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>-fno-monomorphism-restriction</option>:</term>
69 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
71 <para> Switch off the Haskell 98 monomorphism restriction.
72 Independent of the <option>-fglasgow-exts</option>
78 <term><option>-fallow-overlapping-instances</option></term>
79 <term><option>-fallow-undecidable-instances</option></term>
80 <term><option>-fallow-incoherent-instances</option></term>
81 <term><option>-fcontext-stack</option></term>
82 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
83 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
84 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
86 <para> See <xref LinkEnd="instance-decls">. Only relevant
87 if you also use <option>-fglasgow-exts</option>.</para>
92 <term><option>-finline-phase</option></term>
93 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
95 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
96 you also use <option>-fglasgow-exts</option>.</para>
101 <term><option>-farrows</option></term>
102 <indexterm><primary><option>-farrows</option></primary></indexterm>
104 <para>See <xref LinkEnd="arrow-notation">. Independent of
105 <option>-fglasgow-exts</option>.</para>
110 <term><option>-fgenerics</option></term>
111 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
113 <para>See <xref LinkEnd="generic-classes">. Independent of
114 <option>-fglasgow-exts</option>.</para>
119 <term><option>-fno-implicit-prelude</option></term>
121 <para><indexterm><primary>-fno-implicit-prelude
122 option</primary></indexterm> GHC normally imports
123 <filename>Prelude.hi</filename> files for you. If you'd
124 rather it didn't, then give it a
125 <option>-fno-implicit-prelude</option> option. The idea is
126 that you can then import a Prelude of your own. (But don't
127 call it <literal>Prelude</literal>; the Haskell module
128 namespace is flat, and you must not conflict with any
129 Prelude module.)</para>
131 <para>Even though you have not imported the Prelude, most of
132 the built-in syntax still refers to the built-in Haskell
133 Prelude types and values, as specified by the Haskell
134 Report. For example, the type <literal>[Int]</literal>
135 still means <literal>Prelude.[] Int</literal>; tuples
136 continue to refer to the standard Prelude tuples; the
137 translation for list comprehensions continues to use
138 <literal>Prelude.map</literal> etc.</para>
140 <para>However, <option>-fno-implicit-prelude</option> does
141 change the handling of certain built-in syntax: see <xref
142 LinkEnd="rebindable-syntax">.</para>
147 <term><option>-fth</option></term>
149 <para>Enables Template Haskell (see <xref
150 linkend="template-haskell">). Currently also implied by
151 <option>-fglasgow-exts</option>.</para>
156 <term><option>-fimplicit-params</option></term>
158 <para>Enables implicit parameters (see <xref
159 linkend="implicit-parameters">). Currently also implied by
160 <option>-fglasgow-exts</option>.</para>
167 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
168 <!-- included from primitives.sgml -->
169 <!-- &primitives; -->
170 <sect1 id="primitives">
171 <title>Unboxed types and primitive operations</title>
173 <para>GHC is built on a raft of primitive data types and operations.
174 While you really can use this stuff to write fast code,
175 we generally find it a lot less painful, and more satisfying in the
176 long run, to use higher-level language features and libraries. With
177 any luck, the code you write will be optimised to the efficient
178 unboxed version in any case. And if it isn't, we'd like to know
181 <para>We do not currently have good, up-to-date documentation about the
182 primitives, perhaps because they are mainly intended for internal use.
183 There used to be a long section about them here in the User Guide, but it
184 became out of date, and wrong information is worse than none.</para>
186 <para>The Real Truth about what primitive types there are, and what operations
187 work over those types, is held in the file
188 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
189 This file is used directly to generate GHC's primitive-operation definitions, so
190 it is always correct! It is also intended for processing into text.</para>
193 the result of such processing is part of the description of the
195 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
196 Core language</ulink>.
197 So that document is a good place to look for a type-set version.
198 We would be very happy if someone wanted to volunteer to produce an SGML
199 back end to the program that processes <filename>primops.txt</filename> so that
200 we could include the results here in the User Guide.</para>
202 <para>What follows here is a brief summary of some main points.</para>
204 <sect2 id="glasgow-unboxed">
209 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
212 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
213 that values of that type are represented by a pointer to a heap
214 object. The representation of a Haskell <literal>Int</literal>, for
215 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
216 type, however, is represented by the value itself, no pointers or heap
217 allocation are involved.
221 Unboxed types correspond to the “raw machine” types you
222 would use in C: <literal>Int#</literal> (long int),
223 <literal>Double#</literal> (double), <literal>Addr#</literal>
224 (void *), etc. The <emphasis>primitive operations</emphasis>
225 (PrimOps) on these types are what you might expect; e.g.,
226 <literal>(+#)</literal> is addition on
227 <literal>Int#</literal>s, and is the machine-addition that we all
228 know and love—usually one instruction.
232 Primitive (unboxed) types cannot be defined in Haskell, and are
233 therefore built into the language and compiler. Primitive types are
234 always unlifted; that is, a value of a primitive type cannot be
235 bottom. We use the convention that primitive types, values, and
236 operations have a <literal>#</literal> suffix.
240 Primitive values are often represented by a simple bit-pattern, such
241 as <literal>Int#</literal>, <literal>Float#</literal>,
242 <literal>Double#</literal>. But this is not necessarily the case:
243 a primitive value might be represented by a pointer to a
244 heap-allocated object. Examples include
245 <literal>Array#</literal>, the type of primitive arrays. A
246 primitive array is heap-allocated because it is too big a value to fit
247 in a register, and would be too expensive to copy around; in a sense,
248 it is accidental that it is represented by a pointer. If a pointer
249 represents a primitive value, then it really does point to that value:
250 no unevaluated thunks, no indirections…nothing can be at the
251 other end of the pointer than the primitive value.
255 There are some restrictions on the use of primitive types, the main
256 one being that you can't pass a primitive value to a polymorphic
257 function or store one in a polymorphic data type. This rules out
258 things like <literal>[Int#]</literal> (i.e. lists of primitive
259 integers). The reason for this restriction is that polymorphic
260 arguments and constructor fields are assumed to be pointers: if an
261 unboxed integer is stored in one of these, the garbage collector would
262 attempt to follow it, leading to unpredictable space leaks. Or a
263 <function>seq</function> operation on the polymorphic component may
264 attempt to dereference the pointer, with disastrous results. Even
265 worse, the unboxed value might be larger than a pointer
266 (<literal>Double#</literal> for instance).
270 Nevertheless, A numerically-intensive program using unboxed types can
271 go a <emphasis>lot</emphasis> faster than its “standard”
272 counterpart—we saw a threefold speedup on one example.
277 <sect2 id="unboxed-tuples">
278 <title>Unboxed Tuples
282 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
283 they're available by default with <option>-fglasgow-exts</option>. An
284 unboxed tuple looks like this:
296 where <literal>e_1..e_n</literal> are expressions of any
297 type (primitive or non-primitive). The type of an unboxed tuple looks
302 Unboxed tuples are used for functions that need to return multiple
303 values, but they avoid the heap allocation normally associated with
304 using fully-fledged tuples. When an unboxed tuple is returned, the
305 components are put directly into registers or on the stack; the
306 unboxed tuple itself does not have a composite representation. Many
307 of the primitive operations listed in this section return unboxed
312 There are some pretty stringent restrictions on the use of unboxed tuples:
321 Unboxed tuple types are subject to the same restrictions as
322 other unboxed types; i.e. they may not be stored in polymorphic data
323 structures or passed to polymorphic functions.
330 Unboxed tuples may only be constructed as the direct result of
331 a function, and may only be deconstructed with a <literal>case</literal> expression.
332 eg. the following are valid:
336 f x y = (# x+1, y-1 #)
337 g x = case f x x of { (# a, b #) -> a + b }
341 but the following are invalid:
355 No variable can have an unboxed tuple type. This is illegal:
359 f :: (# Int, Int #) -> (# Int, Int #)
364 because <literal>x</literal> has an unboxed tuple type.
374 Note: we may relax some of these restrictions in the future.
378 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
379 tuples to avoid unnecessary allocation during sequences of operations.
386 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
388 <sect1 id="syntax-extns">
389 <title>Syntactic extensions</title>
391 <!-- ====================== HIERARCHICAL MODULES ======================= -->
393 <sect2 id="hierarchical-modules">
394 <title>Hierarchical Modules</title>
396 <para>GHC supports a small extension to the syntax of module
397 names: a module name is allowed to contain a dot
398 <literal>‘.’</literal>. This is also known as the
399 “hierarchical module namespace” extension, because
400 it extends the normally flat Haskell module namespace into a
401 more flexible hierarchy of modules.</para>
403 <para>This extension has very little impact on the language
404 itself; modules names are <emphasis>always</emphasis> fully
405 qualified, so you can just think of the fully qualified module
406 name as <quote>the module name</quote>. In particular, this
407 means that the full module name must be given after the
408 <literal>module</literal> keyword at the beginning of the
409 module; for example, the module <literal>A.B.C</literal> must
412 <programlisting>module A.B.C</programlisting>
415 <para>It is a common strategy to use the <literal>as</literal>
416 keyword to save some typing when using qualified names with
417 hierarchical modules. For example:</para>
420 import qualified Control.Monad.ST.Strict as ST
423 <para>For details on how GHC searches for source and interface
424 files in the presence of hierarchical modules, see <xref
425 linkend="search-path">.</para>
427 <para>GHC comes with a large collection of libraries arranged
428 hierarchically; see the accompanying library documentation.
429 There is an ongoing project to create and maintain a stable set
430 of <quote>core</quote> libraries used by several Haskell
431 compilers, and the libraries that GHC comes with represent the
432 current status of that project. For more details, see <ulink
433 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
434 Libraries</ulink>.</para>
438 <!-- ====================== PATTERN GUARDS ======================= -->
440 <sect2 id="pattern-guards">
441 <title>Pattern guards</title>
444 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
445 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.)
449 Suppose we have an abstract data type of finite maps, with a
453 lookup :: FiniteMap -> Int -> Maybe Int
456 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
457 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
461 clunky env var1 var2 | ok1 && ok2 = val1 + val2
462 | otherwise = var1 + var2
473 The auxiliary functions are
477 maybeToBool :: Maybe a -> Bool
478 maybeToBool (Just x) = True
479 maybeToBool Nothing = False
481 expectJust :: Maybe a -> a
482 expectJust (Just x) = x
483 expectJust Nothing = error "Unexpected Nothing"
487 What is <function>clunky</function> doing? The guard <literal>ok1 &&
488 ok2</literal> checks that both lookups succeed, using
489 <function>maybeToBool</function> to convert the <function>Maybe</function>
490 types to booleans. The (lazily evaluated) <function>expectJust</function>
491 calls extract the values from the results of the lookups, and binds the
492 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
493 respectively. If either lookup fails, then clunky takes the
494 <literal>otherwise</literal> case and returns the sum of its arguments.
498 This is certainly legal Haskell, but it is a tremendously verbose and
499 un-obvious way to achieve the desired effect. Arguably, a more direct way
500 to write clunky would be to use case expressions:
504 clunky env var1 var1 = case lookup env var1 of
506 Just val1 -> case lookup env var2 of
508 Just val2 -> val1 + val2
514 This is a bit shorter, but hardly better. Of course, we can rewrite any set
515 of pattern-matching, guarded equations as case expressions; that is
516 precisely what the compiler does when compiling equations! The reason that
517 Haskell provides guarded equations is because they allow us to write down
518 the cases we want to consider, one at a time, independently of each other.
519 This structure is hidden in the case version. Two of the right-hand sides
520 are really the same (<function>fail</function>), and the whole expression
521 tends to become more and more indented.
525 Here is how I would write clunky:
530 | Just val1 <- lookup env var1
531 , Just val2 <- lookup env var2
533 ...other equations for clunky...
537 The semantics should be clear enough. The qualifers are matched in order.
538 For a <literal><-</literal> qualifier, which I call a pattern guard, the
539 right hand side is evaluated and matched against the pattern on the left.
540 If the match fails then the whole guard fails and the next equation is
541 tried. If it succeeds, then the appropriate binding takes place, and the
542 next qualifier is matched, in the augmented environment. Unlike list
543 comprehensions, however, the type of the expression to the right of the
544 <literal><-</literal> is the same as the type of the pattern to its
545 left. The bindings introduced by pattern guards scope over all the
546 remaining guard qualifiers, and over the right hand side of the equation.
550 Just as with list comprehensions, boolean expressions can be freely mixed
551 with among the pattern guards. For example:
562 Haskell's current guards therefore emerge as a special case, in which the
563 qualifier list has just one element, a boolean expression.
567 <!-- ===================== Recursive do-notation =================== -->
569 <sect2 id="mdo-notation">
570 <title>The recursive do-notation
573 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
574 "A recursive do for Haskell",
575 Levent Erkok, John Launchbury",
576 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
579 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
580 that is, the variables bound in a do-expression are visible only in the textually following
581 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
582 group. It turns out that several applications can benefit from recursive bindings in
583 the do-notation, and this extension provides the necessary syntactic support.
586 Here is a simple (yet contrived) example:
589 import Control.Monad.Fix
591 justOnes = mdo xs <- Just (1:xs)
595 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
599 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
602 class Monad m => MonadFix m where
603 mfix :: (a -> m a) -> m a
606 The function <literal>mfix</literal>
607 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
608 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
609 For details, see the above mentioned reference.
612 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
613 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
614 for Haskell's internal state monad (strict and lazy, respectively).
617 There are three important points in using the recursive-do notation:
620 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
621 than <literal>do</literal>).
625 You should <literal>import Control.Monad.Fix</literal>.
626 (Note: Strictly speaking, this import is required only when you need to refer to the name
627 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
628 are encouraged to always import this module when using the mdo-notation.)
632 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
638 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
639 contains up to date information on recursive monadic bindings.
643 Historical note: The old implementation of the mdo-notation (and most
644 of the existing documents) used the name
645 <literal>MonadRec</literal> for the class and the corresponding library.
646 This name is not supported by GHC.
652 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
654 <sect2 id="parallel-list-comprehensions">
655 <title>Parallel List Comprehensions</title>
656 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
658 <indexterm><primary>parallel list comprehensions</primary>
661 <para>Parallel list comprehensions are a natural extension to list
662 comprehensions. List comprehensions can be thought of as a nice
663 syntax for writing maps and filters. Parallel comprehensions
664 extend this to include the zipWith family.</para>
666 <para>A parallel list comprehension has multiple independent
667 branches of qualifier lists, each separated by a `|' symbol. For
668 example, the following zips together two lists:</para>
671 [ (x, y) | x <- xs | y <- ys ]
674 <para>The behavior of parallel list comprehensions follows that of
675 zip, in that the resulting list will have the same length as the
676 shortest branch.</para>
678 <para>We can define parallel list comprehensions by translation to
679 regular comprehensions. Here's the basic idea:</para>
681 <para>Given a parallel comprehension of the form: </para>
684 [ e | p1 <- e11, p2 <- e12, ...
685 | q1 <- e21, q2 <- e22, ...
690 <para>This will be translated to: </para>
693 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
694 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
699 <para>where `zipN' is the appropriate zip for the given number of
704 <sect2 id="rebindable-syntax">
705 <title>Rebindable syntax</title>
708 <para>GHC allows most kinds of built-in syntax to be rebound by
709 the user, to facilitate replacing the <literal>Prelude</literal>
710 with a home-grown version, for example.</para>
712 <para>You may want to define your own numeric class
713 hierarchy. It completely defeats that purpose if the
714 literal "1" means "<literal>Prelude.fromInteger
715 1</literal>", which is what the Haskell Report specifies.
716 So the <option>-fno-implicit-prelude</option> flag causes
717 the following pieces of built-in syntax to refer to
718 <emphasis>whatever is in scope</emphasis>, not the Prelude
723 <para>Integer and fractional literals mean
724 "<literal>fromInteger 1</literal>" and
725 "<literal>fromRational 3.2</literal>", not the
726 Prelude-qualified versions; both in expressions and in
728 <para>However, the standard Prelude <literal>Eq</literal> class
729 is still used for the equality test necessary for literal patterns.</para>
733 <para>Negation (e.g. "<literal>- (f x)</literal>")
734 means "<literal>negate (f x)</literal>" (not
735 <literal>Prelude.negate</literal>).</para>
739 <para>In an n+k pattern, the standard Prelude
740 <literal>Ord</literal> class is still used for comparison,
741 but the necessary subtraction uses whatever
742 "<literal>(-)</literal>" is in scope (not
743 "<literal>Prelude.(-)</literal>").</para>
747 <para>"Do" notation is translated using whatever
748 functions <literal>(>>=)</literal>,
749 <literal>(>>)</literal>, <literal>fail</literal>, and
750 <literal>return</literal>, are in scope (not the Prelude
751 versions). List comprehensions, and parallel array
752 comprehensions, are unaffected. </para></listitem>
755 <para>Be warned: this is an experimental facility, with fewer checks than
756 usual. In particular, it is essential that the functions GHC finds in scope
757 must have the appropriate types, namely:
759 fromInteger :: forall a. (...) => Integer -> a
760 fromRational :: forall a. (...) => Rational -> a
761 negate :: forall a. (...) => a -> a
762 (-) :: forall a. (...) => a -> a -> a
763 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
764 (>>) :: forall m a. (...) => m a -> m b -> m b
765 return :: forall m a. (...) => a -> m a
766 fail :: forall m a. (...) => String -> m a
768 (The (...) part can be any context including the empty context; that part
770 If the functions don't have the right type, very peculiar things may
771 happen. Use <literal>-dcore-lint</literal> to
772 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
778 <!-- TYPE SYSTEM EXTENSIONS -->
779 <sect1 id="type-extensions">
780 <title>Type system extensions</title>
784 <title>Data types and type synonyms</title>
786 <sect3 id="nullary-types">
787 <title>Data types with no constructors</title>
789 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
790 a data type with no constructors. For example:</para>
794 data T a -- T :: * -> *
797 <para>Syntactically, the declaration lacks the "= constrs" part. The
798 type can be parameterised over types of any kind, but if the kind is
799 not <literal>*</literal> then an explicit kind annotation must be used
800 (see <xref linkend="sec-kinding">).</para>
802 <para>Such data types have only one value, namely bottom.
803 Nevertheless, they can be useful when defining "phantom types".</para>
806 <sect3 id="infix-tycons">
807 <title>Infix type constructors</title>
810 GHC allows type constructors to be operators, and to be written infix, very much
811 like expressions. More specifically:
814 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
815 The lexical syntax is the same as that for data constructors.
818 Types can be written infix. For example <literal>Int :*: Bool</literal>.
822 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
823 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
826 Fixities may be declared for type constructors just as for data constructors. However,
827 one cannot distinguish between the two in a fixity declaration; a fixity declaration
828 sets the fixity for a data constructor and the corresponding type constructor. For example:
832 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
833 and similarly for <literal>:*:</literal>.
834 <literal>Int `a` Bool</literal>.
837 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
840 Data type and type-synonym declarations can be written infix. E.g.
842 data a :*: b = Foo a b
843 type a :+: b = Either a b
847 The only thing that differs between operators in types and operators in expressions is that
848 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
849 are not allowed in types. Reason: the uniform thing to do would be to make them type
850 variables, but that's not very useful. A less uniform but more useful thing would be to
851 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
852 lists. So for now we just exclude them.
859 <sect3 id="type-synonyms">
860 <title>Liberalised type synonyms</title>
863 Type synonmys are like macros at the type level, and
864 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
865 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
867 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
868 in a type synonym, thus:
870 type Discard a = forall b. Show b => a -> b -> (a, String)
875 g :: Discard Int -> (Int,Bool) -- A rank-2 type
882 You can write an unboxed tuple in a type synonym:
884 type Pr = (# Int, Int #)
892 You can apply a type synonym to a forall type:
894 type Foo a = a -> a -> Bool
896 f :: Foo (forall b. b->b)
898 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
900 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
905 You can apply a type synonym to a partially applied type synonym:
907 type Generic i o = forall x. i x -> o x
912 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
914 foo :: forall x. x -> [x]
922 GHC currently does kind checking before expanding synonyms (though even that
926 After expanding type synonyms, GHC does validity checking on types, looking for
927 the following mal-formedness which isn't detected simply by kind checking:
930 Type constructor applied to a type involving for-alls.
933 Unboxed tuple on left of an arrow.
936 Partially-applied type synonym.
940 this will be rejected:
942 type Pr = (# Int, Int #)
947 because GHC does not allow unboxed tuples on the left of a function arrow.
952 <sect3 id="existential-quantification">
953 <title>Existentially quantified data constructors
957 The idea of using existential quantification in data type declarations
958 was suggested by Laufer (I believe, thought doubtless someone will
959 correct me), and implemented in Hope+. It's been in Lennart
960 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
961 proved very useful. Here's the idea. Consider the declaration:
967 data Foo = forall a. MkFoo a (a -> Bool)
974 The data type <literal>Foo</literal> has two constructors with types:
980 MkFoo :: forall a. a -> (a -> Bool) -> Foo
987 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
988 does not appear in the data type itself, which is plain <literal>Foo</literal>.
989 For example, the following expression is fine:
995 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
1001 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
1002 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
1003 isUpper</function> packages a character with a compatible function. These
1004 two things are each of type <literal>Foo</literal> and can be put in a list.
1008 What can we do with a value of type <literal>Foo</literal>?. In particular,
1009 what happens when we pattern-match on <function>MkFoo</function>?
1015 f (MkFoo val fn) = ???
1021 Since all we know about <literal>val</literal> and <function>fn</function> is that they
1022 are compatible, the only (useful) thing we can do with them is to
1023 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
1030 f (MkFoo val fn) = fn val
1036 What this allows us to do is to package heterogenous values
1037 together with a bunch of functions that manipulate them, and then treat
1038 that collection of packages in a uniform manner. You can express
1039 quite a bit of object-oriented-like programming this way.
1042 <sect4 id="existential">
1043 <title>Why existential?
1047 What has this to do with <emphasis>existential</emphasis> quantification?
1048 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
1054 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
1060 But Haskell programmers can safely think of the ordinary
1061 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
1062 adding a new existential quantification construct.
1068 <title>Type classes</title>
1071 An easy extension (implemented in <Command>hbc</Command>) is to allow
1072 arbitrary contexts before the constructor. For example:
1078 data Baz = forall a. Eq a => Baz1 a a
1079 | forall b. Show b => Baz2 b (b -> b)
1085 The two constructors have the types you'd expect:
1091 Baz1 :: forall a. Eq a => a -> a -> Baz
1092 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
1098 But when pattern matching on <function>Baz1</function> the matched values can be compared
1099 for equality, and when pattern matching on <function>Baz2</function> the first matched
1100 value can be converted to a string (as well as applying the function to it).
1101 So this program is legal:
1108 f (Baz1 p q) | p == q = "Yes"
1110 f (Baz2 v fn) = show (fn v)
1116 Operationally, in a dictionary-passing implementation, the
1117 constructors <function>Baz1</function> and <function>Baz2</function> must store the
1118 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
1119 extract it on pattern matching.
1123 Notice the way that the syntax fits smoothly with that used for
1124 universal quantification earlier.
1130 <title>Restrictions</title>
1133 There are several restrictions on the ways in which existentially-quantified
1134 constructors can be use.
1143 When pattern matching, each pattern match introduces a new,
1144 distinct, type for each existential type variable. These types cannot
1145 be unified with any other type, nor can they escape from the scope of
1146 the pattern match. For example, these fragments are incorrect:
1154 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
1155 is the result of <function>f1</function>. One way to see why this is wrong is to
1156 ask what type <function>f1</function> has:
1160 f1 :: Foo -> a -- Weird!
1164 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
1169 f1 :: forall a. Foo -> a -- Wrong!
1173 The original program is just plain wrong. Here's another sort of error
1177 f2 (Baz1 a b) (Baz1 p q) = a==q
1181 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
1182 <literal>a==q</literal> is wrong because it equates the two distinct types arising
1183 from the two <function>Baz1</function> constructors.
1191 You can't pattern-match on an existentially quantified
1192 constructor in a <literal>let</literal> or <literal>where</literal> group of
1193 bindings. So this is illegal:
1197 f3 x = a==b where { Baz1 a b = x }
1200 Instead, use a <literal>case</literal> expression:
1203 f3 x = case x of Baz1 a b -> a==b
1206 In general, you can only pattern-match
1207 on an existentially-quantified constructor in a <literal>case</literal> expression or
1208 in the patterns of a function definition.
1210 The reason for this restriction is really an implementation one.
1211 Type-checking binding groups is already a nightmare without
1212 existentials complicating the picture. Also an existential pattern
1213 binding at the top level of a module doesn't make sense, because it's
1214 not clear how to prevent the existentially-quantified type "escaping".
1215 So for now, there's a simple-to-state restriction. We'll see how
1223 You can't use existential quantification for <literal>newtype</literal>
1224 declarations. So this is illegal:
1228 newtype T = forall a. Ord a => MkT a
1232 Reason: a value of type <literal>T</literal> must be represented as a pair
1233 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
1234 That contradicts the idea that <literal>newtype</literal> should have no
1235 concrete representation. You can get just the same efficiency and effect
1236 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
1237 overloading involved, then there is more of a case for allowing
1238 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
1239 because the <literal>data</literal> version does carry an implementation cost,
1240 but single-field existentially quantified constructors aren't much
1241 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
1242 stands, unless there are convincing reasons to change it.
1250 You can't use <literal>deriving</literal> to define instances of a
1251 data type with existentially quantified data constructors.
1253 Reason: in most cases it would not make sense. For example:#
1256 data T = forall a. MkT [a] deriving( Eq )
1259 To derive <literal>Eq</literal> in the standard way we would need to have equality
1260 between the single component of two <function>MkT</function> constructors:
1264 (MkT a) == (MkT b) = ???
1267 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1268 It's just about possible to imagine examples in which the derived instance
1269 would make sense, but it seems altogether simpler simply to prohibit such
1270 declarations. Define your own instances!
1285 <sect2 id="multi-param-type-classes">
1286 <title>Class declarations</title>
1289 This section documents GHC's implementation of multi-parameter type
1290 classes. There's lots of background in the paper <ULink
1291 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1292 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
1293 Jones, Erik Meijer).
1296 There are the following constraints on class declarations:
1301 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1305 class Collection c a where
1306 union :: c a -> c a -> c a
1317 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1318 of "acyclic" involves only the superclass relationships. For example,
1324 op :: D b => a -> b -> b
1327 class C a => D a where { ... }
1331 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1332 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1333 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1340 <emphasis>There are no restrictions on the context in a class declaration
1341 (which introduces superclasses), except that the class hierarchy must
1342 be acyclic</emphasis>. So these class declarations are OK:
1346 class Functor (m k) => FiniteMap m k where
1349 class (Monad m, Monad (t m)) => Transform t m where
1350 lift :: m a -> (t m) a
1360 <emphasis>All of the class type variables must be reachable (in the sense
1361 mentioned in <xref linkend="type-restrictions">)
1362 from the free varibles of each method type
1363 </emphasis>. For example:
1367 class Coll s a where
1369 insert :: s -> a -> s
1373 is not OK, because the type of <literal>empty</literal> doesn't mention
1374 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1375 types, and has the same motivation.
1377 Sometimes, offending class declarations exhibit misunderstandings. For
1378 example, <literal>Coll</literal> might be rewritten
1382 class Coll s a where
1384 insert :: s a -> a -> s a
1388 which makes the connection between the type of a collection of
1389 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1390 Occasionally this really doesn't work, in which case you can split the
1398 class CollE s => Coll s a where
1399 insert :: s -> a -> s
1409 <sect3 id="class-method-types">
1410 <title>Class method types</title>
1412 Haskell 98 prohibits class method types to mention constraints on the
1413 class type variable, thus:
1416 fromList :: [a] -> s a
1417 elem :: Eq a => a -> s a -> Bool
1419 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1420 contains the constraint <literal>Eq a</literal>, constrains only the
1421 class type variable (in this case <literal>a</literal>).
1424 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1431 <sect2 id="type-restrictions">
1432 <title>Type signatures</title>
1434 <sect3><title>The context of a type signature</title>
1436 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1437 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1440 f :: Eq (m a) => [m a] -> [m a]
1443 This choice recovers principal types, a property that Haskell 1.4 does not have.
1446 GHC imposes the following restrictions on the constraints in a type signature.
1450 forall tv1..tvn (c1, ...,cn) => type
1453 (Here, we write the "foralls" explicitly, although the Haskell source
1454 language omits them; in Haskell 1.4, all the free type variables of an
1455 explicit source-language type signature are universally quantified,
1456 except for the class type variables in a class declaration. However,
1457 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
1466 <emphasis>Each universally quantified type variable
1467 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1469 A type variable is "reachable" if it it is functionally dependent
1470 (see <xref linkend="functional-dependencies">)
1471 on the type variables free in <literal>type</literal>.
1472 The reason for this is that a value with a type that does not obey
1473 this restriction could not be used without introducing
1475 Here, for example, is an illegal type:
1479 forall a. Eq a => Int
1483 When a value with this type was used, the constraint <literal>Eq tv</literal>
1484 would be introduced where <literal>tv</literal> is a fresh type variable, and
1485 (in the dictionary-translation implementation) the value would be
1486 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1487 can never know which instance of <literal>Eq</literal> to use because we never
1488 get any more information about <literal>tv</literal>.
1495 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1496 universally quantified type variables <literal>tvi</literal></emphasis>.
1498 For example, this type is OK because <literal>C a b</literal> mentions the
1499 universally quantified type variable <literal>b</literal>:
1503 forall a. C a b => burble
1507 The next type is illegal because the constraint <literal>Eq b</literal> does not
1508 mention <literal>a</literal>:
1512 forall a. Eq b => burble
1516 The reason for this restriction is milder than the other one. The
1517 excluded types are never useful or necessary (because the offending
1518 context doesn't need to be witnessed at this point; it can be floated
1519 out). Furthermore, floating them out increases sharing. Lastly,
1520 excluding them is a conservative choice; it leaves a patch of
1521 territory free in case we need it later.
1532 <title>For-all hoisting</title>
1534 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms">) at the right hand
1535 end of an arrow, thus:
1537 type Discard a = forall b. a -> b -> a
1539 g :: Int -> Discard Int
1542 Simply expanding the type synonym would give
1544 g :: Int -> (forall b. Int -> b -> Int)
1546 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1548 g :: forall b. Int -> Int -> b -> Int
1550 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1551 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1552 performs the transformation:</emphasis>
1554 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1556 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1558 (In fact, GHC tries to retain as much synonym information as possible for use in
1559 error messages, but that is a usability issue.) This rule applies, of course, whether
1560 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1561 valid way to write <literal>g</literal>'s type signature:
1563 g :: Int -> Int -> forall b. b -> Int
1567 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1570 type Foo a = (?x::Int) => Bool -> a
1575 g :: (?x::Int) => Bool -> Bool -> Int
1583 <sect2 id="instance-decls">
1584 <title>Instance declarations</title>
1587 <title>Overlapping instances</title>
1589 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1594 instance context1 => C type1 where ...
1595 instance context2 => C type2 where ...
1599 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1601 However, if you give the command line option
1602 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1603 option</primary></indexterm> then overlapping instance declarations are permitted.
1604 However, GHC arranges never to commit to using an instance declaration
1605 if another instance declaration also applies, either now or later.
1611 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1617 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1618 (but not identical to <literal>type1</literal>), or vice versa.
1622 Notice that these rules
1627 make it clear which instance decl to use
1628 (pick the most specific one that matches)
1635 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1636 Reason: you can pick which instance decl
1637 "matches" based on the type.
1642 However the rules are over-conservative. Two instance declarations can overlap,
1643 but it can still be clear in particular situations which to use. For example:
1645 instance C (Int,a) where ...
1646 instance C (a,Bool) where ...
1648 These are rejected by GHC's rules, but it is clear what to do when trying
1649 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1650 cannot apply. Yell if this restriction bites you.
1653 GHC is also conservative about committing to an overlapping instance. For example:
1655 class C a where { op :: a -> a }
1656 instance C [Int] where ...
1657 instance C a => C [a] where ...
1659 f :: C b => [b] -> [b]
1662 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1663 GHC does not commit to the second instance declaration, because in a paricular
1664 call of f, b might be instantiate to Int, so the first instance declaration
1665 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1666 GHC will instead silently pick the second instance, without complaining about
1667 the problem of subsequent instantiations.
1670 Regrettably, GHC doesn't guarantee to detect overlapping instance
1671 declarations if they appear in different modules. GHC can "see" the
1672 instance declarations in the transitive closure of all the modules
1673 imported by the one being compiled, so it can "see" all instance decls
1674 when it is compiling <literal>Main</literal>. However, it currently chooses not
1675 to look at ones that can't possibly be of use in the module currently
1676 being compiled, in the interests of efficiency. (Perhaps we should
1677 change that decision, at least for <literal>Main</literal>.)
1682 <title>Type synonyms in the instance head</title>
1685 <emphasis>Unlike Haskell 1.4, instance heads may use type
1686 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1687 As always, using a type synonym is just shorthand for
1688 writing the RHS of the type synonym definition. For example:
1692 type Point = (Int,Int)
1693 instance C Point where ...
1694 instance C [Point] where ...
1698 is legal. However, if you added
1702 instance C (Int,Int) where ...
1706 as well, then the compiler will complain about the overlapping
1707 (actually, identical) instance declarations. As always, type synonyms
1708 must be fully applied. You cannot, for example, write:
1713 instance Monad P where ...
1717 This design decision is independent of all the others, and easily
1718 reversed, but it makes sense to me.
1723 <sect3 id="undecidable-instances">
1724 <title>Undecidable instances</title>
1726 <para>An instance declaration must normally obey the following rules:
1728 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1729 an instance declaration <emphasis>must not</emphasis> be a type variable.
1730 For example, these are OK:
1733 instance C Int a where ...
1735 instance D (Int, Int) where ...
1737 instance E [[a]] where ...
1741 instance F a where ...
1743 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1744 For example, this is OK:
1746 instance Stateful (ST s) (MutVar s) where ...
1753 <para>All of the types in the <emphasis>context</emphasis> of
1754 an instance declaration <emphasis>must</emphasis> be type variables.
1757 instance C a b => Eq (a,b) where ...
1761 instance C Int b => Foo b where ...
1767 These restrictions ensure that
1768 context reduction terminates: each reduction step removes one type
1769 constructor. For example, the following would make the type checker
1770 loop if it wasn't excluded:
1772 instance C a => C a where ...
1774 There are two situations in which the rule is a bit of a pain. First,
1775 if one allows overlapping instance declarations then it's quite
1776 convenient to have a "default instance" declaration that applies if
1777 something more specific does not:
1786 Second, sometimes you might want to use the following to get the
1787 effect of a "class synonym":
1791 class (C1 a, C2 a, C3 a) => C a where { }
1793 instance (C1 a, C2 a, C3 a) => C a where { }
1797 This allows you to write shorter signatures:
1809 f :: (C1 a, C2 a, C3 a) => ...
1813 Voluminous correspondence on the Haskell mailing list has convinced me
1814 that it's worth experimenting with more liberal rules. If you use
1815 the experimental flag <option>-fallow-undecidable-instances</option>
1816 <indexterm><primary>-fallow-undecidable-instances
1817 option</primary></indexterm>, you can use arbitrary
1818 types in both an instance context and instance head. Termination is ensured by having a
1819 fixed-depth recursion stack. If you exceed the stack depth you get a
1820 sort of backtrace, and the opportunity to increase the stack depth
1821 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1824 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1825 allowing these idioms interesting idioms.
1832 <sect2 id="implicit-parameters">
1833 <title>Implicit parameters</title>
1835 <para> Implicit paramters are implemented as described in
1836 "Implicit parameters: dynamic scoping with static types",
1837 J Lewis, MB Shields, E Meijer, J Launchbury,
1838 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1842 <para>(Most of the following, stil rather incomplete, documentation is
1843 due to Jeff Lewis.)</para>
1845 <para>Implicit parameter support is enabled with the option
1846 <option>-fimplicit-params</option>.</para>
1849 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1850 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1851 context. In Haskell, all variables are statically bound. Dynamic
1852 binding of variables is a notion that goes back to Lisp, but was later
1853 discarded in more modern incarnations, such as Scheme. Dynamic binding
1854 can be very confusing in an untyped language, and unfortunately, typed
1855 languages, in particular Hindley-Milner typed languages like Haskell,
1856 only support static scoping of variables.
1859 However, by a simple extension to the type class system of Haskell, we
1860 can support dynamic binding. Basically, we express the use of a
1861 dynamically bound variable as a constraint on the type. These
1862 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1863 function uses a dynamically-bound variable <literal>?x</literal>
1864 of type <literal>t'</literal>". For
1865 example, the following expresses the type of a sort function,
1866 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1868 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1870 The dynamic binding constraints are just a new form of predicate in the type class system.
1873 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1874 where <literal>x</literal> is
1875 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1876 Use of this construct also introduces a new
1877 dynamic-binding constraint in the type of the expression.
1878 For example, the following definition
1879 shows how we can define an implicitly parameterized sort function in
1880 terms of an explicitly parameterized <literal>sortBy</literal> function:
1882 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1884 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1890 <title>Implicit-parameter type constraints</title>
1892 Dynamic binding constraints behave just like other type class
1893 constraints in that they are automatically propagated. Thus, when a
1894 function is used, its implicit parameters are inherited by the
1895 function that called it. For example, our <literal>sort</literal> function might be used
1896 to pick out the least value in a list:
1898 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1899 least xs = fst (sort xs)
1901 Without lifting a finger, the <literal>?cmp</literal> parameter is
1902 propagated to become a parameter of <literal>least</literal> as well. With explicit
1903 parameters, the default is that parameters must always be explicit
1904 propagated. With implicit parameters, the default is to always
1908 An implicit-parameter type constraint differs from other type class constraints in the
1909 following way: All uses of a particular implicit parameter must have
1910 the same type. This means that the type of <literal>(?x, ?x)</literal>
1911 is <literal>(?x::a) => (a,a)</literal>, and not
1912 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1916 <para> You can't have an implicit parameter in the context of a class or instance
1917 declaration. For example, both these declarations are illegal:
1919 class (?x::Int) => C a where ...
1920 instance (?x::a) => Foo [a] where ...
1922 Reason: exactly which implicit parameter you pick up depends on exactly where
1923 you invoke a function. But the ``invocation'' of instance declarations is done
1924 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1925 Easiest thing is to outlaw the offending types.</para>
1927 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1929 f :: (?x :: [a]) => Int -> Int
1932 g :: (Read a, Show a) => String -> String
1935 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1936 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1937 quite unambiguous, and fixes the type <literal>a</literal>.
1942 <title>Implicit-parameter bindings</title>
1945 An implicit parameter is <emphasis>bound</emphasis> using the standard
1946 <literal>let</literal> or <literal>where</literal> binding forms.
1947 For example, we define the <literal>min</literal> function by binding
1948 <literal>cmp</literal>.
1951 min = let ?cmp = (<=) in least
1955 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1956 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1957 (including in a list comprehension, or do-notation, or pattern guards),
1958 or a <literal>where</literal> clause.
1959 Note the following points:
1962 An implicit-parameter binding group must be a
1963 collection of simple bindings to implicit-style variables (no
1964 function-style bindings, and no type signatures); these bindings are
1965 neither polymorphic or recursive.
1968 You may not mix implicit-parameter bindings with ordinary bindings in a
1969 single <literal>let</literal>
1970 expression; use two nested <literal>let</literal>s instead.
1971 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1975 You may put multiple implicit-parameter bindings in a
1976 single binding group; but they are <emphasis>not</emphasis> treated
1977 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1978 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1979 parameter. The bindings are not nested, and may be re-ordered without changing
1980 the meaning of the program.
1981 For example, consider:
1983 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1985 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1986 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1988 f :: (?x::Int) => Int -> Int
1997 <sect2 id="linear-implicit-parameters">
1998 <title>Linear implicit parameters</title>
2000 Linear implicit parameters are an idea developed by Koen Claessen,
2001 Mark Shields, and Simon PJ. They address the long-standing
2002 problem that monads seem over-kill for certain sorts of problem, notably:
2005 <listitem> <para> distributing a supply of unique names </para> </listitem>
2006 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2007 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2011 Linear implicit parameters are just like ordinary implicit parameters,
2012 except that they are "linear" -- that is, they cannot be copied, and
2013 must be explicitly "split" instead. Linear implicit parameters are
2014 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2015 (The '/' in the '%' suggests the split!)
2020 import GHC.Exts( Splittable )
2022 data NameSupply = ...
2024 splitNS :: NameSupply -> (NameSupply, NameSupply)
2025 newName :: NameSupply -> Name
2027 instance Splittable NameSupply where
2031 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2032 f env (Lam x e) = Lam x' (f env e)
2035 env' = extend env x x'
2036 ...more equations for f...
2038 Notice that the implicit parameter %ns is consumed
2040 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2041 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2045 So the translation done by the type checker makes
2046 the parameter explicit:
2048 f :: NameSupply -> Env -> Expr -> Expr
2049 f ns env (Lam x e) = Lam x' (f ns1 env e)
2051 (ns1,ns2) = splitNS ns
2053 env = extend env x x'
2055 Notice the call to 'split' introduced by the type checker.
2056 How did it know to use 'splitNS'? Because what it really did
2057 was to introduce a call to the overloaded function 'split',
2058 defined by the class <literal>Splittable</literal>:
2060 class Splittable a where
2063 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2064 split for name supplies. But we can simply write
2070 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2072 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2073 <literal>GHC.Exts</literal>.
2078 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2079 are entirely distinct implicit parameters: you
2080 can use them together and they won't intefere with each other. </para>
2083 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2085 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2086 in the context of a class or instance declaration. </para></listitem>
2090 <sect3><title>Warnings</title>
2093 The monomorphism restriction is even more important than usual.
2094 Consider the example above:
2096 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2097 f env (Lam x e) = Lam x' (f env e)
2100 env' = extend env x x'
2102 If we replaced the two occurrences of x' by (newName %ns), which is
2103 usually a harmless thing to do, we get:
2105 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2106 f env (Lam x e) = Lam (newName %ns) (f env e)
2108 env' = extend env x (newName %ns)
2110 But now the name supply is consumed in <emphasis>three</emphasis> places
2111 (the two calls to newName,and the recursive call to f), so
2112 the result is utterly different. Urk! We don't even have
2116 Well, this is an experimental change. With implicit
2117 parameters we have already lost beta reduction anyway, and
2118 (as John Launchbury puts it) we can't sensibly reason about
2119 Haskell programs without knowing their typing.
2124 <sect3><title>Recursive functions</title>
2125 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2128 foo :: %x::T => Int -> [Int]
2130 foo n = %x : foo (n-1)
2132 where T is some type in class Splittable.</para>
2134 Do you get a list of all the same T's or all different T's
2135 (assuming that split gives two distinct T's back)?
2137 If you supply the type signature, taking advantage of polymorphic
2138 recursion, you get what you'd probably expect. Here's the
2139 translated term, where the implicit param is made explicit:
2142 foo x n = let (x1,x2) = split x
2143 in x1 : foo x2 (n-1)
2145 But if you don't supply a type signature, GHC uses the Hindley
2146 Milner trick of using a single monomorphic instance of the function
2147 for the recursive calls. That is what makes Hindley Milner type inference
2148 work. So the translation becomes
2152 foom n = x : foom (n-1)
2156 Result: 'x' is not split, and you get a list of identical T's. So the
2157 semantics of the program depends on whether or not foo has a type signature.
2160 You may say that this is a good reason to dislike linear implicit parameters
2161 and you'd be right. That is why they are an experimental feature.
2167 <sect2 id="functional-dependencies">
2168 <title>Functional dependencies
2171 <para> Functional dependencies are implemented as described by Mark Jones
2172 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2173 In Proceedings of the 9th European Symposium on Programming,
2174 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2178 Functional dependencies are introduced by a vertical bar in the syntax of a
2179 class declaration; e.g.
2181 class (Monad m) => MonadState s m | m -> s where ...
2183 class Foo a b c | a b -> c where ...
2185 There should be more documentation, but there isn't (yet). Yell if you need it.
2191 <sect2 id="sec-kinding">
2192 <title>Explicitly-kinded quantification</title>
2195 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2196 to give the kind explicitly as (machine-checked) documentation,
2197 just as it is nice to give a type signature for a function. On some occasions,
2198 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2199 John Hughes had to define the data type:
2201 data Set cxt a = Set [a]
2202 | Unused (cxt a -> ())
2204 The only use for the <literal>Unused</literal> constructor was to force the correct
2205 kind for the type variable <literal>cxt</literal>.
2208 GHC now instead allows you to specify the kind of a type variable directly, wherever
2209 a type variable is explicitly bound. Namely:
2211 <listitem><para><literal>data</literal> declarations:
2213 data Set (cxt :: * -> *) a = Set [a]
2214 </Screen></para></listitem>
2215 <listitem><para><literal>type</literal> declarations:
2217 type T (f :: * -> *) = f Int
2218 </Screen></para></listitem>
2219 <listitem><para><literal>class</literal> declarations:
2221 class (Eq a) => C (f :: * -> *) a where ...
2222 </Screen></para></listitem>
2223 <listitem><para><literal>forall</literal>'s in type signatures:
2225 f :: forall (cxt :: * -> *). Set cxt Int
2226 </Screen></para></listitem>
2231 The parentheses are required. Some of the spaces are required too, to
2232 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2233 will get a parse error, because "<literal>::*->*</literal>" is a
2234 single lexeme in Haskell.
2238 As part of the same extension, you can put kind annotations in types
2241 f :: (Int :: *) -> Int
2242 g :: forall a. a -> (a :: *)
2246 atype ::= '(' ctype '::' kind ')
2248 The parentheses are required.
2253 <sect2 id="universal-quantification">
2254 <title>Arbitrary-rank polymorphism
2258 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2259 allows us to say exactly what this means. For example:
2267 g :: forall b. (b -> b)
2269 The two are treated identically.
2273 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2274 explicit universal quantification in
2276 For example, all the following types are legal:
2278 f1 :: forall a b. a -> b -> a
2279 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2281 f2 :: (forall a. a->a) -> Int -> Int
2282 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2284 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2286 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2287 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2288 The <literal>forall</literal> makes explicit the universal quantification that
2289 is implicitly added by Haskell.
2292 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2293 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2294 shows, the polymorphic type on the left of the function arrow can be overloaded.
2297 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
2298 they have rank-2 types on the left of a function arrow.
2301 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2302 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2303 that restriction has now been lifted.)
2304 In particular, a forall-type (also called a "type scheme"),
2305 including an operational type class context, is legal:
2307 <listitem> <para> On the left of a function arrow </para> </listitem>
2308 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
2309 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2310 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
2311 field type signatures.</para> </listitem>
2312 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2313 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
2315 There is one place you cannot put a <literal>forall</literal>:
2316 you cannot instantiate a type variable with a forall-type. So you cannot
2317 make a forall-type the argument of a type constructor. So these types are illegal:
2319 x1 :: [forall a. a->a]
2320 x2 :: (forall a. a->a, Int)
2321 x3 :: Maybe (forall a. a->a)
2323 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2324 a type variable any more!
2333 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2334 the types of the constructor arguments. Here are several examples:
2340 data T a = T1 (forall b. b -> b -> b) a
2342 data MonadT m = MkMonad { return :: forall a. a -> m a,
2343 bind :: forall a b. m a -> (a -> m b) -> m b
2346 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2352 The constructors have rank-2 types:
2358 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2359 MkMonad :: forall m. (forall a. a -> m a)
2360 -> (forall a b. m a -> (a -> m b) -> m b)
2362 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2368 Notice that you don't need to use a <literal>forall</literal> if there's an
2369 explicit context. For example in the first argument of the
2370 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2371 prefixed to the argument type. The implicit <literal>forall</literal>
2372 quantifies all type variables that are not already in scope, and are
2373 mentioned in the type quantified over.
2377 As for type signatures, implicit quantification happens for non-overloaded
2378 types too. So if you write this:
2381 data T a = MkT (Either a b) (b -> b)
2384 it's just as if you had written this:
2387 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2390 That is, since the type variable <literal>b</literal> isn't in scope, it's
2391 implicitly universally quantified. (Arguably, it would be better
2392 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2393 where that is what is wanted. Feedback welcomed.)
2397 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2398 the constructor to suitable values, just as usual. For example,
2409 a3 = MkSwizzle reverse
2412 a4 = let r x = Just x
2419 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2420 mkTs f x y = [T1 f x, T1 f y]
2426 The type of the argument can, as usual, be more general than the type
2427 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2428 does not need the <literal>Ord</literal> constraint.)
2432 When you use pattern matching, the bound variables may now have
2433 polymorphic types. For example:
2439 f :: T a -> a -> (a, Char)
2440 f (T1 w k) x = (w k x, w 'c' 'd')
2442 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2443 g (MkSwizzle s) xs f = s (map f (s xs))
2445 h :: MonadT m -> [m a] -> m [a]
2446 h m [] = return m []
2447 h m (x:xs) = bind m x $ \y ->
2448 bind m (h m xs) $ \ys ->
2455 In the function <function>h</function> we use the record selectors <literal>return</literal>
2456 and <literal>bind</literal> to extract the polymorphic bind and return functions
2457 from the <literal>MonadT</literal> data structure, rather than using pattern
2463 <title>Type inference</title>
2466 In general, type inference for arbitrary-rank types is undecideable.
2467 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2468 to get a decidable algorithm by requiring some help from the programmer.
2469 We do not yet have a formal specification of "some help" but the rule is this:
2472 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2473 provides an explicit polymorphic type for x, or GHC's type inference will assume
2474 that x's type has no foralls in it</emphasis>.
2477 What does it mean to "provide" an explicit type for x? You can do that by
2478 giving a type signature for x directly, using a pattern type signature
2479 (<xref linkend="scoped-type-variables">), thus:
2481 \ f :: (forall a. a->a) -> (f True, f 'c')
2483 Alternatively, you can give a type signature to the enclosing
2484 context, which GHC can "push down" to find the type for the variable:
2486 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2488 Here the type signature on the expression can be pushed inwards
2489 to give a type signature for f. Similarly, and more commonly,
2490 one can give a type signature for the function itself:
2492 h :: (forall a. a->a) -> (Bool,Char)
2493 h f = (f True, f 'c')
2495 You don't need to give a type signature if the lambda bound variable
2496 is a constructor argument. Here is an example we saw earlier:
2498 f :: T a -> a -> (a, Char)
2499 f (T1 w k) x = (w k x, w 'c' 'd')
2501 Here we do not need to give a type signature to <literal>w</literal>, because
2502 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2509 <sect3 id="implicit-quant">
2510 <title>Implicit quantification</title>
2513 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2514 user-written types, if and only if there is no explicit <literal>forall</literal>,
2515 GHC finds all the type variables mentioned in the type that are not already
2516 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2520 f :: forall a. a -> a
2527 h :: forall b. a -> b -> b
2533 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2536 f :: (a -> a) -> Int
2538 f :: forall a. (a -> a) -> Int
2540 f :: (forall a. a -> a) -> Int
2543 g :: (Ord a => a -> a) -> Int
2544 -- MEANS the illegal type
2545 g :: forall a. (Ord a => a -> a) -> Int
2547 g :: (forall a. Ord a => a -> a) -> Int
2549 The latter produces an illegal type, which you might think is silly,
2550 but at least the rule is simple. If you want the latter type, you
2551 can write your for-alls explicitly. Indeed, doing so is strongly advised
2560 <sect2 id="scoped-type-variables">
2561 <title>Scoped type variables
2565 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2566 variable</emphasis>. For example
2572 f (xs::[a]) = ys ++ ys
2581 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2582 This brings the type variable <literal>a</literal> into scope; it scopes over
2583 all the patterns and right hand sides for this equation for <function>f</function>.
2584 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2588 Pattern type signatures are completely orthogonal to ordinary, separate
2589 type signatures. The two can be used independently or together.
2590 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2591 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2592 implicitly universally quantified. (If there are no type variables in
2593 scope, all type variables mentioned in the signature are universally
2594 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2595 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2596 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2597 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2598 it becomes possible to do so.
2602 Scoped type variables are implemented in both GHC and Hugs. Where the
2603 implementations differ from the specification below, those differences
2608 So much for the basic idea. Here are the details.
2612 <title>What a pattern type signature means</title>
2614 A type variable brought into scope by a pattern type signature is simply
2615 the name for a type. The restriction they express is that all occurrences
2616 of the same name mean the same type. For example:
2618 f :: [Int] -> Int -> Int
2619 f (xs::[a]) (y::a) = (head xs + y) :: a
2621 The pattern type signatures on the left hand side of
2622 <literal>f</literal> express the fact that <literal>xs</literal>
2623 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2624 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2625 specifies that this expression must have the same type <literal>a</literal>.
2626 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2627 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2628 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2629 rules, which specified that a pattern-bound type variable should be universally quantified.)
2630 For example, all of these are legal:</para>
2633 t (x::a) (y::a) = x+y*2
2635 f (x::a) (y::b) = [x,y] -- a unifies with b
2637 g (x::a) = x + 1::Int -- a unifies with Int
2639 h x = let k (y::a) = [x,y] -- a is free in the
2640 in k x -- environment
2642 k (x::a) True = ... -- a unifies with Int
2643 k (x::Int) False = ...
2646 w (x::a) = x -- a unifies with [b]
2652 <title>Scope and implicit quantification</title>
2660 All the type variables mentioned in a pattern,
2661 that are not already in scope,
2662 are brought into scope by the pattern. We describe this set as
2663 the <emphasis>type variables bound by the pattern</emphasis>.
2666 f (x::a) = let g (y::(a,b)) = fst y
2670 The pattern <literal>(x::a)</literal> brings the type variable
2671 <literal>a</literal> into scope, as well as the term
2672 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2673 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2674 and brings into scope the type variable <literal>b</literal>.
2680 The type variable(s) bound by the pattern have the same scope
2681 as the term variable(s) bound by the pattern. For example:
2684 f (x::a) = <...rhs of f...>
2685 (p::b, q::b) = (1,2)
2686 in <...body of let...>
2688 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2689 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2690 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2691 just like <literal>p</literal> and <literal>q</literal> do.
2692 Indeed, the newly bound type variables also scope over any ordinary, separate
2693 type signatures in the <literal>let</literal> group.
2700 The type variables bound by the pattern may be
2701 mentioned in ordinary type signatures or pattern
2702 type signatures anywhere within their scope.
2709 In ordinary type signatures, any type variable mentioned in the
2710 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2718 Ordinary type signatures do not bring any new type variables
2719 into scope (except in the type signature itself!). So this is illegal:
2726 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2727 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2728 and that is an incorrect typing.
2735 The pattern type signature is a monotype:
2740 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2744 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2745 not to type schemes.
2749 There is no implicit universal quantification on pattern type signatures (in contrast to
2750 ordinary type signatures).
2760 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2761 scope over the methods defined in the <literal>where</literal> part. For example:
2775 (Not implemented in Hugs yet, Dec 98).
2786 <title>Where a pattern type signature can occur</title>
2789 A pattern type signature can occur in any pattern. For example:
2794 A pattern type signature can be on an arbitrary sub-pattern, not
2799 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2808 Pattern type signatures, including the result part, can be used
2809 in lambda abstractions:
2812 (\ (x::a, y) :: a -> x)
2819 Pattern type signatures, including the result part, can be used
2820 in <literal>case</literal> expressions:
2824 case e of { (x::a, y) :: a -> x }
2832 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2833 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2834 token or a parenthesised type of some sort). To see why,
2835 consider how one would parse this:
2849 Pattern type signatures can bind existential type variables.
2854 data T = forall a. MkT [a]
2857 f (MkT [t::a]) = MkT t3
2870 Pattern type signatures
2871 can be used in pattern bindings:
2874 f x = let (y, z::a) = x in ...
2875 f1 x = let (y, z::Int) = x in ...
2876 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2877 f3 :: (b->b) = \x -> x
2880 In all such cases, the binding is not generalised over the pattern-bound
2881 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2882 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2883 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2884 In contrast, the binding
2889 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2890 in <literal>f4</literal>'s scope.
2900 <title>Result type signatures</title>
2903 The result type of a function can be given a signature, thus:
2907 f (x::a) :: [a] = [x,x,x]
2911 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2912 result type. Sometimes this is the only way of naming the type variable
2917 f :: Int -> [a] -> [a]
2918 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2919 in \xs -> map g (reverse xs `zip` xs)
2924 The type variables bound in a result type signature scope over the right hand side
2925 of the definition. However, consider this corner-case:
2927 rev1 :: [a] -> [a] = \xs -> reverse xs
2929 foo ys = rev (ys::[a])
2931 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2932 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2933 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2934 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2935 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2938 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2939 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2943 rev1 :: [a] -> [a] = \xs -> reverse xs
2948 Result type signatures are not yet implemented in Hugs.
2955 <sect2 id="deriving-typeable">
2956 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2959 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2960 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2961 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2962 classes <literal>Eq</literal>, <literal>Ord</literal>,
2963 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2966 GHC extends this list with two more classes that may be automatically derived
2967 (provided the <option>-fglasgow-exts</option> flag is specified):
2968 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2969 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
2970 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2974 <sect2 id="newtype-deriving">
2975 <title>Generalised derived instances for newtypes</title>
2978 When you define an abstract type using <literal>newtype</literal>, you may want
2979 the new type to inherit some instances from its representation. In
2980 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2981 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2982 other classes you have to write an explicit instance declaration. For
2983 example, if you define
2986 newtype Dollars = Dollars Int
2989 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2990 explicitly define an instance of <literal>Num</literal>:
2993 instance Num Dollars where
2994 Dollars a + Dollars b = Dollars (a+b)
2997 All the instance does is apply and remove the <literal>newtype</literal>
2998 constructor. It is particularly galling that, since the constructor
2999 doesn't appear at run-time, this instance declaration defines a
3000 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3001 dictionary, only slower!
3005 <sect3> <title> Generalising the deriving clause </title>
3007 GHC now permits such instances to be derived instead, so one can write
3009 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3012 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3013 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3014 derives an instance declaration of the form
3017 instance Num Int => Num Dollars
3020 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3024 We can also derive instances of constructor classes in a similar
3025 way. For example, suppose we have implemented state and failure monad
3026 transformers, such that
3029 instance Monad m => Monad (State s m)
3030 instance Monad m => Monad (Failure m)
3032 In Haskell 98, we can define a parsing monad by
3034 type Parser tok m a = State [tok] (Failure m) a
3037 which is automatically a monad thanks to the instance declarations
3038 above. With the extension, we can make the parser type abstract,
3039 without needing to write an instance of class <literal>Monad</literal>, via
3042 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3045 In this case the derived instance declaration is of the form
3047 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3050 Notice that, since <literal>Monad</literal> is a constructor class, the
3051 instance is a <emphasis>partial application</emphasis> of the new type, not the
3052 entire left hand side. We can imagine that the type declaration is
3053 ``eta-converted'' to generate the context of the instance
3058 We can even derive instances of multi-parameter classes, provided the
3059 newtype is the last class parameter. In this case, a ``partial
3060 application'' of the class appears in the <literal>deriving</literal>
3061 clause. For example, given the class
3064 class StateMonad s m | m -> s where ...
3065 instance Monad m => StateMonad s (State s m) where ...
3067 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3069 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3070 deriving (Monad, StateMonad [tok])
3073 The derived instance is obtained by completing the application of the
3074 class to the new type:
3077 instance StateMonad [tok] (State [tok] (Failure m)) =>
3078 StateMonad [tok] (Parser tok m)
3083 As a result of this extension, all derived instances in newtype
3084 declarations are treated uniformly (and implemented just by reusing
3085 the dictionary for the representation type), <emphasis>except</emphasis>
3086 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3087 the newtype and its representation.
3091 <sect3> <title> A more precise specification </title>
3093 Derived instance declarations are constructed as follows. Consider the
3094 declaration (after expansion of any type synonyms)
3097 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3103 <literal>S</literal> is a type constructor,
3106 <literal>t1...tk</literal> are types,
3109 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3110 the <literal>ti</literal>, and
3113 the <literal>ci</literal> are partial applications of
3114 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3115 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3118 Then, for each <literal>ci</literal>, the derived instance
3121 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3123 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3124 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3128 As an example which does <emphasis>not</emphasis> work, consider
3130 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3132 Here we cannot derive the instance
3134 instance Monad (State s m) => Monad (NonMonad m)
3137 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3138 and so cannot be "eta-converted" away. It is a good thing that this
3139 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3140 not, in fact, a monad --- for the same reason. Try defining
3141 <literal>>>=</literal> with the correct type: you won't be able to.
3145 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3146 important, since we can only derive instances for the last one. If the
3147 <literal>StateMonad</literal> class above were instead defined as
3150 class StateMonad m s | m -> s where ...
3153 then we would not have been able to derive an instance for the
3154 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3155 classes usually have one "main" parameter for which deriving new
3156 instances is most interesting.
3164 <!-- ==================== End of type system extensions ================= -->
3166 <!-- ====================== TEMPLATE HASKELL ======================= -->
3168 <sect1 id="template-haskell">
3169 <title>Template Haskell</title>
3171 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3172 Template Haskell at <ulink url="http://www.haskell.org/th/">
3173 http://www.haskell.org/th/</ulink>, while
3175 the main technical innovations is discussed in "<ulink
3176 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3177 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3180 <para> The first example from that paper is set out below as a worked example to help get you started.
3184 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3185 Tim Sheard is going to expand it.)
3189 <title>Syntax</title>
3191 <para> Template Haskell has the following new syntactic
3192 constructions. You need to use the flag
3193 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3194 </indexterm>to switch these syntactic extensions on
3195 (<option>-fth</option> is currently implied by
3196 <option>-fglasgow-exts</option>, but you are encouraged to
3197 specify it explicitly).</para>
3201 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3202 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3203 There must be no space between the "$" and the identifier or parenthesis. This use
3204 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3205 of "." as an infix operator. If you want the infix operator, put spaces around it.
3207 <para> A splice can occur in place of
3209 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3210 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3211 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3213 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3214 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3220 A expression quotation is written in Oxford brackets, thus:
3222 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3223 the quotation has type <literal>Expr</literal>.</para></listitem>
3224 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3225 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3226 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3227 the quotation has type <literal>Type</literal>.</para></listitem>
3228 </itemizedlist></para></listitem>
3231 Reification is written thus:
3233 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3234 has type <literal>Dec</literal>. </para></listitem>
3235 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3236 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3237 <listitem><para> Still to come: fixities </para></listitem>
3239 </itemizedlist></para>
3246 <sect2> <title> Using Template Haskell </title>
3250 The data types and monadic constructor functions for Template Haskell are in the library
3251 <literal>Language.Haskell.THSyntax</literal>.
3255 You can only run a function at compile time if it is imported from another module. That is,
3256 you can't define a function in a module, and call it from within a splice in the same module.
3257 (It would make sense to do so, but it's hard to implement.)
3261 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3264 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3265 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3266 compiles and runs a program, and then looks at the result. So it's important that
3267 the program it compiles produces results whose representations are identical to
3268 those of the compiler itself.
3272 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3273 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3278 <sect2> <title> A Template Haskell Worked Example </title>
3279 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3280 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3286 -- Import our template "pr"
3287 import Printf ( pr )
3289 -- The splice operator $ takes the Haskell source code
3290 -- generated at compile time by "pr" and splices it into
3291 -- the argument of "putStrLn".
3292 main = putStrLn ( $(pr "Hello") )
3299 -- Skeletal printf from the paper.
3300 -- It needs to be in a separate module to the one where
3301 -- you intend to use it.
3303 -- Import some Template Haskell syntax
3304 import Language.Haskell.THSyntax
3306 -- Describe a format string
3307 data Format = D | S | L String
3309 -- Parse a format string. This is left largely to you
3310 -- as we are here interested in building our first ever
3311 -- Template Haskell program and not in building printf.
3312 parse :: String -> [Format]
3315 -- Generate Haskell source code from a parsed representation
3316 -- of the format string. This code will be spliced into
3317 -- the module which calls "pr", at compile time.
3318 gen :: [Format] -> Expr
3319 gen [D] = [| \n -> show n |]
3320 gen [S] = [| \s -> s |]
3321 gen [L s] = string s
3323 -- Here we generate the Haskell code for the splice
3324 -- from an input format string.
3325 pr :: String -> Expr
3326 pr s = gen (parse s)
3329 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3332 $ ghc --make -fth main.hs -o main.exe
3335 <para>Run "main.exe" and here is your output:</para>
3346 <!-- ===================== Arrow notation =================== -->
3348 <sect1 id="arrow-notation">
3349 <title>Arrow notation
3352 <para>Arrows are a generalization of monads introduced by John Hughes.
3353 For more details, see
3358 “Generalising Monads to Arrows”,
3359 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3360 pp67–111, May 2000.
3366 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3367 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3373 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3374 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3380 and the arrows web page at
3381 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3382 With the <option>-farrows</option> flag, GHC supports the arrow
3383 notation described in the second of these papers.
3384 What follows is a brief introduction to the notation;
3385 it won't make much sense unless you've read Hughes's paper.
3386 This notation is translated to ordinary Haskell,
3387 using combinators from the
3388 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3392 <para>The extension adds a new kind of expression for defining arrows,
3393 of the form <literal>proc pat -> cmd</literal>,
3394 where <literal>proc</literal> is a new keyword.
3395 The variables of the pattern are bound in the body of the
3396 <literal>proc</literal>-expression,
3397 which is a new sort of thing called a <firstterm>command</firstterm>.
3398 The syntax of commands is as follows:
3400 cmd ::= exp1 -< exp2
3401 | exp1 -<< exp2
3402 | do { cstmt1 .. cstmtn ; cmd }
3404 | if exp then cmd1 else cmd2
3405 | case exp of { calts }
3407 | (| aexp cmd1 .. cmdn |)
3408 | \ pat1 .. patn -> cmd
3414 | rec { cstmt1 .. cstmtn }
3417 Commands produce values, but (like monadic computations)
3418 may yield more than one value,
3419 or none, and may do other things as well.
3420 For the most part, familiarity with monadic notation is a good guide to
3422 However the values of expressions, even monadic ones,
3423 are determined by the values of the variables they contain;
3424 this is not necessarily the case for commands.
3428 A simple example of the new notation is the expression
3430 proc x -> f -< x+1
3432 We call this a <firstterm>procedure</firstterm> or
3433 <firstterm>arrow abstraction</firstterm>.
3434 As with a lambda expression, the variable <literal>x</literal>
3435 is a new variable bound within the <literal>proc</literal>-expression.
3436 It refers to the input to the arrow.
3437 In the above example, <literal>-<</literal> is not an identifier but an
3438 new reserved symbol used for building commands from an expression of arrow
3439 type and an expression to be fed as input to that arrow.
3440 (The weird look will make more sense later.)
3441 It may be read as analogue of application for arrows.
3442 The above example is equivalent to the Haskell expression
3444 arr (\ x -> x+1) >>> f
3446 That would make no sense if the expression to the left of
3447 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3448 More generally, the expression to the left of <literal>-<</literal>
3449 may not involve any <firstterm>local variable</firstterm>,
3450 i.e. a variable bound in the current arrow abstraction.
3451 For such a situation there is a variant <literal>-<<</literal>, as in
3453 proc x -> f x -<< x+1
3455 which is equivalent to
3457 arr (\ x -> (f, x+1)) >>> app
3459 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3461 Such an arrow is equivalent to a monad, so if you're using this form
3462 you may find a monadic formulation more convenient.
3466 <title>do-notation for commands</title>
3469 Another form of command is a form of <literal>do</literal>-notation.
3470 For example, you can write
3479 You can read this much like ordinary <literal>do</literal>-notation,
3480 but with commands in place of monadic expressions.
3481 The first line sends the value of <literal>x+1</literal> as an input to
3482 the arrow <literal>f</literal>, and matches its output against
3483 <literal>y</literal>.
3484 In the next line, the output is discarded.
3485 The arrow <literal>returnA</literal> is defined in the
3486 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3487 module as <literal>arr id</literal>.
3488 The above example is treated as an abbreviation for
3490 arr (\ x -> (x, x)) >>>
3491 first (arr (\ x -> x+1) >>> f) >>>
3492 arr (\ (y, x) -> (y, (x, y))) >>>
3493 first (arr (\ y -> 2*y) >>> g) >>>
3495 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3496 first (arr (\ (x, z) -> x*z) >>> h) >>>
3497 arr (\ (t, z) -> t+z) >>>
3500 Note that variables not used later in the composition are projected out.
3501 After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
3503 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3504 module, this reduces to
3506 arr (\ x -> (x+1, x)) >>>
3508 arr (\ (y, x) -> (2*y, (x, y))) >>>
3510 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3512 arr (\ (t, z) -> t+z)
3514 which is what you might have written by hand.
3515 With arrow notation, GHC keeps track of all those tuples of variables for you.
3519 Note that although the above translation suggests that
3520 <literal>let</literal>-bound variables like <literal>z</literal> must be
3521 monomorphic, the actual translation produces Core,
3522 so polymorphic variables are allowed.
3526 It's also possible to have mutually recursive bindings,
3527 using the new <literal>rec</literal> keyword, as in the following example:
3529 counter :: ArrowCircuit a => a Bool Int
3530 counter = proc reset -> do
3531 rec output <- returnA -< if reset then 0 else next
3532 next <- delay 0 -< output+1
3533 returnA -< output
3535 The translation of such forms uses the <literal>loop</literal> combinator,
3536 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3542 <title>Conditional commands</title>
3545 In the previous example, we used a conditional expression to construct the
3547 Sometimes we want to conditionally execute different commands, as in
3554 which is translated to
3556 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3557 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3559 Since the translation uses <literal>|||</literal>,
3560 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3564 There are also <literal>case</literal> commands, like
3570 y <- h -< (x1, x2)
3574 The syntax is the same as for <literal>case</literal> expressions,
3575 except that the bodies of the alternatives are commands rather than expressions.
3576 The translation is similar to that of <literal>if</literal> commands.
3582 <title>Defining your own control structures</title>
3585 As we're seen, arrow notation provides constructs,
3586 modelled on those for expressions,
3587 for sequencing, value recursion and conditionals.
3588 But suitable combinators,
3589 which you can define in ordinary Haskell,
3590 may also be used to build new commands out of existing ones.
3591 The basic idea is that a command defines an arrow from environments to values.
3592 These environments assign values to the free local variables of the command.
3593 Thus combinators that produce arrows from arrows
3594 may also be used to build commands from commands.
3595 For example, the <literal>ArrowChoice</literal> class includes a combinator
3597 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3599 so we can use it to build commands:
3604 symbol Plus -< ()
3605 y <- term -< ()
3608 symbol Minus -< ()
3609 y <- term -< ()
3612 This is equivalent to
3614 expr' = (proc x -> returnA -< x)
3615 <+> (proc x -> do
3616 symbol Plus -< ()
3617 y <- term -< ()
3619 <+> (proc x -> do
3620 symbol Minus -< ()
3621 y <- term -< ()
3624 It is essential that this operator be polymorphic in <literal>e</literal>
3625 (representing the environment input to the command
3626 and thence to its subcommands)
3627 and satisfy the corresponding naturality property
3629 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3631 at least for strict <literal>k</literal>.
3632 (This should be automatic if you're not using <literal>seq</literal>.)
3633 This ensures that environments seen by the subcommands are environments
3634 of the whole command,
3635 and also allows the translation to safely trim these environments.
3636 The operator must also not use any variable defined within the current
3641 We could define our own operator
3643 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3644 untilA body cond = proc x ->
3645 if cond x then returnA -< ()
3648 untilA body cond -< x
3650 and use it in the same way.
3651 Of course this infix syntax only makes sense for binary operators;
3652 there is also a more general syntax involving special brackets:
3656 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3663 <title>Primitive constructs</title>
3666 Some operators will need to pass additional inputs to their subcommands.
3667 For example, in an arrow type supporting exceptions,
3668 the operator that attaches an exception handler will wish to pass the
3669 exception that occurred to the handler.
3670 Such an operator might have a type
3672 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3674 where <literal>Ex</literal> is the type of exceptions handled.
3675 You could then use this with arrow notation by writing a command
3677 body `handleA` \ ex -> handler
3679 so that if an exception is raised in the command <literal>body</literal>,
3680 the variable <literal>ex</literal> is bound to the value of the exception
3681 and the command <literal>handler</literal>,
3682 which typically refers to <literal>ex</literal>, is entered.
3683 Though the syntax here looks like a functional lambda,
3684 we are talking about commands, and something different is going on.
3685 The input to the arrow represented by a command consists of values for
3686 the free local variables in the command, plus a stack of anonymous values.
3687 In all the prior examples, this stack was empty.
3688 In the second argument to <literal>handleA</literal>,
3689 this stack consists of one value, the value of the exception.
3690 The command form of lambda merely gives this value a name.
3695 the values on the stack are paired to the right of the environment.
3696 So when designing operators like <literal>handleA</literal> that pass
3697 extra inputs to their subcommands,
3698 More precisely, the type of each argument of the operator (and its result)
3699 should have the form
3701 a (...(e,t1), ... tn) t
3703 where <replaceable>e</replaceable> is a polymorphic variable
3704 (representing the environment)
3705 and <replaceable>ti</replaceable> are the types of the values on the stack,
3706 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3707 The polymorphic variable <replaceable>e</replaceable> must not occur in
3708 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3709 <replaceable>t</replaceable>.
3710 However the arrows involved need not be the same.
3711 Here are some more examples of suitable operators:
3713 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3714 runReader :: ... => a e c -> a' (e,State) c
3715 runState :: ... => a e c -> a' (e,State) (c,State)
3717 We can supply the extra input required by commands built with the last two
3718 by applying them to ordinary expressions, as in
3722 (|runReader (do { ... })|) s
3724 which adds <literal>s</literal> to the stack of inputs to the command
3725 built using <literal>runReader</literal>.
3729 The command versions of lambda abstraction and application are analogous to
3730 the expression versions.
3731 In particular, the beta and eta rules describe equivalences of commands.
3732 These three features (operators, lambda abstraction and application)
3733 are the core of the notation; everything else can be built using them,
3734 though the results would be somewhat clumsy.
3735 For example, we could simulate <literal>do</literal>-notation by defining
3737 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3738 u `bind` f = returnA &&& u >>> f
3740 bind_ :: Arrow a => a e b -> a e c -> a e c
3741 u `bind_` f = u `bind` (arr fst >>> f)
3743 We could simulate <literal>do</literal> by defining
3745 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3746 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3753 <title>Differences with the paper</title>
3758 <para>Instead of a single form of arrow application (arrow tail) with two
3759 translations, the implementation provides two forms
3760 <quote><literal>-<</literal></quote> (first-order)
3761 and <quote><literal>-<<</literal></quote> (higher-order).
3766 <para>User-defined operators are flagged with banana brackets instead of
3767 a new <literal>form</literal> keyword.
3776 <title>Portability</title>
3779 Although only GHC implements arrow notation directly,
3780 there is also a preprocessor
3782 <ulink url="http://www.haskell.org/arrows/">arrows web page></ulink>)
3783 that translates arrow notation into Haskell 98
3784 for use with other Haskell systems.
3785 You would still want to check arrow programs with GHC;
3786 tracing type errors in the preprocessor output is not easy.
3787 Modules intended for both GHC and the preprocessor must observe some
3788 additional restrictions:
3793 The module must import
3794 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3800 The preprocessor cannot cope with other Haskell extensions.
3801 These would have to go in separate modules.
3807 Because the preprocessor targets Haskell (rather than Core),
3808 <literal>let</literal>-bound variables are monomorphic.
3819 <!-- ==================== ASSERTIONS ================= -->
3821 <sect1 id="sec-assertions">
3823 <indexterm><primary>Assertions</primary></indexterm>
3827 If you want to make use of assertions in your standard Haskell code, you
3828 could define a function like the following:
3834 assert :: Bool -> a -> a
3835 assert False x = error "assertion failed!"
3842 which works, but gives you back a less than useful error message --
3843 an assertion failed, but which and where?
3847 One way out is to define an extended <function>assert</function> function which also
3848 takes a descriptive string to include in the error message and
3849 perhaps combine this with the use of a pre-processor which inserts
3850 the source location where <function>assert</function> was used.
3854 Ghc offers a helping hand here, doing all of this for you. For every
3855 use of <function>assert</function> in the user's source:
3861 kelvinToC :: Double -> Double
3862 kelvinToC k = assert (k >= 0.0) (k+273.15)
3868 Ghc will rewrite this to also include the source location where the
3875 assert pred val ==> assertError "Main.hs|15" pred val
3881 The rewrite is only performed by the compiler when it spots
3882 applications of <function>Control.Exception.assert</function>, so you
3883 can still define and use your own versions of
3884 <function>assert</function>, should you so wish. If not, import
3885 <literal>Control.Exception</literal> to make use
3886 <function>assert</function> in your code.
3890 To have the compiler ignore uses of assert, use the compiler option
3891 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3892 option</primary></indexterm> That is, expressions of the form
3893 <literal>assert pred e</literal> will be rewritten to
3894 <literal>e</literal>.
3898 Assertion failures can be caught, see the documentation for the
3899 <literal>Control.Exception</literal> library for the details.
3905 <!-- =============================== PRAGMAS =========================== -->
3907 <sect1 id="pragmas">
3908 <title>Pragmas</title>
3910 <indexterm><primary>pragma</primary></indexterm>
3912 <para>GHC supports several pragmas, or instructions to the
3913 compiler placed in the source code. Pragmas don't normally affect
3914 the meaning of the program, but they might affect the efficiency
3915 of the generated code.</para>
3917 <para>Pragmas all take the form
3919 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3921 where <replaceable>word</replaceable> indicates the type of
3922 pragma, and is followed optionally by information specific to that
3923 type of pragma. Case is ignored in
3924 <replaceable>word</replaceable>. The various values for
3925 <replaceable>word</replaceable> that GHC understands are described
3926 in the following sections; any pragma encountered with an
3927 unrecognised <replaceable>word</replaceable> is (silently)
3930 <sect2 id="deprecated-pragma">
3931 <title>DEPRECATED pragma</title>
3932 <indexterm><primary>DEPRECATED</primary>
3935 <para>The DEPRECATED pragma lets you specify that a particular
3936 function, class, or type, is deprecated. There are two
3941 <para>You can deprecate an entire module thus:</para>
3943 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3946 <para>When you compile any module that import
3947 <literal>Wibble</literal>, GHC will print the specified
3952 <para>You can deprecate a function, class, or type, with the
3953 following top-level declaration:</para>
3955 {-# DEPRECATED f, C, T "Don't use these" #-}
3957 <para>When you compile any module that imports and uses any
3958 of the specifed entities, GHC will print the specified
3963 <para>You can suppress the warnings with the flag
3964 <option>-fno-warn-deprecations</option>.</para>
3967 <sect2 id="inline-noinline-pragma">
3968 <title>INLINE and NOINLINE pragmas</title>
3970 <para>These pragmas control the inlining of function
3973 <sect3 id="inline-pragma">
3974 <title>INLINE pragma</title>
3975 <indexterm><primary>INLINE</primary></indexterm>
3977 <para>GHC (with <option>-O</option>, as always) tries to
3978 inline (or “unfold”) functions/values that are
3979 “small enough,” thus avoiding the call overhead
3980 and possibly exposing other more-wonderful optimisations.
3981 Normally, if GHC decides a function is “too
3982 expensive” to inline, it will not do so, nor will it
3983 export that unfolding for other modules to use.</para>
3985 <para>The sledgehammer you can bring to bear is the
3986 <literal>INLINE</literal><indexterm><primary>INLINE
3987 pragma</primary></indexterm> pragma, used thusly:</para>
3990 key_function :: Int -> String -> (Bool, Double)
3992 #ifdef __GLASGOW_HASKELL__
3993 {-# INLINE key_function #-}
3997 <para>(You don't need to do the C pre-processor carry-on
3998 unless you're going to stick the code through HBC—it
3999 doesn't like <literal>INLINE</literal> pragmas.)</para>
4001 <para>The major effect of an <literal>INLINE</literal> pragma
4002 is to declare a function's “cost” to be very low.
4003 The normal unfolding machinery will then be very keen to
4006 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4007 function can be put anywhere its type signature could be
4010 <para><literal>INLINE</literal> pragmas are a particularly
4012 <literal>then</literal>/<literal>return</literal> (or
4013 <literal>bind</literal>/<literal>unit</literal>) functions in
4014 a monad. For example, in GHC's own
4015 <literal>UniqueSupply</literal> monad code, we have:</para>
4018 #ifdef __GLASGOW_HASKELL__
4019 {-# INLINE thenUs #-}
4020 {-# INLINE returnUs #-}
4024 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4025 linkend="noinline-pragma">).</para>
4028 <sect3 id="noinline-pragma">
4029 <title>NOINLINE pragma</title>
4031 <indexterm><primary>NOINLINE</primary></indexterm>
4032 <indexterm><primary>NOTINLINE</primary></indexterm>
4034 <para>The <literal>NOINLINE</literal> pragma does exactly what
4035 you'd expect: it stops the named function from being inlined
4036 by the compiler. You shouldn't ever need to do this, unless
4037 you're very cautious about code size.</para>
4039 <para><literal>NOTINLINE</literal> is a synonym for
4040 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4041 specified by Haskell 98 as the standard way to disable
4042 inlining, so it should be used if you want your code to be
4046 <sect3 id="phase-control">
4047 <title>Phase control</title>
4049 <para> Sometimes you want to control exactly when in GHC's
4050 pipeline the INLINE pragma is switched on. Inlining happens
4051 only during runs of the <emphasis>simplifier</emphasis>. Each
4052 run of the simplifier has a different <emphasis>phase
4053 number</emphasis>; the phase number decreases towards zero.
4054 If you use <option>-dverbose-core2core</option> you'll see the
4055 sequence of phase numbers for successive runs of the
4056 simpifier. In an INLINE pragma you can optionally specify a
4057 phase number, thus:</para>
4061 <para>You can say "inline <literal>f</literal> in Phase 2
4062 and all subsequent phases":
4064 {-# INLINE [2] f #-}
4070 <para>You can say "inline <literal>g</literal> in all
4071 phases up to, but not including, Phase 3":
4073 {-# INLINE [~3] g #-}
4079 <para>If you omit the phase indicator, you mean "inline in
4084 <para>You can use a phase number on a NOINLINE pragma too:</para>
4088 <para>You can say "do not inline <literal>f</literal>
4089 until Phase 2; in Phase 2 and subsequently behave as if
4090 there was no pragma at all":
4092 {-# NOINLINE [2] f #-}
4098 <para>You can say "do not inline <literal>g</literal> in
4099 Phase 3 or any subsequent phase; before that, behave as if
4100 there was no pragma":
4102 {-# NOINLINE [~3] g #-}
4108 <para>If you omit the phase indicator, you mean "never
4109 inline this function".</para>
4113 <para>The same phase-numbering control is available for RULES
4114 (<xref LinkEnd="rewrite-rules">).</para>
4118 <sect2 id="line-pragma">
4119 <title>LINE pragma</title>
4121 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4122 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4123 <para>This pragma is similar to C's <literal>#line</literal>
4124 pragma, and is mainly for use in automatically generated Haskell
4125 code. It lets you specify the line number and filename of the
4126 original code; for example</para>
4129 {-# LINE 42 "Foo.vhs" #-}
4132 <para>if you'd generated the current file from something called
4133 <filename>Foo.vhs</filename> and this line corresponds to line
4134 42 in the original. GHC will adjust its error messages to refer
4135 to the line/file named in the <literal>LINE</literal>
4139 <sect2 id="options-pragma">
4140 <title>OPTIONS pragma</title>
4141 <indexterm><primary>OPTIONS</primary>
4143 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4146 <para>The <literal>OPTIONS</literal> pragma is used to specify
4147 additional options that are given to the compiler when compiling
4148 this source file. See <xref linkend="source-file-options"> for
4153 <title>RULES pragma</title>
4155 <para>The RULES pragma lets you specify rewrite rules. It is
4156 described in <xref LinkEnd="rewrite-rules">.</para>
4159 <sect2 id="specialize-pragma">
4160 <title>SPECIALIZE pragma</title>
4162 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4163 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4164 <indexterm><primary>overloading, death to</primary></indexterm>
4166 <para>(UK spelling also accepted.) For key overloaded
4167 functions, you can create extra versions (NB: more code space)
4168 specialised to particular types. Thus, if you have an
4169 overloaded function:</para>
4172 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4175 <para>If it is heavily used on lists with
4176 <literal>Widget</literal> keys, you could specialise it as
4180 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4183 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4184 be put anywhere its type signature could be put.</para>
4186 <para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
4187 version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
4188 rewrites a call to the un-specialised function into a call to the specialised
4189 one. You can, instead, provide your own specialised function and your own rewrite rule.
4190 For example, suppose that:
4192 genericLookup :: Ord a => Table a b -> a -> b
4193 intLookup :: Table Int b -> Int -> b
4195 where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
4196 that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
4198 {-# RULES "intLookup" genericLookup = intLookup #-}
4200 (see <xref linkend="rule-spec">). It is <emphasis>Your
4201 Responsibility</emphasis> to make sure that
4202 <function>intLookup</function> really behaves as a specialised
4203 version of <function>genericLookup</function>!!!</para>
4205 <para>An example in which using <literal>RULES</literal> for
4206 specialisation will Win Big:
4209 toDouble :: Real a => a -> Double
4210 toDouble = fromRational . toRational
4212 {-# RULES "toDouble/Int" toDouble = i2d #-}
4213 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4216 The <function>i2d</function> function is virtually one machine
4217 instruction; the default conversion—via an intermediate
4218 <literal>Rational</literal>—is obscenely expensive by
4223 <sect2 id="specialize-instance-pragma">
4224 <title>SPECIALIZE instance pragma
4228 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4229 <indexterm><primary>overloading, death to</primary></indexterm>
4230 Same idea, except for instance declarations. For example:
4233 instance (Eq a) => Eq (Foo a) where {
4234 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4238 The pragma must occur inside the <literal>where</literal> part
4239 of the instance declaration.
4242 Compatible with HBC, by the way, except perhaps in the placement
4252 <!-- ======================= REWRITE RULES ======================== -->
4254 <sect1 id="rewrite-rules">
4255 <title>Rewrite rules
4257 <indexterm><primary>RULES pagma</primary></indexterm>
4258 <indexterm><primary>pragma, RULES</primary></indexterm>
4259 <indexterm><primary>rewrite rules</primary></indexterm></title>
4262 The programmer can specify rewrite rules as part of the source program
4263 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4264 the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
4265 and (b) the <option>-frules-off</option> flag
4266 (<xref LinkEnd="options-f">) is not specified.
4274 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4281 <title>Syntax</title>
4284 From a syntactic point of view:
4290 There may be zero or more rules in a <literal>RULES</literal> pragma.
4297 Each rule has a name, enclosed in double quotes. The name itself has
4298 no significance at all. It is only used when reporting how many times the rule fired.
4304 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
4305 immediately after the name of the rule. Thus:
4308 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4311 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4312 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4321 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4322 is set, so you must lay out your rules starting in the same column as the
4323 enclosing definitions.
4330 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4331 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4332 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4333 by spaces, just like in a type <literal>forall</literal>.
4339 A pattern variable may optionally have a type signature.
4340 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4341 For example, here is the <literal>foldr/build</literal> rule:
4344 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4345 foldr k z (build g) = g k z
4348 Since <function>g</function> has a polymorphic type, it must have a type signature.
4355 The left hand side of a rule must consist of a top-level variable applied
4356 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4359 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4360 "wrong2" forall f. f True = True
4363 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4370 A rule does not need to be in the same module as (any of) the
4371 variables it mentions, though of course they need to be in scope.
4377 Rules are automatically exported from a module, just as instance declarations are.
4388 <title>Semantics</title>
4391 From a semantic point of view:
4397 Rules are only applied if you use the <option>-O</option> flag.
4403 Rules are regarded as left-to-right rewrite rules.
4404 When GHC finds an expression that is a substitution instance of the LHS
4405 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4406 By "a substitution instance" we mean that the LHS can be made equal to the
4407 expression by substituting for the pattern variables.
4414 The LHS and RHS of a rule are typechecked, and must have the
4422 GHC makes absolutely no attempt to verify that the LHS and RHS
4423 of a rule have the same meaning. That is undecideable in general, and
4424 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4431 GHC makes no attempt to make sure that the rules are confluent or
4432 terminating. For example:
4435 "loop" forall x,y. f x y = f y x
4438 This rule will cause the compiler to go into an infinite loop.
4445 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4451 GHC currently uses a very simple, syntactic, matching algorithm
4452 for matching a rule LHS with an expression. It seeks a substitution
4453 which makes the LHS and expression syntactically equal modulo alpha
4454 conversion. The pattern (rule), but not the expression, is eta-expanded if
4455 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4456 But not beta conversion (that's called higher-order matching).
4460 Matching is carried out on GHC's intermediate language, which includes
4461 type abstractions and applications. So a rule only matches if the
4462 types match too. See <xref LinkEnd="rule-spec"> below.
4468 GHC keeps trying to apply the rules as it optimises the program.
4469 For example, consider:
4478 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4479 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4480 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4481 not be substituted, and the rule would not fire.
4488 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4489 that appears on the LHS of a rule</emphasis>, because once you have substituted
4490 for something you can't match against it (given the simple minded
4491 matching). So if you write the rule
4494 "map/map" forall f,g. map f . map g = map (f.g)
4497 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4498 It will only match something written with explicit use of ".".
4499 Well, not quite. It <emphasis>will</emphasis> match the expression
4505 where <function>wibble</function> is defined:
4508 wibble f g = map f . map g
4511 because <function>wibble</function> will be inlined (it's small).
4513 Later on in compilation, GHC starts inlining even things on the
4514 LHS of rules, but still leaves the rules enabled. This inlining
4515 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4522 All rules are implicitly exported from the module, and are therefore
4523 in force in any module that imports the module that defined the rule, directly
4524 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4525 in force when compiling A.) The situation is very similar to that for instance
4537 <title>List fusion</title>
4540 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4541 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4542 intermediate list should be eliminated entirely.
4546 The following are good producers:
4558 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4564 Explicit lists (e.g. <literal>[True, False]</literal>)
4570 The cons constructor (e.g <literal>3:4:[]</literal>)
4576 <function>++</function>
4582 <function>map</function>
4588 <function>filter</function>
4594 <function>iterate</function>, <function>repeat</function>
4600 <function>zip</function>, <function>zipWith</function>
4609 The following are good consumers:
4621 <function>array</function> (on its second argument)
4627 <function>length</function>
4633 <function>++</function> (on its first argument)
4639 <function>foldr</function>
4645 <function>map</function>
4651 <function>filter</function>
4657 <function>concat</function>
4663 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4669 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4670 will fuse with one but not the other)
4676 <function>partition</function>
4682 <function>head</function>
4688 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4694 <function>sequence_</function>
4700 <function>msum</function>
4706 <function>sortBy</function>
4715 So, for example, the following should generate no intermediate lists:
4718 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4724 This list could readily be extended; if there are Prelude functions that you use
4725 a lot which are not included, please tell us.
4729 If you want to write your own good consumers or producers, look at the
4730 Prelude definitions of the above functions to see how to do so.
4735 <sect2 id="rule-spec">
4736 <title>Specialisation
4740 Rewrite rules can be used to get the same effect as a feature
4741 present in earlier version of GHC:
4744 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4747 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4748 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4749 specialising the original definition of <function>fromIntegral</function> the programmer is
4750 promising that it is safe to use <function>int8ToInt16</function> instead.
4754 This feature is no longer in GHC. But rewrite rules let you do the
4759 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4763 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4764 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4765 GHC adds the type and dictionary applications to get the typed rule
4768 forall (d1::Integral Int8) (d2::Num Int16) .
4769 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4773 this rule does not need to be in the same file as fromIntegral,
4774 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4775 have an original definition available to specialise).
4781 <title>Controlling what's going on</title>
4789 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4795 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4796 If you add <option>-dppr-debug</option> you get a more detailed listing.
4802 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4805 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4806 {-# INLINE build #-}
4810 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4811 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4812 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4813 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4820 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4821 see how to write rules that will do fusion and yet give an efficient
4822 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4832 <sect2 id="core-pragma">
4833 <title>CORE pragma</title>
4835 <indexterm><primary>CORE pragma</primary></indexterm>
4836 <indexterm><primary>pragma, CORE</primary></indexterm>
4837 <indexterm><primary>core, annotation</primary></indexterm>
4840 The external core format supports <quote>Note</quote> annotations;
4841 the <literal>CORE</literal> pragma gives a way to specify what these
4842 should be in your Haskell source code. Syntactically, core
4843 annotations are attached to expressions and take a Haskell string
4844 literal as an argument. The following function definition shows an
4848 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4851 Sematically, this is equivalent to:
4859 However, when external for is generated (via
4860 <option>-fext-core</option>), there will be Notes attached to the
4861 expressions <function>show</function> and <VarName>x</VarName>.
4862 The core function declaration for <function>f</function> is:
4866 f :: %forall a . GHCziShow.ZCTShow a ->
4867 a -> GHCziBase.ZMZN GHCziBase.Char =
4868 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4870 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4872 (tpl1::GHCziBase.Int ->
4874 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4876 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4877 (tpl3::GHCziBase.ZMZN a ->
4878 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4886 Here, we can see that the function <function>show</function> (which
4887 has been expanded out to a case expression over the Show dictionary)
4888 has a <literal>%note</literal> attached to it, as does the
4889 expression <VarName>eta</VarName> (which used to be called
4890 <VarName>x</VarName>).
4897 <sect1 id="generic-classes">
4898 <title>Generic classes</title>
4900 <para>(Note: support for generic classes is currently broken in
4904 The ideas behind this extension are described in detail in "Derivable type classes",
4905 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4906 An example will give the idea:
4914 fromBin :: [Int] -> (a, [Int])
4916 toBin {| Unit |} Unit = []
4917 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4918 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4919 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4921 fromBin {| Unit |} bs = (Unit, bs)
4922 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4923 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4924 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4925 (y,bs'') = fromBin bs'
4928 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4929 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4930 which are defined thus in the library module <literal>Generics</literal>:
4934 data a :+: b = Inl a | Inr b
4935 data a :*: b = a :*: b
4938 Now you can make a data type into an instance of Bin like this:
4940 instance (Bin a, Bin b) => Bin (a,b)
4941 instance Bin a => Bin [a]
4943 That is, just leave off the "where" clause. Of course, you can put in the
4944 where clause and over-ride whichever methods you please.
4948 <title> Using generics </title>
4949 <para>To use generics you need to</para>
4952 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4953 <option>-fgenerics</option> (to generate extra per-data-type code),
4954 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4958 <para>Import the module <literal>Generics</literal> from the
4959 <literal>lang</literal> package. This import brings into
4960 scope the data types <literal>Unit</literal>,
4961 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4962 don't need this import if you don't mention these types
4963 explicitly; for example, if you are simply giving instance
4964 declarations.)</para>
4969 <sect2> <title> Changes wrt the paper </title>
4971 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4972 can be written infix (indeed, you can now use
4973 any operator starting in a colon as an infix type constructor). Also note that
4974 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4975 Finally, note that the syntax of the type patterns in the class declaration
4976 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4977 alone would ambiguous when they appear on right hand sides (an extension we
4978 anticipate wanting).
4982 <sect2> <title>Terminology and restrictions</title>
4984 Terminology. A "generic default method" in a class declaration
4985 is one that is defined using type patterns as above.
4986 A "polymorphic default method" is a default method defined as in Haskell 98.
4987 A "generic class declaration" is a class declaration with at least one
4988 generic default method.
4996 Alas, we do not yet implement the stuff about constructor names and
5003 A generic class can have only one parameter; you can't have a generic
5004 multi-parameter class.
5010 A default method must be defined entirely using type patterns, or entirely
5011 without. So this is illegal:
5014 op :: a -> (a, Bool)
5015 op {| Unit |} Unit = (Unit, True)
5018 However it is perfectly OK for some methods of a generic class to have
5019 generic default methods and others to have polymorphic default methods.
5025 The type variable(s) in the type pattern for a generic method declaration
5026 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:
5030 op {| p :*: q |} (x :*: y) = op (x :: p)
5038 The type patterns in a generic default method must take one of the forms:
5044 where "a" and "b" are type variables. Furthermore, all the type patterns for
5045 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5046 must use the same type variables. So this is illegal:
5050 op {| a :+: b |} (Inl x) = True
5051 op {| p :+: q |} (Inr y) = False
5053 The type patterns must be identical, even in equations for different methods of the class.
5054 So this too is illegal:
5058 op1 {| a :*: b |} (x :*: y) = True
5061 op2 {| p :*: q |} (x :*: y) = False
5063 (The reason for this restriction is that we gather all the equations for a particular type consructor
5064 into a single generic instance declaration.)
5070 A generic method declaration must give a case for each of the three type constructors.
5076 The type for a generic method can be built only from:
5078 <listitem> <para> Function arrows </para> </listitem>
5079 <listitem> <para> Type variables </para> </listitem>
5080 <listitem> <para> Tuples </para> </listitem>
5081 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5083 Here are some example type signatures for generic methods:
5086 op2 :: Bool -> (a,Bool)
5087 op3 :: [Int] -> a -> a
5090 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5094 This restriction is an implementation restriction: we just havn't got around to
5095 implementing the necessary bidirectional maps over arbitrary type constructors.
5096 It would be relatively easy to add specific type constructors, such as Maybe and list,
5097 to the ones that are allowed.</para>
5102 In an instance declaration for a generic class, the idea is that the compiler
5103 will fill in the methods for you, based on the generic templates. However it can only
5108 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5113 No constructor of the instance type has unboxed fields.
5117 (Of course, these things can only arise if you are already using GHC extensions.)
5118 However, you can still give an instance declarations for types which break these rules,
5119 provided you give explicit code to override any generic default methods.
5127 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5128 what the compiler does with generic declarations.
5133 <sect2> <title> Another example </title>
5135 Just to finish with, here's another example I rather like:
5139 nCons {| Unit |} _ = 1
5140 nCons {| a :*: b |} _ = 1
5141 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5144 tag {| Unit |} _ = 1
5145 tag {| a :*: b |} _ = 1
5146 tag {| a :+: b |} (Inl x) = tag x
5147 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5156 ;;; Local Variables: ***
5158 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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