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 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
640 <sect2 id="parallel-list-comprehensions">
641 <title>Parallel List Comprehensions</title>
642 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
644 <indexterm><primary>parallel list comprehensions</primary>
647 <para>Parallel list comprehensions are a natural extension to list
648 comprehensions. List comprehensions can be thought of as a nice
649 syntax for writing maps and filters. Parallel comprehensions
650 extend this to include the zipWith family.</para>
652 <para>A parallel list comprehension has multiple independent
653 branches of qualifier lists, each separated by a `|' symbol. For
654 example, the following zips together two lists:</para>
657 [ (x, y) | x <- xs | y <- ys ]
660 <para>The behavior of parallel list comprehensions follows that of
661 zip, in that the resulting list will have the same length as the
662 shortest branch.</para>
664 <para>We can define parallel list comprehensions by translation to
665 regular comprehensions. Here's the basic idea:</para>
667 <para>Given a parallel comprehension of the form: </para>
670 [ e | p1 <- e11, p2 <- e12, ...
671 | q1 <- e21, q2 <- e22, ...
676 <para>This will be translated to: </para>
679 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
680 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
685 <para>where `zipN' is the appropriate zip for the given number of
690 <sect2 id="rebindable-syntax">
691 <title>Rebindable syntax</title>
694 <para>GHC allows most kinds of built-in syntax to be rebound by
695 the user, to facilitate replacing the <literal>Prelude</literal>
696 with a home-grown version, for example.</para>
698 <para>You may want to define your own numeric class
699 hierarchy. It completely defeats that purpose if the
700 literal "1" means "<literal>Prelude.fromInteger
701 1</literal>", which is what the Haskell Report specifies.
702 So the <option>-fno-implicit-prelude</option> flag causes
703 the following pieces of built-in syntax to refer to
704 <emphasis>whatever is in scope</emphasis>, not the Prelude
709 <para>Integer and fractional literals mean
710 "<literal>fromInteger 1</literal>" and
711 "<literal>fromRational 3.2</literal>", not the
712 Prelude-qualified versions; both in expressions and in
714 <para>However, the standard Prelude <literal>Eq</literal> class
715 is still used for the equality test necessary for literal patterns.</para>
719 <para>Negation (e.g. "<literal>- (f x)</literal>")
720 means "<literal>negate (f x)</literal>" (not
721 <literal>Prelude.negate</literal>).</para>
725 <para>In an n+k pattern, the standard Prelude
726 <literal>Ord</literal> class is still used for comparison,
727 but the necessary subtraction uses whatever
728 "<literal>(-)</literal>" is in scope (not
729 "<literal>Prelude.(-)</literal>").</para>
733 <para>"Do" notation is translated using whatever
734 functions <literal>(>>=)</literal>,
735 <literal>(>>)</literal>, <literal>fail</literal>, and
736 <literal>return</literal>, are in scope (not the Prelude
737 versions). List comprehensions, and parallel array
738 comprehensions, are unaffected. </para></listitem>
741 <para>Be warned: this is an experimental facility, with fewer checks than
742 usual. In particular, it is essential that the functions GHC finds in scope
743 must have the appropriate types, namely:
745 fromInteger :: forall a. (...) => Integer -> a
746 fromRational :: forall a. (...) => Rational -> a
747 negate :: forall a. (...) => a -> a
748 (-) :: forall a. (...) => a -> a -> a
749 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
750 (>>) :: forall m a. (...) => m a -> m b -> m b
751 return :: forall m a. (...) => a -> m a
752 fail :: forall m a. (...) => String -> m a
754 (The (...) part can be any context including the empty context; that part
756 If the functions don't have the right type, very peculiar things may
757 happen. Use <literal>-dcore-lint</literal> to
758 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
764 <!-- TYPE SYSTEM EXTENSIONS -->
765 <sect1 id="type-extensions">
766 <title>Type system extensions</title>
768 <sect2 id="nullary-types">
769 <title>Data types with no constructors</title>
771 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
772 a data type with no constructors. For example:</para>
776 data T a -- T :: * -> *
779 <para>Syntactically, the declaration lacks the "= constrs" part. The
780 type can be parameterised over types of any kind, but if the kind is
781 not <literal>*</literal> then an explicit kind annotation must be used
782 (see <xref linkend="sec-kinding">).</para>
784 <para>Such data types have only one value, namely bottom.
785 Nevertheless, they can be useful when defining "phantom types".</para>
788 <sect2 id="infix-tycons">
789 <title>Infix type constructors</title>
792 GHC allows type constructors to be operators, and to be written infix, very much
793 like expressions. More specifically:
796 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
797 The lexical syntax is the same as that for data constructors.
800 Types can be written infix. For example <literal>Int :*: Bool</literal>.
804 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
805 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
808 Fixities may be declared for type constructors just as for data constructors. However,
809 one cannot distinguish between the two in a fixity declaration; a fixity declaration
810 sets the fixity for a data constructor and the corresponding type constructor. For example:
814 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
815 and similarly for <literal>:*:</literal>.
816 <literal>Int `a` Bool</literal>.
819 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
822 Data type and type-synonym declarations can be written infix. E.g.
824 data a :*: b = Foo a b
825 type a :+: b = Either a b
829 The only thing that differs between operators in types and operators in expressions is that
830 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
831 are not allowed in types. Reason: the uniform thing to do would be to make them type
832 variables, but that's not very useful. A less uniform but more useful thing would be to
833 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
834 lists. So for now we just exclude them.
841 <sect2 id="sec-kinding">
842 <title>Explicitly-kinded quantification</title>
845 Haskell infers the kind of each type variable. Sometimes it is nice to be able
846 to give the kind explicitly as (machine-checked) documentation,
847 just as it is nice to give a type signature for a function. On some occasions,
848 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
849 John Hughes had to define the data type:
851 data Set cxt a = Set [a]
852 | Unused (cxt a -> ())
854 The only use for the <literal>Unused</literal> constructor was to force the correct
855 kind for the type variable <literal>cxt</literal>.
858 GHC now instead allows you to specify the kind of a type variable directly, wherever
859 a type variable is explicitly bound. Namely:
861 <listitem><para><literal>data</literal> declarations:
863 data Set (cxt :: * -> *) a = Set [a]
864 </Screen></para></listitem>
865 <listitem><para><literal>type</literal> declarations:
867 type T (f :: * -> *) = f Int
868 </Screen></para></listitem>
869 <listitem><para><literal>class</literal> declarations:
871 class (Eq a) => C (f :: * -> *) a where ...
872 </Screen></para></listitem>
873 <listitem><para><literal>forall</literal>'s in type signatures:
875 f :: forall (cxt :: * -> *). Set cxt Int
876 </Screen></para></listitem>
881 The parentheses are required. Some of the spaces are required too, to
882 separate the lexemes. If you write <literal>(f::*->*)</literal> you
883 will get a parse error, because "<literal>::*->*</literal>" is a
884 single lexeme in Haskell.
888 As part of the same extension, you can put kind annotations in types
891 f :: (Int :: *) -> Int
892 g :: forall a. a -> (a :: *)
896 atype ::= '(' ctype '::' kind ')
898 The parentheses are required.
903 <sect2 id="class-method-types">
904 <title>Class method types
907 Haskell 98 prohibits class method types to mention constraints on the
908 class type variable, thus:
911 fromList :: [a] -> s a
912 elem :: Eq a => a -> s a -> Bool
914 The type of <literal>elem</literal> is illegal in Haskell 98, because it
915 contains the constraint <literal>Eq a</literal>, constrains only the
916 class type variable (in this case <literal>a</literal>).
919 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
924 <sect2 id="multi-param-type-classes">
925 <title>Multi-parameter type classes
929 This section documents GHC's implementation of multi-parameter type
930 classes. There's lots of background in the paper <ULink
931 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
932 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
937 <sect3 id="type-restrictions">
941 GHC imposes the following restrictions on the form of a qualified
942 type, whether declared in a type signature
943 or inferred. Consider the type:
946 forall tv1..tvn (c1, ...,cn) => type
949 (Here, I write the "foralls" explicitly, although the Haskell source
950 language omits them; in Haskell 1.4, all the free type variables of an
951 explicit source-language type signature are universally quantified,
952 except for the class type variables in a class declaration. However,
953 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
962 <emphasis>Each universally quantified type variable
963 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
965 A type variable is "reachable" if it it is functionally dependent
966 (see <xref linkend="functional-dependencies">)
967 on the type variables free in <literal>type</literal>.
968 The reason for this is that a value with a type that does not obey
969 this restriction could not be used without introducing
971 Here, for example, is an illegal type:
975 forall a. Eq a => Int
979 When a value with this type was used, the constraint <literal>Eq tv</literal>
980 would be introduced where <literal>tv</literal> is a fresh type variable, and
981 (in the dictionary-translation implementation) the value would be
982 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
983 can never know which instance of <literal>Eq</literal> to use because we never
984 get any more information about <literal>tv</literal>.
991 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
992 universally quantified type variables <literal>tvi</literal></emphasis>.
994 For example, this type is OK because <literal>C a b</literal> mentions the
995 universally quantified type variable <literal>b</literal>:
999 forall a. C a b => burble
1003 The next type is illegal because the constraint <literal>Eq b</literal> does not
1004 mention <literal>a</literal>:
1008 forall a. Eq b => burble
1012 The reason for this restriction is milder than the other one. The
1013 excluded types are never useful or necessary (because the offending
1014 context doesn't need to be witnessed at this point; it can be floated
1015 out). Furthermore, floating them out increases sharing. Lastly,
1016 excluding them is a conservative choice; it leaves a patch of
1017 territory free in case we need it later.
1028 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1029 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1036 f :: Eq (m a) => [m a] -> [m a]
1043 This choice recovers principal types, a property that Haskell 1.4 does not have.
1049 <title>Class declarations</title>
1057 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1061 class Collection c a where
1062 union :: c a -> c a -> c a
1073 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1074 of "acyclic" involves only the superclass relationships. For example,
1080 op :: D b => a -> b -> b
1083 class C a => D a where { ... }
1087 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1088 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1089 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1096 <emphasis>There are no restrictions on the context in a class declaration
1097 (which introduces superclasses), except that the class hierarchy must
1098 be acyclic</emphasis>. So these class declarations are OK:
1102 class Functor (m k) => FiniteMap m k where
1105 class (Monad m, Monad (t m)) => Transform t m where
1106 lift :: m a -> (t m) a
1116 <emphasis>All of the class type variables must be reachable (in the sense
1117 mentioned in <xref linkend="type-restrictions">)
1118 from the free varibles of each method type
1119 </emphasis>. For example:
1123 class Coll s a where
1125 insert :: s -> a -> s
1129 is not OK, because the type of <literal>empty</literal> doesn't mention
1130 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1131 types, and has the same motivation.
1133 Sometimes, offending class declarations exhibit misunderstandings. For
1134 example, <literal>Coll</literal> might be rewritten
1138 class Coll s a where
1140 insert :: s a -> a -> s a
1144 which makes the connection between the type of a collection of
1145 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1146 Occasionally this really doesn't work, in which case you can split the
1154 class CollE s => Coll s a where
1155 insert :: s -> a -> s
1168 <sect3 id="instance-decls">
1169 <title>Instance declarations</title>
1177 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1182 instance context1 => C type1 where ...
1183 instance context2 => C type2 where ...
1187 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1189 However, if you give the command line option
1190 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1191 option</primary></indexterm> then overlapping instance declarations are permitted.
1192 However, GHC arranges never to commit to using an instance declaration
1193 if another instance declaration also applies, either now or later.
1199 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1205 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1206 (but not identical to <literal>type1</literal>), or vice versa.
1210 Notice that these rules
1215 make it clear which instance decl to use
1216 (pick the most specific one that matches)
1223 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1224 Reason: you can pick which instance decl
1225 "matches" based on the type.
1230 However the rules are over-conservative. Two instance declarations can overlap,
1231 but it can still be clear in particular situations which to use. For example:
1233 instance C (Int,a) where ...
1234 instance C (a,Bool) where ...
1236 These are rejected by GHC's rules, but it is clear what to do when trying
1237 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1238 cannot apply. Yell if this restriction bites you.
1241 GHC is also conservative about committing to an overlapping instance. For example:
1243 class C a where { op :: a -> a }
1244 instance C [Int] where ...
1245 instance C a => C [a] where ...
1247 f :: C b => [b] -> [b]
1250 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1251 GHC does not commit to the second instance declaration, because in a paricular
1252 call of f, b might be instantiate to Int, so the first instance declaration
1253 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1254 GHC will instead silently pick the second instance, without complaining about
1255 the problem of subsequent instantiations.
1258 Regrettably, GHC doesn't guarantee to detect overlapping instance
1259 declarations if they appear in different modules. GHC can "see" the
1260 instance declarations in the transitive closure of all the modules
1261 imported by the one being compiled, so it can "see" all instance decls
1262 when it is compiling <literal>Main</literal>. However, it currently chooses not
1263 to look at ones that can't possibly be of use in the module currently
1264 being compiled, in the interests of efficiency. (Perhaps we should
1265 change that decision, at least for <literal>Main</literal>.)
1272 <emphasis>There are no restrictions on the type in an instance
1273 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1274 The instance "head" is the bit after the "=>" in an instance decl. For
1275 example, these are OK:
1279 instance C Int a where ...
1281 instance D (Int, Int) where ...
1283 instance E [[a]] where ...
1287 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1288 For example, this is OK:
1292 instance Stateful (ST s) (MutVar s) where ...
1295 See <xref linkend="undecidable-instances"> for an experimental
1296 extension to lift this restriction.
1302 <emphasis>Unlike Haskell 1.4, instance heads may use type
1303 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1304 writing the RHS of the type synonym definition. For example:
1308 type Point = (Int,Int)
1309 instance C Point where ...
1310 instance C [Point] where ...
1314 is legal. However, if you added
1318 instance C (Int,Int) where ...
1322 as well, then the compiler will complain about the overlapping
1323 (actually, identical) instance declarations. As always, type synonyms
1324 must be fully applied. You cannot, for example, write:
1329 instance Monad P where ...
1333 This design decision is independent of all the others, and easily
1334 reversed, but it makes sense to me.
1341 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1342 be type variables</emphasis>. Thus
1346 instance C a b => Eq (a,b) where ...
1354 instance C Int b => Foo b where ...
1358 is not OK. See <xref linkend="undecidable-instances"> for an experimental
1359 extension to lift this restriction.
1374 <sect2 id="undecidable-instances">
1375 <title>Undecidable instances</title>
1377 <para>The rules for instance declarations state that:
1379 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1380 an instance declaration <emphasis>must not</emphasis> be a type variable.
1382 <listitem><para>All of the types in the <emphasis>context</emphasis> of
1383 an instance declaration <emphasis>must</emphasis> be type variables.
1386 These restrictions ensure that
1387 context reduction terminates: each reduction step removes one type
1388 constructor. For example, the following would make the type checker
1389 loop if it wasn't excluded:
1391 instance C a => C a where ...
1393 There are two situations in which the rule is a bit of a pain. First,
1394 if one allows overlapping instance declarations then it's quite
1395 convenient to have a "default instance" declaration that applies if
1396 something more specific does not:
1405 Second, sometimes you might want to use the following to get the
1406 effect of a "class synonym":
1410 class (C1 a, C2 a, C3 a) => C a where { }
1412 instance (C1 a, C2 a, C3 a) => C a where { }
1416 This allows you to write shorter signatures:
1428 f :: (C1 a, C2 a, C3 a) => ...
1432 Voluminous correspondence on the Haskell mailing list has convinced me
1433 that it's worth experimenting with more liberal rules. If you use
1434 the experimental flag <option>-fallow-undecidable-instances</option>
1435 <indexterm><primary>-fallow-undecidable-instances
1436 option</primary></indexterm>, you can use arbitrary
1437 types in both an instance context and instance head. Termination is ensured by having a
1438 fixed-depth recursion stack. If you exceed the stack depth you get a
1439 sort of backtrace, and the opportunity to increase the stack depth
1440 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1443 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1444 allowing these idioms interesting idioms.
1448 <sect2 id="implicit-parameters">
1449 <title>Implicit parameters
1452 <para> Implicit paramters are implemented as described in
1453 "Implicit parameters: dynamic scoping with static types",
1454 J Lewis, MB Shields, E Meijer, J Launchbury,
1455 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1458 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1460 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1461 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1462 context. In Haskell, all variables are statically bound. Dynamic
1463 binding of variables is a notion that goes back to Lisp, but was later
1464 discarded in more modern incarnations, such as Scheme. Dynamic binding
1465 can be very confusing in an untyped language, and unfortunately, typed
1466 languages, in particular Hindley-Milner typed languages like Haskell,
1467 only support static scoping of variables.
1470 However, by a simple extension to the type class system of Haskell, we
1471 can support dynamic binding. Basically, we express the use of a
1472 dynamically bound variable as a constraint on the type. These
1473 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1474 function uses a dynamically-bound variable <literal>?x</literal>
1475 of type <literal>t'</literal>". For
1476 example, the following expresses the type of a sort function,
1477 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1479 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1481 The dynamic binding constraints are just a new form of predicate in the type class system.
1484 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1485 where <literal>x</literal> is
1486 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1487 Use of this construct also introduces a new
1488 dynamic-binding constraint in the type of the expression.
1489 For example, the following definition
1490 shows how we can define an implicitly parameterized sort function in
1491 terms of an explicitly parameterized <literal>sortBy</literal> function:
1493 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1495 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1501 <title>Implicit-parameter type constraints</title>
1503 Dynamic binding constraints behave just like other type class
1504 constraints in that they are automatically propagated. Thus, when a
1505 function is used, its implicit parameters are inherited by the
1506 function that called it. For example, our <literal>sort</literal> function might be used
1507 to pick out the least value in a list:
1509 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1510 least xs = fst (sort xs)
1512 Without lifting a finger, the <literal>?cmp</literal> parameter is
1513 propagated to become a parameter of <literal>least</literal> as well. With explicit
1514 parameters, the default is that parameters must always be explicit
1515 propagated. With implicit parameters, the default is to always
1519 An implicit-parameter type constraint differs from other type class constraints in the
1520 following way: All uses of a particular implicit parameter must have
1521 the same type. This means that the type of <literal>(?x, ?x)</literal>
1522 is <literal>(?x::a) => (a,a)</literal>, and not
1523 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1527 <para> You can't have an implicit parameter in the context of a class or instance
1528 declaration. For example, both these declarations are illegal:
1530 class (?x::Int) => C a where ...
1531 instance (?x::a) => Foo [a] where ...
1533 Reason: exactly which implicit parameter you pick up depends on exactly where
1534 you invoke a function. But the ``invocation'' of instance declarations is done
1535 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1536 Easiest thing is to outlaw the offending types.</para>
1538 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1540 f :: (?x :: [a]) => Int -> Int
1543 g :: (Read a, Show a) => String -> String
1546 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1547 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1548 quite unambiguous, and fixes the type <literal>a</literal>.
1553 <title>Implicit-parameter bindings</title>
1556 An implicit parameter is <emphasis>bound</emphasis> using the standard
1557 <literal>let</literal> or <literal>where</literal> binding forms.
1558 For example, we define the <literal>min</literal> function by binding
1559 <literal>cmp</literal>.
1562 min = let ?cmp = (<=) in least
1566 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1567 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1568 (including in a list comprehension, or do-notation, or pattern guards),
1569 or a <literal>where</literal> clause.
1570 Note the following points:
1573 An implicit-parameter binding group must be a
1574 collection of simple bindings to implicit-style variables (no
1575 function-style bindings, and no type signatures); these bindings are
1576 neither polymorphic or recursive.
1579 You may not mix implicit-parameter bindings with ordinary bindings in a
1580 single <literal>let</literal>
1581 expression; use two nested <literal>let</literal>s instead.
1582 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1586 You may put multiple implicit-parameter bindings in a
1587 single binding group; but they are <emphasis>not</emphasis> treated
1588 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1589 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1590 parameter. The bindings are not nested, and may be re-ordered without changing
1591 the meaning of the program.
1592 For example, consider:
1594 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1596 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1597 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1599 f :: (?x::Int) => Int -> Int
1608 <sect2 id="linear-implicit-parameters">
1609 <title>Linear implicit parameters
1612 Linear implicit parameters are an idea developed by Koen Claessen,
1613 Mark Shields, and Simon PJ. They address the long-standing
1614 problem that monads seem over-kill for certain sorts of problem, notably:
1617 <listitem> <para> distributing a supply of unique names </para> </listitem>
1618 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1619 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1623 Linear implicit parameters are just like ordinary implicit parameters,
1624 except that they are "linear" -- that is, they cannot be copied, and
1625 must be explicitly "split" instead. Linear implicit parameters are
1626 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1627 (The '/' in the '%' suggests the split!)
1632 import GHC.Exts( Splittable )
1634 data NameSupply = ...
1636 splitNS :: NameSupply -> (NameSupply, NameSupply)
1637 newName :: NameSupply -> Name
1639 instance Splittable NameSupply where
1643 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1644 f env (Lam x e) = Lam x' (f env e)
1647 env' = extend env x x'
1648 ...more equations for f...
1650 Notice that the implicit parameter %ns is consumed
1652 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1653 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1657 So the translation done by the type checker makes
1658 the parameter explicit:
1660 f :: NameSupply -> Env -> Expr -> Expr
1661 f ns env (Lam x e) = Lam x' (f ns1 env e)
1663 (ns1,ns2) = splitNS ns
1665 env = extend env x x'
1667 Notice the call to 'split' introduced by the type checker.
1668 How did it know to use 'splitNS'? Because what it really did
1669 was to introduce a call to the overloaded function 'split',
1670 defined by the class <literal>Splittable</literal>:
1672 class Splittable a where
1675 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1676 split for name supplies. But we can simply write
1682 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1684 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1685 <literal>GHC.Exts</literal>.
1690 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1691 are entirely distinct implicit parameters: you
1692 can use them together and they won't intefere with each other. </para>
1695 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1697 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1698 in the context of a class or instance declaration. </para></listitem>
1702 <sect3><title>Warnings</title>
1705 The monomorphism restriction is even more important than usual.
1706 Consider the example above:
1708 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1709 f env (Lam x e) = Lam x' (f env e)
1712 env' = extend env x x'
1714 If we replaced the two occurrences of x' by (newName %ns), which is
1715 usually a harmless thing to do, we get:
1717 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1718 f env (Lam x e) = Lam (newName %ns) (f env e)
1720 env' = extend env x (newName %ns)
1722 But now the name supply is consumed in <emphasis>three</emphasis> places
1723 (the two calls to newName,and the recursive call to f), so
1724 the result is utterly different. Urk! We don't even have
1728 Well, this is an experimental change. With implicit
1729 parameters we have already lost beta reduction anyway, and
1730 (as John Launchbury puts it) we can't sensibly reason about
1731 Haskell programs without knowing their typing.
1736 <sect3><title>Recursive functions</title>
1737 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1740 foo :: %x::T => Int -> [Int]
1742 foo n = %x : foo (n-1)
1744 where T is some type in class Splittable.</para>
1746 Do you get a list of all the same T's or all different T's
1747 (assuming that split gives two distinct T's back)?
1749 If you supply the type signature, taking advantage of polymorphic
1750 recursion, you get what you'd probably expect. Here's the
1751 translated term, where the implicit param is made explicit:
1754 foo x n = let (x1,x2) = split x
1755 in x1 : foo x2 (n-1)
1757 But if you don't supply a type signature, GHC uses the Hindley
1758 Milner trick of using a single monomorphic instance of the function
1759 for the recursive calls. That is what makes Hindley Milner type inference
1760 work. So the translation becomes
1764 foom n = x : foom (n-1)
1768 Result: 'x' is not split, and you get a list of identical T's. So the
1769 semantics of the program depends on whether or not foo has a type signature.
1772 You may say that this is a good reason to dislike linear implicit parameters
1773 and you'd be right. That is why they are an experimental feature.
1779 <sect2 id="functional-dependencies">
1780 <title>Functional dependencies
1783 <para> Functional dependencies are implemented as described by Mark Jones
1784 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1785 In Proceedings of the 9th European Symposium on Programming,
1786 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1790 Functional dependencies are introduced by a vertical bar in the syntax of a
1791 class declaration; e.g.
1793 class (Monad m) => MonadState s m | m -> s where ...
1795 class Foo a b c | a b -> c where ...
1797 There should be more documentation, but there isn't (yet). Yell if you need it.
1802 <sect2 id="universal-quantification">
1803 <title>Arbitrary-rank polymorphism
1807 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1808 allows us to say exactly what this means. For example:
1816 g :: forall b. (b -> b)
1818 The two are treated identically.
1822 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1823 explicit universal quantification in
1825 For example, all the following types are legal:
1827 f1 :: forall a b. a -> b -> a
1828 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1830 f2 :: (forall a. a->a) -> Int -> Int
1831 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1833 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1835 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1836 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1837 The <literal>forall</literal> makes explicit the universal quantification that
1838 is implicitly added by Haskell.
1841 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1842 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1843 shows, the polymorphic type on the left of the function arrow can be overloaded.
1846 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1847 they have rank-2 types on the left of a function arrow.
1850 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1851 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1852 that restriction has now been lifted.)
1853 In particular, a forall-type (also called a "type scheme"),
1854 including an operational type class context, is legal:
1856 <listitem> <para> On the left of a function arrow </para> </listitem>
1857 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1858 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1859 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1860 field type signatures.</para> </listitem>
1861 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1862 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1864 There is one place you cannot put a <literal>forall</literal>:
1865 you cannot instantiate a type variable with a forall-type. So you cannot
1866 make a forall-type the argument of a type constructor. So these types are illegal:
1868 x1 :: [forall a. a->a]
1869 x2 :: (forall a. a->a, Int)
1870 x3 :: Maybe (forall a. a->a)
1872 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1873 a type variable any more!
1882 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1883 the types of the constructor arguments. Here are several examples:
1889 data T a = T1 (forall b. b -> b -> b) a
1891 data MonadT m = MkMonad { return :: forall a. a -> m a,
1892 bind :: forall a b. m a -> (a -> m b) -> m b
1895 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1901 The constructors have rank-2 types:
1907 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1908 MkMonad :: forall m. (forall a. a -> m a)
1909 -> (forall a b. m a -> (a -> m b) -> m b)
1911 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1917 Notice that you don't need to use a <literal>forall</literal> if there's an
1918 explicit context. For example in the first argument of the
1919 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1920 prefixed to the argument type. The implicit <literal>forall</literal>
1921 quantifies all type variables that are not already in scope, and are
1922 mentioned in the type quantified over.
1926 As for type signatures, implicit quantification happens for non-overloaded
1927 types too. So if you write this:
1930 data T a = MkT (Either a b) (b -> b)
1933 it's just as if you had written this:
1936 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1939 That is, since the type variable <literal>b</literal> isn't in scope, it's
1940 implicitly universally quantified. (Arguably, it would be better
1941 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1942 where that is what is wanted. Feedback welcomed.)
1946 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1947 the constructor to suitable values, just as usual. For example,
1958 a3 = MkSwizzle reverse
1961 a4 = let r x = Just x
1968 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1969 mkTs f x y = [T1 f x, T1 f y]
1975 The type of the argument can, as usual, be more general than the type
1976 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1977 does not need the <literal>Ord</literal> constraint.)
1981 When you use pattern matching, the bound variables may now have
1982 polymorphic types. For example:
1988 f :: T a -> a -> (a, Char)
1989 f (T1 w k) x = (w k x, w 'c' 'd')
1991 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
1992 g (MkSwizzle s) xs f = s (map f (s xs))
1994 h :: MonadT m -> [m a] -> m [a]
1995 h m [] = return m []
1996 h m (x:xs) = bind m x $ \y ->
1997 bind m (h m xs) $ \ys ->
2004 In the function <function>h</function> we use the record selectors <literal>return</literal>
2005 and <literal>bind</literal> to extract the polymorphic bind and return functions
2006 from the <literal>MonadT</literal> data structure, rather than using pattern
2012 <title>Type inference</title>
2015 In general, type inference for arbitrary-rank types is undecideable.
2016 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2017 to get a decidable algorithm by requiring some help from the programmer.
2018 We do not yet have a formal specification of "some help" but the rule is this:
2021 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2022 provides an explicit polymorphic type for x, or GHC's type inference will assume
2023 that x's type has no foralls in it</emphasis>.
2026 What does it mean to "provide" an explicit type for x? You can do that by
2027 giving a type signature for x directly, using a pattern type signature
2028 (<xref linkend="scoped-type-variables">), thus:
2030 \ f :: (forall a. a->a) -> (f True, f 'c')
2032 Alternatively, you can give a type signature to the enclosing
2033 context, which GHC can "push down" to find the type for the variable:
2035 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2037 Here the type signature on the expression can be pushed inwards
2038 to give a type signature for f. Similarly, and more commonly,
2039 one can give a type signature for the function itself:
2041 h :: (forall a. a->a) -> (Bool,Char)
2042 h f = (f True, f 'c')
2044 You don't need to give a type signature if the lambda bound variable
2045 is a constructor argument. Here is an example we saw earlier:
2047 f :: T a -> a -> (a, Char)
2048 f (T1 w k) x = (w k x, w 'c' 'd')
2050 Here we do not need to give a type signature to <literal>w</literal>, because
2051 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2058 <sect3 id="implicit-quant">
2059 <title>Implicit quantification</title>
2062 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2063 user-written types, if and only if there is no explicit <literal>forall</literal>,
2064 GHC finds all the type variables mentioned in the type that are not already
2065 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2069 f :: forall a. a -> a
2076 h :: forall b. a -> b -> b
2082 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2085 f :: (a -> a) -> Int
2087 f :: forall a. (a -> a) -> Int
2089 f :: (forall a. a -> a) -> Int
2092 g :: (Ord a => a -> a) -> Int
2093 -- MEANS the illegal type
2094 g :: forall a. (Ord a => a -> a) -> Int
2096 g :: (forall a. Ord a => a -> a) -> Int
2098 The latter produces an illegal type, which you might think is silly,
2099 but at least the rule is simple. If you want the latter type, you
2100 can write your for-alls explicitly. Indeed, doing so is strongly advised
2106 <sect2 id="type-synonyms">
2107 <title>Liberalised type synonyms
2111 Type synonmys are like macros at the type level, and
2112 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2113 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
2115 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2116 in a type synonym, thus:
2118 type Discard a = forall b. Show b => a -> b -> (a, String)
2123 g :: Discard Int -> (Int,Bool) -- A rank-2 type
2130 You can write an unboxed tuple in a type synonym:
2132 type Pr = (# Int, Int #)
2140 You can apply a type synonym to a forall type:
2142 type Foo a = a -> a -> Bool
2144 f :: Foo (forall b. b->b)
2146 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2148 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2153 You can apply a type synonym to a partially applied type synonym:
2155 type Generic i o = forall x. i x -> o x
2158 foo :: Generic Id []
2160 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2162 foo :: forall x. x -> [x]
2170 GHC currently does kind checking before expanding synonyms (though even that
2174 After expanding type synonyms, GHC does validity checking on types, looking for
2175 the following mal-formedness which isn't detected simply by kind checking:
2178 Type constructor applied to a type involving for-alls.
2181 Unboxed tuple on left of an arrow.
2184 Partially-applied type synonym.
2188 this will be rejected:
2190 type Pr = (# Int, Int #)
2195 because GHC does not allow unboxed tuples on the left of a function arrow.
2200 <title>For-all hoisting</title>
2202 It is often convenient to use generalised type synonyms at the right hand
2203 end of an arrow, thus:
2205 type Discard a = forall b. a -> b -> a
2207 g :: Int -> Discard Int
2210 Simply expanding the type synonym would give
2212 g :: Int -> (forall b. Int -> b -> Int)
2214 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2216 g :: forall b. Int -> Int -> b -> Int
2218 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2219 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2220 performs the transformation:</emphasis>
2222 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2224 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2226 (In fact, GHC tries to retain as much synonym information as possible for use in
2227 error messages, but that is a usability issue.) This rule applies, of course, whether
2228 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2229 valid way to write <literal>g</literal>'s type signature:
2231 g :: Int -> Int -> forall b. b -> Int
2235 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2238 type Foo a = (?x::Int) => Bool -> a
2243 g :: (?x::Int) => Bool -> Bool -> Int
2249 <sect2 id="existential-quantification">
2250 <title>Existentially quantified data constructors
2254 The idea of using existential quantification in data type declarations
2255 was suggested by Laufer (I believe, thought doubtless someone will
2256 correct me), and implemented in Hope+. It's been in Lennart
2257 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2258 proved very useful. Here's the idea. Consider the declaration:
2264 data Foo = forall a. MkFoo a (a -> Bool)
2271 The data type <literal>Foo</literal> has two constructors with types:
2277 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2284 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2285 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2286 For example, the following expression is fine:
2292 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2298 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2299 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2300 isUpper</function> packages a character with a compatible function. These
2301 two things are each of type <literal>Foo</literal> and can be put in a list.
2305 What can we do with a value of type <literal>Foo</literal>?. In particular,
2306 what happens when we pattern-match on <function>MkFoo</function>?
2312 f (MkFoo val fn) = ???
2318 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2319 are compatible, the only (useful) thing we can do with them is to
2320 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2327 f (MkFoo val fn) = fn val
2333 What this allows us to do is to package heterogenous values
2334 together with a bunch of functions that manipulate them, and then treat
2335 that collection of packages in a uniform manner. You can express
2336 quite a bit of object-oriented-like programming this way.
2339 <sect3 id="existential">
2340 <title>Why existential?
2344 What has this to do with <emphasis>existential</emphasis> quantification?
2345 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2351 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2357 But Haskell programmers can safely think of the ordinary
2358 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2359 adding a new existential quantification construct.
2365 <title>Type classes</title>
2368 An easy extension (implemented in <Command>hbc</Command>) is to allow
2369 arbitrary contexts before the constructor. For example:
2375 data Baz = forall a. Eq a => Baz1 a a
2376 | forall b. Show b => Baz2 b (b -> b)
2382 The two constructors have the types you'd expect:
2388 Baz1 :: forall a. Eq a => a -> a -> Baz
2389 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2395 But when pattern matching on <function>Baz1</function> the matched values can be compared
2396 for equality, and when pattern matching on <function>Baz2</function> the first matched
2397 value can be converted to a string (as well as applying the function to it).
2398 So this program is legal:
2405 f (Baz1 p q) | p == q = "Yes"
2407 f (Baz2 v fn) = show (fn v)
2413 Operationally, in a dictionary-passing implementation, the
2414 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2415 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2416 extract it on pattern matching.
2420 Notice the way that the syntax fits smoothly with that used for
2421 universal quantification earlier.
2427 <title>Restrictions</title>
2430 There are several restrictions on the ways in which existentially-quantified
2431 constructors can be use.
2440 When pattern matching, each pattern match introduces a new,
2441 distinct, type for each existential type variable. These types cannot
2442 be unified with any other type, nor can they escape from the scope of
2443 the pattern match. For example, these fragments are incorrect:
2451 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2452 is the result of <function>f1</function>. One way to see why this is wrong is to
2453 ask what type <function>f1</function> has:
2457 f1 :: Foo -> a -- Weird!
2461 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2466 f1 :: forall a. Foo -> a -- Wrong!
2470 The original program is just plain wrong. Here's another sort of error
2474 f2 (Baz1 a b) (Baz1 p q) = a==q
2478 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2479 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2480 from the two <function>Baz1</function> constructors.
2488 You can't pattern-match on an existentially quantified
2489 constructor in a <literal>let</literal> or <literal>where</literal> group of
2490 bindings. So this is illegal:
2494 f3 x = a==b where { Baz1 a b = x }
2497 Instead, use a <literal>case</literal> expression:
2500 f3 x = case x of Baz1 a b -> a==b
2503 In general, you can only pattern-match
2504 on an existentially-quantified constructor in a <literal>case</literal> expression or
2505 in the patterns of a function definition.
2507 The reason for this restriction is really an implementation one.
2508 Type-checking binding groups is already a nightmare without
2509 existentials complicating the picture. Also an existential pattern
2510 binding at the top level of a module doesn't make sense, because it's
2511 not clear how to prevent the existentially-quantified type "escaping".
2512 So for now, there's a simple-to-state restriction. We'll see how
2520 You can't use existential quantification for <literal>newtype</literal>
2521 declarations. So this is illegal:
2525 newtype T = forall a. Ord a => MkT a
2529 Reason: a value of type <literal>T</literal> must be represented as a pair
2530 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2531 That contradicts the idea that <literal>newtype</literal> should have no
2532 concrete representation. You can get just the same efficiency and effect
2533 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2534 overloading involved, then there is more of a case for allowing
2535 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2536 because the <literal>data</literal> version does carry an implementation cost,
2537 but single-field existentially quantified constructors aren't much
2538 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2539 stands, unless there are convincing reasons to change it.
2547 You can't use <literal>deriving</literal> to define instances of a
2548 data type with existentially quantified data constructors.
2550 Reason: in most cases it would not make sense. For example:#
2553 data T = forall a. MkT [a] deriving( Eq )
2556 To derive <literal>Eq</literal> in the standard way we would need to have equality
2557 between the single component of two <function>MkT</function> constructors:
2561 (MkT a) == (MkT b) = ???
2564 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2565 It's just about possible to imagine examples in which the derived instance
2566 would make sense, but it seems altogether simpler simply to prohibit such
2567 declarations. Define your own instances!
2579 <sect2 id="scoped-type-variables">
2580 <title>Scoped type variables
2584 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2585 variable</emphasis>. For example
2591 f (xs::[a]) = ys ++ ys
2600 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2601 This brings the type variable <literal>a</literal> into scope; it scopes over
2602 all the patterns and right hand sides for this equation for <function>f</function>.
2603 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2607 Pattern type signatures are completely orthogonal to ordinary, separate
2608 type signatures. The two can be used independently or together.
2609 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2610 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2611 implicitly universally quantified. (If there are no type variables in
2612 scope, all type variables mentioned in the signature are universally
2613 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2614 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2615 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2616 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2617 it becomes possible to do so.
2621 Scoped type variables are implemented in both GHC and Hugs. Where the
2622 implementations differ from the specification below, those differences
2627 So much for the basic idea. Here are the details.
2631 <title>What a pattern type signature means</title>
2633 A type variable brought into scope by a pattern type signature is simply
2634 the name for a type. The restriction they express is that all occurrences
2635 of the same name mean the same type. For example:
2637 f :: [Int] -> Int -> Int
2638 f (xs::[a]) (y::a) = (head xs + y) :: a
2640 The pattern type signatures on the left hand side of
2641 <literal>f</literal> express the fact that <literal>xs</literal>
2642 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2643 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2644 specifies that this expression must have the same type <literal>a</literal>.
2645 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2646 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2647 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2648 rules, which specified that a pattern-bound type variable should be universally quantified.)
2649 For example, all of these are legal:</para>
2652 t (x::a) (y::a) = x+y*2
2654 f (x::a) (y::b) = [x,y] -- a unifies with b
2656 g (x::a) = x + 1::Int -- a unifies with Int
2658 h x = let k (y::a) = [x,y] -- a is free in the
2659 in k x -- environment
2661 k (x::a) True = ... -- a unifies with Int
2662 k (x::Int) False = ...
2665 w (x::a) = x -- a unifies with [b]
2671 <title>Scope and implicit quantification</title>
2679 All the type variables mentioned in a pattern,
2680 that are not already in scope,
2681 are brought into scope by the pattern. We describe this set as
2682 the <emphasis>type variables bound by the pattern</emphasis>.
2685 f (x::a) = let g (y::(a,b)) = fst y
2689 The pattern <literal>(x::a)</literal> brings the type variable
2690 <literal>a</literal> into scope, as well as the term
2691 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2692 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2693 and brings into scope the type variable <literal>b</literal>.
2699 The type variable(s) bound by the pattern have the same scope
2700 as the term variable(s) bound by the pattern. For example:
2703 f (x::a) = <...rhs of f...>
2704 (p::b, q::b) = (1,2)
2705 in <...body of let...>
2707 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2708 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2709 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2710 just like <literal>p</literal> and <literal>q</literal> do.
2711 Indeed, the newly bound type variables also scope over any ordinary, separate
2712 type signatures in the <literal>let</literal> group.
2719 The type variables bound by the pattern may be
2720 mentioned in ordinary type signatures or pattern
2721 type signatures anywhere within their scope.
2728 In ordinary type signatures, any type variable mentioned in the
2729 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2737 Ordinary type signatures do not bring any new type variables
2738 into scope (except in the type signature itself!). So this is illegal:
2745 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2746 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2747 and that is an incorrect typing.
2754 The pattern type signature is a monotype:
2759 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2763 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2764 not to type schemes.
2768 There is no implicit universal quantification on pattern type signatures (in contrast to
2769 ordinary type signatures).
2779 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2780 scope over the methods defined in the <literal>where</literal> part. For example:
2794 (Not implemented in Hugs yet, Dec 98).
2805 <title>Where a pattern type signature can occur</title>
2808 A pattern type signature can occur in any pattern. For example:
2813 A pattern type signature can be on an arbitrary sub-pattern, not
2818 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2827 Pattern type signatures, including the result part, can be used
2828 in lambda abstractions:
2831 (\ (x::a, y) :: a -> x)
2838 Pattern type signatures, including the result part, can be used
2839 in <literal>case</literal> expressions:
2843 case e of { (x::a, y) :: a -> x }
2851 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2852 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2853 token or a parenthesised type of some sort). To see why,
2854 consider how one would parse this:
2868 Pattern type signatures can bind existential type variables.
2873 data T = forall a. MkT [a]
2876 f (MkT [t::a]) = MkT t3
2889 Pattern type signatures
2890 can be used in pattern bindings:
2893 f x = let (y, z::a) = x in ...
2894 f1 x = let (y, z::Int) = x in ...
2895 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2896 f3 :: (b->b) = \x -> x
2899 In all such cases, the binding is not generalised over the pattern-bound
2900 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2901 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2902 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2903 In contrast, the binding
2908 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2909 in <literal>f4</literal>'s scope.
2919 <title>Result type signatures</title>
2922 The result type of a function can be given a signature, thus:
2926 f (x::a) :: [a] = [x,x,x]
2930 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2931 result type. Sometimes this is the only way of naming the type variable
2936 f :: Int -> [a] -> [a]
2937 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2938 in \xs -> map g (reverse xs `zip` xs)
2943 The type variables bound in a result type signature scope over the right hand side
2944 of the definition. However, consider this corner-case:
2946 rev1 :: [a] -> [a] = \xs -> reverse xs
2948 foo ys = rev (ys::[a])
2950 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2951 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2952 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2953 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2954 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2957 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2958 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2962 rev1 :: [a] -> [a] = \xs -> reverse xs
2967 Result type signatures are not yet implemented in Hugs.
2974 <sect2 id="newtype-deriving">
2975 <title>Generalised derived instances for newtypes</title>
2978 When you define an abstract type using <literal>newtype</literal>, you may want
2979 the new type to inherit some instances from its representation. In
2980 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2981 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2982 other classes you have to write an explicit instance declaration. For
2983 example, if you define
2986 newtype Dollars = Dollars Int
2989 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2990 explicitly define an instance of <literal>Num</literal>:
2993 instance Num Dollars where
2994 Dollars a + Dollars b = Dollars (a+b)
2997 All the instance does is apply and remove the <literal>newtype</literal>
2998 constructor. It is particularly galling that, since the constructor
2999 doesn't appear at run-time, this instance declaration defines a
3000 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3001 dictionary, only slower!
3005 <sect3> <title> Generalising the deriving clause </title>
3007 GHC now permits such instances to be derived instead, so one can write
3009 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3012 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3013 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3014 derives an instance declaration of the form
3017 instance Num Int => Num Dollars
3020 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3024 We can also derive instances of constructor classes in a similar
3025 way. For example, suppose we have implemented state and failure monad
3026 transformers, such that
3029 instance Monad m => Monad (State s m)
3030 instance Monad m => Monad (Failure m)
3032 In Haskell 98, we can define a parsing monad by
3034 type Parser tok m a = State [tok] (Failure m) a
3037 which is automatically a monad thanks to the instance declarations
3038 above. With the extension, we can make the parser type abstract,
3039 without needing to write an instance of class <literal>Monad</literal>, via
3042 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3045 In this case the derived instance declaration is of the form
3047 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3050 Notice that, since <literal>Monad</literal> is a constructor class, the
3051 instance is a <emphasis>partial application</emphasis> of the new type, not the
3052 entire left hand side. We can imagine that the type declaration is
3053 ``eta-converted'' to generate the context of the instance
3058 We can even derive instances of multi-parameter classes, provided the
3059 newtype is the last class parameter. In this case, a ``partial
3060 application'' of the class appears in the <literal>deriving</literal>
3061 clause. For example, given the class
3064 class StateMonad s m | m -> s where ...
3065 instance Monad m => StateMonad s (State s m) where ...
3067 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3069 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3070 deriving (Monad, StateMonad [tok])
3073 The derived instance is obtained by completing the application of the
3074 class to the new type:
3077 instance StateMonad [tok] (State [tok] (Failure m)) =>
3078 StateMonad [tok] (Parser tok m)
3083 As a result of this extension, all derived instances in newtype
3084 declarations are treated uniformly (and implemented just by reusing
3085 the dictionary for the representation type), <emphasis>except</emphasis>
3086 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3087 the newtype and its representation.
3091 <sect3> <title> A more precise specification </title>
3093 Derived instance declarations are constructed as follows. Consider the
3094 declaration (after expansion of any type synonyms)
3097 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3103 <literal>S</literal> is a type constructor,
3106 <literal>t1...tk</literal> are types,
3109 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3110 the <literal>ti</literal>, and
3113 the <literal>ci</literal> are partial applications of
3114 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3115 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3118 Then, for each <literal>ci</literal>, the derived instance
3121 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3123 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3124 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3128 As an example which does <emphasis>not</emphasis> work, consider
3130 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3132 Here we cannot derive the instance
3134 instance Monad (State s m) => Monad (NonMonad m)
3137 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3138 and so cannot be "eta-converted" away. It is a good thing that this
3139 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3140 not, in fact, a monad --- for the same reason. Try defining
3141 <literal>>>=</literal> with the correct type: you won't be able to.
3145 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3146 important, since we can only derive instances for the last one. If the
3147 <literal>StateMonad</literal> class above were instead defined as
3150 class StateMonad m s | m -> s where ...
3153 then we would not have been able to derive an instance for the
3154 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3155 classes usually have one "main" parameter for which deriving new
3156 instances is most interesting.
3164 <!-- ==================== End of type system extensions ================= -->
3166 <!-- ====================== TEMPLATE HASKELL ======================= -->
3168 <sect1 id="template-haskell">
3169 <title>Template Haskell</title>
3171 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
3172 the main technical innovations are discussed in "<ulink
3173 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3174 Template Meta-programming for Haskell</ulink>", in
3175 Proc Haskell Workshop 2002.
3178 <para> The first example from that paper is set out below as a worked example to help get you started.
3182 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3183 Tim Sheard is going to expand it.)
3186 <sect2> <title> Syntax </title>
3188 Template Haskell has the following new syntactic constructions. You need to use the flag
3189 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
3193 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3194 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3195 There must be no space between the "$" and the identifier or parenthesis. This use
3196 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3197 of "." as an infix operator. If you want the infix operator, put spaces around it.
3199 <para> A splice can occur in place of
3201 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3202 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3203 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3205 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3206 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3212 A expression quotation is written in Oxford brackets, thus:
3214 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3215 the quotation has type <literal>Expr</literal>.</para></listitem>
3216 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3217 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3218 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3219 the quotation has type <literal>Type</literal>.</para></listitem>
3220 </itemizedlist></para></listitem>
3223 Reification is written thus:
3225 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3226 has type <literal>Dec</literal>. </para></listitem>
3227 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3228 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3229 <listitem><para> Still to come: fixities </para></listitem>
3231 </itemizedlist></para>
3239 <sect2> <title> Using Template Haskell </title>
3243 The data types and monadic constructor functions for Template Haskell are in the library
3244 <literal>Language.Haskell.THSyntax</literal>.
3248 You can only run a function at compile time if it is imported from another module. That is,
3249 you can't define a function in a module, and call it from within a splice in the same module.
3250 (It would make sense to do so, but it's hard to implement.)
3254 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3257 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3258 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3259 compiles and runs a program, and then looks at the result. So it's important that
3260 the program it compiles produces results whose representations are identical to
3261 those of the compiler itself.
3265 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3266 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3271 <sect2> <title> A Template Haskell Worked Example </title>
3272 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3273 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3279 -- Import our template "pr"
3280 import Printf ( pr )
3282 -- The splice operator $ takes the Haskell source code
3283 -- generated at compile time by "pr" and splices it into
3284 -- the argument of "putStrLn".
3285 main = putStrLn ( $(pr "Hello") )
3292 -- Skeletal printf from the paper.
3293 -- It needs to be in a separate module to the one where
3294 -- you intend to use it.
3296 -- Import some Template Haskell syntax
3297 import Language.Haskell.THSyntax
3299 -- Describe a format string
3300 data Format = D | S | L String
3302 -- Parse a format string. This is left largely to you
3303 -- as we are here interested in building our first ever
3304 -- Template Haskell program and not in building printf.
3305 parse :: String -> [Format]
3308 -- Generate Haskell source code from a parsed representation
3309 -- of the format string. This code will be spliced into
3310 -- the module which calls "pr", at compile time.
3311 gen :: [Format] -> Expr
3312 gen [D] = [| \n -> show n |]
3313 gen [S] = [| \s -> s |]
3314 gen [L s] = string s
3316 -- Here we generate the Haskell code for the splice
3317 -- from an input format string.
3318 pr :: String -> Expr
3319 pr s = gen (parse s)
3322 <para>Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows):
3325 ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe
3328 <para>Run "main.exe" and here is your output:
3340 <!-- ==================== ASSERTIONS ================= -->
3342 <sect1 id="sec-assertions">
3344 <indexterm><primary>Assertions</primary></indexterm>
3348 If you want to make use of assertions in your standard Haskell code, you
3349 could define a function like the following:
3355 assert :: Bool -> a -> a
3356 assert False x = error "assertion failed!"
3363 which works, but gives you back a less than useful error message --
3364 an assertion failed, but which and where?
3368 One way out is to define an extended <function>assert</function> function which also
3369 takes a descriptive string to include in the error message and
3370 perhaps combine this with the use of a pre-processor which inserts
3371 the source location where <function>assert</function> was used.
3375 Ghc offers a helping hand here, doing all of this for you. For every
3376 use of <function>assert</function> in the user's source:
3382 kelvinToC :: Double -> Double
3383 kelvinToC k = assert (k >= 0.0) (k+273.15)
3389 Ghc will rewrite this to also include the source location where the
3396 assert pred val ==> assertError "Main.hs|15" pred val
3402 The rewrite is only performed by the compiler when it spots
3403 applications of <function>Control.Exception.assert</function>, so you
3404 can still define and use your own versions of
3405 <function>assert</function>, should you so wish. If not, import
3406 <literal>Control.Exception</literal> to make use
3407 <function>assert</function> in your code.
3411 To have the compiler ignore uses of assert, use the compiler option
3412 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3413 option</primary></indexterm> That is, expressions of the form
3414 <literal>assert pred e</literal> will be rewritten to
3415 <literal>e</literal>.
3419 Assertion failures can be caught, see the documentation for the
3420 <literal>Control.Exception</literal> library for the details.
3426 <!-- =============================== PRAGMAS =========================== -->
3428 <sect1 id="pragmas">
3429 <title>Pragmas</title>
3431 <indexterm><primary>pragma</primary></indexterm>
3433 <para>GHC supports several pragmas, or instructions to the
3434 compiler placed in the source code. Pragmas don't normally affect
3435 the meaning of the program, but they might affect the efficiency
3436 of the generated code.</para>
3438 <para>Pragmas all take the form
3440 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3442 where <replaceable>word</replaceable> indicates the type of
3443 pragma, and is followed optionally by information specific to that
3444 type of pragma. Case is ignored in
3445 <replaceable>word</replaceable>. The various values for
3446 <replaceable>word</replaceable> that GHC understands are described
3447 in the following sections; any pragma encountered with an
3448 unrecognised <replaceable>word</replaceable> is (silently)
3451 <sect2 id="deprecated-pragma">
3452 <title>DEPRECATED pragma</title>
3453 <indexterm><primary>DEPRECATED</primary>
3456 <para>The DEPRECATED pragma lets you specify that a particular
3457 function, class, or type, is deprecated. There are two
3462 <para>You can deprecate an entire module thus:</para>
3464 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3467 <para>When you compile any module that import
3468 <literal>Wibble</literal>, GHC will print the specified
3473 <para>You can deprecate a function, class, or type, with the
3474 following top-level declaration:</para>
3476 {-# DEPRECATED f, C, T "Don't use these" #-}
3478 <para>When you compile any module that imports and uses any
3479 of the specifed entities, GHC will print the specified
3484 <para>You can suppress the warnings with the flag
3485 <option>-fno-warn-deprecations</option>.</para>
3488 <sect2 id="inline-noinline-pragma">
3489 <title>INLINE and NOINLINE pragmas</title>
3491 <para>These pragmas control the inlining of function
3494 <sect3 id="inline-pragma">
3495 <title>INLINE pragma</title>
3496 <indexterm><primary>INLINE</primary></indexterm>
3498 <para>GHC (with <option>-O</option>, as always) tries to
3499 inline (or “unfold”) functions/values that are
3500 “small enough,” thus avoiding the call overhead
3501 and possibly exposing other more-wonderful optimisations.
3502 Normally, if GHC decides a function is “too
3503 expensive” to inline, it will not do so, nor will it
3504 export that unfolding for other modules to use.</para>
3506 <para>The sledgehammer you can bring to bear is the
3507 <literal>INLINE</literal><indexterm><primary>INLINE
3508 pragma</primary></indexterm> pragma, used thusly:</para>
3511 key_function :: Int -> String -> (Bool, Double)
3513 #ifdef __GLASGOW_HASKELL__
3514 {-# INLINE key_function #-}
3518 <para>(You don't need to do the C pre-processor carry-on
3519 unless you're going to stick the code through HBC—it
3520 doesn't like <literal>INLINE</literal> pragmas.)</para>
3522 <para>The major effect of an <literal>INLINE</literal> pragma
3523 is to declare a function's “cost” to be very low.
3524 The normal unfolding machinery will then be very keen to
3527 <para>Syntactially, an <literal>INLINE</literal> pragma for a
3528 function can be put anywhere its type signature could be
3531 <para><literal>INLINE</literal> pragmas are a particularly
3533 <literal>then</literal>/<literal>return</literal> (or
3534 <literal>bind</literal>/<literal>unit</literal>) functions in
3535 a monad. For example, in GHC's own
3536 <literal>UniqueSupply</literal> monad code, we have:</para>
3539 #ifdef __GLASGOW_HASKELL__
3540 {-# INLINE thenUs #-}
3541 {-# INLINE returnUs #-}
3545 <para>See also the <literal>NOINLINE</literal> pragma (<xref
3546 linkend="noinline-pragma">).</para>
3549 <sect3 id="noinline-pragma">
3550 <title>NOINLINE pragma</title>
3552 <indexterm><primary>NOINLINE</primary></indexterm>
3553 <indexterm><primary>NOTINLINE</primary></indexterm>
3555 <para>The <literal>NOINLINE</literal> pragma does exactly what
3556 you'd expect: it stops the named function from being inlined
3557 by the compiler. You shouldn't ever need to do this, unless
3558 you're very cautious about code size.</para>
3560 <para><literal>NOTINLINE</literal> is a synonym for
3561 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
3562 specified by Haskell 98 as the standard way to disable
3563 inlining, so it should be used if you want your code to be
3567 <sect3 id="phase-control">
3568 <title>Phase control</title>
3570 <para> Sometimes you want to control exactly when in GHC's
3571 pipeline the INLINE pragma is switched on. Inlining happens
3572 only during runs of the <emphasis>simplifier</emphasis>. Each
3573 run of the simplifier has a different <emphasis>phase
3574 number</emphasis>; the phase number decreases towards zero.
3575 If you use <option>-dverbose-core2core</option> you'll see the
3576 sequence of phase numbers for successive runs of the
3577 simpifier. In an INLINE pragma you can optionally specify a
3578 phase number, thus:</para>
3582 <para>You can say "inline <literal>f</literal> in Phase 2
3583 and all subsequent phases":
3585 {-# INLINE [2] f #-}
3591 <para>You can say "inline <literal>g</literal> in all
3592 phases up to, but not including, Phase 3":
3594 {-# INLINE [~3] g #-}
3600 <para>If you omit the phase indicator, you mean "inline in
3605 <para>You can use a phase number on a NOINLINE pragma too:</para>
3609 <para>You can say "do not inline <literal>f</literal>
3610 until Phase 2; in Phase 2 and subsequently behave as if
3611 there was no pragma at all":
3613 {-# NOINLINE [2] f #-}
3619 <para>You can say "do not inline <literal>g</literal> in
3620 Phase 3 or any subsequent phase; before that, behave as if
3621 there was no pragma":
3623 {-# NOINLINE [~3] g #-}
3629 <para>If you omit the phase indicator, you mean "never
3630 inline this function".</para>
3634 <para>The same phase-numbering control is available for RULES
3635 (<xref LinkEnd="rewrite-rules">).</para>
3639 <sect2 id="line-pragma">
3640 <title>LINE pragma</title>
3642 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
3643 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
3644 <para>This pragma is similar to C's <literal>#line</literal>
3645 pragma, and is mainly for use in automatically generated Haskell
3646 code. It lets you specify the line number and filename of the
3647 original code; for example</para>
3650 {-# LINE 42 "Foo.vhs" #-}
3653 <para>if you'd generated the current file from something called
3654 <filename>Foo.vhs</filename> and this line corresponds to line
3655 42 in the original. GHC will adjust its error messages to refer
3656 to the line/file named in the <literal>LINE</literal>
3660 <sect2 id="options-pragma">
3661 <title>OPTIONS pragma</title>
3662 <indexterm><primary>OPTIONS</primary>
3664 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
3667 <para>The <literal>OPTIONS</literal> pragma is used to specify
3668 additional options that are given to the compiler when compiling
3669 this source file. See <xref linkend="source-file-options"> for
3674 <title>RULES pragma</title>
3676 <para>The RULES pragma lets you specify rewrite rules. It is
3677 described in <xref LinkEnd="rewrite-rules">.</para>
3680 <sect2 id="specialize-pragma">
3681 <title>SPECIALIZE pragma</title>
3683 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3684 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
3685 <indexterm><primary>overloading, death to</primary></indexterm>
3687 <para>(UK spelling also accepted.) For key overloaded
3688 functions, you can create extra versions (NB: more code space)
3689 specialised to particular types. Thus, if you have an
3690 overloaded function:</para>
3693 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3696 <para>If it is heavily used on lists with
3697 <literal>Widget</literal> keys, you could specialise it as
3701 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3704 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3705 be put anywhere its type signature could be put.</para>
3707 <para>To get very fancy, you can also specify a named function
3708 to use for the specialised value, as in:</para>
3711 {-# RULES "hammeredLookup" hammeredLookup = blah #-}
3714 <para>where <literal>blah</literal> is an implementation of
3715 <literal>hammerdLookup</literal> written specialy for
3716 <literal>Widget</literal> lookups. It's <emphasis>Your
3717 Responsibility</emphasis> to make sure that
3718 <function>blah</function> really behaves as a specialised
3719 version of <function>hammeredLookup</function>!!!</para>
3721 <para>Note we use the <literal>RULE</literal> pragma here to
3722 indicate that <literal>hammeredLookup</literal> applied at a
3723 certain type should be replaced by <literal>blah</literal>. See
3724 <xref linkend="rules"> for more information on
3725 <literal>RULES</literal>.</para>
3727 <para>An example in which using <literal>RULES</literal> for
3728 specialisation will Win Big:
3731 toDouble :: Real a => a -> Double
3732 toDouble = fromRational . toRational
3734 {-# RULES "toDouble/Int" toDouble = i2d #-}
3735 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3738 The <function>i2d</function> function is virtually one machine
3739 instruction; the default conversion—via an intermediate
3740 <literal>Rational</literal>—is obscenely expensive by
3745 <sect2 id="specialize-instance-pragma">
3746 <title>SPECIALIZE instance pragma
3750 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3751 <indexterm><primary>overloading, death to</primary></indexterm>
3752 Same idea, except for instance declarations. For example:
3755 instance (Eq a) => Eq (Foo a) where {
3756 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3760 The pragma must occur inside the <literal>where</literal> part
3761 of the instance declaration.
3764 Compatible with HBC, by the way, except perhaps in the placement
3774 <!-- ======================= REWRITE RULES ======================== -->
3776 <sect1 id="rewrite-rules">
3777 <title>Rewrite rules
3779 <indexterm><primary>RULES pagma</primary></indexterm>
3780 <indexterm><primary>pragma, RULES</primary></indexterm>
3781 <indexterm><primary>rewrite rules</primary></indexterm></title>
3784 The programmer can specify rewrite rules as part of the source program
3785 (in a pragma). GHC applies these rewrite rules wherever it can.
3793 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3800 <title>Syntax</title>
3803 From a syntactic point of view:
3809 There may be zero or more rules in a <literal>RULES</literal> pragma.
3816 Each rule has a name, enclosed in double quotes. The name itself has
3817 no significance at all. It is only used when reporting how many times the rule fired.
3823 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
3824 immediately after the name of the rule. Thus:
3827 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
3830 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
3831 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
3840 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3841 is set, so you must lay out your rules starting in the same column as the
3842 enclosing definitions.
3849 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3850 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3851 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3852 by spaces, just like in a type <literal>forall</literal>.
3858 A pattern variable may optionally have a type signature.
3859 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3860 For example, here is the <literal>foldr/build</literal> rule:
3863 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3864 foldr k z (build g) = g k z
3867 Since <function>g</function> has a polymorphic type, it must have a type signature.
3874 The left hand side of a rule must consist of a top-level variable applied
3875 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3878 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3879 "wrong2" forall f. f True = True
3882 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3889 A rule does not need to be in the same module as (any of) the
3890 variables it mentions, though of course they need to be in scope.
3896 Rules are automatically exported from a module, just as instance declarations are.
3907 <title>Semantics</title>
3910 From a semantic point of view:
3916 Rules are only applied if you use the <option>-O</option> flag.
3922 Rules are regarded as left-to-right rewrite rules.
3923 When GHC finds an expression that is a substitution instance of the LHS
3924 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3925 By "a substitution instance" we mean that the LHS can be made equal to the
3926 expression by substituting for the pattern variables.
3933 The LHS and RHS of a rule are typechecked, and must have the
3941 GHC makes absolutely no attempt to verify that the LHS and RHS
3942 of a rule have the same meaning. That is undecideable in general, and
3943 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3950 GHC makes no attempt to make sure that the rules are confluent or
3951 terminating. For example:
3954 "loop" forall x,y. f x y = f y x
3957 This rule will cause the compiler to go into an infinite loop.
3964 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3970 GHC currently uses a very simple, syntactic, matching algorithm
3971 for matching a rule LHS with an expression. It seeks a substitution
3972 which makes the LHS and expression syntactically equal modulo alpha
3973 conversion. The pattern (rule), but not the expression, is eta-expanded if
3974 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3975 But not beta conversion (that's called higher-order matching).
3979 Matching is carried out on GHC's intermediate language, which includes
3980 type abstractions and applications. So a rule only matches if the
3981 types match too. See <xref LinkEnd="rule-spec"> below.
3987 GHC keeps trying to apply the rules as it optimises the program.
3988 For example, consider:
3997 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
3998 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
3999 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4000 not be substituted, and the rule would not fire.
4007 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4008 that appears on the LHS of a rule</emphasis>, because once you have substituted
4009 for something you can't match against it (given the simple minded
4010 matching). So if you write the rule
4013 "map/map" forall f,g. map f . map g = map (f.g)
4016 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4017 It will only match something written with explicit use of ".".
4018 Well, not quite. It <emphasis>will</emphasis> match the expression
4024 where <function>wibble</function> is defined:
4027 wibble f g = map f . map g
4030 because <function>wibble</function> will be inlined (it's small).
4032 Later on in compilation, GHC starts inlining even things on the
4033 LHS of rules, but still leaves the rules enabled. This inlining
4034 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4041 All rules are implicitly exported from the module, and are therefore
4042 in force in any module that imports the module that defined the rule, directly
4043 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4044 in force when compiling A.) The situation is very similar to that for instance
4056 <title>List fusion</title>
4059 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4060 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4061 intermediate list should be eliminated entirely.
4065 The following are good producers:
4077 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4083 Explicit lists (e.g. <literal>[True, False]</literal>)
4089 The cons constructor (e.g <literal>3:4:[]</literal>)
4095 <function>++</function>
4101 <function>map</function>
4107 <function>filter</function>
4113 <function>iterate</function>, <function>repeat</function>
4119 <function>zip</function>, <function>zipWith</function>
4128 The following are good consumers:
4140 <function>array</function> (on its second argument)
4146 <function>length</function>
4152 <function>++</function> (on its first argument)
4158 <function>foldr</function>
4164 <function>map</function>
4170 <function>filter</function>
4176 <function>concat</function>
4182 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4188 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4189 will fuse with one but not the other)
4195 <function>partition</function>
4201 <function>head</function>
4207 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4213 <function>sequence_</function>
4219 <function>msum</function>
4225 <function>sortBy</function>
4234 So, for example, the following should generate no intermediate lists:
4237 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4243 This list could readily be extended; if there are Prelude functions that you use
4244 a lot which are not included, please tell us.
4248 If you want to write your own good consumers or producers, look at the
4249 Prelude definitions of the above functions to see how to do so.
4254 <sect2 id="rule-spec">
4255 <title>Specialisation
4259 Rewrite rules can be used to get the same effect as a feature
4260 present in earlier version of GHC:
4263 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4266 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4267 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4268 specialising the original definition of <function>fromIntegral</function> the programmer is
4269 promising that it is safe to use <function>int8ToInt16</function> instead.
4273 This feature is no longer in GHC. But rewrite rules let you do the
4278 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4282 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4283 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4284 GHC adds the type and dictionary applications to get the typed rule
4287 forall (d1::Integral Int8) (d2::Num Int16) .
4288 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4292 this rule does not need to be in the same file as fromIntegral,
4293 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4294 have an original definition available to specialise).
4300 <title>Controlling what's going on</title>
4308 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4314 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4315 If you add <option>-dppr-debug</option> you get a more detailed listing.
4321 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4324 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4325 {-# INLINE build #-}
4329 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4330 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4331 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4332 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4339 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4340 see how to write rules that will do fusion and yet give an efficient
4341 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4351 <sect2 id="core-pragma">
4352 <title>CORE pragma</title>
4354 <indexterm><primary>CORE pragma</primary></indexterm>
4355 <indexterm><primary>pragma, CORE</primary></indexterm>
4356 <indexterm><primary>core, annotation</primary></indexterm>
4359 The external core format supports <quote>Note</quote> annotations;
4360 the <literal>CORE</literal> pragma gives a way to specify what these
4361 should be in your Haskell source code. Syntactically, core
4362 annotations are attached to expressions and take a Haskell string
4363 literal as an argument. The following function definition shows an
4367 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4370 Sematically, this is equivalent to:
4378 However, when external for is generated (via
4379 <option>-fext-core</option>), there will be Notes attached to the
4380 expressions <function>show</function> and <VarName>x</VarName>.
4381 The core function declaration for <function>f</function> is:
4385 f :: %forall a . GHCziShow.ZCTShow a ->
4386 a -> GHCziBase.ZMZN GHCziBase.Char =
4387 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4389 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4391 (tpl1::GHCziBase.Int ->
4393 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4395 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4396 (tpl3::GHCziBase.ZMZN a ->
4397 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4405 Here, we can see that the function <function>show</function> (which
4406 has been expanded out to a case expression over the Show dictionary)
4407 has a <literal>%note</literal> attached to it, as does the
4408 expression <VarName>eta</VarName> (which used to be called
4409 <VarName>x</VarName>).
4416 <sect1 id="generic-classes">
4417 <title>Generic classes</title>
4419 <para>(Note: support for generic classes is currently broken in
4423 The ideas behind this extension are described in detail in "Derivable type classes",
4424 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4425 An example will give the idea:
4433 fromBin :: [Int] -> (a, [Int])
4435 toBin {| Unit |} Unit = []
4436 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4437 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4438 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4440 fromBin {| Unit |} bs = (Unit, bs)
4441 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4442 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4443 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4444 (y,bs'') = fromBin bs'
4447 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4448 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4449 which are defined thus in the library module <literal>Generics</literal>:
4453 data a :+: b = Inl a | Inr b
4454 data a :*: b = a :*: b
4457 Now you can make a data type into an instance of Bin like this:
4459 instance (Bin a, Bin b) => Bin (a,b)
4460 instance Bin a => Bin [a]
4462 That is, just leave off the "where" clause. Of course, you can put in the
4463 where clause and over-ride whichever methods you please.
4467 <title> Using generics </title>
4468 <para>To use generics you need to</para>
4471 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4472 <option>-fgenerics</option> (to generate extra per-data-type code),
4473 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4477 <para>Import the module <literal>Generics</literal> from the
4478 <literal>lang</literal> package. This import brings into
4479 scope the data types <literal>Unit</literal>,
4480 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4481 don't need this import if you don't mention these types
4482 explicitly; for example, if you are simply giving instance
4483 declarations.)</para>
4488 <sect2> <title> Changes wrt the paper </title>
4490 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4491 can be written infix (indeed, you can now use
4492 any operator starting in a colon as an infix type constructor). Also note that
4493 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4494 Finally, note that the syntax of the type patterns in the class declaration
4495 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4496 alone would ambiguous when they appear on right hand sides (an extension we
4497 anticipate wanting).
4501 <sect2> <title>Terminology and restrictions</title>
4503 Terminology. A "generic default method" in a class declaration
4504 is one that is defined using type patterns as above.
4505 A "polymorphic default method" is a default method defined as in Haskell 98.
4506 A "generic class declaration" is a class declaration with at least one
4507 generic default method.
4515 Alas, we do not yet implement the stuff about constructor names and
4522 A generic class can have only one parameter; you can't have a generic
4523 multi-parameter class.
4529 A default method must be defined entirely using type patterns, or entirely
4530 without. So this is illegal:
4533 op :: a -> (a, Bool)
4534 op {| Unit |} Unit = (Unit, True)
4537 However it is perfectly OK for some methods of a generic class to have
4538 generic default methods and others to have polymorphic default methods.
4544 The type variable(s) in the type pattern for a generic method declaration
4545 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:
4549 op {| p :*: q |} (x :*: y) = op (x :: p)
4557 The type patterns in a generic default method must take one of the forms:
4563 where "a" and "b" are type variables. Furthermore, all the type patterns for
4564 a single type constructor (<literal>:*:</literal>, say) must be identical; they
4565 must use the same type variables. So this is illegal:
4569 op {| a :+: b |} (Inl x) = True
4570 op {| p :+: q |} (Inr y) = False
4572 The type patterns must be identical, even in equations for different methods of the class.
4573 So this too is illegal:
4577 op1 {| a :*: b |} (x :*: y) = True
4580 op2 {| p :*: q |} (x :*: y) = False
4582 (The reason for this restriction is that we gather all the equations for a particular type consructor
4583 into a single generic instance declaration.)
4589 A generic method declaration must give a case for each of the three type constructors.
4595 The type for a generic method can be built only from:
4597 <listitem> <para> Function arrows </para> </listitem>
4598 <listitem> <para> Type variables </para> </listitem>
4599 <listitem> <para> Tuples </para> </listitem>
4600 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
4602 Here are some example type signatures for generic methods:
4605 op2 :: Bool -> (a,Bool)
4606 op3 :: [Int] -> a -> a
4609 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
4613 This restriction is an implementation restriction: we just havn't got around to
4614 implementing the necessary bidirectional maps over arbitrary type constructors.
4615 It would be relatively easy to add specific type constructors, such as Maybe and list,
4616 to the ones that are allowed.</para>
4621 In an instance declaration for a generic class, the idea is that the compiler
4622 will fill in the methods for you, based on the generic templates. However it can only
4627 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4632 No constructor of the instance type has unboxed fields.
4636 (Of course, these things can only arise if you are already using GHC extensions.)
4637 However, you can still give an instance declarations for types which break these rules,
4638 provided you give explicit code to override any generic default methods.
4646 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
4647 what the compiler does with generic declarations.
4652 <sect2> <title> Another example </title>
4654 Just to finish with, here's another example I rather like:
4658 nCons {| Unit |} _ = 1
4659 nCons {| a :*: b |} _ = 1
4660 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4663 tag {| Unit |} _ = 1
4664 tag {| a :*: b |} _ = 1
4665 tag {| a :+: b |} (Inl x) = tag x
4666 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4675 ;;; Local Variables: ***
4677 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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