphasis>primitive operations</emphasis>
211 (PrimOps) on these types are what you might expect; e.g.,
212 <literal>(+#)</literal> is addition on
213 <literal>Int#</literal>s, and is the machine-addition that we all
214 know and love—usually one instruction.
218 Primitive (unboxed) types cannot be defined in Haskell, and are
219 therefore built into the language and compiler. Primitive types are
220 always unlifted; that is, a value of a primitive type cannot be
221 bottom. We use the convention that primitive types, values, and
222 operations have a <literal>#</literal> suffix.
226 Primitive values are often represented by a simple bit-pattern, such
227 as <literal>Int#</literal>, <literal>Float#</literal>,
228 <literal>Double#</literal>. But this is not necessarily the case:
229 a primitive value might be represented by a pointer to a
230 heap-allocated object. Examples include
231 <literal>Array#</literal>, the type of primitive arrays. A
232 primitive array is heap-allocated because it is too big a value to fit
233 in a register, and would be too expensive to copy around; in a sense,
234 it is accidental that it is represented by a pointer. If a pointer
235 represents a primitive value, then it really does point to that value:
236 no unevaluated thunks, no indirections…nothing can be at the
237 other end of the pointer than the primitive value.
241 There are some restrictions on the use of primitive types, the main
242 one being that you can't pass a primitive value to a polymorphic
243 function or store one in a polymorphic data type. This rules out
244 things like <literal>[Int#]</literal> (i.e. lists of primitive
245 integers). The reason for this restriction is that polymorphic
246 arguments and constructor fields are assumed to be pointers: if an
247 unboxed integer is stored in one of these, the garbage collector would
248 attempt to follow it, leading to unpredictable space leaks. Or a
249 <function>seq</function> operation on the polymorphic component may
250 attempt to dereference the pointer, with disastrous results. Even
251 worse, the unboxed value might be larger than a pointer
252 (<literal>Double#</literal> for instance).
256 Nevertheless, A numerically-intensive program using unboxed types can
257 go a <emphasis>lot</emphasis> faster than its “standard”
258 counterpart—we saw a threefold speedup on one example.
263 <sect2 id="unboxed-tuples">
264 <title>Unboxed Tuples
268 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
269 they're available by default with <option>-fglasgow-exts</option>. An
270 unboxed tuple looks like this:
282 where <literal>e_1..e_n</literal> are expressions of any
283 type (primitive or non-primitive). The type of an unboxed tuple looks
288 Unboxed tuples are used for functions that need to return multiple
289 values, but they avoid the heap allocation normally associated with
290 using fully-fledged tuples. When an unboxed tuple is returned, the
291 components are put directly into registers or on the stack; the
292 unboxed tuple itself does not have a composite representation. Many
293 of the primitive operations listed in this section return unboxed
298 There are some pretty stringent restrictions on the use of unboxed tuples:
307 Unboxed tuple types are subject to the same restrictions as
308 other unboxed types; i.e. they may not be stored in polymorphic data
309 structures or passed to polymorphic functions.
316 Unboxed tuples may only be constructed as the direct result of
317 a function, and may only be deconstructed with a <literal>case</literal> expression.
318 eg. the following are valid:
322 f x y = (# x+1, y-1 #)
323 g x = case f x x of { (# a, b #) -> a + b }
327 but the following are invalid:
341 No variable can have an unboxed tuple type. This is illegal:
345 f :: (# Int, Int #) -> (# Int, Int #)
350 because <literal>x</literal> has an unboxed tuple type.
360 Note: we may relax some of these restrictions in the future.
364 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
365 tuples to avoid unnecessary allocation during sequences of operations.
372 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
374 <sect1 id="syntax-extns">
375 <title>Syntactic extensions</title>
377 <!-- ====================== HIERARCHICAL MODULES ======================= -->
379 <sect2 id="hierarchical-modules">
380 <title>Hierarchical Modules</title>
382 <para>GHC supports a small extension to the syntax of module
383 names: a module name is allowed to contain a dot
384 <literal>‘.’</literal>. This is also known as the
385 “hierarchical module namespace” extension, because
386 it extends the normally flat Haskell module namespace into a
387 more flexible hierarchy of modules.</para>
389 <para>This extension has very little impact on the language
390 itself; modules names are <emphasis>always</emphasis> fully
391 qualified, so you can just think of the fully qualified module
392 name as <quote>the module name</quote>. In particular, this
393 means that the full module name must be given after the
394 <literal>module</literal> keyword at the beginning of the
395 module; for example, the module <literal>A.B.C</literal> must
398 <programlisting>module A.B.C</programlisting>
401 <para>It is a common strategy to use the <literal>as</literal>
402 keyword to save some typing when using qualified names with
403 hierarchical modules. For example:</para>
406 import qualified Control.Monad.ST.Strict as ST
409 <para>Hierarchical modules have an impact on the way that GHC
410 searches for files. For a description, see <xref
411 linkend="finding-hierarchical-modules">.</para>
413 <para>GHC comes with a large collection of libraries arranged
414 hierarchically; see the accompanying library documentation.
415 There is an ongoing project to create and maintain a stable set
416 of <quote>core</quote> libraries used by several Haskell
417 compilers, and the libraries that GHC comes with represent the
418 current status of that project. For more details, see <ulink
419 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
420 Libraries</ulink>.</para>
424 <!-- ====================== PATTERN GUARDS ======================= -->
426 <sect2 id="pattern-guards">
427 <title>Pattern guards</title>
430 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
431 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.)
435 Suppose we have an abstract data type of finite maps, with a
439 lookup :: FiniteMap -> Int -> Maybe Int
442 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
443 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
447 clunky env var1 var2 | ok1 && ok2 = val1 + val2
448 | otherwise = var1 + var2
459 The auxiliary functions are
463 maybeToBool :: Maybe a -> Bool
464 maybeToBool (Just x) = True
465 maybeToBool Nothing = False
467 expectJust :: Maybe a -> a
468 expectJust (Just x) = x
469 expectJust Nothing = error "Unexpected Nothing"
473 What is <function>clunky</function> doing? The guard <literal>ok1 &&
474 ok2</literal> checks that both lookups succeed, using
475 <function>maybeToBool</function> to convert the <function>Maybe</function>
476 types to booleans. The (lazily evaluated) <function>expectJust</function>
477 calls extract the values from the results of the lookups, and binds the
478 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
479 respectively. If either lookup fails, then clunky takes the
480 <literal>otherwise</literal> case and returns the sum of its arguments.
484 This is certainly legal Haskell, but it is a tremendously verbose and
485 un-obvious way to achieve the desired effect. Arguably, a more direct way
486 to write clunky would be to use case expressions:
490 clunky env var1 var1 = case lookup env var1 of
492 Just val1 -> case lookup env var2 of
494 Just val2 -> val1 + val2
500 This is a bit shorter, but hardly better. Of course, we can rewrite any set
501 of pattern-matching, guarded equations as case expressions; that is
502 precisely what the compiler does when compiling equations! The reason that
503 Haskell provides guarded equations is because they allow us to write down
504 the cases we want to consider, one at a time, independently of each other.
505 This structure is hidden in the case version. Two of the right-hand sides
506 are really the same (<function>fail</function>), and the whole expression
507 tends to become more and more indented.
511 Here is how I would write clunky:
516 | Just val1 <- lookup env var1
517 , Just val2 <- lookup env var2
519 ...other equations for clunky...
523 The semantics should be clear enough. The qualifers are matched in order.
524 For a <literal><-</literal> qualifier, which I call a pattern guard, the
525 right hand side is evaluated and matched against the pattern on the left.
526 If the match fails then the whole guard fails and the next equation is
527 tried. If it succeeds, then the appropriate binding takes place, and the
528 next qualifier is matched, in the augmented environment. Unlike list
529 comprehensions, however, the type of the expression to the right of the
530 <literal><-</literal> is the same as the type of the pattern to its
531 left. The bindings introduced by pattern guards scope over all the
532 remaining guard qualifiers, and over the right hand side of the equation.
536 Just as with list comprehensions, boolean expressions can be freely mixed
537 with among the pattern guards. For example:
548 Haskell's current guards therefore emerge as a special case, in which the
549 qualifier list has just one element, a boolean expression.
553 <!-- ===================== Recursive do-notation =================== -->
555 <sect2 id="mdo-notation">
556 <title>The recursive do-notation
559 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
560 "A recursive do for Haskell",
561 Levent Erkok, John Launchbury",
562 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
565 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
566 that is, the variables bound in a do-expression are visible only in the textually following
567 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
568 group. It turns out that several applications can benefit from recursive bindings in
569 the do-notation, and this extension provides the necessary syntactic support.
572 Here is a simple (yet contrived) example:
575 import Control.Monad.Fix
577 justOnes = mdo xs <- Just (1:xs)
581 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
585 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
588 class Monad m => MonadFix m where
589 mfix :: (a -> m a) -> m a
592 The function <literal>mfix</literal>
593 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
594 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
595 For details, see the above mentioned reference.
598 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
599 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
600 for Haskell's internal state monad (strict and lazy, respectively).
603 There are three important points in using the recursive-do notation:
606 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
607 than <literal>do</literal>).
611 You should <literal>import Control.Monad.Fix</literal>.
612 (Note: Strictly speaking, this import is required only when you need to refer to the name
613 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
614 are encouraged to always import this module when using the mdo-notation.)
618 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
624 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
625 contains up to date information on recursive monadic bindings.
629 Historical note: The old implementation of the mdo-notation (and most
630 of the existing documents) used the name
631 <literal>MonadRec</literal> for the class and the corresponding library.
632 This name is not supported by GHC.
638 <sect2> <title> Infix type constructors </title>
640 <para>GHC supports infix type constructors, much as it supports infix data constructors. For example:
644 data a :+: b = Inl a | Inr b
646 f :: a `Either` b -> a :+: b
651 syntax of an infix type constructor is just like that of an infix data constructor: either
652 it's an operator beginning with ":", or it is an ordinary (alphabetic) type constructor enclosed in
656 When you give a fixity declaration, the fixity applies to both the data constructor and the
657 type constructor with the specified name. You cannot give different fixities to the type constructor T
658 and the data constructor T.
664 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
666 <sect2 id="parallel-list-comprehensions">
667 <title>Parallel List Comprehensions</title>
668 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
670 <indexterm><primary>parallel list comprehensions</primary>
673 <para>Parallel list comprehensions are a natural extension to list
674 comprehensions. List comprehensions can be thought of as a nice
675 syntax for writing maps and filters. Parallel comprehensions
676 extend this to include the zipWith family.</para>
678 <para>A parallel list comprehension has multiple independent
679 branches of qualifier lists, each separated by a `|' symbol. For
680 example, the following zips together two lists:</para>
683 [ (x, y) | x <- xs | y <- ys ]
686 <para>The behavior of parallel list comprehensions follows that of
687 zip, in that the resulting list will have the same length as the
688 shortest branch.</para>
690 <para>We can define parallel list comprehensions by translation to
691 regular comprehensions. Here's the basic idea:</para>
693 <para>Given a parallel comprehension of the form: </para>
696 [ e | p1 <- e11, p2 <- e12, ...
697 | q1 <- e21, q2 <- e22, ...
702 <para>This will be translated to: </para>
705 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
706 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
711 <para>where `zipN' is the appropriate zip for the given number of
716 <sect2 id="rebindable-syntax">
717 <title>Rebindable syntax</title>
720 <para>GHC allows most kinds of built-in syntax to be rebound by
721 the user, to facilitate replacing the <literal>Prelude</literal>
722 with a home-grown version, for example.</para>
724 <para>You may want to define your own numeric class
725 hierarchy. It completely defeats that purpose if the
726 literal "1" means "<literal>Prelude.fromInteger
727 1</literal>", which is what the Haskell Report specifies.
728 So the <option>-fno-implicit-prelude</option> flag causes
729 the following pieces of built-in syntax to refer to
730 <emphasis>whatever is in scope</emphasis>, not the Prelude
735 <para>Integer and fractional literals mean
736 "<literal>fromInteger 1</literal>" and
737 "<literal>fromRational 3.2</literal>", not the
738 Prelude-qualified versions; both in expressions and in
740 <para>However, the standard Prelude <literal>Eq</literal> class
741 is still used for the equality test necessary for literal patterns.</para>
745 <para>Negation (e.g. "<literal>- (f x)</literal>")
746 means "<literal>negate (f x)</literal>" (not
747 <literal>Prelude.negate</literal>).</para>
751 <para>In an n+k pattern, the standard Prelude
752 <literal>Ord</literal> class is still used for comparison,
753 but the necessary subtraction uses whatever
754 "<literal>(-)</literal>" is in scope (not
755 "<literal>Prelude.(-)</literal>").</para>
759 <para>"Do" notation is translated using whatever
760 functions <literal>(>>=)</literal>,
761 <literal>(>>)</literal>, <literal>fail</literal>, and
762 <literal>return</literal>, are in scope (not the Prelude
763 versions). List comprehensions, and parallel array
764 comprehensions, are unaffected. </para></listitem>
767 <para>Be warned: this is an experimental facility, with fewer checks than
768 usual. In particular, it is essential that the functions GHC finds in scope
769 must have the appropriate types, namely:
771 fromInteger :: forall a. (...) => Integer -> a
772 fromRational :: forall a. (...) => Rational -> a
773 negate :: forall a. (...) => a -> a
774 (-) :: forall a. (...) => a -> a -> a
775 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
776 (>>) :: forall m a. (...) => m a -> m b -> m b
777 return :: forall m a. (...) => a -> m a
778 fail :: forall m a. (...) => String -> m a
780 (The (...) part can be any context including the empty context; that part
782 If the functions don't have the right type, very peculiar things may
783 happen. Use <literal>-dcore-lint</literal> to
784 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
790 <!-- TYPE SYSTEM EXTENSIONS -->
791 <sect1 id="type-extensions">
792 <title>Type system extensions</title>
794 <sect2 id="nullary-types">
795 <title>Data types with no constructors</title>
797 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
798 a data type with no constructors. For example:</para>
802 data T a -- T :: * -> *
805 <para>Syntactically, the declaration lacks the "= constrs" part. The
806 type can be parameterised over types of any kind, but if the kind is
807 not <literal>*</literal> then an explicit kind annotation must be used
808 (see <xref linkend="sec-kinding">).</para>
810 <para>Such data types have only one value, namely bottom.
811 Nevertheless, they can be useful when defining "phantom types".</para>
814 <sect2 id="infix-tycons">
815 <title>Infix type constructors</title>
818 GHC allows type constructors to be operators, and to be written infix, very much
819 like expressions. More specifically:
822 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
823 The lexical syntax is the same as that for data constructors.
826 Types can be written infix. For example <literal>Int :*: Bool</literal>.
830 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
831 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
834 Fixities may be declared for type constructors just as for data constructors. However,
835 one cannot distinguish between the two in a fixity declaration; a fixity declaration
836 sets the fixity for a data constructor and the corresponding type constructor. For example:
840 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
841 and similarly for <literal>:*:</literal>.
842 <literal>Int `a` Bool</literal>.
845 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
848 Data type and type-synonym declarations can be written infix. E.g.
850 data a :*: b = Foo a b
851 type a :+: b = Either a b
855 The only thing that differs between operators in types and operators in expressions is that
856 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
857 are not allowed in types. Reason: the uniform thing to do would be to make them type
858 variables, but that's not very useful. A less uniform but more useful thing would be to
859 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
860 lists. So for now we just exclude them.
867 <sect2 id="sec-kinding">
868 <title>Explicitly-kinded quantification</title>
871 Haskell infers the kind of each type variable. Sometimes it is nice to be able
872 to give the kind explicitly as (machine-checked) documentation,
873 just as it is nice to give a type signature for a function. On some occasions,
874 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
875 John Hughes had to define the data type:
877 data Set cxt a = Set [a]
878 | Unused (cxt a -> ())
880 The only use for the <literal>Unused</literal> constructor was to force the correct
881 kind for the type variable <literal>cxt</literal>.
884 GHC now instead allows you to specify the kind of a type variable directly, wherever
885 a type variable is explicitly bound. Namely:
887 <listitem><para><literal>data</literal> declarations:
889 data Set (cxt :: * -> *) a = Set [a]
890 </Screen></para></listitem>
891 <listitem><para><literal>type</literal> declarations:
893 type T (f :: * -> *) = f Int
894 </Screen></para></listitem>
895 <listitem><para><literal>class</literal> declarations:
897 class (Eq a) => C (f :: * -> *) a where ...
898 </Screen></para></listitem>
899 <listitem><para><literal>forall</literal>'s in type signatures:
901 f :: forall (cxt :: * -> *). Set cxt Int
902 </Screen></para></listitem>
907 The parentheses are required. Some of the spaces are required too, to
908 separate the lexemes. If you write <literal>(f::*->*)</literal> you
909 will get a parse error, because "<literal>::*->*</literal>" is a
910 single lexeme in Haskell.
914 As part of the same extension, you can put kind annotations in types
917 f :: (Int :: *) -> Int
918 g :: forall a. a -> (a :: *)
922 atype ::= '(' ctype '::' kind ')
924 The parentheses are required.
929 <sect2 id="class-method-types">
930 <title>Class method types
933 Haskell 98 prohibits class method types to mention constraints on the
934 class type variable, thus:
937 fromList :: [a] -> s a
938 elem :: Eq a => a -> s a -> Bool
940 The type of <literal>elem</literal> is illegal in Haskell 98, because it
941 contains the constraint <literal>Eq a</literal>, constrains only the
942 class type variable (in this case <literal>a</literal>).
945 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
950 <sect2 id="multi-param-type-classes">
951 <title>Multi-parameter type classes
955 This section documents GHC's implementation of multi-parameter type
956 classes. There's lots of background in the paper <ULink
957 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
958 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
963 I'd like to thank people who reported shorcomings in the GHC 3.02
964 implementation. Our default decisions were all conservative ones, and
965 the experience of these heroic pioneers has given useful concrete
966 examples to support several generalisations. (These appear below as
967 design choices not implemented in 3.02.)
971 I've discussed these notes with Mark Jones, and I believe that Hugs
972 will migrate towards the same design choices as I outline here.
973 Thanks to him, and to many others who have offered very useful
981 There are the following restrictions on the form of a qualified
988 forall tv1..tvn (c1, ...,cn) => type
994 (Here, I write the "foralls" explicitly, although the Haskell source
995 language omits them; in Haskell 1.4, all the free type variables of an
996 explicit source-language type signature are universally quantified,
997 except for the class type variables in a class declaration. However,
998 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
1007 <emphasis>Each universally quantified type variable
1008 <literal>tvi</literal> must be mentioned (i.e. appear free) in <literal>type</literal></emphasis>.
1010 The reason for this is that a value with a type that does not obey
1011 this restriction could not be used without introducing
1012 ambiguity. Here, for example, is an illegal type:
1016 forall a. Eq a => Int
1020 When a value with this type was used, the constraint <literal>Eq tv</literal>
1021 would be introduced where <literal>tv</literal> is a fresh type variable, and
1022 (in the dictionary-translation implementation) the value would be
1023 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1024 can never know which instance of <literal>Eq</literal> to use because we never
1025 get any more information about <literal>tv</literal>.
1032 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1033 universally quantified type variables <literal>tvi</literal></emphasis>.
1035 For example, this type is OK because <literal>C a b</literal> mentions the
1036 universally quantified type variable <literal>b</literal>:
1040 forall a. C a b => burble
1044 The next type is illegal because the constraint <literal>Eq b</literal> does not
1045 mention <literal>a</literal>:
1049 forall a. Eq b => burble
1053 The reason for this restriction is milder than the other one. The
1054 excluded types are never useful or necessary (because the offending
1055 context doesn't need to be witnessed at this point; it can be floated
1056 out). Furthermore, floating them out increases sharing. Lastly,
1057 excluding them is a conservative choice; it leaves a patch of
1058 territory free in case we need it later.
1068 These restrictions apply to all types, whether declared in a type signature
1073 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1074 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1081 f :: Eq (m a) => [m a] -> [m a]
1088 This choice recovers principal types, a property that Haskell 1.4 does not have.
1094 <title>Class declarations</title>
1102 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1106 class Collection c a where
1107 union :: c a -> c a -> c a
1118 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1119 of "acyclic" involves only the superclass relationships. For example,
1125 op :: D b => a -> b -> b
1128 class C a => D a where { ... }
1132 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1133 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1134 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1141 <emphasis>There are no restrictions on the context in a class declaration
1142 (which introduces superclasses), except that the class hierarchy must
1143 be acyclic</emphasis>. So these class declarations are OK:
1147 class Functor (m k) => FiniteMap m k where
1150 class (Monad m, Monad (t m)) => Transform t m where
1151 lift :: m a -> (t m) a
1160 <emphasis>In the signature of a class operation, every constraint
1161 must mention at least one type variable that is not a class type
1162 variable</emphasis>.
1168 class Collection c a where
1169 mapC :: Collection c b => (a->b) -> c a -> c b
1173 is OK because the constraint <literal>(Collection a b)</literal> mentions
1174 <literal>b</literal>, even though it also mentions the class variable
1175 <literal>a</literal>. On the other hand:
1180 op :: Eq a => (a,b) -> (a,b)
1184 is not OK because the constraint <literal>(Eq a)</literal> mentions on the class
1185 type variable <literal>a</literal>, but not <literal>b</literal>. However, any such
1186 example is easily fixed by moving the offending context up to the
1191 class Eq a => C a where
1196 A yet more relaxed rule would allow the context of a class-op signature
1197 to mention only class type variables. However, that conflicts with
1198 Rule 1(b) for types above.
1205 <emphasis>The type of each class operation must mention <emphasis>all</emphasis> of
1206 the class type variables</emphasis>. For example:
1210 class Coll s a where
1212 insert :: s -> a -> s
1216 is not OK, because the type of <literal>empty</literal> doesn't mention
1217 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1218 types, and has the same motivation.
1220 Sometimes, offending class declarations exhibit misunderstandings. For
1221 example, <literal>Coll</literal> might be rewritten
1225 class Coll s a where
1227 insert :: s a -> a -> s a
1231 which makes the connection between the type of a collection of
1232 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1233 Occasionally this really doesn't work, in which case you can split the
1241 class CollE s => Coll s a where
1242 insert :: s -> a -> s
1255 <sect3 id="instance-decls">
1256 <title>Instance declarations</title>
1264 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1269 instance context1 => C type1 where ...
1270 instance context2 => C type2 where ...
1274 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1276 However, if you give the command line option
1277 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1278 option</primary></indexterm> then overlapping instance declarations are permitted.
1279 However, GHC arranges never to commit to using an instance declaration
1280 if another instance declaration also applies, either now or later.
1286 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1292 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1293 (but not identical to <literal>type1</literal>), or vice versa.
1297 Notice that these rules
1302 make it clear which instance decl to use
1303 (pick the most specific one that matches)
1310 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1311 Reason: you can pick which instance decl
1312 "matches" based on the type.
1317 However the rules are over-conservative. Two instance declarations can overlap,
1318 but it can still be clear in particular situations which to use. For example:
1320 instance C (Int,a) where ...
1321 instance C (a,Bool) where ...
1323 These are rejected by GHC's rules, but it is clear what to do when trying
1324 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1325 cannot apply. Yell if this restriction bites you.
1328 GHC is also conservative about committing to an overlapping instance. For example:
1330 class C a where { op :: a -> a }
1331 instance C [Int] where ...
1332 instance C a => C [a] where ...
1334 f :: C b => [b] -> [b]
1337 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1338 GHC does not commit to the second instance declaration, because in a paricular
1339 call of f, b might be instantiate to Int, so the first instance declaration
1340 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1341 GHC will instead silently pick the second instance, without complaining about
1342 the problem of subsequent instantiations.
1345 Regrettably, GHC doesn't guarantee to detect overlapping instance
1346 declarations if they appear in different modules. GHC can "see" the
1347 instance declarations in the transitive closure of all the modules
1348 imported by the one being compiled, so it can "see" all instance decls
1349 when it is compiling <literal>Main</literal>. However, it currently chooses not
1350 to look at ones that can't possibly be of use in the module currently
1351 being compiled, in the interests of efficiency. (Perhaps we should
1352 change that decision, at least for <literal>Main</literal>.)
1359 <emphasis>There are no restrictions on the type in an instance
1360 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1361 The instance "head" is the bit after the "=>" in an instance decl. For
1362 example, these are OK:
1366 instance C Int a where ...
1368 instance D (Int, Int) where ...
1370 instance E [[a]] where ...
1374 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1375 For example, this is OK:
1379 instance Stateful (ST s) (MutVar s) where ...
1383 The "at least one not a type variable" restriction is to ensure that
1384 context reduction terminates: each reduction step removes one type
1385 constructor. For example, the following would make the type checker
1386 loop if it wasn't excluded:
1390 instance C a => C a where ...
1394 There are two situations in which the rule is a bit of a pain. First,
1395 if one allows overlapping instance declarations then it's quite
1396 convenient to have a "default instance" declaration that applies if
1397 something more specific does not:
1406 Second, sometimes you might want to use the following to get the
1407 effect of a "class synonym":
1411 class (C1 a, C2 a, C3 a) => C a where { }
1413 instance (C1 a, C2 a, C3 a) => C a where { }
1417 This allows you to write shorter signatures:
1429 f :: (C1 a, C2 a, C3 a) => ...
1433 I'm on the lookout for a simple rule that preserves decidability while
1434 allowing these idioms. The experimental flag
1435 <option>-fallow-undecidable-instances</option><indexterm><primary>-fallow-undecidable-instances
1436 option</primary></indexterm> lifts this restriction, allowing all the types in an
1437 instance head to be type variables.
1444 <emphasis>Unlike Haskell 1.4, instance heads may use type
1445 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1446 writing the RHS of the type synonym definition. For example:
1450 type Point = (Int,Int)
1451 instance C Point where ...
1452 instance C [Point] where ...
1456 is legal. However, if you added
1460 instance C (Int,Int) where ...
1464 as well, then the compiler will complain about the overlapping
1465 (actually, identical) instance declarations. As always, type synonyms
1466 must be fully applied. You cannot, for example, write:
1471 instance Monad P where ...
1475 This design decision is independent of all the others, and easily
1476 reversed, but it makes sense to me.
1483 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1484 be type variables</emphasis>. Thus
1488 instance C a b => Eq (a,b) where ...
1496 instance C Int b => Foo b where ...
1500 is not OK. Again, the intent here is to make sure that context
1501 reduction terminates.
1503 Voluminous correspondence on the Haskell mailing list has convinced me
1504 that it's worth experimenting with a more liberal rule. If you use
1505 the flag <option>-fallow-undecidable-instances</option> can use arbitrary
1506 types in an instance context. Termination is ensured by having a
1507 fixed-depth recursion stack. If you exceed the stack depth you get a
1508 sort of backtrace, and the opportunity to increase the stack depth
1509 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1522 <sect2 id="implicit-parameters">
1523 <title>Implicit parameters
1526 <para> Implicit paramters are implemented as described in
1527 "Implicit parameters: dynamic scoping with static types",
1528 J Lewis, MB Shields, E Meijer, J Launchbury,
1529 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1532 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1534 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1535 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1536 context. In Haskell, all variables are statically bound. Dynamic
1537 binding of variables is a notion that goes back to Lisp, but was later
1538 discarded in more modern incarnations, such as Scheme. Dynamic binding
1539 can be very confusing in an untyped language, and unfortunately, typed
1540 languages, in particular Hindley-Milner typed languages like Haskell,
1541 only support static scoping of variables.
1544 However, by a simple extension to the type class system of Haskell, we
1545 can support dynamic binding. Basically, we express the use of a
1546 dynamically bound variable as a constraint on the type. These
1547 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1548 function uses a dynamically-bound variable <literal>?x</literal>
1549 of type <literal>t'</literal>". For
1550 example, the following expresses the type of a sort function,
1551 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1553 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1555 The dynamic binding constraints are just a new form of predicate in the type class system.
1558 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1559 where <literal>x</literal> is
1560 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1561 Use of this construct also introduces a new
1562 dynamic-binding constraint in the type of the expression.
1563 For example, the following definition
1564 shows how we can define an implicitly parameterized sort function in
1565 terms of an explicitly parameterized <literal>sortBy</literal> function:
1567 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1569 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1575 <title>Implicit-parameter type constraints</title>
1577 Dynamic binding constraints behave just like other type class
1578 constraints in that they are automatically propagated. Thus, when a
1579 function is used, its implicit parameters are inherited by the
1580 function that called it. For example, our <literal>sort</literal> function might be used
1581 to pick out the least value in a list:
1583 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1584 least xs = fst (sort xs)
1586 Without lifting a finger, the <literal>?cmp</literal> parameter is
1587 propagated to become a parameter of <literal>least</literal> as well. With explicit
1588 parameters, the default is that parameters must always be explicit
1589 propagated. With implicit parameters, the default is to always
1593 An implicit-parameter type constraint differs from other type class constraints in the
1594 following way: All uses of a particular implicit parameter must have
1595 the same type. This means that the type of <literal>(?x, ?x)</literal>
1596 is <literal>(?x::a) => (a,a)</literal>, and not
1597 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1601 <para> You can't have an implicit parameter in the context of a class or instance
1602 declaration. For example, both these declarations are illegal:
1604 class (?x::Int) => C a where ...
1605 instance (?x::a) => Foo [a] where ...
1607 Reason: exactly which implicit parameter you pick up depends on exactly where
1608 you invoke a function. But the ``invocation'' of instance declarations is done
1609 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1610 Easiest thing is to outlaw the offending types.</para>
1612 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1614 f :: (?x :: [a]) => Int -> Int
1617 g :: (Read a, Show a) => String -> String
1620 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1621 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1622 quite unambiguous, and fixes the type <literal>a</literal>.
1627 <title>Implicit-parameter bindings</title>
1630 An implicit parameter is <emphasis>bound</emphasis> using the standard
1631 <literal>let</literal> or <literal>where</literal> binding forms.
1632 For example, we define the <literal>min</literal> function by binding
1633 <literal>cmp</literal>.
1636 min = let ?cmp = (<=) in least
1640 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1641 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1642 (including in a list comprehension, or do-notation, or pattern guards),
1643 or a <literal>where</literal> clause.
1644 Note the following points:
1647 An implicit-parameter binding group must be a
1648 collection of simple bindings to implicit-style variables (no
1649 function-style bindings, and no type signatures); these bindings are
1650 neither polymorphic or recursive.
1653 You may not mix implicit-parameter bindings with ordinary bindings in a
1654 single <literal>let</literal>
1655 expression; use two nested <literal>let</literal>s instead.
1656 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1660 You may put multiple implicit-parameter bindings in a
1661 single binding group; but they are <emphasis>not</emphasis> treated
1662 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1663 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1664 parameter. The bindings are not nested, and may be re-ordered without changing
1665 the meaning of the program.
1666 For example, consider:
1668 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1670 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1671 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1673 f :: (?x::Int) => Int -> Int
1682 <sect2 id="linear-implicit-parameters">
1683 <title>Linear implicit parameters
1686 Linear implicit parameters are an idea developed by Koen Claessen,
1687 Mark Shields, and Simon PJ. They address the long-standing
1688 problem that monads seem over-kill for certain sorts of problem, notably:
1691 <listitem> <para> distributing a supply of unique names </para> </listitem>
1692 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1693 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1697 Linear implicit parameters are just like ordinary implicit parameters,
1698 except that they are "linear" -- that is, they cannot be copied, and
1699 must be explicitly "split" instead. Linear implicit parameters are
1700 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1701 (The '/' in the '%' suggests the split!)
1706 import GHC.Exts( Splittable )
1708 data NameSupply = ...
1710 splitNS :: NameSupply -> (NameSupply, NameSupply)
1711 newName :: NameSupply -> Name
1713 instance Splittable NameSupply where
1717 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1718 f env (Lam x e) = Lam x' (f env e)
1721 env' = extend env x x'
1722 ...more equations for f...
1724 Notice that the implicit parameter %ns is consumed
1726 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1727 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1731 So the translation done by the type checker makes
1732 the parameter explicit:
1734 f :: NameSupply -> Env -> Expr -> Expr
1735 f ns env (Lam x e) = Lam x' (f ns1 env e)
1737 (ns1,ns2) = splitNS ns
1739 env = extend env x x'
1741 Notice the call to 'split' introduced by the type checker.
1742 How did it know to use 'splitNS'? Because what it really did
1743 was to introduce a call to the overloaded function 'split',
1744 defined by the class <literal>Splittable</literal>:
1746 class Splittable a where
1749 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1750 split for name supplies. But we can simply write
1756 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1758 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1759 <literal>GHC.Exts</literal>.
1764 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1765 are entirely distinct implicit parameters: you
1766 can use them together and they won't intefere with each other. </para>
1769 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1771 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1772 in the context of a class or instance declaration. </para></listitem>
1776 <sect3><title>Warnings</title>
1779 The monomorphism restriction is even more important than usual.
1780 Consider the example above:
1782 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1783 f env (Lam x e) = Lam x' (f env e)
1786 env' = extend env x x'
1788 If we replaced the two occurrences of x' by (newName %ns), which is
1789 usually a harmless thing to do, we get:
1791 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1792 f env (Lam x e) = Lam (newName %ns) (f env e)
1794 env' = extend env x (newName %ns)
1796 But now the name supply is consumed in <emphasis>three</emphasis> places
1797 (the two calls to newName,and the recursive call to f), so
1798 the result is utterly different. Urk! We don't even have
1802 Well, this is an experimental change. With implicit
1803 parameters we have already lost beta reduction anyway, and
1804 (as John Launchbury puts it) we can't sensibly reason about
1805 Haskell programs without knowing their typing.
1810 <sect3><title>Recursive functions</title>
1811 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1814 foo :: %x::T => Int -> [Int]
1816 foo n = %x : foo (n-1)
1818 where T is some type in class Splittable.</para>
1820 Do you get a list of all the same T's or all different T's
1821 (assuming that split gives two distinct T's back)?
1823 If you supply the type signature, taking advantage of polymorphic
1824 recursion, you get what you'd probably expect. Here's the
1825 translated term, where the implicit param is made explicit:
1828 foo x n = let (x1,x2) = split x
1829 in x1 : foo x2 (n-1)
1831 But if you don't supply a type signature, GHC uses the Hindley
1832 Milner trick of using a single monomorphic instance of the function
1833 for the recursive calls. That is what makes Hindley Milner type inference
1834 work. So the translation becomes
1838 foom n = x : foom (n-1)
1842 Result: 'x' is not split, and you get a list of identical T's. So the
1843 semantics of the program depends on whether or not foo has a type signature.
1846 You may say that this is a good reason to dislike linear implicit parameters
1847 and you'd be right. That is why they are an experimental feature.
1853 <sect2 id="functional-dependencies">
1854 <title>Functional dependencies
1857 <para> Functional dependencies are implemented as described by Mark Jones
1858 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1859 In Proceedings of the 9th European Symposium on Programming,
1860 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1865 There should be more documentation, but there isn't (yet). Yell if you need it.
1870 <sect2 id="universal-quantification">
1871 <title>Arbitrary-rank polymorphism
1875 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1876 allows us to say exactly what this means. For example:
1884 g :: forall b. (b -> b)
1886 The two are treated identically.
1890 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1891 explicit universal quantification in
1893 For example, all the following types are legal:
1895 f1 :: forall a b. a -> b -> a
1896 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1898 f2 :: (forall a. a->a) -> Int -> Int
1899 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1901 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1903 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1904 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1905 The <literal>forall</literal> makes explicit the universal quantification that
1906 is implicitly added by Haskell.
1909 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1910 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1911 shows, the polymorphic type on the left of the function arrow can be overloaded.
1914 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1915 they have rank-2 types on the left of a function arrow.
1918 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1919 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1920 that restriction has now been lifted.)
1921 In particular, a forall-type (also called a "type scheme"),
1922 including an operational type class context, is legal:
1924 <listitem> <para> On the left of a function arrow </para> </listitem>
1925 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1926 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1927 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1928 field type signatures.</para> </listitem>
1929 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1930 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1932 There is one place you cannot put a <literal>forall</literal>:
1933 you cannot instantiate a type variable with a forall-type. So you cannot
1934 make a forall-type the argument of a type constructor. So these types are illegal:
1936 x1 :: [forall a. a->a]
1937 x2 :: (forall a. a->a, Int)
1938 x3 :: Maybe (forall a. a->a)
1940 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1941 a type variable any more!
1950 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1951 the types of the constructor arguments. Here are several examples:
1957 data T a = T1 (forall b. b -> b -> b) a
1959 data MonadT m = MkMonad { return :: forall a. a -> m a,
1960 bind :: forall a b. m a -> (a -> m b) -> m b
1963 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1969 The constructors have rank-2 types:
1975 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1976 MkMonad :: forall m. (forall a. a -> m a)
1977 -> (forall a b. m a -> (a -> m b) -> m b)
1979 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1985 Notice that you don't need to use a <literal>forall</literal> if there's an
1986 explicit context. For example in the first argument of the
1987 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1988 prefixed to the argument type. The implicit <literal>forall</literal>
1989 quantifies all type variables that are not already in scope, and are
1990 mentioned in the type quantified over.
1994 As for type signatures, implicit quantification happens for non-overloaded
1995 types too. So if you write this:
1998 data T a = MkT (Either a b) (b -> b)
2001 it's just as if you had written this:
2004 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2007 That is, since the type variable <literal>b</literal> isn't in scope, it's
2008 implicitly universally quantified. (Arguably, it would be better
2009 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2010 where that is what is wanted. Feedback welcomed.)
2014 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2015 the constructor to suitable values, just as usual. For example,
2026 a3 = MkSwizzle reverse
2029 a4 = let r x = Just x
2036 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2037 mkTs f x y = [T1 f x, T1 f y]
2043 The type of the argument can, as usual, be more general than the type
2044 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2045 does not need the <literal>Ord</literal> constraint.)
2049 When you use pattern matching, the bound variables may now have
2050 polymorphic types. For example:
2056 f :: T a -> a -> (a, Char)
2057 f (T1 w k) x = (w k x, w 'c' 'd')
2059 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2060 g (MkSwizzle s) xs f = s (map f (s xs))
2062 h :: MonadT m -> [m a] -> m [a]
2063 h m [] = return m []
2064 h m (x:xs) = bind m x $ \y ->
2065 bind m (h m xs) $ \ys ->
2072 In the function <function>h</function> we use the record selectors <literal>return</literal>
2073 and <literal>bind</literal> to extract the polymorphic bind and return functions
2074 from the <literal>MonadT</literal> data structure, rather than using pattern
2080 <title>Type inference</title>
2083 In general, type inference for arbitrary-rank types is undecideable.
2084 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2085 to get a decidable algorithm by requiring some help from the programmer.
2086 We do not yet have a formal specification of "some help" but the rule is this:
2089 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2090 provides an explicit polymorphic type for x, or GHC's type inference will assume
2091 that x's type has no foralls in it</emphasis>.
2094 What does it mean to "provide" an explicit type for x? You can do that by
2095 giving a type signature for x directly, using a pattern type signature
2096 (<xref linkend="scoped-type-variables">), thus:
2098 \ f :: (forall a. a->a) -> (f True, f 'c')
2100 Alternatively, you can give a type signature to the enclosing
2101 context, which GHC can "push down" to find the type for the variable:
2103 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2105 Here the type signature on the expression can be pushed inwards
2106 to give a type signature for f. Similarly, and more commonly,
2107 one can give a type signature for the function itself:
2109 h :: (forall a. a->a) -> (Bool,Char)
2110 h f = (f True, f 'c')
2112 You don't need to give a type signature if the lambda bound variable
2113 is a constructor argument. Here is an example we saw earlier:
2115 f :: T a -> a -> (a, Char)
2116 f (T1 w k) x = (w k x, w 'c' 'd')
2118 Here we do not need to give a type signature to <literal>w</literal>, because
2119 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2126 <sect3 id="implicit-quant">
2127 <title>Implicit quantification</title>
2130 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2131 user-written types, if and only if there is no explicit <literal>forall</literal>,
2132 GHC finds all the type variables mentioned in the type that are not already
2133 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2137 f :: forall a. a -> a
2144 h :: forall b. a -> b -> b
2150 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2153 f :: (a -> a) -> Int
2155 f :: forall a. (a -> a) -> Int
2157 f :: (forall a. a -> a) -> Int
2160 g :: (Ord a => a -> a) -> Int
2161 -- MEANS the illegal type
2162 g :: forall a. (Ord a => a -> a) -> Int
2164 g :: (forall a. Ord a => a -> a) -> Int
2166 The latter produces an illegal type, which you might think is silly,
2167 but at least the rule is simple. If you want the latter type, you
2168 can write your for-alls explicitly. Indeed, doing so is strongly advised
2174 <sect2 id="type-synonyms">
2175 <title>Liberalised type synonyms
2179 Type synonmys are like macros at the type level, and
2180 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2181 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
2183 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2184 in a type synonym, thus:
2186 type Discard a = forall b. Show b => a -> b -> (a, String)
2191 g :: Discard Int -> (Int,Bool) -- A rank-2 type
2198 You can write an unboxed tuple in a type synonym:
2200 type Pr = (# Int, Int #)
2208 You can apply a type synonym to a forall type:
2210 type Foo a = a -> a -> Bool
2212 f :: Foo (forall b. b->b)
2214 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2216 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2221 You can apply a type synonym to a partially applied type synonym:
2223 type Generic i o = forall x. i x -> o x
2226 foo :: Generic Id []
2228 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2230 foo :: forall x. x -> [x]
2238 GHC currently does kind checking before expanding synonyms (though even that
2242 After expanding type synonyms, GHC does validity checking on types, looking for
2243 the following mal-formedness which isn't detected simply by kind checking:
2246 Type constructor applied to a type involving for-alls.
2249 Unboxed tuple on left of an arrow.
2252 Partially-applied type synonym.
2256 this will be rejected:
2258 type Pr = (# Int, Int #)
2263 because GHC does not allow unboxed tuples on the left of a function arrow.
2268 <title>For-all hoisting</title>
2270 It is often convenient to use generalised type synonyms at the right hand
2271 end of an arrow, thus:
2273 type Discard a = forall b. a -> b -> a
2275 g :: Int -> Discard Int
2278 Simply expanding the type synonym would give
2280 g :: Int -> (forall b. Int -> b -> Int)
2282 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2284 g :: forall b. Int -> Int -> b -> Int
2286 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2287 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2288 performs the transformation:</emphasis>
2290 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2292 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2294 (In fact, GHC tries to retain as much synonym information as possible for use in
2295 error messages, but that is a usability issue.) This rule applies, of course, whether
2296 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2297 valid way to write <literal>g</literal>'s type signature:
2299 g :: Int -> Int -> forall b. b -> Int
2303 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2306 type Foo a = (?x::Int) => Bool -> a
2311 g :: (?x::Int) => Bool -> Bool -> Int
2317 <sect2 id="existential-quantification">
2318 <title>Existentially quantified data constructors
2322 The idea of using existential quantification in data type declarations
2323 was suggested by Laufer (I believe, thought doubtless someone will
2324 correct me), and implemented in Hope+. It's been in Lennart
2325 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2326 proved very useful. Here's the idea. Consider the declaration:
2332 data Foo = forall a. MkFoo a (a -> Bool)
2339 The data type <literal>Foo</literal> has two constructors with types:
2345 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2352 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2353 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2354 For example, the following expression is fine:
2360 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2366 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2367 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2368 isUpper</function> packages a character with a compatible function. These
2369 two things are each of type <literal>Foo</literal> and can be put in a list.
2373 What can we do with a value of type <literal>Foo</literal>?. In particular,
2374 what happens when we pattern-match on <function>MkFoo</function>?
2380 f (MkFoo val fn) = ???
2386 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2387 are compatible, the only (useful) thing we can do with them is to
2388 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2395 f (MkFoo val fn) = fn val
2401 What this allows us to do is to package heterogenous values
2402 together with a bunch of functions that manipulate them, and then treat
2403 that collection of packages in a uniform manner. You can express
2404 quite a bit of object-oriented-like programming this way.
2407 <sect3 id="existential">
2408 <title>Why existential?
2412 What has this to do with <emphasis>existential</emphasis> quantification?
2413 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2419 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2425 But Haskell programmers can safely think of the ordinary
2426 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2427 adding a new existential quantification construct.
2433 <title>Type classes</title>
2436 An easy extension (implemented in <Command>hbc</Command>) is to allow
2437 arbitrary contexts before the constructor. For example:
2443 data Baz = forall a. Eq a => Baz1 a a
2444 | forall b. Show b => Baz2 b (b -> b)
2450 The two constructors have the types you'd expect:
2456 Baz1 :: forall a. Eq a => a -> a -> Baz
2457 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2463 But when pattern matching on <function>Baz1</function> the matched values can be compared
2464 for equality, and when pattern matching on <function>Baz2</function> the first matched
2465 value can be converted to a string (as well as applying the function to it).
2466 So this program is legal:
2473 f (Baz1 p q) | p == q = "Yes"
2475 f (Baz2 v fn) = show (fn v)
2481 Operationally, in a dictionary-passing implementation, the
2482 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2483 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2484 extract it on pattern matching.
2488 Notice the way that the syntax fits smoothly with that used for
2489 universal quantification earlier.
2495 <title>Restrictions</title>
2498 There are several restrictions on the ways in which existentially-quantified
2499 constructors can be use.
2508 When pattern matching, each pattern match introduces a new,
2509 distinct, type for each existential type variable. These types cannot
2510 be unified with any other type, nor can they escape from the scope of
2511 the pattern match. For example, these fragments are incorrect:
2519 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2520 is the result of <function>f1</function>. One way to see why this is wrong is to
2521 ask what type <function>f1</function> has:
2525 f1 :: Foo -> a -- Weird!
2529 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2534 f1 :: forall a. Foo -> a -- Wrong!
2538 The original program is just plain wrong. Here's another sort of error
2542 f2 (Baz1 a b) (Baz1 p q) = a==q
2546 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2547 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2548 from the two <function>Baz1</function> constructors.
2556 You can't pattern-match on an existentially quantified
2557 constructor in a <literal>let</literal> or <literal>where</literal> group of
2558 bindings. So this is illegal:
2562 f3 x = a==b where { Baz1 a b = x }
2565 Instead, use a <literal>case</literal> expression:
2568 f3 x = case x of Baz1 a b -> a==b
2571 In general, you can only pattern-match
2572 on an existentially-quantified constructor in a <literal>case</literal> expression or
2573 in the patterns of a function definition.
2575 The reason for this restriction is really an implementation one.
2576 Type-checking binding groups is already a nightmare without
2577 existentials complicating the picture. Also an existential pattern
2578 binding at the top level of a module doesn't make sense, because it's
2579 not clear how to prevent the existentially-quantified type "escaping".
2580 So for now, there's a simple-to-state restriction. We'll see how
2588 You can't use existential quantification for <literal>newtype</literal>
2589 declarations. So this is illegal:
2593 newtype T = forall a. Ord a => MkT a
2597 Reason: a value of type <literal>T</literal> must be represented as a pair
2598 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2599 That contradicts the idea that <literal>newtype</literal> should have no
2600 concrete representation. You can get just the same efficiency and effect
2601 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2602 overloading involved, then there is more of a case for allowing
2603 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2604 because the <literal>data</literal> version does carry an implementation cost,
2605 but single-field existentially quantified constructors aren't much
2606 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2607 stands, unless there are convincing reasons to change it.
2615 You can't use <literal>deriving</literal> to define instances of a
2616 data type with existentially quantified data constructors.
2618 Reason: in most cases it would not make sense. For example:#
2621 data T = forall a. MkT [a] deriving( Eq )
2624 To derive <literal>Eq</literal> in the standard way we would need to have equality
2625 between the single component of two <function>MkT</function> constructors:
2629 (MkT a) == (MkT b) = ???
2632 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2633 It's just about possible to imagine examples in which the derived instance
2634 would make sense, but it seems altogether simpler simply to prohibit such
2635 declarations. Define your own instances!
2647 <sect2 id="scoped-type-variables">
2648 <title>Scoped type variables
2652 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2653 variable</emphasis>. For example
2659 f (xs::[a]) = ys ++ ys
2668 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2669 This brings the type variable <literal>a</literal> into scope; it scopes over
2670 all the patterns and right hand sides for this equation for <function>f</function>.
2671 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2675 Pattern type signatures are completely orthogonal to ordinary, separate
2676 type signatures. The two can be used independently or together.
2677 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2678 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2679 implicitly universally quantified. (If there are no type variables in
2680 scope, all type variables mentioned in the signature are universally
2681 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2682 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2683 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2684 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2685 it becomes possible to do so.
2689 Scoped type variables are implemented in both GHC and Hugs. Where the
2690 implementations differ from the specification below, those differences
2695 So much for the basic idea. Here are the details.
2699 <title>What a pattern type signature means</title>
2701 A type variable brought into scope by a pattern type signature is simply
2702 the name for a type. The restriction they express is that all occurrences
2703 of the same name mean the same type. For example:
2705 f :: [Int] -> Int -> Int
2706 f (xs::[a]) (y::a) = (head xs + y) :: a
2708 The pattern type signatures on the left hand side of
2709 <literal>f</literal> express the fact that <literal>xs</literal>
2710 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2711 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2712 specifies that this expression must have the same type <literal>a</literal>.
2713 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2714 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2715 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2716 rules, which specified that a pattern-bound type variable should be universally quantified.)
2717 For example, all of these are legal:</para>
2720 t (x::a) (y::a) = x+y*2
2722 f (x::a) (y::b) = [x,y] -- a unifies with b
2724 g (x::a) = x + 1::Int -- a unifies with Int
2726 h x = let k (y::a) = [x,y] -- a is free in the
2727 in k x -- environment
2729 k (x::a) True = ... -- a unifies with Int
2730 k (x::Int) False = ...
2733 w (x::a) = x -- a unifies with [b]
2739 <title>Scope and implicit quantification</title>
2747 All the type variables mentioned in a pattern,
2748 that are not already in scope,
2749 are brought into scope by the pattern. We describe this set as
2750 the <emphasis>type variables bound by the pattern</emphasis>.
2753 f (x::a) = let g (y::(a,b)) = fst y
2757 The pattern <literal>(x::a)</literal> brings the type variable
2758 <literal>a</literal> into scope, as well as the term
2759 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2760 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2761 and brings into scope the type variable <literal>b</literal>.
2767 The type variable(s) bound by the pattern have the same scope
2768 as the term variable(s) bound by the pattern. For example:
2771 f (x::a) = <...rhs of f...>
2772 (p::b, q::b) = (1,2)
2773 in <...body of let...>
2775 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2776 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2777 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2778 just like <literal>p</literal> and <literal>q</literal> do.
2779 Indeed, the newly bound type variables also scope over any ordinary, separate
2780 type signatures in the <literal>let</literal> group.
2787 The type variables bound by the pattern may be
2788 mentioned in ordinary type signatures or pattern
2789 type signatures anywhere within their scope.
2796 In ordinary type signatures, any type variable mentioned in the
2797 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2805 Ordinary type signatures do not bring any new type variables
2806 into scope (except in the type signature itself!). So this is illegal:
2813 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2814 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2815 and that is an incorrect typing.
2822 The pattern type signature is a monotype:
2827 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2831 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2832 not to type schemes.
2836 There is no implicit universal quantification on pattern type signatures (in contrast to
2837 ordinary type signatures).
2847 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2848 scope over the methods defined in the <literal>where</literal> part. For example:
2862 (Not implemented in Hugs yet, Dec 98).
2873 <title>Result type signatures</title>
2881 The result type of a function can be given a signature,
2886 f (x::a) :: [a] = [x,x,x]
2890 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2891 result type. Sometimes this is the only way of naming the type variable
2896 f :: Int -> [a] -> [a]
2897 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2898 in \xs -> map g (reverse xs `zip` xs)
2910 Result type signatures are not yet implemented in Hugs.
2916 <title>Where a pattern type signature can occur</title>
2919 A pattern type signature can occur in any pattern. For example:
2924 A pattern type signature can be on an arbitrary sub-pattern, not
2929 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2938 Pattern type signatures, including the result part, can be used
2939 in lambda abstractions:
2942 (\ (x::a, y) :: a -> x)
2949 Pattern type signatures, including the result part, can be used
2950 in <literal>case</literal> expressions:
2954 case e of { (x::a, y) :: a -> x }
2962 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2963 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2964 token or a parenthesised type of some sort). To see why,
2965 consider how one would parse this:
2979 Pattern type signatures can bind existential type variables.
2984 data T = forall a. MkT [a]
2987 f (MkT [t::a]) = MkT t3
3000 Pattern type signatures
3001 can be used in pattern bindings:
3004 f x = let (y, z::a) = x in ...
3005 f1 x = let (y, z::Int) = x in ...
3006 f2 (x::(Int,a)) = let (y, z::a) = x in ...
3007 f3 :: (b->b) = \x -> x
3010 In all such cases, the binding is not generalised over the pattern-bound
3011 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
3012 has type <literal>b -> b</literal> for some type <literal>b</literal>,
3013 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
3014 In contrast, the binding
3019 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
3020 in <literal>f4</literal>'s scope.
3030 <sect2 id="newtype-deriving">
3031 <title>Generalised derived instances for newtypes</title>
3034 When you define an abstract type using <literal>newtype</literal>, you may want
3035 the new type to inherit some instances from its representation. In
3036 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3037 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3038 other classes you have to write an explicit instance declaration. For
3039 example, if you define
3042 newtype Dollars = Dollars Int
3045 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3046 explicitly define an instance of <literal>Num</literal>:
3049 instance Num Dollars where
3050 Dollars a + Dollars b = Dollars (a+b)
3053 All the instance does is apply and remove the <literal>newtype</literal>
3054 constructor. It is particularly galling that, since the constructor
3055 doesn't appear at run-time, this instance declaration defines a
3056 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3057 dictionary, only slower!
3061 <sect3> <title> Generalising the deriving clause </title>
3063 GHC now permits such instances to be derived instead, so one can write
3065 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3068 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3069 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3070 derives an instance declaration of the form
3073 instance Num Int => Num Dollars
3076 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3080 We can also derive instances of constructor classes in a similar
3081 way. For example, suppose we have implemented state and failure monad
3082 transformers, such that
3085 instance Monad m => Monad (State s m)
3086 instance Monad m => Monad (Failure m)
3088 In Haskell 98, we can define a parsing monad by
3090 type Parser tok m a = State [tok] (Failure m) a
3093 which is automatically a monad thanks to the instance declarations
3094 above. With the extension, we can make the parser type abstract,
3095 without needing to write an instance of class <literal>Monad</literal>, via
3098 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3101 In this case the derived instance declaration is of the form
3103 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3106 Notice that, since <literal>Monad</literal> is a constructor class, the
3107 instance is a <emphasis>partial application</emphasis> of the new type, not the
3108 entire left hand side. We can imagine that the type declaration is
3109 ``eta-converted'' to generate the context of the instance
3114 We can even derive instances of multi-parameter classes, provided the
3115 newtype is the last class parameter. In this case, a ``partial
3116 application'' of the class appears in the <literal>deriving</literal>
3117 clause. For example, given the class
3120 class StateMonad s m | m -> s where ...
3121 instance Monad m => StateMonad s (State s m) where ...
3123 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3125 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3126 deriving (Monad, StateMonad [tok])
3129 The derived instance is obtained by completing the application of the
3130 class to the new type:
3133 instance StateMonad [tok] (State [tok] (Failure m)) =>
3134 StateMonad [tok] (Parser tok m)
3139 As a result of this extension, all derived instances in newtype
3140 declarations are treated uniformly (and implemented just by reusing
3141 the dictionary for the representation type), <emphasis>except</emphasis>
3142 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3143 the newtype and its representation.
3147 <sect3> <title> A more precise specification </title>
3149 Derived instance declarations are constructed as follows. Consider the
3150 declaration (after expansion of any type synonyms)
3153 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3156 where <literal>S</literal> is a type constructor, <literal>t1...tk</literal> are
3158 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3159 the <literal>ti</literal>, and the <literal>ci</literal> are partial applications of
3160 classes of the form <literal>C t1'...tj'</literal>. The derived instance
3161 declarations are, for each <literal>ci</literal>,
3164 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3166 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3167 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3171 As an example which does <emphasis>not</emphasis> work, consider
3173 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3175 Here we cannot derive the instance
3177 instance Monad (State s m) => Monad (NonMonad m)
3180 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3181 and so cannot be "eta-converted" away. It is a good thing that this
3182 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3183 not, in fact, a monad --- for the same reason. Try defining
3184 <literal>>>=</literal> with the correct type: you won't be able to.
3188 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3189 important, since we can only derive instances for the last one. If the
3190 <literal>StateMonad</literal> class above were instead defined as
3193 class StateMonad m s | m -> s where ...
3196 then we would not have been able to derive an instance for the
3197 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3198 classes usually have one "main" parameter for which deriving new
3199 instances is most interesting.
3207 <!-- ==================== End of type system extensions ================= -->
3209 <!-- ====================== TEMPLATE HASKELL ======================= -->
3211 <sect1 id="template-haskell">
3212 <title>Template Haskell</title>
3214 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
3215 the main technical innovations are discussed in "<ulink
3216 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3217 Template Meta-programming for Haskell</ulink>", in
3218 Proc Haskell Workshop 2002.
3222 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3223 Tim Sheard is going to expand it.)
3226 <sect2> <title> Syntax </title>
3228 Template Haskell has the following new syntactic constructions. You need to use the flag
3229 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
3233 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3234 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3235 There must be no space between the "$" and the identifier or parenthesis. This use
3236 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3237 of "." as an infix operator. If you want the infix operator, put spaces around it.
3239 <para> A splice can occur in place of
3241 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3242 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3243 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3245 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3246 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3252 A expression quotation is written in Oxford brackets, thus:
3254 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3255 the quotation has type <literal>Expr</literal>.</para></listitem>
3256 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3257 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3258 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3259 the quotation has type <literal>Type</literal>.</para></listitem>
3260 </itemizedlist></para></listitem>
3263 Reification is written thus:
3265 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3266 has type <literal>Dec</literal>. </para></listitem>
3267 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3268 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3269 <listitem><para> Still to come: fixities </para></listitem>
3271 </itemizedlist></para>
3279 <sect2> <title> Using Template Haskell </title>
3283 The data types and monadic constructor functions for Template Haskell are in the library
3284 <literal>Language.Haskell.THSyntax</literal>.
3288 You can only run a function at compile time if it is imported from another module. That is,
3289 you can't define a function in a module, and call it from within a splice in the same module.
3290 (It would make sense to do so, but it's hard to implement.)
3294 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3298 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3299 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3306 <!-- ==================== ASSERTIONS ================= -->
3308 <sect1 id="sec-assertions">
3310 <indexterm><primary>Assertions</primary></indexterm>
3314 If you want to make use of assertions in your standard Haskell code, you
3315 could define a function like the following:
3321 assert :: Bool -> a -> a
3322 assert False x = error "assertion failed!"
3329 which works, but gives you back a less than useful error message --
3330 an assertion failed, but which and where?
3334 One way out is to define an extended <function>assert</function> function which also
3335 takes a descriptive string to include in the error message and
3336 perhaps combine this with the use of a pre-processor which inserts
3337 the source location where <function>assert</function> was used.
3341 Ghc offers a helping hand here, doing all of this for you. For every
3342 use of <function>assert</function> in the user's source:
3348 kelvinToC :: Double -> Double
3349 kelvinToC k = assert (k >= 0.0) (k+273.15)
3355 Ghc will rewrite this to also include the source location where the
3362 assert pred val ==> assertError "Main.hs|15" pred val
3368 The rewrite is only performed by the compiler when it spots
3369 applications of <function>Control.Exception.assert</function>, so you
3370 can still define and use your own versions of
3371 <function>assert</function>, should you so wish. If not, import
3372 <literal>Control.Exception</literal> to make use
3373 <function>assert</function> in your code.
3377 To have the compiler ignore uses of assert, use the compiler option
3378 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3379 option</primary></indexterm> That is, expressions of the form
3380 <literal>assert pred e</literal> will be rewritten to
3381 <literal>e</literal>.
3385 Assertion failures can be caught, see the documentation for the
3386 <literal>Control.Exception</literal> library for the details.
3392 <!-- =============================== PRAGMAS =========================== -->
3394 <sect1 id="pragmas">
3395 <title>Pragmas</title>
3397 <indexterm><primary>pragma</primary></indexterm>
3399 <para>GHC supports several pragmas, or instructions to the
3400 compiler placed in the source code. Pragmas don't normally affect
3401 the meaning of the program, but they might affect the efficiency
3402 of the generated code.</para>
3404 <para>Pragmas all take the form
3406 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3408 where <replaceable>word</replaceable> indicates the type of
3409 pragma, and is followed optionally by information specific to that
3410 type of pragma. Case is ignored in
3411 <replaceable>word</replaceable>. The various values for
3412 <replaceable>word</replaceable> that GHC understands are described
3413 in the following sections; any pragma encountered with an
3414 unrecognised <replaceable>word</replaceable> is (silently)
3417 <sect2 id="inline-pragma">
3418 <title>INLINE pragma
3420 <indexterm><primary>INLINE pragma</primary></indexterm>
3421 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
3424 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
3425 functions/values that are “small enough,” thus avoiding the call
3426 overhead and possibly exposing other more-wonderful optimisations.
3430 You will probably see these unfoldings (in Core syntax) in your
3435 Normally, if GHC decides a function is “too expensive” to inline, it
3436 will not do so, nor will it export that unfolding for other modules to
3441 The sledgehammer you can bring to bear is the
3442 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
3445 key_function :: Int -> String -> (Bool, Double)
3447 #ifdef __GLASGOW_HASKELL__
3448 {-# INLINE key_function #-}
3452 (You don't need to do the C pre-processor carry-on unless you're going
3453 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
3457 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
3458 “cost” to be very low. The normal unfolding machinery will then be
3459 very keen to inline it.
3463 An <literal>INLINE</literal> pragma for a function can be put anywhere its type
3464 signature could be put.
3468 <literal>INLINE</literal> pragmas are a particularly good idea for the
3469 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
3470 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
3473 #ifdef __GLASGOW_HASKELL__
3474 {-# INLINE thenUs #-}
3475 {-# INLINE returnUs #-}
3483 <sect2 id="noinline-pragma">
3484 <title>NOINLINE pragma
3487 <indexterm><primary>NOINLINE pragma</primary></indexterm>
3488 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
3489 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
3490 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
3493 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
3494 it stops the named function from being inlined by the compiler. You
3495 shouldn't ever need to do this, unless you're very cautious about code
3499 <para><literal>NOTINLINE</literal> is a synonym for
3500 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
3501 by Haskell 98 as the standard way to disable inlining, so it should be
3502 used if you want your code to be portable).</para>
3506 <sect2 id="specialize-pragma">
3507 <title>SPECIALIZE pragma</title>
3509 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3510 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
3511 <indexterm><primary>overloading, death to</primary></indexterm>
3513 <para>(UK spelling also accepted.) For key overloaded
3514 functions, you can create extra versions (NB: more code space)
3515 specialised to particular types. Thus, if you have an
3516 overloaded function:</para>
3519 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3522 <para>If it is heavily used on lists with
3523 <literal>Widget</literal> keys, you could specialise it as
3527 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3530 <para>To get very fancy, you can also specify a named function
3531 to use for the specialised value, as in:</para>
3534 {-# RULES hammeredLookup = blah #-}
3537 <para>where <literal>blah</literal> is an implementation of
3538 <literal>hammerdLookup</literal> written specialy for
3539 <literal>Widget</literal> lookups. It's <emphasis>Your
3540 Responsibility</emphasis> to make sure that
3541 <function>blah</function> really behaves as a specialised
3542 version of <function>hammeredLookup</function>!!!</para>
3544 <para>Note we use the <literal>RULE</literal> pragma here to
3545 indicate that <literal>hammeredLookup</literal> applied at a
3546 certain type should be replaced by <literal>blah</literal>. See
3547 <xref linkend="rules"> for more information on
3548 <literal>RULES</literal>.</para>
3550 <para>An example in which using <literal>RULES</literal> for
3551 specialisation will Win Big:
3554 toDouble :: Real a => a -> Double
3555 toDouble = fromRational . toRational
3557 {-# SPECIALIZE toDouble :: Int -> Double = i2d #-}
3558 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3561 The <function>i2d</function> function is virtually one machine
3562 instruction; the default conversion—via an intermediate
3563 <literal>Rational</literal>—is obscenely expensive by
3566 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3567 be put anywhere its type signature could be put.</para>
3571 <sect2 id="specialize-instance-pragma">
3572 <title>SPECIALIZE instance pragma
3576 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3577 <indexterm><primary>overloading, death to</primary></indexterm>
3578 Same idea, except for instance declarations. For example:
3581 instance (Eq a) => Eq (Foo a) where {
3582 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3586 The pragma must occur inside the <literal>where</literal> part
3587 of the instance declaration.
3590 Compatible with HBC, by the way, except perhaps in the placement
3596 <sect2 id="line-pragma">
3601 <indexterm><primary>LINE pragma</primary></indexterm>
3602 <indexterm><primary>pragma, LINE</primary></indexterm>
3606 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
3607 automatically generated Haskell code. It lets you specify the line
3608 number and filename of the original code; for example
3614 {-# LINE 42 "Foo.vhs" #-}
3620 if you'd generated the current file from something called <filename>Foo.vhs</filename>
3621 and this line corresponds to line 42 in the original. GHC will adjust
3622 its error messages to refer to the line/file named in the <literal>LINE</literal>
3629 <title>RULES pragma</title>
3632 The RULES pragma lets you specify rewrite rules. It is described in
3633 <xref LinkEnd="rewrite-rules">.
3638 <sect2 id="deprecated-pragma">
3639 <title>DEPRECATED pragma</title>
3642 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
3643 There are two forms.
3647 You can deprecate an entire module thus:</para>
3649 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3653 When you compile any module that import <literal>Wibble</literal>, GHC will print
3654 the specified message.</para>
3659 You can deprecate a function, class, or type, with the following top-level declaration:
3662 {-# DEPRECATED f, C, T "Don't use these" #-}
3665 When you compile any module that imports and uses any of the specifed entities,
3666 GHC will print the specified message.
3670 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
3676 <!-- ======================= REWRITE RULES ======================== -->
3678 <sect1 id="rewrite-rules">
3679 <title>Rewrite rules
3681 <indexterm><primary>RULES pagma</primary></indexterm>
3682 <indexterm><primary>pragma, RULES</primary></indexterm>
3683 <indexterm><primary>rewrite rules</primary></indexterm></title>
3686 The programmer can specify rewrite rules as part of the source program
3687 (in a pragma). GHC applies these rewrite rules wherever it can.
3695 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3702 <title>Syntax</title>
3705 From a syntactic point of view:
3711 Each rule has a name, enclosed in double quotes. The name itself has
3712 no significance at all. It is only used when reporting how many times the rule fired.
3718 There may be zero or more rules in a <literal>RULES</literal> pragma.
3724 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3725 is set, so you must lay out your rules starting in the same column as the
3726 enclosing definitions.
3732 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3733 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3734 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3735 by spaces, just like in a type <literal>forall</literal>.
3741 A pattern variable may optionally have a type signature.
3742 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3743 For example, here is the <literal>foldr/build</literal> rule:
3746 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3747 foldr k z (build g) = g k z
3750 Since <function>g</function> has a polymorphic type, it must have a type signature.
3757 The left hand side of a rule must consist of a top-level variable applied
3758 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3761 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3762 "wrong2" forall f. f True = True
3765 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3772 A rule does not need to be in the same module as (any of) the
3773 variables it mentions, though of course they need to be in scope.
3779 Rules are automatically exported from a module, just as instance declarations are.
3790 <title>Semantics</title>
3793 From a semantic point of view:
3799 Rules are only applied if you use the <option>-O</option> flag.
3805 Rules are regarded as left-to-right rewrite rules.
3806 When GHC finds an expression that is a substitution instance of the LHS
3807 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3808 By "a substitution instance" we mean that the LHS can be made equal to the
3809 expression by substituting for the pattern variables.
3816 The LHS and RHS of a rule are typechecked, and must have the
3824 GHC makes absolutely no attempt to verify that the LHS and RHS
3825 of a rule have the same meaning. That is undecideable in general, and
3826 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3833 GHC makes no attempt to make sure that the rules are confluent or
3834 terminating. For example:
3837 "loop" forall x,y. f x y = f y x
3840 This rule will cause the compiler to go into an infinite loop.
3847 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3853 GHC currently uses a very simple, syntactic, matching algorithm
3854 for matching a rule LHS with an expression. It seeks a substitution
3855 which makes the LHS and expression syntactically equal modulo alpha
3856 conversion. The pattern (rule), but not the expression, is eta-expanded if
3857 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3858 But not beta conversion (that's called higher-order matching).
3862 Matching is carried out on GHC's intermediate language, which includes
3863 type abstractions and applications. So a rule only matches if the
3864 types match too. See <xref LinkEnd="rule-spec"> below.
3870 GHC keeps trying to apply the rules as it optimises the program.
3871 For example, consider:
3880 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3881 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3882 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
3883 not be substituted, and the rule would not fire.
3890 In the earlier phases of compilation, GHC inlines <emphasis>nothing
3891 that appears on the LHS of a rule</emphasis>, because once you have substituted
3892 for something you can't match against it (given the simple minded
3893 matching). So if you write the rule
3896 "map/map" forall f,g. map f . map g = map (f.g)
3899 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
3900 It will only match something written with explicit use of ".".
3901 Well, not quite. It <emphasis>will</emphasis> match the expression
3907 where <function>wibble</function> is defined:
3910 wibble f g = map f . map g
3913 because <function>wibble</function> will be inlined (it's small).
3915 Later on in compilation, GHC starts inlining even things on the
3916 LHS of rules, but still leaves the rules enabled. This inlining
3917 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
3924 All rules are implicitly exported from the module, and are therefore
3925 in force in any module that imports the module that defined the rule, directly
3926 or indirectly. (That is, if A imports B, which imports C, then C's rules are
3927 in force when compiling A.) The situation is very similar to that for instance
3939 <title>List fusion</title>
3942 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
3943 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
3944 intermediate list should be eliminated entirely.
3948 The following are good producers:
3960 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
3966 Explicit lists (e.g. <literal>[True, False]</literal>)
3972 The cons constructor (e.g <literal>3:4:[]</literal>)
3978 <function>++</function>
3984 <function>map</function>
3990 <function>filter</function>
3996 <function>iterate</function>, <function>repeat</function>
4002 <function>zip</function>, <function>zipWith</function>
4011 The following are good consumers:
4023 <function>array</function> (on its second argument)
4029 <function>length</function>
4035 <function>++</function> (on its first argument)
4041 <function>foldr</function>
4047 <function>map</function>
4053 <function>filter</function>
4059 <function>concat</function>
4065 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4071 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4072 will fuse with one but not the other)
4078 <function>partition</function>
4084 <function>head</function>
4090 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4096 <function>sequence_</function>
4102 <function>msum</function>
4108 <function>sortBy</function>
4117 So, for example, the following should generate no intermediate lists:
4120 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4126 This list could readily be extended; if there are Prelude functions that you use
4127 a lot which are not included, please tell us.
4131 If you want to write your own good consumers or producers, look at the
4132 Prelude definitions of the above functions to see how to do so.
4137 <sect2 id="rule-spec">
4138 <title>Specialisation
4142 Rewrite rules can be used to get the same effect as a feature
4143 present in earlier version of GHC:
4146 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4149 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4150 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4151 specialising the original definition of <function>fromIntegral</function> the programmer is
4152 promising that it is safe to use <function>int8ToInt16</function> instead.
4156 This feature is no longer in GHC. But rewrite rules let you do the
4161 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4165 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4166 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4167 GHC adds the type and dictionary applications to get the typed rule
4170 forall (d1::Integral Int8) (d2::Num Int16) .
4171 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4175 this rule does not need to be in the same file as fromIntegral,
4176 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4177 have an original definition available to specialise).
4183 <title>Controlling what's going on</title>
4191 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4197 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4198 If you add <option>-dppr-debug</option> you get a more detailed listing.
4204 The defintion of (say) <function>build</function> in <FileName>PrelBase.lhs</FileName> looks llike this:
4207 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4208 {-# INLINE build #-}
4212 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4213 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4214 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4215 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4222 In <filename>ghc/lib/std/PrelBase.lhs</filename> look at the rules for <function>map</function> to
4223 see how to write rules that will do fusion and yet give an efficient
4224 program even if fusion doesn't happen. More rules in <filename>PrelList.lhs</filename>.
4236 <sect1 id="generic-classes">
4237 <title>Generic classes</title>
4239 <para>(Note: support for generic classes is currently broken in
4243 The ideas behind this extension are described in detail in "Derivable type classes",
4244 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4245 An example will give the idea:
4253 fromBin :: [Int] -> (a, [Int])
4255 toBin {| Unit |} Unit = []
4256 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4257 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4258 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4260 fromBin {| Unit |} bs = (Unit, bs)
4261 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4262 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4263 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4264 (y,bs'') = fromBin bs'
4267 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4268 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4269 which are defined thus in the library module <literal>Generics</literal>:
4273 data a :+: b = Inl a | Inr b
4274 data a :*: b = a :*: b
4277 Now you can make a data type into an instance of Bin like this:
4279 instance (Bin a, Bin b) => Bin (a,b)
4280 instance Bin a => Bin [a]
4282 That is, just leave off the "where" clasuse. Of course, you can put in the
4283 where clause and over-ride whichever methods you please.
4287 <title> Using generics </title>
4288 <para>To use generics you need to</para>
4291 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4292 <option>-fgenerics</option> (to generate extra per-data-type code),
4293 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4297 <para>Import the module <literal>Generics</literal> from the
4298 <literal>lang</literal> package. This import brings into
4299 scope the data types <literal>Unit</literal>,
4300 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4301 don't need this import if you don't mention these types
4302 explicitly; for example, if you are simply giving instance
4303 declarations.)</para>
4308 <sect2> <title> Changes wrt the paper </title>
4310 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4311 can be written infix (indeed, you can now use
4312 any operator starting in a colon as an infix type constructor). Also note that
4313 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4314 Finally, note that the syntax of the type patterns in the class declaration
4315 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4316 alone would ambiguous when they appear on right hand sides (an extension we
4317 anticipate wanting).
4321 <sect2> <title>Terminology and restrictions</title>
4323 Terminology. A "generic default method" in a class declaration
4324 is one that is defined using type patterns as above.
4325 A "polymorphic default method" is a default method defined as in Haskell 98.
4326 A "generic class declaration" is a class declaration with at least one
4327 generic default method.
4335 Alas, we do not yet implement the stuff about constructor names and
4342 A generic class can have only one parameter; you can't have a generic
4343 multi-parameter class.
4349 A default method must be defined entirely using type patterns, or entirely
4350 without. So this is illegal:
4353 op :: a -> (a, Bool)
4354 op {| Unit |} Unit = (Unit, True)
4357 However it is perfectly OK for some methods of a generic class to have
4358 generic default methods and others to have polymorphic default methods.
4364 The type variable(s) in the type pattern for a generic method declaration
4365 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:
4369 op {| p :*: q |} (x :*: y) = op (x :: p)
4377 The type patterns in a generic default method must take one of the forms:
4383 where "a" and "b" are type variables. Furthermore, all the type patterns for
4384 a single type constructor (<literal>:*:</literal>, say) must be identical; they
4385 must use the same type variables. So this is illegal:
4389 op {| a :+: b |} (Inl x) = True
4390 op {| p :+: q |} (Inr y) = False
4392 The type patterns must be identical, even in equations for different methods of the class.
4393 So this too is illegal:
4397 op1 {| a :*: b |} (x :*: y) = True
4400 op2 {| p :*: q |} (x :*: y) = False
4402 (The reason for this restriction is that we gather all the equations for a particular type consructor
4403 into a single generic instance declaration.)
4409 A generic method declaration must give a case for each of the three type constructors.
4415 The type for a generic method can be built only from:
4417 <listitem> <para> Function arrows </para> </listitem>
4418 <listitem> <para> Type variables </para> </listitem>
4419 <listitem> <para> Tuples </para> </listitem>
4420 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
4422 Here are some example type signatures for generic methods:
4425 op2 :: Bool -> (a,Bool)
4426 op3 :: [Int] -> a -> a
4429 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
4433 This restriction is an implementation restriction: we just havn't got around to
4434 implementing the necessary bidirectional maps over arbitrary type constructors.
4435 It would be relatively easy to add specific type constructors, such as Maybe and list,
4436 to the ones that are allowed.</para>
4441 In an instance declaration for a generic class, the idea is that the compiler
4442 will fill in the methods for you, based on the generic templates. However it can only
4447 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4452 No constructor of the instance type has unboxed fields.
4456 (Of course, these things can only arise if you are already using GHC extensions.)
4457 However, you can still give an instance declarations for types which break these rules,
4458 provided you give explicit code to override any generic default methods.
4466 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
4467 what the compiler does with generic declarations.
4472 <sect2> <title> Another example </title>
4474 Just to finish with, here's another example I rather like:
4478 nCons {| Unit |} _ = 1
4479 nCons {| a :*: b |} _ = 1
4480 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4483 tag {| Unit |} _ = 1
4484 tag {| a :*: b |} _ = 1
4485 tag {| a :+: b |} (Inl x) = tag x
4486 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4495 ;;; Local Variables: ***
4497 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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