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>-farrows</option></term>
114 <indexterm><primary><option>-farrows</option></primary></indexterm>
116 <para>See <xref LinkEnd="arrow-notation">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fgenerics</option></term>
123 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
125 <para>See <xref LinkEnd="generic-classes">. Independent of
126 <option>-fglasgow-exts</option>.</para>
131 <term><option>-fno-implicit-prelude</option></term>
133 <para><indexterm><primary>-fno-implicit-prelude
134 option</primary></indexterm> GHC normally imports
135 <filename>Prelude.hi</filename> files for you. If you'd
136 rather it didn't, then give it a
137 <option>-fno-implicit-prelude</option> option. The idea is
138 that you can then import a Prelude of your own. (But don't
139 call it <literal>Prelude</literal>; the Haskell module
140 namespace is flat, and you must not conflict with any
141 Prelude module.)</para>
143 <para>Even though you have not imported the Prelude, most of
144 the built-in syntax still refers to the built-in Haskell
145 Prelude types and values, as specified by the Haskell
146 Report. For example, the type <literal>[Int]</literal>
147 still means <literal>Prelude.[] Int</literal>; tuples
148 continue to refer to the standard Prelude tuples; the
149 translation for list comprehensions continues to use
150 <literal>Prelude.map</literal> etc.</para>
152 <para>However, <option>-fno-implicit-prelude</option> does
153 change the handling of certain built-in syntax: see <xref
154 LinkEnd="rebindable-syntax">.</para>
159 <term><option>-fth</option></term>
161 <para>Enables Template Haskell (see <xref
162 linkend="template-haskell">). Currently also implied by
163 <option>-fglasgow-exts</option>.</para>
168 <term><option>-fimplicit-params</option></term>
170 <para>Enables implicit parameters (see <xref
171 linkend="implicit-parameters">). Currently also implied by
172 <option>-fglasgow-exts</option>.</para>
179 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
180 <!-- included from primitives.sgml -->
181 <!-- &primitives; -->
182 <sect1 id="primitives">
183 <title>Unboxed types and primitive operations</title>
185 <para>GHC is built on a raft of primitive data types and operations.
186 While you really can use this stuff to write fast code,
187 we generally find it a lot less painful, and more satisfying in the
188 long run, to use higher-level language features and libraries. With
189 any luck, the code you write will be optimised to the efficient
190 unboxed version in any case. And if it isn't, we'd like to know
193 <para>We do not currently have good, up-to-date documentation about the
194 primitives, perhaps because they are mainly intended for internal use.
195 There used to be a long section about them here in the User Guide, but it
196 became out of date, and wrong information is worse than none.</para>
198 <para>The Real Truth about what primitive types there are, and what operations
199 work over those types, is held in the file
200 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
201 This file is used directly to generate GHC's primitive-operation definitions, so
202 it is always correct! It is also intended for processing into text.</para>
205 the result of such processing is part of the description of the
207 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
208 Core language</ulink>.
209 So that document is a good place to look for a type-set version.
210 We would be very happy if someone wanted to volunteer to produce an SGML
211 back end to the program that processes <filename>primops.txt</filename> so that
212 we could include the results here in the User Guide.</para>
214 <para>What follows here is a brief summary of some main points.</para>
216 <sect2 id="glasgow-unboxed">
221 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
224 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
225 that values of that type are represented by a pointer to a heap
226 object. The representation of a Haskell <literal>Int</literal>, for
227 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
228 type, however, is represented by the value itself, no pointers or heap
229 allocation are involved.
233 Unboxed types correspond to the “raw machine” types you
234 would use in C: <literal>Int#</literal> (long int),
235 <literal>Double#</literal> (double), <literal>Addr#</literal>
236 (void *), etc. The <emphasis>primitive operations</emphasis>
237 (PrimOps) on these types are what you might expect; e.g.,
238 <literal>(+#)</literal> is addition on
239 <literal>Int#</literal>s, and is the machine-addition that we all
240 know and love—usually one instruction.
244 Primitive (unboxed) types cannot be defined in Haskell, and are
245 therefore built into the language and compiler. Primitive types are
246 always unlifted; that is, a value of a primitive type cannot be
247 bottom. We use the convention that primitive types, values, and
248 operations have a <literal>#</literal> suffix.
252 Primitive values are often represented by a simple bit-pattern, such
253 as <literal>Int#</literal>, <literal>Float#</literal>,
254 <literal>Double#</literal>. But this is not necessarily the case:
255 a primitive value might be represented by a pointer to a
256 heap-allocated object. Examples include
257 <literal>Array#</literal>, the type of primitive arrays. A
258 primitive array is heap-allocated because it is too big a value to fit
259 in a register, and would be too expensive to copy around; in a sense,
260 it is accidental that it is represented by a pointer. If a pointer
261 represents a primitive value, then it really does point to that value:
262 no unevaluated thunks, no indirections…nothing can be at the
263 other end of the pointer than the primitive value.
267 There are some restrictions on the use of primitive types, the main
268 one being that you can't pass a primitive value to a polymorphic
269 function or store one in a polymorphic data type. This rules out
270 things like <literal>[Int#]</literal> (i.e. lists of primitive
271 integers). The reason for this restriction is that polymorphic
272 arguments and constructor fields are assumed to be pointers: if an
273 unboxed integer is stored in one of these, the garbage collector would
274 attempt to follow it, leading to unpredictable space leaks. Or a
275 <function>seq</function> operation on the polymorphic component may
276 attempt to dereference the pointer, with disastrous results. Even
277 worse, the unboxed value might be larger than a pointer
278 (<literal>Double#</literal> for instance).
282 Nevertheless, A numerically-intensive program using unboxed types can
283 go a <emphasis>lot</emphasis> faster than its “standard”
284 counterpart—we saw a threefold speedup on one example.
289 <sect2 id="unboxed-tuples">
290 <title>Unboxed Tuples
294 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
295 they're available by default with <option>-fglasgow-exts</option>. An
296 unboxed tuple looks like this:
308 where <literal>e_1..e_n</literal> are expressions of any
309 type (primitive or non-primitive). The type of an unboxed tuple looks
314 Unboxed tuples are used for functions that need to return multiple
315 values, but they avoid the heap allocation normally associated with
316 using fully-fledged tuples. When an unboxed tuple is returned, the
317 components are put directly into registers or on the stack; the
318 unboxed tuple itself does not have a composite representation. Many
319 of the primitive operations listed in this section return unboxed
324 There are some pretty stringent restrictions on the use of unboxed tuples:
333 Unboxed tuple types are subject to the same restrictions as
334 other unboxed types; i.e. they may not be stored in polymorphic data
335 structures or passed to polymorphic functions.
342 Unboxed tuples may only be constructed as the direct result of
343 a function, and may only be deconstructed with a <literal>case</literal> expression.
344 eg. the following are valid:
348 f x y = (# x+1, y-1 #)
349 g x = case f x x of { (# a, b #) -> a + b }
353 but the following are invalid:
367 No variable can have an unboxed tuple type. This is illegal:
371 f :: (# Int, Int #) -> (# Int, Int #)
376 because <literal>x</literal> has an unboxed tuple type.
386 Note: we may relax some of these restrictions in the future.
390 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
391 tuples to avoid unnecessary allocation during sequences of operations.
398 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
400 <sect1 id="syntax-extns">
401 <title>Syntactic extensions</title>
403 <!-- ====================== HIERARCHICAL MODULES ======================= -->
405 <sect2 id="hierarchical-modules">
406 <title>Hierarchical Modules</title>
408 <para>GHC supports a small extension to the syntax of module
409 names: a module name is allowed to contain a dot
410 <literal>‘.’</literal>. This is also known as the
411 “hierarchical module namespace” extension, because
412 it extends the normally flat Haskell module namespace into a
413 more flexible hierarchy of modules.</para>
415 <para>This extension has very little impact on the language
416 itself; modules names are <emphasis>always</emphasis> fully
417 qualified, so you can just think of the fully qualified module
418 name as <quote>the module name</quote>. In particular, this
419 means that the full module name must be given after the
420 <literal>module</literal> keyword at the beginning of the
421 module; for example, the module <literal>A.B.C</literal> must
424 <programlisting>module A.B.C</programlisting>
427 <para>It is a common strategy to use the <literal>as</literal>
428 keyword to save some typing when using qualified names with
429 hierarchical modules. For example:</para>
432 import qualified Control.Monad.ST.Strict as ST
435 <para>For details on how GHC searches for source and interface
436 files in the presence of hierarchical modules, see <xref
437 linkend="search-path">.</para>
439 <para>GHC comes with a large collection of libraries arranged
440 hierarchically; see the accompanying library documentation.
441 There is an ongoing project to create and maintain a stable set
442 of <quote>core</quote> libraries used by several Haskell
443 compilers, and the libraries that GHC comes with represent the
444 current status of that project. For more details, see <ulink
445 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
446 Libraries</ulink>.</para>
450 <!-- ====================== PATTERN GUARDS ======================= -->
452 <sect2 id="pattern-guards">
453 <title>Pattern guards</title>
456 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
457 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.)
461 Suppose we have an abstract data type of finite maps, with a
465 lookup :: FiniteMap -> Int -> Maybe Int
468 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
469 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
473 clunky env var1 var2 | ok1 && ok2 = val1 + val2
474 | otherwise = var1 + var2
485 The auxiliary functions are
489 maybeToBool :: Maybe a -> Bool
490 maybeToBool (Just x) = True
491 maybeToBool Nothing = False
493 expectJust :: Maybe a -> a
494 expectJust (Just x) = x
495 expectJust Nothing = error "Unexpected Nothing"
499 What is <function>clunky</function> doing? The guard <literal>ok1 &&
500 ok2</literal> checks that both lookups succeed, using
501 <function>maybeToBool</function> to convert the <function>Maybe</function>
502 types to booleans. The (lazily evaluated) <function>expectJust</function>
503 calls extract the values from the results of the lookups, and binds the
504 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
505 respectively. If either lookup fails, then clunky takes the
506 <literal>otherwise</literal> case and returns the sum of its arguments.
510 This is certainly legal Haskell, but it is a tremendously verbose and
511 un-obvious way to achieve the desired effect. Arguably, a more direct way
512 to write clunky would be to use case expressions:
516 clunky env var1 var1 = case lookup env var1 of
518 Just val1 -> case lookup env var2 of
520 Just val2 -> val1 + val2
526 This is a bit shorter, but hardly better. Of course, we can rewrite any set
527 of pattern-matching, guarded equations as case expressions; that is
528 precisely what the compiler does when compiling equations! The reason that
529 Haskell provides guarded equations is because they allow us to write down
530 the cases we want to consider, one at a time, independently of each other.
531 This structure is hidden in the case version. Two of the right-hand sides
532 are really the same (<function>fail</function>), and the whole expression
533 tends to become more and more indented.
537 Here is how I would write clunky:
542 | Just val1 <- lookup env var1
543 , Just val2 <- lookup env var2
545 ...other equations for clunky...
549 The semantics should be clear enough. The qualifers are matched in order.
550 For a <literal><-</literal> qualifier, which I call a pattern guard, the
551 right hand side is evaluated and matched against the pattern on the left.
552 If the match fails then the whole guard fails and the next equation is
553 tried. If it succeeds, then the appropriate binding takes place, and the
554 next qualifier is matched, in the augmented environment. Unlike list
555 comprehensions, however, the type of the expression to the right of the
556 <literal><-</literal> is the same as the type of the pattern to its
557 left. The bindings introduced by pattern guards scope over all the
558 remaining guard qualifiers, and over the right hand side of the equation.
562 Just as with list comprehensions, boolean expressions can be freely mixed
563 with among the pattern guards. For example:
574 Haskell's current guards therefore emerge as a special case, in which the
575 qualifier list has just one element, a boolean expression.
579 <!-- ===================== Recursive do-notation =================== -->
581 <sect2 id="mdo-notation">
582 <title>The recursive do-notation
585 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
586 "A recursive do for Haskell",
587 Levent Erkok, John Launchbury",
588 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
591 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
592 that is, the variables bound in a do-expression are visible only in the textually following
593 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
594 group. It turns out that several applications can benefit from recursive bindings in
595 the do-notation, and this extension provides the necessary syntactic support.
598 Here is a simple (yet contrived) example:
601 import Control.Monad.Fix
603 justOnes = mdo xs <- Just (1:xs)
607 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
611 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
614 class Monad m => MonadFix m where
615 mfix :: (a -> m a) -> m a
618 The function <literal>mfix</literal>
619 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
620 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
621 For details, see the above mentioned reference.
624 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
625 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
626 for Haskell's internal state monad (strict and lazy, respectively).
629 There are three important points in using the recursive-do notation:
632 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
633 than <literal>do</literal>).
637 You should <literal>import Control.Monad.Fix</literal>.
638 (Note: Strictly speaking, this import is required only when you need to refer to the name
639 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
640 are encouraged to always import this module when using the mdo-notation.)
644 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
650 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
651 contains up to date information on recursive monadic bindings.
655 Historical note: The old implementation of the mdo-notation (and most
656 of the existing documents) used the name
657 <literal>MonadRec</literal> for the class and the corresponding library.
658 This name is not supported by GHC.
664 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
666 <sect2 id="parallel-list-comprehensions">
667 <title>Parallel List Comprehensions</title>
668 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
670 <indexterm><primary>parallel list comprehensions</primary>
673 <para>Parallel list comprehensions are a natural extension to list
674 comprehensions. List comprehensions can be thought of as a nice
675 syntax for writing maps and filters. Parallel comprehensions
676 extend this to include the zipWith family.</para>
678 <para>A parallel list comprehension has multiple independent
679 branches of qualifier lists, each separated by a `|' symbol. For
680 example, the following zips together two lists:</para>
683 [ (x, y) | x <- xs | y <- ys ]
686 <para>The behavior of parallel list comprehensions follows that of
687 zip, in that the resulting list will have the same length as the
688 shortest branch.</para>
690 <para>We can define parallel list comprehensions by translation to
691 regular comprehensions. Here's the basic idea:</para>
693 <para>Given a parallel comprehension of the form: </para>
696 [ e | p1 <- e11, p2 <- e12, ...
697 | q1 <- e21, q2 <- e22, ...
702 <para>This will be translated to: </para>
705 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
706 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
711 <para>where `zipN' is the appropriate zip for the given number of
716 <sect2 id="rebindable-syntax">
717 <title>Rebindable syntax</title>
720 <para>GHC allows most kinds of built-in syntax to be rebound by
721 the user, to facilitate replacing the <literal>Prelude</literal>
722 with a home-grown version, for example.</para>
724 <para>You may want to define your own numeric class
725 hierarchy. It completely defeats that purpose if the
726 literal "1" means "<literal>Prelude.fromInteger
727 1</literal>", which is what the Haskell Report specifies.
728 So the <option>-fno-implicit-prelude</option> flag causes
729 the following pieces of built-in syntax to refer to
730 <emphasis>whatever is in scope</emphasis>, not the Prelude
735 <para>Integer and fractional literals mean
736 "<literal>fromInteger 1</literal>" and
737 "<literal>fromRational 3.2</literal>", not the
738 Prelude-qualified versions; both in expressions and in
740 <para>However, the standard Prelude <literal>Eq</literal> class
741 is still used for the equality test necessary for literal patterns.</para>
745 <para>Negation (e.g. "<literal>- (f x)</literal>")
746 means "<literal>negate (f x)</literal>" (not
747 <literal>Prelude.negate</literal>).</para>
751 <para>In an n+k pattern, the standard Prelude
752 <literal>Ord</literal> class is still used for comparison,
753 but the necessary subtraction uses whatever
754 "<literal>(-)</literal>" is in scope (not
755 "<literal>Prelude.(-)</literal>").</para>
759 <para>"Do" notation is translated using whatever
760 functions <literal>(>>=)</literal>,
761 <literal>(>>)</literal>, <literal>fail</literal>, and
762 <literal>return</literal>, are in scope (not the Prelude
763 versions). List comprehensions, and parallel array
764 comprehensions, are unaffected. </para></listitem>
767 <para>Be warned: this is an experimental facility, with fewer checks than
768 usual. In particular, it is essential that the functions GHC finds in scope
769 must have the appropriate types, namely:
771 fromInteger :: forall a. (...) => Integer -> a
772 fromRational :: forall a. (...) => Rational -> a
773 negate :: forall a. (...) => a -> a
774 (-) :: forall a. (...) => a -> a -> a
775 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
776 (>>) :: forall m a. (...) => m a -> m b -> m b
777 return :: forall m a. (...) => a -> m a
778 fail :: forall m a. (...) => String -> m a
780 (The (...) part can be any context including the empty context; that part
782 If the functions don't have the right type, very peculiar things may
783 happen. Use <literal>-dcore-lint</literal> to
784 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
790 <!-- TYPE SYSTEM EXTENSIONS -->
791 <sect1 id="type-extensions">
792 <title>Type system extensions</title>
796 <title>Data types and type synonyms</title>
798 <sect3 id="nullary-types">
799 <title>Data types with no constructors</title>
801 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
802 a data type with no constructors. For example:</para>
806 data T a -- T :: * -> *
809 <para>Syntactically, the declaration lacks the "= constrs" part. The
810 type can be parameterised over types of any kind, but if the kind is
811 not <literal>*</literal> then an explicit kind annotation must be used
812 (see <xref linkend="sec-kinding">).</para>
814 <para>Such data types have only one value, namely bottom.
815 Nevertheless, they can be useful when defining "phantom types".</para>
818 <sect3 id="infix-tycons">
819 <title>Infix type constructors</title>
822 GHC allows type constructors to be operators, and to be written infix, very much
823 like expressions. More specifically:
826 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
827 The lexical syntax is the same as that for data constructors.
830 Types can be written infix. For example <literal>Int :*: Bool</literal>.
834 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
835 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
838 Fixities may be declared for type constructors just as for data constructors. However,
839 one cannot distinguish between the two in a fixity declaration; a fixity declaration
840 sets the fixity for a data constructor and the corresponding type constructor. For example:
844 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
845 and similarly for <literal>:*:</literal>.
846 <literal>Int `a` Bool</literal>.
849 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
852 Data type and type-synonym declarations can be written infix. E.g.
854 data a :*: b = Foo a b
855 type a :+: b = Either a b
859 The only thing that differs between operators in types and operators in expressions is that
860 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
861 are not allowed in types. Reason: the uniform thing to do would be to make them type
862 variables, but that's not very useful. A less uniform but more useful thing would be to
863 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
864 lists. So for now we just exclude them.
871 <sect3 id="type-synonyms">
872 <title>Liberalised type synonyms</title>
875 Type synonmys are like macros at the type level, and
876 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
877 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
879 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
880 in a type synonym, thus:
882 type Discard a = forall b. Show b => a -> b -> (a, String)
887 g :: Discard Int -> (Int,Bool) -- A rank-2 type
894 You can write an unboxed tuple in a type synonym:
896 type Pr = (# Int, Int #)
904 You can apply a type synonym to a forall type:
906 type Foo a = a -> a -> Bool
908 f :: Foo (forall b. b->b)
910 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
912 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
917 You can apply a type synonym to a partially applied type synonym:
919 type Generic i o = forall x. i x -> o x
924 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
926 foo :: forall x. x -> [x]
934 GHC currently does kind checking before expanding synonyms (though even that
938 After expanding type synonyms, GHC does validity checking on types, looking for
939 the following mal-formedness which isn't detected simply by kind checking:
942 Type constructor applied to a type involving for-alls.
945 Unboxed tuple on left of an arrow.
948 Partially-applied type synonym.
952 this will be rejected:
954 type Pr = (# Int, Int #)
959 because GHC does not allow unboxed tuples on the left of a function arrow.
964 <sect3 id="existential-quantification">
965 <title>Existentially quantified data constructors
969 The idea of using existential quantification in data type declarations
970 was suggested by Laufer (I believe, thought doubtless someone will
971 correct me), and implemented in Hope+. It's been in Lennart
972 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
973 proved very useful. Here's the idea. Consider the declaration:
979 data Foo = forall a. MkFoo a (a -> Bool)
986 The data type <literal>Foo</literal> has two constructors with types:
992 MkFoo :: forall a. a -> (a -> Bool) -> Foo
999 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
1000 does not appear in the data type itself, which is plain <literal>Foo</literal>.
1001 For example, the following expression is fine:
1007 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1013 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1014 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1015 isUpper</function> packages a character with a compatible function. These
1016 two things are each of type <literal>Foo</literal> and can be put in a list.
1020 What can we do with a value of type <literal>Foo</literal>?. In particular,
1021 what happens when we pattern-match on <function>MkFoo</function>?
1027 f (MkFoo val fn) = ???
1033 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1034 are compatible, the only (useful) thing we can do with them is to
1035 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1042 f (MkFoo val fn) = fn val
1048 What this allows us to do is to package heterogenous values
1049 together with a bunch of functions that manipulate them, and then treat
1050 that collection of packages in a uniform manner. You can express
1051 quite a bit of object-oriented-like programming this way.
1054 <sect4 id="existential">
1055 <title>Why existential?
1059 What has this to do with <emphasis>existential</emphasis> quantification?
1060 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1066 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1072 But Haskell programmers can safely think of the ordinary
1073 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1074 adding a new existential quantification construct.
1080 <title>Type classes</title>
1083 An easy extension (implemented in <Command>hbc</Command>) is to allow
1084 arbitrary contexts before the constructor. For example:
1090 data Baz = forall a. Eq a => Baz1 a a
1091 | forall b. Show b => Baz2 b (b -> b)
1097 The two constructors have the types you'd expect:
1103 Baz1 :: forall a. Eq a => a -> a -> Baz
1104 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1110 But when pattern matching on <function>Baz1</function> the matched values can be compared
1111 for equality, and when pattern matching on <function>Baz2</function> the first matched
1112 value can be converted to a string (as well as applying the function to it).
1113 So this program is legal:
1120 f (Baz1 p q) | p == q = "Yes"
1122 f (Baz2 v fn) = show (fn v)
1128 Operationally, in a dictionary-passing implementation, the
1129 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1130 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1131 extract it on pattern matching.
1135 Notice the way that the syntax fits smoothly with that used for
1136 universal quantification earlier.
1142 <title>Restrictions</title>
1145 There are several restrictions on the ways in which existentially-quantified
1146 constructors can be use.
1155 When pattern matching, each pattern match introduces a new,
1156 distinct, type for each existential type variable. These types cannot
1157 be unified with any other type, nor can they escape from the scope of
1158 the pattern match. For example, these fragments are incorrect:
1166 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1167 is the result of <function>f1</function>. One way to see why this is wrong is to
1168 ask what type <function>f1</function> has:
1172 f1 :: Foo -> a -- Weird!
1176 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1181 f1 :: forall a. Foo -> a -- Wrong!
1185 The original program is just plain wrong. Here's another sort of error
1189 f2 (Baz1 a b) (Baz1 p q) = a==q
1193 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1194 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1195 from the two <function>Baz1</function> constructors.
1203 You can't pattern-match on an existentially quantified
1204 constructor in a <literal>let</literal> or <literal>where</literal> group of
1205 bindings. So this is illegal:
1209 f3 x = a==b where { Baz1 a b = x }
1212 Instead, use a <literal>case</literal> expression:
1215 f3 x = case x of Baz1 a b -> a==b
1218 In general, you can only pattern-match
1219 on an existentially-quantified constructor in a <literal>case</literal> expression or
1220 in the patterns of a function definition.
1222 The reason for this restriction is really an implementation one.
1223 Type-checking binding groups is already a nightmare without
1224 existentials complicating the picture. Also an existential pattern
1225 binding at the top level of a module doesn't make sense, because it's
1226 not clear how to prevent the existentially-quantified type "escaping".
1227 So for now, there's a simple-to-state restriction. We'll see how
1235 You can't use existential quantification for <literal>newtype</literal>
1236 declarations. So this is illegal:
1240 newtype T = forall a. Ord a => MkT a
1244 Reason: a value of type <literal>T</literal> must be represented as a pair
1245 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1246 That contradicts the idea that <literal>newtype</literal> should have no
1247 concrete representation. You can get just the same efficiency and effect
1248 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1249 overloading involved, then there is more of a case for allowing
1250 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1251 because the <literal>data</literal> version does carry an implementation cost,
1252 but single-field existentially quantified constructors aren't much
1253 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1254 stands, unless there are convincing reasons to change it.
1262 You can't use <literal>deriving</literal> to define instances of a
1263 data type with existentially quantified data constructors.
1265 Reason: in most cases it would not make sense. For example:#
1268 data T = forall a. MkT [a] deriving( Eq )
1271 To derive <literal>Eq</literal> in the standard way we would need to have equality
1272 between the single component of two <function>MkT</function> constructors:
1276 (MkT a) == (MkT b) = ???
1279 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1280 It's just about possible to imagine examples in which the derived instance
1281 would make sense, but it seems altogether simpler simply to prohibit such
1282 declarations. Define your own instances!
1297 <sect2 id="multi-param-type-classes">
1298 <title>Class declarations</title>
1301 This section documents GHC's implementation of multi-parameter type
1302 classes. There's lots of background in the paper <ULink
1303 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1304 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
1305 Jones, Erik Meijer).
1308 There are the following constraints on class declarations:
1313 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1317 class Collection c a where
1318 union :: c a -> c a -> c a
1329 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1330 of "acyclic" involves only the superclass relationships. For example,
1336 op :: D b => a -> b -> b
1339 class C a => D a where { ... }
1343 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1344 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1345 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1352 <emphasis>There are no restrictions on the context in a class declaration
1353 (which introduces superclasses), except that the class hierarchy must
1354 be acyclic</emphasis>. So these class declarations are OK:
1358 class Functor (m k) => FiniteMap m k where
1361 class (Monad m, Monad (t m)) => Transform t m where
1362 lift :: m a -> (t m) a
1372 <emphasis>All of the class type variables must be reachable (in the sense
1373 mentioned in <xref linkend="type-restrictions">)
1374 from the free varibles of each method type
1375 </emphasis>. For example:
1379 class Coll s a where
1381 insert :: s -> a -> s
1385 is not OK, because the type of <literal>empty</literal> doesn't mention
1386 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1387 types, and has the same motivation.
1389 Sometimes, offending class declarations exhibit misunderstandings. For
1390 example, <literal>Coll</literal> might be rewritten
1394 class Coll s a where
1396 insert :: s a -> a -> s a
1400 which makes the connection between the type of a collection of
1401 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1402 Occasionally this really doesn't work, in which case you can split the
1410 class CollE s => Coll s a where
1411 insert :: s -> a -> s
1421 <sect3 id="class-method-types">
1422 <title>Class method types</title>
1424 Haskell 98 prohibits class method types to mention constraints on the
1425 class type variable, thus:
1428 fromList :: [a] -> s a
1429 elem :: Eq a => a -> s a -> Bool
1431 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1432 contains the constraint <literal>Eq a</literal>, constrains only the
1433 class type variable (in this case <literal>a</literal>).
1436 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1443 <sect2 id="type-restrictions">
1444 <title>Type signatures</title>
1446 <sect3><title>The context of a type signature</title>
1448 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1449 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1452 f :: Eq (m a) => [m a] -> [m a]
1455 This choice recovers principal types, a property that Haskell 1.4 does not have.
1458 GHC imposes the following restrictions on the constraints in a type signature.
1462 forall tv1..tvn (c1, ...,cn) => type
1465 (Here, we write the "foralls" explicitly, although the Haskell source
1466 language omits them; in Haskell 1.4, all the free type variables of an
1467 explicit source-language type signature are universally quantified,
1468 except for the class type variables in a class declaration. However,
1469 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
1478 <emphasis>Each universally quantified type variable
1479 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1481 A type variable is "reachable" if it it is functionally dependent
1482 (see <xref linkend="functional-dependencies">)
1483 on the type variables free in <literal>type</literal>.
1484 The reason for this is that a value with a type that does not obey
1485 this restriction could not be used without introducing
1487 Here, for example, is an illegal type:
1491 forall a. Eq a => Int
1495 When a value with this type was used, the constraint <literal>Eq tv</literal>
1496 would be introduced where <literal>tv</literal> is a fresh type variable, and
1497 (in the dictionary-translation implementation) the value would be
1498 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1499 can never know which instance of <literal>Eq</literal> to use because we never
1500 get any more information about <literal>tv</literal>.
1507 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1508 universally quantified type variables <literal>tvi</literal></emphasis>.
1510 For example, this type is OK because <literal>C a b</literal> mentions the
1511 universally quantified type variable <literal>b</literal>:
1515 forall a. C a b => burble
1519 The next type is illegal because the constraint <literal>Eq b</literal> does not
1520 mention <literal>a</literal>:
1524 forall a. Eq b => burble
1528 The reason for this restriction is milder than the other one. The
1529 excluded types are never useful or necessary (because the offending
1530 context doesn't need to be witnessed at this point; it can be floated
1531 out). Furthermore, floating them out increases sharing. Lastly,
1532 excluding them is a conservative choice; it leaves a patch of
1533 territory free in case we need it later.
1544 <title>For-all hoisting</title>
1546 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms">) at the right hand
1547 end of an arrow, thus:
1549 type Discard a = forall b. a -> b -> a
1551 g :: Int -> Discard Int
1554 Simply expanding the type synonym would give
1556 g :: Int -> (forall b. Int -> b -> Int)
1558 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1560 g :: forall b. Int -> Int -> b -> Int
1562 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1563 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1564 performs the transformation:</emphasis>
1566 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1568 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1570 (In fact, GHC tries to retain as much synonym information as possible for use in
1571 error messages, but that is a usability issue.) This rule applies, of course, whether
1572 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1573 valid way to write <literal>g</literal>'s type signature:
1575 g :: Int -> Int -> forall b. b -> Int
1579 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1582 type Foo a = (?x::Int) => Bool -> a
1587 g :: (?x::Int) => Bool -> Bool -> Int
1595 <sect2 id="instance-decls">
1596 <title>Instance declarations</title>
1599 <title>Overlapping instances</title>
1601 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1606 instance context1 => C type1 where ...
1607 instance context2 => C type2 where ...
1611 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1613 However, if you give the command line option
1614 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1615 option</primary></indexterm> then overlapping instance declarations are permitted.
1616 However, GHC arranges never to commit to using an instance declaration
1617 if another instance declaration also applies, either now or later.
1623 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1629 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1630 (but not identical to <literal>type1</literal>), or vice versa.
1634 Notice that these rules
1639 make it clear which instance decl to use
1640 (pick the most specific one that matches)
1647 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1648 Reason: you can pick which instance decl
1649 "matches" based on the type.
1654 However the rules are over-conservative. Two instance declarations can overlap,
1655 but it can still be clear in particular situations which to use. For example:
1657 instance C (Int,a) where ...
1658 instance C (a,Bool) where ...
1660 These are rejected by GHC's rules, but it is clear what to do when trying
1661 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1662 cannot apply. Yell if this restriction bites you.
1665 GHC is also conservative about committing to an overlapping instance. For example:
1667 class C a where { op :: a -> a }
1668 instance C [Int] where ...
1669 instance C a => C [a] where ...
1671 f :: C b => [b] -> [b]
1674 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1675 GHC does not commit to the second instance declaration, because in a paricular
1676 call of f, b might be instantiate to Int, so the first instance declaration
1677 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1678 GHC will instead silently pick the second instance, without complaining about
1679 the problem of subsequent instantiations.
1682 Regrettably, GHC doesn't guarantee to detect overlapping instance
1683 declarations if they appear in different modules. GHC can "see" the
1684 instance declarations in the transitive closure of all the modules
1685 imported by the one being compiled, so it can "see" all instance decls
1686 when it is compiling <literal>Main</literal>. However, it currently chooses not
1687 to look at ones that can't possibly be of use in the module currently
1688 being compiled, in the interests of efficiency. (Perhaps we should
1689 change that decision, at least for <literal>Main</literal>.)
1694 <title>Type synonyms in the instance head</title>
1697 <emphasis>Unlike Haskell 1.4, instance heads may use type
1698 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1699 As always, using a type synonym is just shorthand for
1700 writing the RHS of the type synonym definition. For example:
1704 type Point = (Int,Int)
1705 instance C Point where ...
1706 instance C [Point] where ...
1710 is legal. However, if you added
1714 instance C (Int,Int) where ...
1718 as well, then the compiler will complain about the overlapping
1719 (actually, identical) instance declarations. As always, type synonyms
1720 must be fully applied. You cannot, for example, write:
1725 instance Monad P where ...
1729 This design decision is independent of all the others, and easily
1730 reversed, but it makes sense to me.
1735 <sect3 id="undecidable-instances">
1736 <title>Undecidable instances</title>
1738 <para>An instance declaration must normally obey the following rules:
1740 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1741 an instance declaration <emphasis>must not</emphasis> be a type variable.
1742 For example, these are OK:
1745 instance C Int a where ...
1747 instance D (Int, Int) where ...
1749 instance E [[a]] where ...
1753 instance F a where ...
1755 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1756 For example, this is OK:
1758 instance Stateful (ST s) (MutVar s) where ...
1765 <para>All of the types in the <emphasis>context</emphasis> of
1766 an instance declaration <emphasis>must</emphasis> be type variables.
1769 instance C a b => Eq (a,b) where ...
1773 instance C Int b => Foo b where ...
1779 These restrictions ensure that
1780 context reduction terminates: each reduction step removes one type
1781 constructor. For example, the following would make the type checker
1782 loop if it wasn't excluded:
1784 instance C a => C a where ...
1786 There are two situations in which the rule is a bit of a pain. First,
1787 if one allows overlapping instance declarations then it's quite
1788 convenient to have a "default instance" declaration that applies if
1789 something more specific does not:
1798 Second, sometimes you might want to use the following to get the
1799 effect of a "class synonym":
1803 class (C1 a, C2 a, C3 a) => C a where { }
1805 instance (C1 a, C2 a, C3 a) => C a where { }
1809 This allows you to write shorter signatures:
1821 f :: (C1 a, C2 a, C3 a) => ...
1825 Voluminous correspondence on the Haskell mailing list has convinced me
1826 that it's worth experimenting with more liberal rules. If you use
1827 the experimental flag <option>-fallow-undecidable-instances</option>
1828 <indexterm><primary>-fallow-undecidable-instances
1829 option</primary></indexterm>, you can use arbitrary
1830 types in both an instance context and instance head. Termination is ensured by having a
1831 fixed-depth recursion stack. If you exceed the stack depth you get a
1832 sort of backtrace, and the opportunity to increase the stack depth
1833 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1836 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1837 allowing these idioms interesting idioms.
1844 <sect2 id="implicit-parameters">
1845 <title>Implicit parameters</title>
1847 <para> Implicit paramters are implemented as described in
1848 "Implicit parameters: dynamic scoping with static types",
1849 J Lewis, MB Shields, E Meijer, J Launchbury,
1850 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1854 <para>(Most of the following, stil rather incomplete, documentation is
1855 due to Jeff Lewis.)</para>
1857 <para>Implicit parameter support is enabled with the option
1858 <option>-fimplicit-params</option>.</para>
1861 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1862 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1863 context. In Haskell, all variables are statically bound. Dynamic
1864 binding of variables is a notion that goes back to Lisp, but was later
1865 discarded in more modern incarnations, such as Scheme. Dynamic binding
1866 can be very confusing in an untyped language, and unfortunately, typed
1867 languages, in particular Hindley-Milner typed languages like Haskell,
1868 only support static scoping of variables.
1871 However, by a simple extension to the type class system of Haskell, we
1872 can support dynamic binding. Basically, we express the use of a
1873 dynamically bound variable as a constraint on the type. These
1874 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1875 function uses a dynamically-bound variable <literal>?x</literal>
1876 of type <literal>t'</literal>". For
1877 example, the following expresses the type of a sort function,
1878 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1880 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1882 The dynamic binding constraints are just a new form of predicate in the type class system.
1885 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1886 where <literal>x</literal> is
1887 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1888 Use of this construct also introduces a new
1889 dynamic-binding constraint in the type of the expression.
1890 For example, the following definition
1891 shows how we can define an implicitly parameterized sort function in
1892 terms of an explicitly parameterized <literal>sortBy</literal> function:
1894 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1896 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1902 <title>Implicit-parameter type constraints</title>
1904 Dynamic binding constraints behave just like other type class
1905 constraints in that they are automatically propagated. Thus, when a
1906 function is used, its implicit parameters are inherited by the
1907 function that called it. For example, our <literal>sort</literal> function might be used
1908 to pick out the least value in a list:
1910 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1911 least xs = fst (sort xs)
1913 Without lifting a finger, the <literal>?cmp</literal> parameter is
1914 propagated to become a parameter of <literal>least</literal> as well. With explicit
1915 parameters, the default is that parameters must always be explicit
1916 propagated. With implicit parameters, the default is to always
1920 An implicit-parameter type constraint differs from other type class constraints in the
1921 following way: All uses of a particular implicit parameter must have
1922 the same type. This means that the type of <literal>(?x, ?x)</literal>
1923 is <literal>(?x::a) => (a,a)</literal>, and not
1924 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1928 <para> You can't have an implicit parameter in the context of a class or instance
1929 declaration. For example, both these declarations are illegal:
1931 class (?x::Int) => C a where ...
1932 instance (?x::a) => Foo [a] where ...
1934 Reason: exactly which implicit parameter you pick up depends on exactly where
1935 you invoke a function. But the ``invocation'' of instance declarations is done
1936 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1937 Easiest thing is to outlaw the offending types.</para>
1939 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1941 f :: (?x :: [a]) => Int -> Int
1944 g :: (Read a, Show a) => String -> String
1947 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1948 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1949 quite unambiguous, and fixes the type <literal>a</literal>.
1954 <title>Implicit-parameter bindings</title>
1957 An implicit parameter is <emphasis>bound</emphasis> using the standard
1958 <literal>let</literal> or <literal>where</literal> binding forms.
1959 For example, we define the <literal>min</literal> function by binding
1960 <literal>cmp</literal>.
1963 min = let ?cmp = (<=) in least
1967 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1968 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1969 (including in a list comprehension, or do-notation, or pattern guards),
1970 or a <literal>where</literal> clause.
1971 Note the following points:
1974 An implicit-parameter binding group must be a
1975 collection of simple bindings to implicit-style variables (no
1976 function-style bindings, and no type signatures); these bindings are
1977 neither polymorphic or recursive.
1980 You may not mix implicit-parameter bindings with ordinary bindings in a
1981 single <literal>let</literal>
1982 expression; use two nested <literal>let</literal>s instead.
1983 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1987 You may put multiple implicit-parameter bindings in a
1988 single binding group; but they are <emphasis>not</emphasis> treated
1989 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1990 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1991 parameter. The bindings are not nested, and may be re-ordered without changing
1992 the meaning of the program.
1993 For example, consider:
1995 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1997 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1998 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
2000 f :: (?x::Int) => Int -> Int
2009 <sect2 id="linear-implicit-parameters">
2010 <title>Linear implicit parameters</title>
2012 Linear implicit parameters are an idea developed by Koen Claessen,
2013 Mark Shields, and Simon PJ. They address the long-standing
2014 problem that monads seem over-kill for certain sorts of problem, notably:
2017 <listitem> <para> distributing a supply of unique names </para> </listitem>
2018 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2019 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2023 Linear implicit parameters are just like ordinary implicit parameters,
2024 except that they are "linear" -- that is, they cannot be copied, and
2025 must be explicitly "split" instead. Linear implicit parameters are
2026 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2027 (The '/' in the '%' suggests the split!)
2032 import GHC.Exts( Splittable )
2034 data NameSupply = ...
2036 splitNS :: NameSupply -> (NameSupply, NameSupply)
2037 newName :: NameSupply -> Name
2039 instance Splittable NameSupply where
2043 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2044 f env (Lam x e) = Lam x' (f env e)
2047 env' = extend env x x'
2048 ...more equations for f...
2050 Notice that the implicit parameter %ns is consumed
2052 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2053 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2057 So the translation done by the type checker makes
2058 the parameter explicit:
2060 f :: NameSupply -> Env -> Expr -> Expr
2061 f ns env (Lam x e) = Lam x' (f ns1 env e)
2063 (ns1,ns2) = splitNS ns
2065 env = extend env x x'
2067 Notice the call to 'split' introduced by the type checker.
2068 How did it know to use 'splitNS'? Because what it really did
2069 was to introduce a call to the overloaded function 'split',
2070 defined by the class <literal>Splittable</literal>:
2072 class Splittable a where
2075 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2076 split for name supplies. But we can simply write
2082 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2084 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2085 <literal>GHC.Exts</literal>.
2090 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2091 are entirely distinct implicit parameters: you
2092 can use them together and they won't intefere with each other. </para>
2095 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2097 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2098 in the context of a class or instance declaration. </para></listitem>
2102 <sect3><title>Warnings</title>
2105 The monomorphism restriction is even more important than usual.
2106 Consider the example above:
2108 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2109 f env (Lam x e) = Lam x' (f env e)
2112 env' = extend env x x'
2114 If we replaced the two occurrences of x' by (newName %ns), which is
2115 usually a harmless thing to do, we get:
2117 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2118 f env (Lam x e) = Lam (newName %ns) (f env e)
2120 env' = extend env x (newName %ns)
2122 But now the name supply is consumed in <emphasis>three</emphasis> places
2123 (the two calls to newName,and the recursive call to f), so
2124 the result is utterly different. Urk! We don't even have
2128 Well, this is an experimental change. With implicit
2129 parameters we have already lost beta reduction anyway, and
2130 (as John Launchbury puts it) we can't sensibly reason about
2131 Haskell programs without knowing their typing.
2136 <sect3><title>Recursive functions</title>
2137 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2140 foo :: %x::T => Int -> [Int]
2142 foo n = %x : foo (n-1)
2144 where T is some type in class Splittable.</para>
2146 Do you get a list of all the same T's or all different T's
2147 (assuming that split gives two distinct T's back)?
2149 If you supply the type signature, taking advantage of polymorphic
2150 recursion, you get what you'd probably expect. Here's the
2151 translated term, where the implicit param is made explicit:
2154 foo x n = let (x1,x2) = split x
2155 in x1 : foo x2 (n-1)
2157 But if you don't supply a type signature, GHC uses the Hindley
2158 Milner trick of using a single monomorphic instance of the function
2159 for the recursive calls. That is what makes Hindley Milner type inference
2160 work. So the translation becomes
2164 foom n = x : foom (n-1)
2168 Result: 'x' is not split, and you get a list of identical T's. So the
2169 semantics of the program depends on whether or not foo has a type signature.
2172 You may say that this is a good reason to dislike linear implicit parameters
2173 and you'd be right. That is why they are an experimental feature.
2179 <sect2 id="functional-dependencies">
2180 <title>Functional dependencies
2183 <para> Functional dependencies are implemented as described by Mark Jones
2184 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2185 In Proceedings of the 9th European Symposium on Programming,
2186 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2190 Functional dependencies are introduced by a vertical bar in the syntax of a
2191 class declaration; e.g.
2193 class (Monad m) => MonadState s m | m -> s where ...
2195 class Foo a b c | a b -> c where ...
2197 There should be more documentation, but there isn't (yet). Yell if you need it.
2203 <sect2 id="sec-kinding">
2204 <title>Explicitly-kinded quantification</title>
2207 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2208 to give the kind explicitly as (machine-checked) documentation,
2209 just as it is nice to give a type signature for a function. On some occasions,
2210 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2211 John Hughes had to define the data type:
2213 data Set cxt a = Set [a]
2214 | Unused (cxt a -> ())
2216 The only use for the <literal>Unused</literal> constructor was to force the correct
2217 kind for the type variable <literal>cxt</literal>.
2220 GHC now instead allows you to specify the kind of a type variable directly, wherever
2221 a type variable is explicitly bound. Namely:
2223 <listitem><para><literal>data</literal> declarations:
2225 data Set (cxt :: * -> *) a = Set [a]
2226 </Screen></para></listitem>
2227 <listitem><para><literal>type</literal> declarations:
2229 type T (f :: * -> *) = f Int
2230 </Screen></para></listitem>
2231 <listitem><para><literal>class</literal> declarations:
2233 class (Eq a) => C (f :: * -> *) a where ...
2234 </Screen></para></listitem>
2235 <listitem><para><literal>forall</literal>'s in type signatures:
2237 f :: forall (cxt :: * -> *). Set cxt Int
2238 </Screen></para></listitem>
2243 The parentheses are required. Some of the spaces are required too, to
2244 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2245 will get a parse error, because "<literal>::*->*</literal>" is a
2246 single lexeme in Haskell.
2250 As part of the same extension, you can put kind annotations in types
2253 f :: (Int :: *) -> Int
2254 g :: forall a. a -> (a :: *)
2258 atype ::= '(' ctype '::' kind ')
2260 The parentheses are required.
2265 <sect2 id="universal-quantification">
2266 <title>Arbitrary-rank polymorphism
2270 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2271 allows us to say exactly what this means. For example:
2279 g :: forall b. (b -> b)
2281 The two are treated identically.
2285 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2286 explicit universal quantification in
2288 For example, all the following types are legal:
2290 f1 :: forall a b. a -> b -> a
2291 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2293 f2 :: (forall a. a->a) -> Int -> Int
2294 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2296 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2298 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2299 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2300 The <literal>forall</literal> makes explicit the universal quantification that
2301 is implicitly added by Haskell.
2304 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2305 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2306 shows, the polymorphic type on the left of the function arrow can be overloaded.
2309 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
2310 they have rank-2 types on the left of a function arrow.
2313 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2314 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2315 that restriction has now been lifted.)
2316 In particular, a forall-type (also called a "type scheme"),
2317 including an operational type class context, is legal:
2319 <listitem> <para> On the left of a function arrow </para> </listitem>
2320 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
2321 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2322 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
2323 field type signatures.</para> </listitem>
2324 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2325 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
2327 There is one place you cannot put a <literal>forall</literal>:
2328 you cannot instantiate a type variable with a forall-type. So you cannot
2329 make a forall-type the argument of a type constructor. So these types are illegal:
2331 x1 :: [forall a. a->a]
2332 x2 :: (forall a. a->a, Int)
2333 x3 :: Maybe (forall a. a->a)
2335 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2336 a type variable any more!
2345 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2346 the types of the constructor arguments. Here are several examples:
2352 data T a = T1 (forall b. b -> b -> b) a
2354 data MonadT m = MkMonad { return :: forall a. a -> m a,
2355 bind :: forall a b. m a -> (a -> m b) -> m b
2358 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2364 The constructors have rank-2 types:
2370 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2371 MkMonad :: forall m. (forall a. a -> m a)
2372 -> (forall a b. m a -> (a -> m b) -> m b)
2374 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2380 Notice that you don't need to use a <literal>forall</literal> if there's an
2381 explicit context. For example in the first argument of the
2382 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2383 prefixed to the argument type. The implicit <literal>forall</literal>
2384 quantifies all type variables that are not already in scope, and are
2385 mentioned in the type quantified over.
2389 As for type signatures, implicit quantification happens for non-overloaded
2390 types too. So if you write this:
2393 data T a = MkT (Either a b) (b -> b)
2396 it's just as if you had written this:
2399 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2402 That is, since the type variable <literal>b</literal> isn't in scope, it's
2403 implicitly universally quantified. (Arguably, it would be better
2404 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2405 where that is what is wanted. Feedback welcomed.)
2409 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2410 the constructor to suitable values, just as usual. For example,
2421 a3 = MkSwizzle reverse
2424 a4 = let r x = Just x
2431 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2432 mkTs f x y = [T1 f x, T1 f y]
2438 The type of the argument can, as usual, be more general than the type
2439 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2440 does not need the <literal>Ord</literal> constraint.)
2444 When you use pattern matching, the bound variables may now have
2445 polymorphic types. For example:
2451 f :: T a -> a -> (a, Char)
2452 f (T1 w k) x = (w k x, w 'c' 'd')
2454 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2455 g (MkSwizzle s) xs f = s (map f (s xs))
2457 h :: MonadT m -> [m a] -> m [a]
2458 h m [] = return m []
2459 h m (x:xs) = bind m x $ \y ->
2460 bind m (h m xs) $ \ys ->
2467 In the function <function>h</function> we use the record selectors <literal>return</literal>
2468 and <literal>bind</literal> to extract the polymorphic bind and return functions
2469 from the <literal>MonadT</literal> data structure, rather than using pattern
2475 <title>Type inference</title>
2478 In general, type inference for arbitrary-rank types is undecideable.
2479 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2480 to get a decidable algorithm by requiring some help from the programmer.
2481 We do not yet have a formal specification of "some help" but the rule is this:
2484 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2485 provides an explicit polymorphic type for x, or GHC's type inference will assume
2486 that x's type has no foralls in it</emphasis>.
2489 What does it mean to "provide" an explicit type for x? You can do that by
2490 giving a type signature for x directly, using a pattern type signature
2491 (<xref linkend="scoped-type-variables">), thus:
2493 \ f :: (forall a. a->a) -> (f True, f 'c')
2495 Alternatively, you can give a type signature to the enclosing
2496 context, which GHC can "push down" to find the type for the variable:
2498 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2500 Here the type signature on the expression can be pushed inwards
2501 to give a type signature for f. Similarly, and more commonly,
2502 one can give a type signature for the function itself:
2504 h :: (forall a. a->a) -> (Bool,Char)
2505 h f = (f True, f 'c')
2507 You don't need to give a type signature if the lambda bound variable
2508 is a constructor argument. Here is an example we saw earlier:
2510 f :: T a -> a -> (a, Char)
2511 f (T1 w k) x = (w k x, w 'c' 'd')
2513 Here we do not need to give a type signature to <literal>w</literal>, because
2514 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2521 <sect3 id="implicit-quant">
2522 <title>Implicit quantification</title>
2525 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2526 user-written types, if and only if there is no explicit <literal>forall</literal>,
2527 GHC finds all the type variables mentioned in the type that are not already
2528 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2532 f :: forall a. a -> a
2539 h :: forall b. a -> b -> b
2545 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2548 f :: (a -> a) -> Int
2550 f :: forall a. (a -> a) -> Int
2552 f :: (forall a. a -> a) -> Int
2555 g :: (Ord a => a -> a) -> Int
2556 -- MEANS the illegal type
2557 g :: forall a. (Ord a => a -> a) -> Int
2559 g :: (forall a. Ord a => a -> a) -> Int
2561 The latter produces an illegal type, which you might think is silly,
2562 but at least the rule is simple. If you want the latter type, you
2563 can write your for-alls explicitly. Indeed, doing so is strongly advised
2572 <sect2 id="scoped-type-variables">
2573 <title>Scoped type variables
2577 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2578 variable</emphasis>. For example
2584 f (xs::[a]) = ys ++ ys
2593 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2594 This brings the type variable <literal>a</literal> into scope; it scopes over
2595 all the patterns and right hand sides for this equation for <function>f</function>.
2596 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2600 Pattern type signatures are completely orthogonal to ordinary, separate
2601 type signatures. The two can be used independently or together.
2602 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2603 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2604 implicitly universally quantified. (If there are no type variables in
2605 scope, all type variables mentioned in the signature are universally
2606 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2607 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2608 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2609 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2610 it becomes possible to do so.
2614 Scoped type variables are implemented in both GHC and Hugs. Where the
2615 implementations differ from the specification below, those differences
2620 So much for the basic idea. Here are the details.
2624 <title>What a pattern type signature means</title>
2626 A type variable brought into scope by a pattern type signature is simply
2627 the name for a type. The restriction they express is that all occurrences
2628 of the same name mean the same type. For example:
2630 f :: [Int] -> Int -> Int
2631 f (xs::[a]) (y::a) = (head xs + y) :: a
2633 The pattern type signatures on the left hand side of
2634 <literal>f</literal> express the fact that <literal>xs</literal>
2635 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2636 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2637 specifies that this expression must have the same type <literal>a</literal>.
2638 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2639 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2640 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2641 rules, which specified that a pattern-bound type variable should be universally quantified.)
2642 For example, all of these are legal:</para>
2645 t (x::a) (y::a) = x+y*2
2647 f (x::a) (y::b) = [x,y] -- a unifies with b
2649 g (x::a) = x + 1::Int -- a unifies with Int
2651 h x = let k (y::a) = [x,y] -- a is free in the
2652 in k x -- environment
2654 k (x::a) True = ... -- a unifies with Int
2655 k (x::Int) False = ...
2658 w (x::a) = x -- a unifies with [b]
2664 <title>Scope and implicit quantification</title>
2672 All the type variables mentioned in a pattern,
2673 that are not already in scope,
2674 are brought into scope by the pattern. We describe this set as
2675 the <emphasis>type variables bound by the pattern</emphasis>.
2678 f (x::a) = let g (y::(a,b)) = fst y
2682 The pattern <literal>(x::a)</literal> brings the type variable
2683 <literal>a</literal> into scope, as well as the term
2684 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2685 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2686 and brings into scope the type variable <literal>b</literal>.
2692 The type variable(s) bound by the pattern have the same scope
2693 as the term variable(s) bound by the pattern. For example:
2696 f (x::a) = <...rhs of f...>
2697 (p::b, q::b) = (1,2)
2698 in <...body of let...>
2700 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2701 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2702 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2703 just like <literal>p</literal> and <literal>q</literal> do.
2704 Indeed, the newly bound type variables also scope over any ordinary, separate
2705 type signatures in the <literal>let</literal> group.
2712 The type variables bound by the pattern may be
2713 mentioned in ordinary type signatures or pattern
2714 type signatures anywhere within their scope.
2721 In ordinary type signatures, any type variable mentioned in the
2722 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2730 Ordinary type signatures do not bring any new type variables
2731 into scope (except in the type signature itself!). So this is illegal:
2738 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2739 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2740 and that is an incorrect typing.
2747 The pattern type signature is a monotype:
2752 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2756 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2757 not to type schemes.
2761 There is no implicit universal quantification on pattern type signatures (in contrast to
2762 ordinary type signatures).
2772 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2773 scope over the methods defined in the <literal>where</literal> part. For example:
2787 (Not implemented in Hugs yet, Dec 98).
2798 <title>Where a pattern type signature can occur</title>
2801 A pattern type signature can occur in any pattern. For example:
2806 A pattern type signature can be on an arbitrary sub-pattern, not
2811 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2820 Pattern type signatures, including the result part, can be used
2821 in lambda abstractions:
2824 (\ (x::a, y) :: a -> x)
2831 Pattern type signatures, including the result part, can be used
2832 in <literal>case</literal> expressions:
2836 case e of { (x::a, y) :: a -> x }
2844 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2845 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2846 token or a parenthesised type of some sort). To see why,
2847 consider how one would parse this:
2861 Pattern type signatures can bind existential type variables.
2866 data T = forall a. MkT [a]
2869 f (MkT [t::a]) = MkT t3
2882 Pattern type signatures
2883 can be used in pattern bindings:
2886 f x = let (y, z::a) = x in ...
2887 f1 x = let (y, z::Int) = x in ...
2888 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2889 f3 :: (b->b) = \x -> x
2892 In all such cases, the binding is not generalised over the pattern-bound
2893 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2894 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2895 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2896 In contrast, the binding
2901 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2902 in <literal>f4</literal>'s scope.
2912 <title>Result type signatures</title>
2915 The result type of a function can be given a signature, thus:
2919 f (x::a) :: [a] = [x,x,x]
2923 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2924 result type. Sometimes this is the only way of naming the type variable
2929 f :: Int -> [a] -> [a]
2930 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2931 in \xs -> map g (reverse xs `zip` xs)
2936 The type variables bound in a result type signature scope over the right hand side
2937 of the definition. However, consider this corner-case:
2939 rev1 :: [a] -> [a] = \xs -> reverse xs
2941 foo ys = rev (ys::[a])
2943 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2944 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2945 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2946 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2947 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2950 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2951 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2955 rev1 :: [a] -> [a] = \xs -> reverse xs
2960 Result type signatures are not yet implemented in Hugs.
2967 <sect2 id="deriving-typeable">
2968 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2971 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2972 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2973 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2974 classes <literal>Eq</literal>, <literal>Ord</literal>,
2975 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2978 GHC extends this list with two more classes that may be automatically derived
2979 (provided the <option>-fglasgow-exts</option> flag is specified):
2980 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2981 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
2982 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2986 <sect2 id="newtype-deriving">
2987 <title>Generalised derived instances for newtypes</title>
2990 When you define an abstract type using <literal>newtype</literal>, you may want
2991 the new type to inherit some instances from its representation. In
2992 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2993 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2994 other classes you have to write an explicit instance declaration. For
2995 example, if you define
2998 newtype Dollars = Dollars Int
3001 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3002 explicitly define an instance of <literal>Num</literal>:
3005 instance Num Dollars where
3006 Dollars a + Dollars b = Dollars (a+b)
3009 All the instance does is apply and remove the <literal>newtype</literal>
3010 constructor. It is particularly galling that, since the constructor
3011 doesn't appear at run-time, this instance declaration defines a
3012 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3013 dictionary, only slower!
3017 <sect3> <title> Generalising the deriving clause </title>
3019 GHC now permits such instances to be derived instead, so one can write
3021 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3024 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3025 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3026 derives an instance declaration of the form
3029 instance Num Int => Num Dollars
3032 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3036 We can also derive instances of constructor classes in a similar
3037 way. For example, suppose we have implemented state and failure monad
3038 transformers, such that
3041 instance Monad m => Monad (State s m)
3042 instance Monad m => Monad (Failure m)
3044 In Haskell 98, we can define a parsing monad by
3046 type Parser tok m a = State [tok] (Failure m) a
3049 which is automatically a monad thanks to the instance declarations
3050 above. With the extension, we can make the parser type abstract,
3051 without needing to write an instance of class <literal>Monad</literal>, via
3054 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3057 In this case the derived instance declaration is of the form
3059 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3062 Notice that, since <literal>Monad</literal> is a constructor class, the
3063 instance is a <emphasis>partial application</emphasis> of the new type, not the
3064 entire left hand side. We can imagine that the type declaration is
3065 ``eta-converted'' to generate the context of the instance
3070 We can even derive instances of multi-parameter classes, provided the
3071 newtype is the last class parameter. In this case, a ``partial
3072 application'' of the class appears in the <literal>deriving</literal>
3073 clause. For example, given the class
3076 class StateMonad s m | m -> s where ...
3077 instance Monad m => StateMonad s (State s m) where ...
3079 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3081 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3082 deriving (Monad, StateMonad [tok])
3085 The derived instance is obtained by completing the application of the
3086 class to the new type:
3089 instance StateMonad [tok] (State [tok] (Failure m)) =>
3090 StateMonad [tok] (Parser tok m)
3095 As a result of this extension, all derived instances in newtype
3096 declarations are treated uniformly (and implemented just by reusing
3097 the dictionary for the representation type), <emphasis>except</emphasis>
3098 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3099 the newtype and its representation.
3103 <sect3> <title> A more precise specification </title>
3105 Derived instance declarations are constructed as follows. Consider the
3106 declaration (after expansion of any type synonyms)
3109 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3115 <literal>S</literal> is a type constructor,
3118 <literal>t1...tk</literal> are types,
3121 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3122 the <literal>ti</literal>, and
3125 the <literal>ci</literal> are partial applications of
3126 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3127 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3130 Then, for each <literal>ci</literal>, the derived instance
3133 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3135 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3136 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3140 As an example which does <emphasis>not</emphasis> work, consider
3142 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3144 Here we cannot derive the instance
3146 instance Monad (State s m) => Monad (NonMonad m)
3149 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3150 and so cannot be "eta-converted" away. It is a good thing that this
3151 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3152 not, in fact, a monad --- for the same reason. Try defining
3153 <literal>>>=</literal> with the correct type: you won't be able to.
3157 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3158 important, since we can only derive instances for the last one. If the
3159 <literal>StateMonad</literal> class above were instead defined as
3162 class StateMonad m s | m -> s where ...
3165 then we would not have been able to derive an instance for the
3166 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3167 classes usually have one "main" parameter for which deriving new
3168 instances is most interesting.
3176 <!-- ==================== End of type system extensions ================= -->
3178 <!-- ====================== TEMPLATE HASKELL ======================= -->
3180 <sect1 id="template-haskell">
3181 <title>Template Haskell</title>
3183 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3184 Template Haskell at <ulink url="http://www.haskell.org/th/">
3185 http://www.haskell.org/th/</ulink>, while
3187 the main technical innovations is discussed in "<ulink
3188 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3189 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3192 <para> The first example from that paper is set out below as a worked example to help get you started.
3196 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3197 Tim Sheard is going to expand it.)
3201 <title>Syntax</title>
3203 <para> Template Haskell has the following new syntactic
3204 constructions. You need to use the flag
3205 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3206 </indexterm>to switch these syntactic extensions on
3207 (<option>-fth</option> is currently implied by
3208 <option>-fglasgow-exts</option>, but you are encouraged to
3209 specify it explicitly).</para>
3213 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3214 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3215 There must be no space between the "$" and the identifier or parenthesis. This use
3216 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3217 of "." as an infix operator. If you want the infix operator, put spaces around it.
3219 <para> A splice can occur in place of
3221 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3222 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3223 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3225 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3226 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3232 A expression quotation is written in Oxford brackets, thus:
3234 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3235 the quotation has type <literal>Expr</literal>.</para></listitem>
3236 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3237 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3238 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3239 the quotation has type <literal>Type</literal>.</para></listitem>
3240 </itemizedlist></para></listitem>
3243 Reification is written thus:
3245 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3246 has type <literal>Dec</literal>. </para></listitem>
3247 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3248 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3249 <listitem><para> Still to come: fixities </para></listitem>
3251 </itemizedlist></para>
3258 <sect2> <title> Using Template Haskell </title>
3262 The data types and monadic constructor functions for Template Haskell are in the library
3263 <literal>Language.Haskell.THSyntax</literal>.
3267 You can only run a function at compile time if it is imported from another module. That is,
3268 you can't define a function in a module, and call it from within a splice in the same module.
3269 (It would make sense to do so, but it's hard to implement.)
3273 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3276 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3277 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3278 compiles and runs a program, and then looks at the result. So it's important that
3279 the program it compiles produces results whose representations are identical to
3280 those of the compiler itself.
3284 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3285 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3290 <sect2> <title> A Template Haskell Worked Example </title>
3291 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3292 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3298 -- Import our template "pr"
3299 import Printf ( pr )
3301 -- The splice operator $ takes the Haskell source code
3302 -- generated at compile time by "pr" and splices it into
3303 -- the argument of "putStrLn".
3304 main = putStrLn ( $(pr "Hello") )
3311 -- Skeletal printf from the paper.
3312 -- It needs to be in a separate module to the one where
3313 -- you intend to use it.
3315 -- Import some Template Haskell syntax
3316 import Language.Haskell.THSyntax
3318 -- Describe a format string
3319 data Format = D | S | L String
3321 -- Parse a format string. This is left largely to you
3322 -- as we are here interested in building our first ever
3323 -- Template Haskell program and not in building printf.
3324 parse :: String -> [Format]
3327 -- Generate Haskell source code from a parsed representation
3328 -- of the format string. This code will be spliced into
3329 -- the module which calls "pr", at compile time.
3330 gen :: [Format] -> Expr
3331 gen [D] = [| \n -> show n |]
3332 gen [S] = [| \s -> s |]
3333 gen [L s] = string s
3335 -- Here we generate the Haskell code for the splice
3336 -- from an input format string.
3337 pr :: String -> Expr
3338 pr s = gen (parse s)
3341 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3344 $ ghc --make -fth main.hs -o main.exe
3347 <para>Run "main.exe" and here is your output:</para>
3358 <!-- ===================== Arrow notation =================== -->
3360 <sect1 id="arrow-notation">
3361 <title>Arrow notation
3364 <para>Arrows are a generalization of monads introduced by John Hughes.
3365 For more details, see
3370 “Generalising Monads to Arrows”,
3371 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3372 pp67–111, May 2000.
3378 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3379 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3385 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3386 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3392 and the arrows web page at
3393 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3394 With the <option>-farrows</option> flag, GHC supports the arrow
3395 notation described in the second of these papers.
3396 What follows is a brief introduction to the notation;
3397 it won't make much sense unless you've read Hughes's paper.
3398 This notation is translated to ordinary Haskell,
3399 using combinators from the
3400 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3404 <para>The extension adds a new kind of expression for defining arrows,
3405 of the form <literal>proc pat -> cmd</literal>,
3406 where <literal>proc</literal> is a new keyword.
3407 The variables of the pattern are bound in the body of the
3408 <literal>proc</literal>-expression,
3409 which is a new sort of thing called a <firstterm>command</firstterm>.
3410 The syntax of commands is as follows:
3412 cmd ::= exp1 -< exp2
3413 | exp1 -<< exp2
3414 | do { cstmt1 .. cstmtn ; cmd }
3416 | if exp then cmd1 else cmd2
3417 | case exp of { calts }
3419 | (| aexp cmd1 .. cmdn |)
3420 | \ pat1 .. patn -> cmd
3426 | rec { cstmt1 .. cstmtn }
3429 Commands produce values, but (like monadic computations)
3430 may yield more than one value,
3431 or none, and may do other things as well.
3432 For the most part, familiarity with monadic notation is a good guide to
3434 However the values of expressions, even monadic ones,
3435 are determined by the values of the variables they contain;
3436 this is not necessarily the case for commands.
3440 A simple example of the new notation is the expression
3442 proc x -> f -< x+1
3444 We call this a <firstterm>procedure</firstterm> or
3445 <firstterm>arrow abstraction</firstterm>.
3446 As with a lambda expression, the variable <literal>x</literal>
3447 is a new variable bound within the <literal>proc</literal>-expression.
3448 It refers to the input to the arrow.
3449 In the above example, <literal>-<</literal> is not an identifier but an
3450 new reserved symbol used for building commands from an expression of arrow
3451 type and an expression to be fed as input to that arrow.
3452 (The weird look will make more sense later.)
3453 It may be read as analogue of application for arrows.
3454 The above example is equivalent to the Haskell expression
3456 arr (\ x -> x+1) >>> f
3458 That would make no sense if the expression to the left of
3459 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3460 More generally, the expression to the left of <literal>-<</literal>
3461 may not involve any <firstterm>local variable</firstterm>,
3462 i.e. a variable bound in the current arrow abstraction.
3463 For such a situation there is a variant <literal>-<<</literal>, as in
3465 proc x -> f x -<< x+1
3467 which is equivalent to
3469 arr (\ x -> (f, x+1)) >>> app
3471 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3473 Such an arrow is equivalent to a monad, so if you're using this form
3474 you may find a monadic formulation more convenient.
3478 <title>do-notation for commands</title>
3481 Another form of command is a form of <literal>do</literal>-notation.
3482 For example, you can write
3491 You can read this much like ordinary <literal>do</literal>-notation,
3492 but with commands in place of monadic expressions.
3493 The first line sends the value of <literal>x+1</literal> as an input to
3494 the arrow <literal>f</literal>, and matches its output against
3495 <literal>y</literal>.
3496 In the next line, the output is discarded.
3497 The arrow <literal>returnA</literal> is defined in the
3498 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3499 module as <literal>arr id</literal>.
3500 The above example is treated as an abbreviation for
3502 arr (\ x -> (x, x)) >>>
3503 first (arr (\ x -> x+1) >>> f) >>>
3504 arr (\ (y, x) -> (y, (x, y))) >>>
3505 first (arr (\ y -> 2*y) >>> g) >>>
3507 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3508 first (arr (\ (x, z) -> x*z) >>> h) >>>
3509 arr (\ (t, z) -> t+z) >>>
3512 Note that variables not used later in the composition are projected out.
3513 After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
3515 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3516 module, this reduces to
3518 arr (\ x -> (x+1, x)) >>>
3520 arr (\ (y, x) -> (2*y, (x, y))) >>>
3522 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3524 arr (\ (t, z) -> t+z)
3526 which is what you might have written by hand.
3527 With arrow notation, GHC keeps track of all those tuples of variables for you.
3531 Note that although the above translation suggests that
3532 <literal>let</literal>-bound variables like <literal>z</literal> must be
3533 monomorphic, the actual translation produces Core,
3534 so polymorphic variables are allowed.
3538 It's also possible to have mutually recursive bindings,
3539 using the new <literal>rec</literal> keyword, as in the following example:
3541 counter :: ArrowCircuit a => a Bool Int
3542 counter = proc reset -> do
3543 rec output <- returnA -< if reset then 0 else next
3544 next <- delay 0 -< output+1
3545 returnA -< output
3547 The translation of such forms uses the <literal>loop</literal> combinator,
3548 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3554 <title>Conditional commands</title>
3557 In the previous example, we used a conditional expression to construct the
3559 Sometimes we want to conditionally execute different commands, as in
3566 which is translated to
3568 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3569 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3571 Since the translation uses <literal>|||</literal>,
3572 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3576 There are also <literal>case</literal> commands, like
3582 y <- h -< (x1, x2)
3586 The syntax is the same as for <literal>case</literal> expressions,
3587 except that the bodies of the alternatives are commands rather than expressions.
3588 The translation is similar to that of <literal>if</literal> commands.
3594 <title>Defining your own control structures</title>
3597 As we're seen, arrow notation provides constructs,
3598 modelled on those for expressions,
3599 for sequencing, value recursion and conditionals.
3600 But suitable combinators,
3601 which you can define in ordinary Haskell,
3602 may also be used to build new commands out of existing ones.
3603 The basic idea is that a command defines an arrow from environments to values.
3604 These environments assign values to the free local variables of the command.
3605 Thus combinators that produce arrows from arrows
3606 may also be used to build commands from commands.
3607 For example, the <literal>ArrowChoice</literal> class includes a combinator
3609 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3611 so we can use it to build commands:
3616 symbol Plus -< ()
3617 y <- term -< ()
3620 symbol Minus -< ()
3621 y <- term -< ()
3624 This is equivalent to
3626 expr' = (proc x -> returnA -< x)
3627 <+> (proc x -> do
3628 symbol Plus -< ()
3629 y <- term -< ()
3631 <+> (proc x -> do
3632 symbol Minus -< ()
3633 y <- term -< ()
3636 It is essential that this operator be polymorphic in <literal>e</literal>
3637 (representing the environment input to the command
3638 and thence to its subcommands)
3639 and satisfy the corresponding naturality property
3641 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3643 at least for strict <literal>k</literal>.
3644 (This should be automatic if you're not using <literal>seq</literal>.)
3645 This ensures that environments seen by the subcommands are environments
3646 of the whole command,
3647 and also allows the translation to safely trim these environments.
3648 The operator must also not use any variable defined within the current
3653 We could define our own operator
3655 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3656 untilA body cond = proc x ->
3657 if cond x then returnA -< ()
3660 untilA body cond -< x
3662 and use it in the same way.
3663 Of course this infix syntax only makes sense for binary operators;
3664 there is also a more general syntax involving special brackets:
3668 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3675 <title>Primitive constructs</title>
3678 Some operators will need to pass additional inputs to their subcommands.
3679 For example, in an arrow type supporting exceptions,
3680 the operator that attaches an exception handler will wish to pass the
3681 exception that occurred to the handler.
3682 Such an operator might have a type
3684 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3686 where <literal>Ex</literal> is the type of exceptions handled.
3687 You could then use this with arrow notation by writing a command
3689 body `handleA` \ ex -> handler
3691 so that if an exception is raised in the command <literal>body</literal>,
3692 the variable <literal>ex</literal> is bound to the value of the exception
3693 and the command <literal>handler</literal>,
3694 which typically refers to <literal>ex</literal>, is entered.
3695 Though the syntax here looks like a functional lambda,
3696 we are talking about commands, and something different is going on.
3697 The input to the arrow represented by a command consists of values for
3698 the free local variables in the command, plus a stack of anonymous values.
3699 In all the prior examples, this stack was empty.
3700 In the second argument to <literal>handleA</literal>,
3701 this stack consists of one value, the value of the exception.
3702 The command form of lambda merely gives this value a name.
3707 the values on the stack are paired to the right of the environment.
3708 So when designing operators like <literal>handleA</literal> that pass
3709 extra inputs to their subcommands,
3710 More precisely, the type of each argument of the operator (and its result)
3711 should have the form
3713 a (...(e,t1), ... tn) t
3715 where <replaceable>e</replaceable> is a polymorphic variable
3716 (representing the environment)
3717 and <replaceable>ti</replaceable> are the types of the values on the stack,
3718 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3719 The polymorphic variable <replaceable>e</replaceable> must not occur in
3720 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3721 <replaceable>t</replaceable>.
3722 However the arrows involved need not be the same.
3723 Here are some more examples of suitable operators:
3725 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3726 runReader :: ... => a e c -> a' (e,State) c
3727 runState :: ... => a e c -> a' (e,State) (c,State)
3729 We can supply the extra input required by commands built with the last two
3730 by applying them to ordinary expressions, as in
3734 (|runReader (do { ... })|) s
3736 which adds <literal>s</literal> to the stack of inputs to the command
3737 built using <literal>runReader</literal>.
3741 The command versions of lambda abstraction and application are analogous to
3742 the expression versions.
3743 In particular, the beta and eta rules describe equivalences of commands.
3744 These three features (operators, lambda abstraction and application)
3745 are the core of the notation; everything else can be built using them,
3746 though the results would be somewhat clumsy.
3747 For example, we could simulate <literal>do</literal>-notation by defining
3749 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3750 u `bind` f = returnA &&& u >>> f
3752 bind_ :: Arrow a => a e b -> a e c -> a e c
3753 u `bind_` f = u `bind` (arr fst >>> f)
3755 We could simulate <literal>do</literal> by defining
3757 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3758 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3765 <title>Differences with the paper</title>
3770 <para>Instead of a single form of arrow application (arrow tail) with two
3771 translations, the implementation provides two forms
3772 <quote><literal>-<</literal></quote> (first-order)
3773 and <quote><literal>-<<</literal></quote> (higher-order).
3778 <para>User-defined operators are flagged with banana brackets instead of
3779 a new <literal>form</literal> keyword.
3788 <title>Portability</title>
3791 Although only GHC implements arrow notation directly,
3792 there is also a preprocessor
3794 <ulink url="http://www.haskell.org/arrows/">arrows web page></ulink>)
3795 that translates arrow notation into Haskell 98
3796 for use with other Haskell systems.
3797 You would still want to check arrow programs with GHC;
3798 tracing type errors in the preprocessor output is not easy.
3799 Modules intended for both GHC and the preprocessor must observe some
3800 additional restrictions:
3805 The module must import
3806 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3812 The preprocessor cannot cope with other Haskell extensions.
3813 These would have to go in separate modules.
3819 Because the preprocessor targets Haskell (rather than Core),
3820 <literal>let</literal>-bound variables are monomorphic.
3831 <!-- ==================== ASSERTIONS ================= -->
3833 <sect1 id="sec-assertions">
3835 <indexterm><primary>Assertions</primary></indexterm>
3839 If you want to make use of assertions in your standard Haskell code, you
3840 could define a function like the following:
3846 assert :: Bool -> a -> a
3847 assert False x = error "assertion failed!"
3854 which works, but gives you back a less than useful error message --
3855 an assertion failed, but which and where?
3859 One way out is to define an extended <function>assert</function> function which also
3860 takes a descriptive string to include in the error message and
3861 perhaps combine this with the use of a pre-processor which inserts
3862 the source location where <function>assert</function> was used.
3866 Ghc offers a helping hand here, doing all of this for you. For every
3867 use of <function>assert</function> in the user's source:
3873 kelvinToC :: Double -> Double
3874 kelvinToC k = assert (k >= 0.0) (k+273.15)
3880 Ghc will rewrite this to also include the source location where the
3887 assert pred val ==> assertError "Main.hs|15" pred val
3893 The rewrite is only performed by the compiler when it spots
3894 applications of <function>Control.Exception.assert</function>, so you
3895 can still define and use your own versions of
3896 <function>assert</function>, should you so wish. If not, import
3897 <literal>Control.Exception</literal> to make use
3898 <function>assert</function> in your code.
3902 To have the compiler ignore uses of assert, use the compiler option
3903 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3904 option</primary></indexterm> That is, expressions of the form
3905 <literal>assert pred e</literal> will be rewritten to
3906 <literal>e</literal>.
3910 Assertion failures can be caught, see the documentation for the
3911 <literal>Control.Exception</literal> library for the details.
3917 <!-- =============================== PRAGMAS =========================== -->
3919 <sect1 id="pragmas">
3920 <title>Pragmas</title>
3922 <indexterm><primary>pragma</primary></indexterm>
3924 <para>GHC supports several pragmas, or instructions to the
3925 compiler placed in the source code. Pragmas don't normally affect
3926 the meaning of the program, but they might affect the efficiency
3927 of the generated code.</para>
3929 <para>Pragmas all take the form
3931 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3933 where <replaceable>word</replaceable> indicates the type of
3934 pragma, and is followed optionally by information specific to that
3935 type of pragma. Case is ignored in
3936 <replaceable>word</replaceable>. The various values for
3937 <replaceable>word</replaceable> that GHC understands are described
3938 in the following sections; any pragma encountered with an
3939 unrecognised <replaceable>word</replaceable> is (silently)
3942 <sect2 id="deprecated-pragma">
3943 <title>DEPRECATED pragma</title>
3944 <indexterm><primary>DEPRECATED</primary>
3947 <para>The DEPRECATED pragma lets you specify that a particular
3948 function, class, or type, is deprecated. There are two
3953 <para>You can deprecate an entire module thus:</para>
3955 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3958 <para>When you compile any module that import
3959 <literal>Wibble</literal>, GHC will print the specified
3964 <para>You can deprecate a function, class, or type, with the
3965 following top-level declaration:</para>
3967 {-# DEPRECATED f, C, T "Don't use these" #-}
3969 <para>When you compile any module that imports and uses any
3970 of the specifed entities, GHC will print the specified
3975 <para>You can suppress the warnings with the flag
3976 <option>-fno-warn-deprecations</option>.</para>
3979 <sect2 id="inline-noinline-pragma">
3980 <title>INLINE and NOINLINE pragmas</title>
3982 <para>These pragmas control the inlining of function
3985 <sect3 id="inline-pragma">
3986 <title>INLINE pragma</title>
3987 <indexterm><primary>INLINE</primary></indexterm>
3989 <para>GHC (with <option>-O</option>, as always) tries to
3990 inline (or “unfold”) functions/values that are
3991 “small enough,” thus avoiding the call overhead
3992 and possibly exposing other more-wonderful optimisations.
3993 Normally, if GHC decides a function is “too
3994 expensive” to inline, it will not do so, nor will it
3995 export that unfolding for other modules to use.</para>
3997 <para>The sledgehammer you can bring to bear is the
3998 <literal>INLINE</literal><indexterm><primary>INLINE
3999 pragma</primary></indexterm> pragma, used thusly:</para>
4002 key_function :: Int -> String -> (Bool, Double)
4004 #ifdef __GLASGOW_HASKELL__
4005 {-# INLINE key_function #-}
4009 <para>(You don't need to do the C pre-processor carry-on
4010 unless you're going to stick the code through HBC—it
4011 doesn't like <literal>INLINE</literal> pragmas.)</para>
4013 <para>The major effect of an <literal>INLINE</literal> pragma
4014 is to declare a function's “cost” to be very low.
4015 The normal unfolding machinery will then be very keen to
4018 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4019 function can be put anywhere its type signature could be
4022 <para><literal>INLINE</literal> pragmas are a particularly
4024 <literal>then</literal>/<literal>return</literal> (or
4025 <literal>bind</literal>/<literal>unit</literal>) functions in
4026 a monad. For example, in GHC's own
4027 <literal>UniqueSupply</literal> monad code, we have:</para>
4030 #ifdef __GLASGOW_HASKELL__
4031 {-# INLINE thenUs #-}
4032 {-# INLINE returnUs #-}
4036 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4037 linkend="noinline-pragma">).</para>
4040 <sect3 id="noinline-pragma">
4041 <title>NOINLINE pragma</title>
4043 <indexterm><primary>NOINLINE</primary></indexterm>
4044 <indexterm><primary>NOTINLINE</primary></indexterm>
4046 <para>The <literal>NOINLINE</literal> pragma does exactly what
4047 you'd expect: it stops the named function from being inlined
4048 by the compiler. You shouldn't ever need to do this, unless
4049 you're very cautious about code size.</para>
4051 <para><literal>NOTINLINE</literal> is a synonym for
4052 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4053 specified by Haskell 98 as the standard way to disable
4054 inlining, so it should be used if you want your code to be
4058 <sect3 id="phase-control">
4059 <title>Phase control</title>
4061 <para> Sometimes you want to control exactly when in GHC's
4062 pipeline the INLINE pragma is switched on. Inlining happens
4063 only during runs of the <emphasis>simplifier</emphasis>. Each
4064 run of the simplifier has a different <emphasis>phase
4065 number</emphasis>; the phase number decreases towards zero.
4066 If you use <option>-dverbose-core2core</option> you'll see the
4067 sequence of phase numbers for successive runs of the
4068 simpifier. In an INLINE pragma you can optionally specify a
4069 phase number, thus:</para>
4073 <para>You can say "inline <literal>f</literal> in Phase 2
4074 and all subsequent phases":
4076 {-# INLINE [2] f #-}
4082 <para>You can say "inline <literal>g</literal> in all
4083 phases up to, but not including, Phase 3":
4085 {-# INLINE [~3] g #-}
4091 <para>If you omit the phase indicator, you mean "inline in
4096 <para>You can use a phase number on a NOINLINE pragma too:</para>
4100 <para>You can say "do not inline <literal>f</literal>
4101 until Phase 2; in Phase 2 and subsequently behave as if
4102 there was no pragma at all":
4104 {-# NOINLINE [2] f #-}
4110 <para>You can say "do not inline <literal>g</literal> in
4111 Phase 3 or any subsequent phase; before that, behave as if
4112 there was no pragma":
4114 {-# NOINLINE [~3] g #-}
4120 <para>If you omit the phase indicator, you mean "never
4121 inline this function".</para>
4125 <para>The same phase-numbering control is available for RULES
4126 (<xref LinkEnd="rewrite-rules">).</para>
4130 <sect2 id="line-pragma">
4131 <title>LINE pragma</title>
4133 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4134 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4135 <para>This pragma is similar to C's <literal>#line</literal>
4136 pragma, and is mainly for use in automatically generated Haskell
4137 code. It lets you specify the line number and filename of the
4138 original code; for example</para>
4141 {-# LINE 42 "Foo.vhs" #-}
4144 <para>if you'd generated the current file from something called
4145 <filename>Foo.vhs</filename> and this line corresponds to line
4146 42 in the original. GHC will adjust its error messages to refer
4147 to the line/file named in the <literal>LINE</literal>
4151 <sect2 id="options-pragma">
4152 <title>OPTIONS pragma</title>
4153 <indexterm><primary>OPTIONS</primary>
4155 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4158 <para>The <literal>OPTIONS</literal> pragma is used to specify
4159 additional options that are given to the compiler when compiling
4160 this source file. See <xref linkend="source-file-options"> for
4165 <title>RULES pragma</title>
4167 <para>The RULES pragma lets you specify rewrite rules. It is
4168 described in <xref LinkEnd="rewrite-rules">.</para>
4171 <sect2 id="specialize-pragma">
4172 <title>SPECIALIZE pragma</title>
4174 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4175 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4176 <indexterm><primary>overloading, death to</primary></indexterm>
4178 <para>(UK spelling also accepted.) For key overloaded
4179 functions, you can create extra versions (NB: more code space)
4180 specialised to particular types. Thus, if you have an
4181 overloaded function:</para>
4184 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4187 <para>If it is heavily used on lists with
4188 <literal>Widget</literal> keys, you could specialise it as
4192 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4195 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4196 be put anywhere its type signature could be put.</para>
4198 <para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
4199 version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
4200 rewrites a call to the un-specialised function into a call to the specialised
4201 one. You can, instead, provide your own specialised function and your own rewrite rule.
4202 For example, suppose that:
4204 genericLookup :: Ord a => Table a b -> a -> b
4205 intLookup :: Table Int b -> Int -> b
4207 where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
4208 that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
4210 {-# RULES "intLookup" genericLookup = intLookup #-}
4212 (see <xref linkend="rule-spec">). It is <emphasis>Your
4213 Responsibility</emphasis> to make sure that
4214 <function>intLookup</function> really behaves as a specialised
4215 version of <function>genericLookup</function>!!!</para>
4217 <para>An example in which using <literal>RULES</literal> for
4218 specialisation will Win Big:
4221 toDouble :: Real a => a -> Double
4222 toDouble = fromRational . toRational
4224 {-# RULES "toDouble/Int" toDouble = i2d #-}
4225 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4228 The <function>i2d</function> function is virtually one machine
4229 instruction; the default conversion—via an intermediate
4230 <literal>Rational</literal>—is obscenely expensive by
4235 <sect2 id="specialize-instance-pragma">
4236 <title>SPECIALIZE instance pragma
4240 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4241 <indexterm><primary>overloading, death to</primary></indexterm>
4242 Same idea, except for instance declarations. For example:
4245 instance (Eq a) => Eq (Foo a) where {
4246 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4250 The pragma must occur inside the <literal>where</literal> part
4251 of the instance declaration.
4254 Compatible with HBC, by the way, except perhaps in the placement
4264 <!-- ======================= REWRITE RULES ======================== -->
4266 <sect1 id="rewrite-rules">
4267 <title>Rewrite rules
4269 <indexterm><primary>RULES pagma</primary></indexterm>
4270 <indexterm><primary>pragma, RULES</primary></indexterm>
4271 <indexterm><primary>rewrite rules</primary></indexterm></title>
4274 The programmer can specify rewrite rules as part of the source program
4275 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4276 the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
4277 and (b) the <option>-frules-off</option> flag
4278 (<xref LinkEnd="options-f">) is not specified.
4286 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4293 <title>Syntax</title>
4296 From a syntactic point of view:
4302 There may be zero or more rules in a <literal>RULES</literal> pragma.
4309 Each rule has a name, enclosed in double quotes. The name itself has
4310 no significance at all. It is only used when reporting how many times the rule fired.
4316 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
4317 immediately after the name of the rule. Thus:
4320 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4323 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4324 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4333 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4334 is set, so you must lay out your rules starting in the same column as the
4335 enclosing definitions.
4342 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4343 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4344 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4345 by spaces, just like in a type <literal>forall</literal>.
4351 A pattern variable may optionally have a type signature.
4352 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4353 For example, here is the <literal>foldr/build</literal> rule:
4356 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4357 foldr k z (build g) = g k z
4360 Since <function>g</function> has a polymorphic type, it must have a type signature.
4367 The left hand side of a rule must consist of a top-level variable applied
4368 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4371 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4372 "wrong2" forall f. f True = True
4375 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4382 A rule does not need to be in the same module as (any of) the
4383 variables it mentions, though of course they need to be in scope.
4389 Rules are automatically exported from a module, just as instance declarations are.
4400 <title>Semantics</title>
4403 From a semantic point of view:
4409 Rules are only applied if you use the <option>-O</option> flag.
4415 Rules are regarded as left-to-right rewrite rules.
4416 When GHC finds an expression that is a substitution instance of the LHS
4417 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4418 By "a substitution instance" we mean that the LHS can be made equal to the
4419 expression by substituting for the pattern variables.
4426 The LHS and RHS of a rule are typechecked, and must have the
4434 GHC makes absolutely no attempt to verify that the LHS and RHS
4435 of a rule have the same meaning. That is undecideable in general, and
4436 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4443 GHC makes no attempt to make sure that the rules are confluent or
4444 terminating. For example:
4447 "loop" forall x,y. f x y = f y x
4450 This rule will cause the compiler to go into an infinite loop.
4457 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4463 GHC currently uses a very simple, syntactic, matching algorithm
4464 for matching a rule LHS with an expression. It seeks a substitution
4465 which makes the LHS and expression syntactically equal modulo alpha
4466 conversion. The pattern (rule), but not the expression, is eta-expanded if
4467 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4468 But not beta conversion (that's called higher-order matching).
4472 Matching is carried out on GHC's intermediate language, which includes
4473 type abstractions and applications. So a rule only matches if the
4474 types match too. See <xref LinkEnd="rule-spec"> below.
4480 GHC keeps trying to apply the rules as it optimises the program.
4481 For example, consider:
4490 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4491 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4492 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4493 not be substituted, and the rule would not fire.
4500 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4501 that appears on the LHS of a rule</emphasis>, because once you have substituted
4502 for something you can't match against it (given the simple minded
4503 matching). So if you write the rule
4506 "map/map" forall f,g. map f . map g = map (f.g)
4509 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4510 It will only match something written with explicit use of ".".
4511 Well, not quite. It <emphasis>will</emphasis> match the expression
4517 where <function>wibble</function> is defined:
4520 wibble f g = map f . map g
4523 because <function>wibble</function> will be inlined (it's small).
4525 Later on in compilation, GHC starts inlining even things on the
4526 LHS of rules, but still leaves the rules enabled. This inlining
4527 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4534 All rules are implicitly exported from the module, and are therefore
4535 in force in any module that imports the module that defined the rule, directly
4536 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4537 in force when compiling A.) The situation is very similar to that for instance
4549 <title>List fusion</title>
4552 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4553 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4554 intermediate list should be eliminated entirely.
4558 The following are good producers:
4570 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4576 Explicit lists (e.g. <literal>[True, False]</literal>)
4582 The cons constructor (e.g <literal>3:4:[]</literal>)
4588 <function>++</function>
4594 <function>map</function>
4600 <function>filter</function>
4606 <function>iterate</function>, <function>repeat</function>
4612 <function>zip</function>, <function>zipWith</function>
4621 The following are good consumers:
4633 <function>array</function> (on its second argument)
4639 <function>length</function>
4645 <function>++</function> (on its first argument)
4651 <function>foldr</function>
4657 <function>map</function>
4663 <function>filter</function>
4669 <function>concat</function>
4675 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4681 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4682 will fuse with one but not the other)
4688 <function>partition</function>
4694 <function>head</function>
4700 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4706 <function>sequence_</function>
4712 <function>msum</function>
4718 <function>sortBy</function>
4727 So, for example, the following should generate no intermediate lists:
4730 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4736 This list could readily be extended; if there are Prelude functions that you use
4737 a lot which are not included, please tell us.
4741 If you want to write your own good consumers or producers, look at the
4742 Prelude definitions of the above functions to see how to do so.
4747 <sect2 id="rule-spec">
4748 <title>Specialisation
4752 Rewrite rules can be used to get the same effect as a feature
4753 present in earlier version of GHC:
4756 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4759 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4760 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4761 specialising the original definition of <function>fromIntegral</function> the programmer is
4762 promising that it is safe to use <function>int8ToInt16</function> instead.
4766 This feature is no longer in GHC. But rewrite rules let you do the
4771 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4775 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4776 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4777 GHC adds the type and dictionary applications to get the typed rule
4780 forall (d1::Integral Int8) (d2::Num Int16) .
4781 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4785 this rule does not need to be in the same file as fromIntegral,
4786 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4787 have an original definition available to specialise).
4793 <title>Controlling what's going on</title>
4801 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4807 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4808 If you add <option>-dppr-debug</option> you get a more detailed listing.
4814 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4817 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4818 {-# INLINE build #-}
4822 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4823 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4824 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4825 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4832 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4833 see how to write rules that will do fusion and yet give an efficient
4834 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4844 <sect2 id="core-pragma">
4845 <title>CORE pragma</title>
4847 <indexterm><primary>CORE pragma</primary></indexterm>
4848 <indexterm><primary>pragma, CORE</primary></indexterm>
4849 <indexterm><primary>core, annotation</primary></indexterm>
4852 The external core format supports <quote>Note</quote> annotations;
4853 the <literal>CORE</literal> pragma gives a way to specify what these
4854 should be in your Haskell source code. Syntactically, core
4855 annotations are attached to expressions and take a Haskell string
4856 literal as an argument. The following function definition shows an
4860 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4863 Sematically, this is equivalent to:
4871 However, when external for is generated (via
4872 <option>-fext-core</option>), there will be Notes attached to the
4873 expressions <function>show</function> and <VarName>x</VarName>.
4874 The core function declaration for <function>f</function> is:
4878 f :: %forall a . GHCziShow.ZCTShow a ->
4879 a -> GHCziBase.ZMZN GHCziBase.Char =
4880 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4882 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4884 (tpl1::GHCziBase.Int ->
4886 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4888 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4889 (tpl3::GHCziBase.ZMZN a ->
4890 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4898 Here, we can see that the function <function>show</function> (which
4899 has been expanded out to a case expression over the Show dictionary)
4900 has a <literal>%note</literal> attached to it, as does the
4901 expression <VarName>eta</VarName> (which used to be called
4902 <VarName>x</VarName>).
4909 <sect1 id="generic-classes">
4910 <title>Generic classes</title>
4912 <para>(Note: support for generic classes is currently broken in
4916 The ideas behind this extension are described in detail in "Derivable type classes",
4917 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4918 An example will give the idea:
4926 fromBin :: [Int] -> (a, [Int])
4928 toBin {| Unit |} Unit = []
4929 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4930 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4931 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4933 fromBin {| Unit |} bs = (Unit, bs)
4934 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4935 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4936 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4937 (y,bs'') = fromBin bs'
4940 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4941 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4942 which are defined thus in the library module <literal>Generics</literal>:
4946 data a :+: b = Inl a | Inr b
4947 data a :*: b = a :*: b
4950 Now you can make a data type into an instance of Bin like this:
4952 instance (Bin a, Bin b) => Bin (a,b)
4953 instance Bin a => Bin [a]
4955 That is, just leave off the "where" clause. Of course, you can put in the
4956 where clause and over-ride whichever methods you please.
4960 <title> Using generics </title>
4961 <para>To use generics you need to</para>
4964 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4965 <option>-fgenerics</option> (to generate extra per-data-type code),
4966 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4970 <para>Import the module <literal>Generics</literal> from the
4971 <literal>lang</literal> package. This import brings into
4972 scope the data types <literal>Unit</literal>,
4973 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4974 don't need this import if you don't mention these types
4975 explicitly; for example, if you are simply giving instance
4976 declarations.)</para>
4981 <sect2> <title> Changes wrt the paper </title>
4983 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4984 can be written infix (indeed, you can now use
4985 any operator starting in a colon as an infix type constructor). Also note that
4986 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4987 Finally, note that the syntax of the type patterns in the class declaration
4988 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4989 alone would ambiguous when they appear on right hand sides (an extension we
4990 anticipate wanting).
4994 <sect2> <title>Terminology and restrictions</title>
4996 Terminology. A "generic default method" in a class declaration
4997 is one that is defined using type patterns as above.
4998 A "polymorphic default method" is a default method defined as in Haskell 98.
4999 A "generic class declaration" is a class declaration with at least one
5000 generic default method.
5008 Alas, we do not yet implement the stuff about constructor names and
5015 A generic class can have only one parameter; you can't have a generic
5016 multi-parameter class.
5022 A default method must be defined entirely using type patterns, or entirely
5023 without. So this is illegal:
5026 op :: a -> (a, Bool)
5027 op {| Unit |} Unit = (Unit, True)
5030 However it is perfectly OK for some methods of a generic class to have
5031 generic default methods and others to have polymorphic default methods.
5037 The type variable(s) in the type pattern for a generic method declaration
5038 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:
5042 op {| p :*: q |} (x :*: y) = op (x :: p)
5050 The type patterns in a generic default method must take one of the forms:
5056 where "a" and "b" are type variables. Furthermore, all the type patterns for
5057 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5058 must use the same type variables. So this is illegal:
5062 op {| a :+: b |} (Inl x) = True
5063 op {| p :+: q |} (Inr y) = False
5065 The type patterns must be identical, even in equations for different methods of the class.
5066 So this too is illegal:
5070 op1 {| a :*: b |} (x :*: y) = True
5073 op2 {| p :*: q |} (x :*: y) = False
5075 (The reason for this restriction is that we gather all the equations for a particular type consructor
5076 into a single generic instance declaration.)
5082 A generic method declaration must give a case for each of the three type constructors.
5088 The type for a generic method can be built only from:
5090 <listitem> <para> Function arrows </para> </listitem>
5091 <listitem> <para> Type variables </para> </listitem>
5092 <listitem> <para> Tuples </para> </listitem>
5093 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5095 Here are some example type signatures for generic methods:
5098 op2 :: Bool -> (a,Bool)
5099 op3 :: [Int] -> a -> a
5102 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5106 This restriction is an implementation restriction: we just havn't got around to
5107 implementing the necessary bidirectional maps over arbitrary type constructors.
5108 It would be relatively easy to add specific type constructors, such as Maybe and list,
5109 to the ones that are allowed.</para>
5114 In an instance declaration for a generic class, the idea is that the compiler
5115 will fill in the methods for you, based on the generic templates. However it can only
5120 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5125 No constructor of the instance type has unboxed fields.
5129 (Of course, these things can only arise if you are already using GHC extensions.)
5130 However, you can still give an instance declarations for types which break these rules,
5131 provided you give explicit code to override any generic default methods.
5139 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5140 what the compiler does with generic declarations.
5145 <sect2> <title> Another example </title>
5147 Just to finish with, here's another example I rather like:
5151 nCons {| Unit |} _ = 1
5152 nCons {| a :*: b |} _ = 1
5153 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5156 tag {| Unit |} _ = 1
5157 tag {| a :*: b |} _ = 1
5158 tag {| a :+: b |} (Inl x) = tag x
5159 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5168 ;;; Local Variables: ***
5170 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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