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
1233 pair of a dictionary for <literal>Ord t</literal> and a value of type
1234 <literal>t</literal>. That contradicts the idea that
1235 <literal>newtype</literal> should have no concrete representation.
1236 You can get just the same efficiency and effect by using
1237 <literal>data</literal> instead of <literal>newtype</literal>. If
1238 there is no overloading involved, then there is more of a case for
1239 allowing an existentially-quantified <literal>newtype</literal>,
1240 because the <literal>data</literal> version does carry an
1241 implementation cost, but single-field existentially quantified
1242 constructors aren't much use. So the simple restriction (no
1243 existential stuff on <literal>newtype</literal>) stands, unless there
1244 are convincing reasons to change it.
1252 You can't use <literal>deriving</literal> to define instances of a
1253 data type with existentially quantified data constructors.
1255 Reason: in most cases it would not make sense. For example:#
1258 data T = forall a. MkT [a] deriving( Eq )
1261 To derive <literal>Eq</literal> in the standard way we would need to have equality
1262 between the single component of two <function>MkT</function> constructors:
1266 (MkT a) == (MkT b) = ???
1269 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
1270 It's just about possible to imagine examples in which the derived instance
1271 would make sense, but it seems altogether simpler simply to prohibit such
1272 declarations. Define your own instances!
1287 <sect2 id="multi-param-type-classes">
1288 <title>Class declarations</title>
1291 This section documents GHC's implementation of multi-parameter type
1292 classes. There's lots of background in the paper <ULink
1293 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
1294 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
1295 Jones, Erik Meijer).
1298 There are the following constraints on class declarations:
1303 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1307 class Collection c a where
1308 union :: c a -> c a -> c a
1319 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1320 of "acyclic" involves only the superclass relationships. For example,
1326 op :: D b => a -> b -> b
1329 class C a => D a where { ... }
1333 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1334 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1335 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1342 <emphasis>There are no restrictions on the context in a class declaration
1343 (which introduces superclasses), except that the class hierarchy must
1344 be acyclic</emphasis>. So these class declarations are OK:
1348 class Functor (m k) => FiniteMap m k where
1351 class (Monad m, Monad (t m)) => Transform t m where
1352 lift :: m a -> (t m) a
1362 <emphasis>All of the class type variables must be reachable (in the sense
1363 mentioned in <xref linkend="type-restrictions">)
1364 from the free varibles of each method type
1365 </emphasis>. For example:
1369 class Coll s a where
1371 insert :: s -> a -> s
1375 is not OK, because the type of <literal>empty</literal> doesn't mention
1376 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1377 types, and has the same motivation.
1379 Sometimes, offending class declarations exhibit misunderstandings. For
1380 example, <literal>Coll</literal> might be rewritten
1384 class Coll s a where
1386 insert :: s a -> a -> s a
1390 which makes the connection between the type of a collection of
1391 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1392 Occasionally this really doesn't work, in which case you can split the
1400 class CollE s => Coll s a where
1401 insert :: s -> a -> s
1411 <sect3 id="class-method-types">
1412 <title>Class method types</title>
1414 Haskell 98 prohibits class method types to mention constraints on the
1415 class type variable, thus:
1418 fromList :: [a] -> s a
1419 elem :: Eq a => a -> s a -> Bool
1421 The type of <literal>elem</literal> is illegal in Haskell 98, because it
1422 contains the constraint <literal>Eq a</literal>, constrains only the
1423 class type variable (in this case <literal>a</literal>).
1426 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
1433 <sect2 id="type-restrictions">
1434 <title>Type signatures</title>
1436 <sect3><title>The context of a type signature</title>
1438 Unlike Haskell 98, constraints in types do <emphasis>not</emphasis> have to be of
1439 the form <emphasis>(class type-variable)</emphasis> or
1440 <emphasis>(class (type-variable type-variable ...))</emphasis>. Thus,
1441 these type signatures are perfectly OK
1444 g :: Ord (T a ()) => ...
1448 GHC imposes the following restrictions on the constraints in a type signature.
1452 forall tv1..tvn (c1, ...,cn) => type
1455 (Here, we write the "foralls" explicitly, although the Haskell source
1456 language omits them; in Haskell 98, all the free type variables of an
1457 explicit source-language type signature are universally quantified,
1458 except for the class type variables in a class declaration. However,
1459 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
1468 <emphasis>Each universally quantified type variable
1469 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
1471 A type variable is "reachable" if it it is functionally dependent
1472 (see <xref linkend="functional-dependencies">)
1473 on the type variables free in <literal>type</literal>.
1474 The reason for this is that a value with a type that does not obey
1475 this restriction could not be used without introducing
1477 Here, for example, is an illegal type:
1481 forall a. Eq a => Int
1485 When a value with this type was used, the constraint <literal>Eq tv</literal>
1486 would be introduced where <literal>tv</literal> is a fresh type variable, and
1487 (in the dictionary-translation implementation) the value would be
1488 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1489 can never know which instance of <literal>Eq</literal> to use because we never
1490 get any more information about <literal>tv</literal>.
1497 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1498 universally quantified type variables <literal>tvi</literal></emphasis>.
1500 For example, this type is OK because <literal>C a b</literal> mentions the
1501 universally quantified type variable <literal>b</literal>:
1505 forall a. C a b => burble
1509 The next type is illegal because the constraint <literal>Eq b</literal> does not
1510 mention <literal>a</literal>:
1514 forall a. Eq b => burble
1518 The reason for this restriction is milder than the other one. The
1519 excluded types are never useful or necessary (because the offending
1520 context doesn't need to be witnessed at this point; it can be floated
1521 out). Furthermore, floating them out increases sharing. Lastly,
1522 excluding them is a conservative choice; it leaves a patch of
1523 territory free in case we need it later.
1534 <title>For-all hoisting</title>
1536 It is often convenient to use generalised type synonyms (see <xref linkend="type-synonyms">) at the right hand
1537 end of an arrow, thus:
1539 type Discard a = forall b. a -> b -> a
1541 g :: Int -> Discard Int
1544 Simply expanding the type synonym would give
1546 g :: Int -> (forall b. Int -> b -> Int)
1548 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
1550 g :: forall b. Int -> Int -> b -> Int
1552 In general, the rule is this: <emphasis>to determine the type specified by any explicit
1553 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
1554 performs the transformation:</emphasis>
1556 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
1558 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
1560 (In fact, GHC tries to retain as much synonym information as possible for use in
1561 error messages, but that is a usability issue.) This rule applies, of course, whether
1562 or not the <literal>forall</literal> comes from a synonym. For example, here is another
1563 valid way to write <literal>g</literal>'s type signature:
1565 g :: Int -> Int -> forall b. b -> Int
1569 When doing this hoisting operation, GHC eliminates duplicate constraints. For
1572 type Foo a = (?x::Int) => Bool -> a
1577 g :: (?x::Int) => Bool -> Bool -> Int
1585 <sect2 id="instance-decls">
1586 <title>Instance declarations</title>
1589 <title>Overlapping instances</title>
1591 In general, <emphasis>instance declarations may not overlap</emphasis>. The two instance
1596 instance context1 => C type1 where ...
1597 instance context2 => C type2 where ...
1600 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify.
1603 However, if you give the command line option
1604 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1605 option</primary></indexterm> then overlapping instance declarations are permitted.
1606 However, GHC arranges never to commit to using an instance declaration
1607 if another instance declaration also applies, either now or later.
1613 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1619 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1620 (but not identical to <literal>type1</literal>), or vice versa.
1624 Notice that these rules
1629 make it clear which instance decl to use
1630 (pick the most specific one that matches)
1637 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1638 Reason: you can pick which instance decl
1639 "matches" based on the type.
1644 However the rules are over-conservative. Two instance declarations can overlap,
1645 but it can still be clear in particular situations which to use. For example:
1647 instance C (Int,a) where ...
1648 instance C (a,Bool) where ...
1650 These are rejected by GHC's rules, but it is clear what to do when trying
1651 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1652 cannot apply. Yell if this restriction bites you.
1655 GHC is also conservative about committing to an overlapping instance. For example:
1657 class C a where { op :: a -> a }
1658 instance C [Int] where ...
1659 instance C a => C [a] where ...
1661 f :: C b => [b] -> [b]
1664 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1665 GHC does not commit to the second instance declaration, because in a paricular
1666 call of f, b might be instantiate to Int, so the first instance declaration
1667 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1668 GHC will instead silently pick the second instance, without complaining about
1669 the problem of subsequent instantiations.
1672 Regrettably, GHC doesn't guarantee to detect overlapping instance
1673 declarations if they appear in different modules. GHC can "see" the
1674 instance declarations in the transitive closure of all the modules
1675 imported by the one being compiled, so it can "see" all instance decls
1676 when it is compiling <literal>Main</literal>. However, it currently chooses not
1677 to look at ones that can't possibly be of use in the module currently
1678 being compiled, in the interests of efficiency. (Perhaps we should
1679 change that decision, at least for <literal>Main</literal>.)
1684 <title>Type synonyms in the instance head</title>
1687 <emphasis>Unlike Haskell 98, instance heads may use type
1688 synonyms</emphasis>. (The instance "head" is the bit after the "=>" in an instance decl.)
1689 As always, using a type synonym is just shorthand for
1690 writing the RHS of the type synonym definition. For example:
1694 type Point = (Int,Int)
1695 instance C Point where ...
1696 instance C [Point] where ...
1700 is legal. However, if you added
1704 instance C (Int,Int) where ...
1708 as well, then the compiler will complain about the overlapping
1709 (actually, identical) instance declarations. As always, type synonyms
1710 must be fully applied. You cannot, for example, write:
1715 instance Monad P where ...
1719 This design decision is independent of all the others, and easily
1720 reversed, but it makes sense to me.
1725 <sect3 id="undecidable-instances">
1726 <title>Undecidable instances</title>
1728 <para>An instance declaration must normally obey the following rules:
1730 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1731 an instance declaration <emphasis>must not</emphasis> be a type variable.
1732 For example, these are OK:
1735 instance C Int a where ...
1737 instance D (Int, Int) where ...
1739 instance E [[a]] where ...
1743 instance F a where ...
1745 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1746 For example, this is OK:
1748 instance Stateful (ST s) (MutVar s) where ...
1755 <para>All of the types in the <emphasis>context</emphasis> of
1756 an instance declaration <emphasis>must</emphasis> be type variables.
1759 instance C a b => Eq (a,b) where ...
1763 instance C Int b => Foo b where ...
1769 These restrictions ensure that
1770 context reduction terminates: each reduction step removes one type
1771 constructor. For example, the following would make the type checker
1772 loop if it wasn't excluded:
1774 instance C a => C a where ...
1776 There are two situations in which the rule is a bit of a pain. First,
1777 if one allows overlapping instance declarations then it's quite
1778 convenient to have a "default instance" declaration that applies if
1779 something more specific does not:
1788 Second, sometimes you might want to use the following to get the
1789 effect of a "class synonym":
1793 class (C1 a, C2 a, C3 a) => C a where { }
1795 instance (C1 a, C2 a, C3 a) => C a where { }
1799 This allows you to write shorter signatures:
1811 f :: (C1 a, C2 a, C3 a) => ...
1815 Voluminous correspondence on the Haskell mailing list has convinced me
1816 that it's worth experimenting with more liberal rules. If you use
1817 the experimental flag <option>-fallow-undecidable-instances</option>
1818 <indexterm><primary>-fallow-undecidable-instances
1819 option</primary></indexterm>, you can use arbitrary
1820 types in both an instance context and instance head. Termination is ensured by having a
1821 fixed-depth recursion stack. If you exceed the stack depth you get a
1822 sort of backtrace, and the opportunity to increase the stack depth
1823 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1826 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1827 allowing these idioms interesting idioms.
1834 <sect2 id="implicit-parameters">
1835 <title>Implicit parameters</title>
1837 <para> Implicit paramters are implemented as described in
1838 "Implicit parameters: dynamic scoping with static types",
1839 J Lewis, MB Shields, E Meijer, J Launchbury,
1840 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1844 <para>(Most of the following, stil rather incomplete, documentation is
1845 due to Jeff Lewis.)</para>
1847 <para>Implicit parameter support is enabled with the option
1848 <option>-fimplicit-params</option>.</para>
1851 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1852 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1853 context. In Haskell, all variables are statically bound. Dynamic
1854 binding of variables is a notion that goes back to Lisp, but was later
1855 discarded in more modern incarnations, such as Scheme. Dynamic binding
1856 can be very confusing in an untyped language, and unfortunately, typed
1857 languages, in particular Hindley-Milner typed languages like Haskell,
1858 only support static scoping of variables.
1861 However, by a simple extension to the type class system of Haskell, we
1862 can support dynamic binding. Basically, we express the use of a
1863 dynamically bound variable as a constraint on the type. These
1864 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1865 function uses a dynamically-bound variable <literal>?x</literal>
1866 of type <literal>t'</literal>". For
1867 example, the following expresses the type of a sort function,
1868 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1870 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1872 The dynamic binding constraints are just a new form of predicate in the type class system.
1875 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1876 where <literal>x</literal> is
1877 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1878 Use of this construct also introduces a new
1879 dynamic-binding constraint in the type of the expression.
1880 For example, the following definition
1881 shows how we can define an implicitly parameterized sort function in
1882 terms of an explicitly parameterized <literal>sortBy</literal> function:
1884 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1886 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1892 <title>Implicit-parameter type constraints</title>
1894 Dynamic binding constraints behave just like other type class
1895 constraints in that they are automatically propagated. Thus, when a
1896 function is used, its implicit parameters are inherited by the
1897 function that called it. For example, our <literal>sort</literal> function might be used
1898 to pick out the least value in a list:
1900 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1901 least xs = fst (sort xs)
1903 Without lifting a finger, the <literal>?cmp</literal> parameter is
1904 propagated to become a parameter of <literal>least</literal> as well. With explicit
1905 parameters, the default is that parameters must always be explicit
1906 propagated. With implicit parameters, the default is to always
1910 An implicit-parameter type constraint differs from other type class constraints in the
1911 following way: All uses of a particular implicit parameter must have
1912 the same type. This means that the type of <literal>(?x, ?x)</literal>
1913 is <literal>(?x::a) => (a,a)</literal>, and not
1914 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1918 <para> You can't have an implicit parameter in the context of a class or instance
1919 declaration. For example, both these declarations are illegal:
1921 class (?x::Int) => C a where ...
1922 instance (?x::a) => Foo [a] where ...
1924 Reason: exactly which implicit parameter you pick up depends on exactly where
1925 you invoke a function. But the ``invocation'' of instance declarations is done
1926 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1927 Easiest thing is to outlaw the offending types.</para>
1929 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1931 f :: (?x :: [a]) => Int -> Int
1934 g :: (Read a, Show a) => String -> String
1937 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1938 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1939 quite unambiguous, and fixes the type <literal>a</literal>.
1944 <title>Implicit-parameter bindings</title>
1947 An implicit parameter is <emphasis>bound</emphasis> using the standard
1948 <literal>let</literal> or <literal>where</literal> binding forms.
1949 For example, we define the <literal>min</literal> function by binding
1950 <literal>cmp</literal>.
1953 min = let ?cmp = (<=) in least
1957 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1958 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1959 (including in a list comprehension, or do-notation, or pattern guards),
1960 or a <literal>where</literal> clause.
1961 Note the following points:
1964 An implicit-parameter binding group must be a
1965 collection of simple bindings to implicit-style variables (no
1966 function-style bindings, and no type signatures); these bindings are
1967 neither polymorphic or recursive.
1970 You may not mix implicit-parameter bindings with ordinary bindings in a
1971 single <literal>let</literal>
1972 expression; use two nested <literal>let</literal>s instead.
1973 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1977 You may put multiple implicit-parameter bindings in a
1978 single binding group; but they are <emphasis>not</emphasis> treated
1979 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1980 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1981 parameter. The bindings are not nested, and may be re-ordered without changing
1982 the meaning of the program.
1983 For example, consider:
1985 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1987 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1988 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1990 f :: (?x::Int) => Int -> Int
1999 <sect2 id="linear-implicit-parameters">
2000 <title>Linear implicit parameters</title>
2002 Linear implicit parameters are an idea developed by Koen Claessen,
2003 Mark Shields, and Simon PJ. They address the long-standing
2004 problem that monads seem over-kill for certain sorts of problem, notably:
2007 <listitem> <para> distributing a supply of unique names </para> </listitem>
2008 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
2009 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
2013 Linear implicit parameters are just like ordinary implicit parameters,
2014 except that they are "linear" -- that is, they cannot be copied, and
2015 must be explicitly "split" instead. Linear implicit parameters are
2016 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
2017 (The '/' in the '%' suggests the split!)
2022 import GHC.Exts( Splittable )
2024 data NameSupply = ...
2026 splitNS :: NameSupply -> (NameSupply, NameSupply)
2027 newName :: NameSupply -> Name
2029 instance Splittable NameSupply where
2033 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2034 f env (Lam x e) = Lam x' (f env e)
2037 env' = extend env x x'
2038 ...more equations for f...
2040 Notice that the implicit parameter %ns is consumed
2042 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
2043 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
2047 So the translation done by the type checker makes
2048 the parameter explicit:
2050 f :: NameSupply -> Env -> Expr -> Expr
2051 f ns env (Lam x e) = Lam x' (f ns1 env e)
2053 (ns1,ns2) = splitNS ns
2055 env = extend env x x'
2057 Notice the call to 'split' introduced by the type checker.
2058 How did it know to use 'splitNS'? Because what it really did
2059 was to introduce a call to the overloaded function 'split',
2060 defined by the class <literal>Splittable</literal>:
2062 class Splittable a where
2065 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
2066 split for name supplies. But we can simply write
2072 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
2074 The <literal>Splittable</literal> class is built into GHC. It's exported by module
2075 <literal>GHC.Exts</literal>.
2080 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
2081 are entirely distinct implicit parameters: you
2082 can use them together and they won't intefere with each other. </para>
2085 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
2087 <listitem> <para>You cannot have implicit parameters (whether linear or not)
2088 in the context of a class or instance declaration. </para></listitem>
2092 <sect3><title>Warnings</title>
2095 The monomorphism restriction is even more important than usual.
2096 Consider the example above:
2098 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2099 f env (Lam x e) = Lam x' (f env e)
2102 env' = extend env x x'
2104 If we replaced the two occurrences of x' by (newName %ns), which is
2105 usually a harmless thing to do, we get:
2107 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
2108 f env (Lam x e) = Lam (newName %ns) (f env e)
2110 env' = extend env x (newName %ns)
2112 But now the name supply is consumed in <emphasis>three</emphasis> places
2113 (the two calls to newName,and the recursive call to f), so
2114 the result is utterly different. Urk! We don't even have
2118 Well, this is an experimental change. With implicit
2119 parameters we have already lost beta reduction anyway, and
2120 (as John Launchbury puts it) we can't sensibly reason about
2121 Haskell programs without knowing their typing.
2126 <sect3><title>Recursive functions</title>
2127 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
2130 foo :: %x::T => Int -> [Int]
2132 foo n = %x : foo (n-1)
2134 where T is some type in class Splittable.</para>
2136 Do you get a list of all the same T's or all different T's
2137 (assuming that split gives two distinct T's back)?
2139 If you supply the type signature, taking advantage of polymorphic
2140 recursion, you get what you'd probably expect. Here's the
2141 translated term, where the implicit param is made explicit:
2144 foo x n = let (x1,x2) = split x
2145 in x1 : foo x2 (n-1)
2147 But if you don't supply a type signature, GHC uses the Hindley
2148 Milner trick of using a single monomorphic instance of the function
2149 for the recursive calls. That is what makes Hindley Milner type inference
2150 work. So the translation becomes
2154 foom n = x : foom (n-1)
2158 Result: 'x' is not split, and you get a list of identical T's. So the
2159 semantics of the program depends on whether or not foo has a type signature.
2162 You may say that this is a good reason to dislike linear implicit parameters
2163 and you'd be right. That is why they are an experimental feature.
2169 <sect2 id="functional-dependencies">
2170 <title>Functional dependencies
2173 <para> Functional dependencies are implemented as described by Mark Jones
2174 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
2175 In Proceedings of the 9th European Symposium on Programming,
2176 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
2180 Functional dependencies are introduced by a vertical bar in the syntax of a
2181 class declaration; e.g.
2183 class (Monad m) => MonadState s m | m -> s where ...
2185 class Foo a b c | a b -> c where ...
2187 There should be more documentation, but there isn't (yet). Yell if you need it.
2193 <sect2 id="sec-kinding">
2194 <title>Explicitly-kinded quantification</title>
2197 Haskell infers the kind of each type variable. Sometimes it is nice to be able
2198 to give the kind explicitly as (machine-checked) documentation,
2199 just as it is nice to give a type signature for a function. On some occasions,
2200 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
2201 John Hughes had to define the data type:
2203 data Set cxt a = Set [a]
2204 | Unused (cxt a -> ())
2206 The only use for the <literal>Unused</literal> constructor was to force the correct
2207 kind for the type variable <literal>cxt</literal>.
2210 GHC now instead allows you to specify the kind of a type variable directly, wherever
2211 a type variable is explicitly bound. Namely:
2213 <listitem><para><literal>data</literal> declarations:
2215 data Set (cxt :: * -> *) a = Set [a]
2216 </Screen></para></listitem>
2217 <listitem><para><literal>type</literal> declarations:
2219 type T (f :: * -> *) = f Int
2220 </Screen></para></listitem>
2221 <listitem><para><literal>class</literal> declarations:
2223 class (Eq a) => C (f :: * -> *) a where ...
2224 </Screen></para></listitem>
2225 <listitem><para><literal>forall</literal>'s in type signatures:
2227 f :: forall (cxt :: * -> *). Set cxt Int
2228 </Screen></para></listitem>
2233 The parentheses are required. Some of the spaces are required too, to
2234 separate the lexemes. If you write <literal>(f::*->*)</literal> you
2235 will get a parse error, because "<literal>::*->*</literal>" is a
2236 single lexeme in Haskell.
2240 As part of the same extension, you can put kind annotations in types
2243 f :: (Int :: *) -> Int
2244 g :: forall a. a -> (a :: *)
2248 atype ::= '(' ctype '::' kind ')
2250 The parentheses are required.
2255 <sect2 id="universal-quantification">
2256 <title>Arbitrary-rank polymorphism
2260 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
2261 allows us to say exactly what this means. For example:
2269 g :: forall b. (b -> b)
2271 The two are treated identically.
2275 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
2276 explicit universal quantification in
2278 For example, all the following types are legal:
2280 f1 :: forall a b. a -> b -> a
2281 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
2283 f2 :: (forall a. a->a) -> Int -> Int
2284 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
2286 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
2288 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
2289 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
2290 The <literal>forall</literal> makes explicit the universal quantification that
2291 is implicitly added by Haskell.
2294 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
2295 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
2296 shows, the polymorphic type on the left of the function arrow can be overloaded.
2299 The function <literal>f3</literal> has a rank-3 type;
2300 it has rank-2 types on the left of a function arrow.
2303 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
2304 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
2305 that restriction has now been lifted.)
2306 In particular, a forall-type (also called a "type scheme"),
2307 including an operational type class context, is legal:
2309 <listitem> <para> On the left of a function arrow </para> </listitem>
2310 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
2311 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
2312 example, any of the <literal>f1,f2,f3,g1,g2</literal> above would be valid
2313 field type signatures.</para> </listitem>
2314 <listitem> <para> As the type of an implicit parameter </para> </listitem>
2315 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
2317 There is one place you cannot put a <literal>forall</literal>:
2318 you cannot instantiate a type variable with a forall-type. So you cannot
2319 make a forall-type the argument of a type constructor. So these types are illegal:
2321 x1 :: [forall a. a->a]
2322 x2 :: (forall a. a->a, Int)
2323 x3 :: Maybe (forall a. a->a)
2325 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
2326 a type variable any more!
2335 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
2336 the types of the constructor arguments. Here are several examples:
2342 data T a = T1 (forall b. b -> b -> b) a
2344 data MonadT m = MkMonad { return :: forall a. a -> m a,
2345 bind :: forall a b. m a -> (a -> m b) -> m b
2348 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
2354 The constructors have rank-2 types:
2360 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
2361 MkMonad :: forall m. (forall a. a -> m a)
2362 -> (forall a b. m a -> (a -> m b) -> m b)
2364 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
2370 Notice that you don't need to use a <literal>forall</literal> if there's an
2371 explicit context. For example in the first argument of the
2372 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
2373 prefixed to the argument type. The implicit <literal>forall</literal>
2374 quantifies all type variables that are not already in scope, and are
2375 mentioned in the type quantified over.
2379 As for type signatures, implicit quantification happens for non-overloaded
2380 types too. So if you write this:
2383 data T a = MkT (Either a b) (b -> b)
2386 it's just as if you had written this:
2389 data T a = MkT (forall b. Either a b) (forall b. b -> b)
2392 That is, since the type variable <literal>b</literal> isn't in scope, it's
2393 implicitly universally quantified. (Arguably, it would be better
2394 to <emphasis>require</emphasis> explicit quantification on constructor arguments
2395 where that is what is wanted. Feedback welcomed.)
2399 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
2400 the constructor to suitable values, just as usual. For example,
2411 a3 = MkSwizzle reverse
2414 a4 = let r x = Just x
2421 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
2422 mkTs f x y = [T1 f x, T1 f y]
2428 The type of the argument can, as usual, be more general than the type
2429 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2430 does not need the <literal>Ord</literal> constraint.)
2434 When you use pattern matching, the bound variables may now have
2435 polymorphic types. For example:
2441 f :: T a -> a -> (a, Char)
2442 f (T1 w k) x = (w k x, w 'c' 'd')
2444 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2445 g (MkSwizzle s) xs f = s (map f (s xs))
2447 h :: MonadT m -> [m a] -> m [a]
2448 h m [] = return m []
2449 h m (x:xs) = bind m x $ \y ->
2450 bind m (h m xs) $ \ys ->
2457 In the function <function>h</function> we use the record selectors <literal>return</literal>
2458 and <literal>bind</literal> to extract the polymorphic bind and return functions
2459 from the <literal>MonadT</literal> data structure, rather than using pattern
2465 <title>Type inference</title>
2468 In general, type inference for arbitrary-rank types is undecideable.
2469 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2470 to get a decidable algorithm by requiring some help from the programmer.
2471 We do not yet have a formal specification of "some help" but the rule is this:
2474 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2475 provides an explicit polymorphic type for x, or GHC's type inference will assume
2476 that x's type has no foralls in it</emphasis>.
2479 What does it mean to "provide" an explicit type for x? You can do that by
2480 giving a type signature for x directly, using a pattern type signature
2481 (<xref linkend="scoped-type-variables">), thus:
2483 \ f :: (forall a. a->a) -> (f True, f 'c')
2485 Alternatively, you can give a type signature to the enclosing
2486 context, which GHC can "push down" to find the type for the variable:
2488 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2490 Here the type signature on the expression can be pushed inwards
2491 to give a type signature for f. Similarly, and more commonly,
2492 one can give a type signature for the function itself:
2494 h :: (forall a. a->a) -> (Bool,Char)
2495 h f = (f True, f 'c')
2497 You don't need to give a type signature if the lambda bound variable
2498 is a constructor argument. Here is an example we saw earlier:
2500 f :: T a -> a -> (a, Char)
2501 f (T1 w k) x = (w k x, w 'c' 'd')
2503 Here we do not need to give a type signature to <literal>w</literal>, because
2504 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2511 <sect3 id="implicit-quant">
2512 <title>Implicit quantification</title>
2515 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2516 user-written types, if and only if there is no explicit <literal>forall</literal>,
2517 GHC finds all the type variables mentioned in the type that are not already
2518 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2522 f :: forall a. a -> a
2529 h :: forall b. a -> b -> b
2535 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2538 f :: (a -> a) -> Int
2540 f :: forall a. (a -> a) -> Int
2542 f :: (forall a. a -> a) -> Int
2545 g :: (Ord a => a -> a) -> Int
2546 -- MEANS the illegal type
2547 g :: forall a. (Ord a => a -> a) -> Int
2549 g :: (forall a. Ord a => a -> a) -> Int
2551 The latter produces an illegal type, which you might think is silly,
2552 but at least the rule is simple. If you want the latter type, you
2553 can write your for-alls explicitly. Indeed, doing so is strongly advised
2562 <sect2 id="scoped-type-variables">
2563 <title>Scoped type variables
2567 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2568 variable</emphasis>. For example
2574 f (xs::[a]) = ys ++ ys
2583 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2584 This brings the type variable <literal>a</literal> into scope; it scopes over
2585 all the patterns and right hand sides for this equation for <function>f</function>.
2586 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2590 Pattern type signatures are completely orthogonal to ordinary, separate
2591 type signatures. The two can be used independently or together.
2592 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2593 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2594 implicitly universally quantified. (If there are no type variables in
2595 scope, all type variables mentioned in the signature are universally
2596 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2597 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2598 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2599 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2600 it becomes possible to do so.
2604 Scoped type variables are implemented in both GHC and Hugs. Where the
2605 implementations differ from the specification below, those differences
2610 So much for the basic idea. Here are the details.
2614 <title>What a pattern type signature means</title>
2616 A type variable brought into scope by a pattern type signature is simply
2617 the name for a type. The restriction they express is that all occurrences
2618 of the same name mean the same type. For example:
2620 f :: [Int] -> Int -> Int
2621 f (xs::[a]) (y::a) = (head xs + y) :: a
2623 The pattern type signatures on the left hand side of
2624 <literal>f</literal> express the fact that <literal>xs</literal>
2625 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2626 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2627 specifies that this expression must have the same type <literal>a</literal>.
2628 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2629 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2630 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2631 rules, which specified that a pattern-bound type variable should be universally quantified.)
2632 For example, all of these are legal:</para>
2635 t (x::a) (y::a) = x+y*2
2637 f (x::a) (y::b) = [x,y] -- a unifies with b
2639 g (x::a) = x + 1::Int -- a unifies with Int
2641 h x = let k (y::a) = [x,y] -- a is free in the
2642 in k x -- environment
2644 k (x::a) True = ... -- a unifies with Int
2645 k (x::Int) False = ...
2648 w (x::a) = x -- a unifies with [b]
2654 <title>Scope and implicit quantification</title>
2662 All the type variables mentioned in a pattern,
2663 that are not already in scope,
2664 are brought into scope by the pattern. We describe this set as
2665 the <emphasis>type variables bound by the pattern</emphasis>.
2668 f (x::a) = let g (y::(a,b)) = fst y
2672 The pattern <literal>(x::a)</literal> brings the type variable
2673 <literal>a</literal> into scope, as well as the term
2674 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2675 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2676 and brings into scope the type variable <literal>b</literal>.
2682 The type variable(s) bound by the pattern have the same scope
2683 as the term variable(s) bound by the pattern. For example:
2686 f (x::a) = <...rhs of f...>
2687 (p::b, q::b) = (1,2)
2688 in <...body of let...>
2690 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2691 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2692 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2693 just like <literal>p</literal> and <literal>q</literal> do.
2694 Indeed, the newly bound type variables also scope over any ordinary, separate
2695 type signatures in the <literal>let</literal> group.
2702 The type variables bound by the pattern may be
2703 mentioned in ordinary type signatures or pattern
2704 type signatures anywhere within their scope.
2711 In ordinary type signatures, any type variable mentioned in the
2712 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2720 Ordinary type signatures do not bring any new type variables
2721 into scope (except in the type signature itself!). So this is illegal:
2728 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2729 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2730 and that is an incorrect typing.
2737 The pattern type signature is a monotype:
2742 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2746 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2747 not to type schemes.
2751 There is no implicit universal quantification on pattern type signatures (in contrast to
2752 ordinary type signatures).
2762 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2763 scope over the methods defined in the <literal>where</literal> part. For example:
2777 (Not implemented in Hugs yet, Dec 98).
2788 <title>Where a pattern type signature can occur</title>
2791 A pattern type signature can occur in any pattern. For example:
2796 A pattern type signature can be on an arbitrary sub-pattern, not
2801 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2810 Pattern type signatures, including the result part, can be used
2811 in lambda abstractions:
2814 (\ (x::a, y) :: a -> x)
2821 Pattern type signatures, including the result part, can be used
2822 in <literal>case</literal> expressions:
2826 case e of { (x::a, y) :: a -> x }
2834 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2835 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2836 token or a parenthesised type of some sort). To see why,
2837 consider how one would parse this:
2851 Pattern type signatures can bind existential type variables.
2856 data T = forall a. MkT [a]
2859 f (MkT [t::a]) = MkT t3
2872 Pattern type signatures
2873 can be used in pattern bindings:
2876 f x = let (y, z::a) = x in ...
2877 f1 x = let (y, z::Int) = x in ...
2878 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2879 f3 :: (b->b) = \x -> x
2882 In all such cases, the binding is not generalised over the pattern-bound
2883 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2884 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2885 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2886 In contrast, the binding
2891 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2892 in <literal>f4</literal>'s scope.
2902 <title>Result type signatures</title>
2905 The result type of a function can be given a signature, thus:
2909 f (x::a) :: [a] = [x,x,x]
2913 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2914 result type. Sometimes this is the only way of naming the type variable
2919 f :: Int -> [a] -> [a]
2920 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2921 in \xs -> map g (reverse xs `zip` xs)
2926 The type variables bound in a result type signature scope over the right hand side
2927 of the definition. However, consider this corner-case:
2929 rev1 :: [a] -> [a] = \xs -> reverse xs
2931 foo ys = rev (ys::[a])
2933 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2934 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2935 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2936 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2937 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2940 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2941 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2945 rev1 :: [a] -> [a] = \xs -> reverse xs
2950 Result type signatures are not yet implemented in Hugs.
2957 <sect2 id="deriving-typeable">
2958 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2961 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2962 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2963 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2964 classes <literal>Eq</literal>, <literal>Ord</literal>,
2965 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2968 GHC extends this list with two more classes that may be automatically derived
2969 (provided the <option>-fglasgow-exts</option> flag is specified):
2970 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2971 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
2972 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
2976 <sect2 id="newtype-deriving">
2977 <title>Generalised derived instances for newtypes</title>
2980 When you define an abstract type using <literal>newtype</literal>, you may want
2981 the new type to inherit some instances from its representation. In
2982 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
2983 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
2984 other classes you have to write an explicit instance declaration. For
2985 example, if you define
2988 newtype Dollars = Dollars Int
2991 and you want to use arithmetic on <literal>Dollars</literal>, you have to
2992 explicitly define an instance of <literal>Num</literal>:
2995 instance Num Dollars where
2996 Dollars a + Dollars b = Dollars (a+b)
2999 All the instance does is apply and remove the <literal>newtype</literal>
3000 constructor. It is particularly galling that, since the constructor
3001 doesn't appear at run-time, this instance declaration defines a
3002 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3003 dictionary, only slower!
3007 <sect3> <title> Generalising the deriving clause </title>
3009 GHC now permits such instances to be derived instead, so one can write
3011 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3014 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3015 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3016 derives an instance declaration of the form
3019 instance Num Int => Num Dollars
3022 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3026 We can also derive instances of constructor classes in a similar
3027 way. For example, suppose we have implemented state and failure monad
3028 transformers, such that
3031 instance Monad m => Monad (State s m)
3032 instance Monad m => Monad (Failure m)
3034 In Haskell 98, we can define a parsing monad by
3036 type Parser tok m a = State [tok] (Failure m) a
3039 which is automatically a monad thanks to the instance declarations
3040 above. With the extension, we can make the parser type abstract,
3041 without needing to write an instance of class <literal>Monad</literal>, via
3044 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3047 In this case the derived instance declaration is of the form
3049 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3052 Notice that, since <literal>Monad</literal> is a constructor class, the
3053 instance is a <emphasis>partial application</emphasis> of the new type, not the
3054 entire left hand side. We can imagine that the type declaration is
3055 ``eta-converted'' to generate the context of the instance
3060 We can even derive instances of multi-parameter classes, provided the
3061 newtype is the last class parameter. In this case, a ``partial
3062 application'' of the class appears in the <literal>deriving</literal>
3063 clause. For example, given the class
3066 class StateMonad s m | m -> s where ...
3067 instance Monad m => StateMonad s (State s m) where ...
3069 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3071 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3072 deriving (Monad, StateMonad [tok])
3075 The derived instance is obtained by completing the application of the
3076 class to the new type:
3079 instance StateMonad [tok] (State [tok] (Failure m)) =>
3080 StateMonad [tok] (Parser tok m)
3085 As a result of this extension, all derived instances in newtype
3086 declarations are treated uniformly (and implemented just by reusing
3087 the dictionary for the representation type), <emphasis>except</emphasis>
3088 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3089 the newtype and its representation.
3093 <sect3> <title> A more precise specification </title>
3095 Derived instance declarations are constructed as follows. Consider the
3096 declaration (after expansion of any type synonyms)
3099 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3105 <literal>S</literal> is a type constructor,
3108 The <literal>t1...tk</literal> are types,
3111 The <literal>vk+1...vn</literal> are type variables which do not occur in any of
3112 the <literal>ti</literal>, and
3115 The <literal>ci</literal> are partial applications of
3116 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3117 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3120 None of the <literal>ci</literal> is <literal>Read</literal>, <literal>Show</literal>,
3121 <literal>Typeable</literal>, or <literal>Data</literal>. These classes
3122 should not "look through" the type or its constructor. You can still
3123 derive these classes for a newtype, but it happens in the usual way, not
3124 via this new mechanism.
3127 Then, for each <literal>ci</literal>, the derived instance
3130 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3132 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3133 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3137 As an example which does <emphasis>not</emphasis> work, consider
3139 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3141 Here we cannot derive the instance
3143 instance Monad (State s m) => Monad (NonMonad m)
3146 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3147 and so cannot be "eta-converted" away. It is a good thing that this
3148 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3149 not, in fact, a monad --- for the same reason. Try defining
3150 <literal>>>=</literal> with the correct type: you won't be able to.
3154 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3155 important, since we can only derive instances for the last one. If the
3156 <literal>StateMonad</literal> class above were instead defined as
3159 class StateMonad m s | m -> s where ...
3162 then we would not have been able to derive an instance for the
3163 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3164 classes usually have one "main" parameter for which deriving new
3165 instances is most interesting.
3173 <!-- ==================== End of type system extensions ================= -->
3175 <!-- ====================== TEMPLATE HASKELL ======================= -->
3177 <sect1 id="template-haskell">
3178 <title>Template Haskell</title>
3180 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3181 Template Haskell at <ulink url="http://www.haskell.org/th/">
3182 http://www.haskell.org/th/</ulink>, while
3184 the main technical innovations is discussed in "<ulink
3185 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3186 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3187 The details of the Template Haskell design are still in flux. Make sure you
3188 consult the <ulink url="http://www.haskell.org/ghc/docs/latest/html/libraries/index.html">online library reference material</ulink>
3189 (search for the type ExpQ).
3190 [Temporary: many changes to the original design are described in
3191 <ulink url="http://research.microsoft.com/~simonpj/tmp/notes2.ps">"http://research.microsoft.com/~simonpj/tmp/notes2.ps"</ulink>.
3192 Not all of these changes are in GHC 6.2.]
3195 <para> The first example from that paper is set out below as a worked example to help get you started.
3199 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3200 Tim Sheard is going to expand it.)
3204 <title>Syntax</title>
3206 <para> Template Haskell has the following new syntactic
3207 constructions. You need to use the flag
3208 <option>-fth</option><indexterm><primary><option>-fth</option></primary>
3209 </indexterm>to switch these syntactic extensions on
3210 (<option>-fth</option> is currently implied by
3211 <option>-fglasgow-exts</option>, but you are encouraged to
3212 specify it explicitly).</para>
3216 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3217 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3218 There must be no space between the "$" and the identifier or parenthesis. This use
3219 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3220 of "." as an infix operator. If you want the infix operator, put spaces around it.
3222 <para> A splice can occur in place of
3224 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3225 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3226 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3228 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3229 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3235 A expression quotation is written in Oxford brackets, thus:
3237 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3238 the quotation has type <literal>Expr</literal>.</para></listitem>
3239 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3240 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3241 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3242 the quotation has type <literal>Type</literal>.</para></listitem>
3243 </itemizedlist></para></listitem>
3246 Reification is written thus:
3248 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3249 has type <literal>Dec</literal>. </para></listitem>
3250 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3251 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3252 <listitem><para> Still to come: fixities </para></listitem>
3254 </itemizedlist></para>
3261 <sect2> <title> Using Template Haskell </title>
3265 The data types and monadic constructor functions for Template Haskell are in the library
3266 <literal>Language.Haskell.THSyntax</literal>.
3270 You can only run a function at compile time if it is imported from another module. That is,
3271 you can't define a function in a module, and call it from within a splice in the same module.
3272 (It would make sense to do so, but it's hard to implement.)
3276 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3279 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3280 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3281 compiles and runs a program, and then looks at the result. So it's important that
3282 the program it compiles produces results whose representations are identical to
3283 those of the compiler itself.
3287 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3288 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3293 <sect2> <title> A Template Haskell Worked Example </title>
3294 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3295 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3302 -- Import our template "pr"
3303 import Printf ( pr )
3305 -- The splice operator $ takes the Haskell source code
3306 -- generated at compile time by "pr" and splices it into
3307 -- the argument of "putStrLn".
3308 main = putStrLn ( $(pr "Hello") )
3314 -- Skeletal printf from the paper.
3315 -- It needs to be in a separate module to the one where
3316 -- you intend to use it.
3318 -- Import some Template Haskell syntax
3319 import Language.Haskell.THSyntax
3321 -- Describe a format string
3322 data Format = D | S | L String
3324 -- Parse a format string. This is left largely to you
3325 -- as we are here interested in building our first ever
3326 -- Template Haskell program and not in building printf.
3327 parse :: String -> [Format]
3330 -- Generate Haskell source code from a parsed representation
3331 -- of the format string. This code will be spliced into
3332 -- the module which calls "pr", at compile time.
3333 gen :: [Format] -> ExpQ
3334 gen [D] = [| \n -> show n |]
3335 gen [S] = [| \s -> s |]
3336 gen [L s] = stringE s
3338 -- Here we generate the Haskell code for the splice
3339 -- from an input format string.
3340 pr :: String -> ExpQ
3341 pr s = gen (parse s)
3344 <para>Now run the compiler (here we are a Cygwin prompt on Windows):
3347 $ ghc --make -fth main.hs -o main.exe
3350 <para>Run "main.exe" and here is your output:</para>
3361 <!-- ===================== Arrow notation =================== -->
3363 <sect1 id="arrow-notation">
3364 <title>Arrow notation
3367 <para>Arrows are a generalization of monads introduced by John Hughes.
3368 For more details, see
3373 “Generalising Monads to Arrows”,
3374 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3375 pp67–111, May 2000.
3381 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3382 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3388 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3389 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3395 and the arrows web page at
3396 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3397 With the <option>-farrows</option> flag, GHC supports the arrow
3398 notation described in the second of these papers.
3399 What follows is a brief introduction to the notation;
3400 it won't make much sense unless you've read Hughes's paper.
3401 This notation is translated to ordinary Haskell,
3402 using combinators from the
3403 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3407 <para>The extension adds a new kind of expression for defining arrows,
3408 of the form <literal>proc pat -> cmd</literal>,
3409 where <literal>proc</literal> is a new keyword.
3410 The variables of the pattern are bound in the body of the
3411 <literal>proc</literal>-expression,
3412 which is a new sort of thing called a <firstterm>command</firstterm>.
3413 The syntax of commands is as follows:
3415 cmd ::= exp1 -< exp2
3416 | exp1 -<< exp2
3417 | do { cstmt1 .. cstmtn ; cmd }
3419 | if exp then cmd1 else cmd2
3420 | case exp of { calts }
3422 | (| aexp cmd1 .. cmdn |)
3423 | \ pat1 .. patn -> cmd
3429 | rec { cstmt1 .. cstmtn }
3432 Commands produce values, but (like monadic computations)
3433 may yield more than one value,
3434 or none, and may do other things as well.
3435 For the most part, familiarity with monadic notation is a good guide to
3437 However the values of expressions, even monadic ones,
3438 are determined by the values of the variables they contain;
3439 this is not necessarily the case for commands.
3443 A simple example of the new notation is the expression
3445 proc x -> f -< x+1
3447 We call this a <firstterm>procedure</firstterm> or
3448 <firstterm>arrow abstraction</firstterm>.
3449 As with a lambda expression, the variable <literal>x</literal>
3450 is a new variable bound within the <literal>proc</literal>-expression.
3451 It refers to the input to the arrow.
3452 In the above example, <literal>-<</literal> is not an identifier but an
3453 new reserved symbol used for building commands from an expression of arrow
3454 type and an expression to be fed as input to that arrow.
3455 (The weird look will make more sense later.)
3456 It may be read as analogue of application for arrows.
3457 The above example is equivalent to the Haskell expression
3459 arr (\ x -> x+1) >>> f
3461 That would make no sense if the expression to the left of
3462 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3463 More generally, the expression to the left of <literal>-<</literal>
3464 may not involve any <firstterm>local variable</firstterm>,
3465 i.e. a variable bound in the current arrow abstraction.
3466 For such a situation there is a variant <literal>-<<</literal>, as in
3468 proc x -> f x -<< x+1
3470 which is equivalent to
3472 arr (\ x -> (f, x+1)) >>> app
3474 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3476 Such an arrow is equivalent to a monad, so if you're using this form
3477 you may find a monadic formulation more convenient.
3481 <title>do-notation for commands</title>
3484 Another form of command is a form of <literal>do</literal>-notation.
3485 For example, you can write
3494 You can read this much like ordinary <literal>do</literal>-notation,
3495 but with commands in place of monadic expressions.
3496 The first line sends the value of <literal>x+1</literal> as an input to
3497 the arrow <literal>f</literal>, and matches its output against
3498 <literal>y</literal>.
3499 In the next line, the output is discarded.
3500 The arrow <literal>returnA</literal> is defined in the
3501 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3502 module as <literal>arr id</literal>.
3503 The above example is treated as an abbreviation for
3505 arr (\ x -> (x, x)) >>>
3506 first (arr (\ x -> x+1) >>> f) >>>
3507 arr (\ (y, x) -> (y, (x, y))) >>>
3508 first (arr (\ y -> 2*y) >>> g) >>>
3510 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3511 first (arr (\ (x, z) -> x*z) >>> h) >>>
3512 arr (\ (t, z) -> t+z) >>>
3515 Note that variables not used later in the composition are projected out.
3516 After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
3518 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3519 module, this reduces to
3521 arr (\ x -> (x+1, x)) >>>
3523 arr (\ (y, x) -> (2*y, (x, y))) >>>
3525 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3527 arr (\ (t, z) -> t+z)
3529 which is what you might have written by hand.
3530 With arrow notation, GHC keeps track of all those tuples of variables for you.
3534 Note that although the above translation suggests that
3535 <literal>let</literal>-bound variables like <literal>z</literal> must be
3536 monomorphic, the actual translation produces Core,
3537 so polymorphic variables are allowed.
3541 It's also possible to have mutually recursive bindings,
3542 using the new <literal>rec</literal> keyword, as in the following example:
3544 counter :: ArrowCircuit a => a Bool Int
3545 counter = proc reset -> do
3546 rec output <- returnA -< if reset then 0 else next
3547 next <- delay 0 -< output+1
3548 returnA -< output
3550 The translation of such forms uses the <literal>loop</literal> combinator,
3551 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3557 <title>Conditional commands</title>
3560 In the previous example, we used a conditional expression to construct the
3562 Sometimes we want to conditionally execute different commands, as in
3569 which is translated to
3571 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3572 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3574 Since the translation uses <literal>|||</literal>,
3575 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3579 There are also <literal>case</literal> commands, like
3585 y <- h -< (x1, x2)
3589 The syntax is the same as for <literal>case</literal> expressions,
3590 except that the bodies of the alternatives are commands rather than expressions.
3591 The translation is similar to that of <literal>if</literal> commands.
3597 <title>Defining your own control structures</title>
3600 As we're seen, arrow notation provides constructs,
3601 modelled on those for expressions,
3602 for sequencing, value recursion and conditionals.
3603 But suitable combinators,
3604 which you can define in ordinary Haskell,
3605 may also be used to build new commands out of existing ones.
3606 The basic idea is that a command defines an arrow from environments to values.
3607 These environments assign values to the free local variables of the command.
3608 Thus combinators that produce arrows from arrows
3609 may also be used to build commands from commands.
3610 For example, the <literal>ArrowChoice</literal> class includes a combinator
3612 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3614 so we can use it to build commands:
3619 symbol Plus -< ()
3620 y <- term -< ()
3623 symbol Minus -< ()
3624 y <- term -< ()
3627 This is equivalent to
3629 expr' = (proc x -> returnA -< x)
3630 <+> (proc x -> do
3631 symbol Plus -< ()
3632 y <- term -< ()
3634 <+> (proc x -> do
3635 symbol Minus -< ()
3636 y <- term -< ()
3639 It is essential that this operator be polymorphic in <literal>e</literal>
3640 (representing the environment input to the command
3641 and thence to its subcommands)
3642 and satisfy the corresponding naturality property
3644 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3646 at least for strict <literal>k</literal>.
3647 (This should be automatic if you're not using <literal>seq</literal>.)
3648 This ensures that environments seen by the subcommands are environments
3649 of the whole command,
3650 and also allows the translation to safely trim these environments.
3651 The operator must also not use any variable defined within the current
3656 We could define our own operator
3658 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3659 untilA body cond = proc x ->
3660 if cond x then returnA -< ()
3663 untilA body cond -< x
3665 and use it in the same way.
3666 Of course this infix syntax only makes sense for binary operators;
3667 there is also a more general syntax involving special brackets:
3671 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3678 <title>Primitive constructs</title>
3681 Some operators will need to pass additional inputs to their subcommands.
3682 For example, in an arrow type supporting exceptions,
3683 the operator that attaches an exception handler will wish to pass the
3684 exception that occurred to the handler.
3685 Such an operator might have a type
3687 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3689 where <literal>Ex</literal> is the type of exceptions handled.
3690 You could then use this with arrow notation by writing a command
3692 body `handleA` \ ex -> handler
3694 so that if an exception is raised in the command <literal>body</literal>,
3695 the variable <literal>ex</literal> is bound to the value of the exception
3696 and the command <literal>handler</literal>,
3697 which typically refers to <literal>ex</literal>, is entered.
3698 Though the syntax here looks like a functional lambda,
3699 we are talking about commands, and something different is going on.
3700 The input to the arrow represented by a command consists of values for
3701 the free local variables in the command, plus a stack of anonymous values.
3702 In all the prior examples, this stack was empty.
3703 In the second argument to <literal>handleA</literal>,
3704 this stack consists of one value, the value of the exception.
3705 The command form of lambda merely gives this value a name.
3710 the values on the stack are paired to the right of the environment.
3711 So when designing operators like <literal>handleA</literal> that pass
3712 extra inputs to their subcommands,
3713 More precisely, the type of each argument of the operator (and its result)
3714 should have the form
3716 a (...(e,t1), ... tn) t
3718 where <replaceable>e</replaceable> is a polymorphic variable
3719 (representing the environment)
3720 and <replaceable>ti</replaceable> are the types of the values on the stack,
3721 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3722 The polymorphic variable <replaceable>e</replaceable> must not occur in
3723 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3724 <replaceable>t</replaceable>.
3725 However the arrows involved need not be the same.
3726 Here are some more examples of suitable operators:
3728 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3729 runReader :: ... => a e c -> a' (e,State) c
3730 runState :: ... => a e c -> a' (e,State) (c,State)
3732 We can supply the extra input required by commands built with the last two
3733 by applying them to ordinary expressions, as in
3737 (|runReader (do { ... })|) s
3739 which adds <literal>s</literal> to the stack of inputs to the command
3740 built using <literal>runReader</literal>.
3744 The command versions of lambda abstraction and application are analogous to
3745 the expression versions.
3746 In particular, the beta and eta rules describe equivalences of commands.
3747 These three features (operators, lambda abstraction and application)
3748 are the core of the notation; everything else can be built using them,
3749 though the results would be somewhat clumsy.
3750 For example, we could simulate <literal>do</literal>-notation by defining
3752 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3753 u `bind` f = returnA &&& u >>> f
3755 bind_ :: Arrow a => a e b -> a e c -> a e c
3756 u `bind_` f = u `bind` (arr fst >>> f)
3758 We could simulate <literal>do</literal> by defining
3760 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3761 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3768 <title>Differences with the paper</title>
3773 <para>Instead of a single form of arrow application (arrow tail) with two
3774 translations, the implementation provides two forms
3775 <quote><literal>-<</literal></quote> (first-order)
3776 and <quote><literal>-<<</literal></quote> (higher-order).
3781 <para>User-defined operators are flagged with banana brackets instead of
3782 a new <literal>form</literal> keyword.
3791 <title>Portability</title>
3794 Although only GHC implements arrow notation directly,
3795 there is also a preprocessor
3797 <ulink url="http://www.haskell.org/arrows/">arrows web page</ulink>)
3798 that translates arrow notation into Haskell 98
3799 for use with other Haskell systems.
3800 You would still want to check arrow programs with GHC;
3801 tracing type errors in the preprocessor output is not easy.
3802 Modules intended for both GHC and the preprocessor must observe some
3803 additional restrictions:
3808 The module must import
3809 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3815 The preprocessor cannot cope with other Haskell extensions.
3816 These would have to go in separate modules.
3822 Because the preprocessor targets Haskell (rather than Core),
3823 <literal>let</literal>-bound variables are monomorphic.
3834 <!-- ==================== ASSERTIONS ================= -->
3836 <sect1 id="sec-assertions">
3838 <indexterm><primary>Assertions</primary></indexterm>
3842 If you want to make use of assertions in your standard Haskell code, you
3843 could define a function like the following:
3849 assert :: Bool -> a -> a
3850 assert False x = error "assertion failed!"
3857 which works, but gives you back a less than useful error message --
3858 an assertion failed, but which and where?
3862 One way out is to define an extended <function>assert</function> function which also
3863 takes a descriptive string to include in the error message and
3864 perhaps combine this with the use of a pre-processor which inserts
3865 the source location where <function>assert</function> was used.
3869 Ghc offers a helping hand here, doing all of this for you. For every
3870 use of <function>assert</function> in the user's source:
3876 kelvinToC :: Double -> Double
3877 kelvinToC k = assert (k >= 0.0) (k+273.15)
3883 Ghc will rewrite this to also include the source location where the
3890 assert pred val ==> assertError "Main.hs|15" pred val
3896 The rewrite is only performed by the compiler when it spots
3897 applications of <function>Control.Exception.assert</function>, so you
3898 can still define and use your own versions of
3899 <function>assert</function>, should you so wish. If not, import
3900 <literal>Control.Exception</literal> to make use
3901 <function>assert</function> in your code.
3905 To have the compiler ignore uses of assert, use the compiler option
3906 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3907 option</primary></indexterm> That is, expressions of the form
3908 <literal>assert pred e</literal> will be rewritten to
3909 <literal>e</literal>.
3913 Assertion failures can be caught, see the documentation for the
3914 <literal>Control.Exception</literal> library for the details.
3920 <!-- =============================== PRAGMAS =========================== -->
3922 <sect1 id="pragmas">
3923 <title>Pragmas</title>
3925 <indexterm><primary>pragma</primary></indexterm>
3927 <para>GHC supports several pragmas, or instructions to the
3928 compiler placed in the source code. Pragmas don't normally affect
3929 the meaning of the program, but they might affect the efficiency
3930 of the generated code.</para>
3932 <para>Pragmas all take the form
3934 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3936 where <replaceable>word</replaceable> indicates the type of
3937 pragma, and is followed optionally by information specific to that
3938 type of pragma. Case is ignored in
3939 <replaceable>word</replaceable>. The various values for
3940 <replaceable>word</replaceable> that GHC understands are described
3941 in the following sections; any pragma encountered with an
3942 unrecognised <replaceable>word</replaceable> is (silently)
3945 <sect2 id="deprecated-pragma">
3946 <title>DEPRECATED pragma</title>
3947 <indexterm><primary>DEPRECATED</primary>
3950 <para>The DEPRECATED pragma lets you specify that a particular
3951 function, class, or type, is deprecated. There are two
3956 <para>You can deprecate an entire module thus:</para>
3958 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3961 <para>When you compile any module that import
3962 <literal>Wibble</literal>, GHC will print the specified
3967 <para>You can deprecate a function, class, or type, with the
3968 following top-level declaration:</para>
3970 {-# DEPRECATED f, C, T "Don't use these" #-}
3972 <para>When you compile any module that imports and uses any
3973 of the specifed entities, GHC will print the specified
3977 Any use of the deprecated item, or of anything from a deprecated
3978 module, will be flagged with an appropriate message. However,
3979 deprecations are not reported for
3980 (a) uses of a deprecated function within its defining module, and
3981 (b) uses of a deprecated function in an export list.
3982 The latter reduces spurious complaints within a library
3983 in which one module gathers together and re-exports
3984 the exports of several others.
3986 <para>You can suppress the warnings with the flag
3987 <option>-fno-warn-deprecations</option>.</para>
3990 <sect2 id="inline-noinline-pragma">
3991 <title>INLINE and NOINLINE pragmas</title>
3993 <para>These pragmas control the inlining of function
3996 <sect3 id="inline-pragma">
3997 <title>INLINE pragma</title>
3998 <indexterm><primary>INLINE</primary></indexterm>
4000 <para>GHC (with <option>-O</option>, as always) tries to
4001 inline (or “unfold”) functions/values that are
4002 “small enough,” thus avoiding the call overhead
4003 and possibly exposing other more-wonderful optimisations.
4004 Normally, if GHC decides a function is “too
4005 expensive” to inline, it will not do so, nor will it
4006 export that unfolding for other modules to use.</para>
4008 <para>The sledgehammer you can bring to bear is the
4009 <literal>INLINE</literal><indexterm><primary>INLINE
4010 pragma</primary></indexterm> pragma, used thusly:</para>
4013 key_function :: Int -> String -> (Bool, Double)
4015 #ifdef __GLASGOW_HASKELL__
4016 {-# INLINE key_function #-}
4020 <para>(You don't need to do the C pre-processor carry-on
4021 unless you're going to stick the code through HBC—it
4022 doesn't like <literal>INLINE</literal> pragmas.)</para>
4024 <para>The major effect of an <literal>INLINE</literal> pragma
4025 is to declare a function's “cost” to be very low.
4026 The normal unfolding machinery will then be very keen to
4029 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4030 function can be put anywhere its type signature could be
4033 <para><literal>INLINE</literal> pragmas are a particularly
4035 <literal>then</literal>/<literal>return</literal> (or
4036 <literal>bind</literal>/<literal>unit</literal>) functions in
4037 a monad. For example, in GHC's own
4038 <literal>UniqueSupply</literal> monad code, we have:</para>
4041 #ifdef __GLASGOW_HASKELL__
4042 {-# INLINE thenUs #-}
4043 {-# INLINE returnUs #-}
4047 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4048 linkend="noinline-pragma">).</para>
4051 <sect3 id="noinline-pragma">
4052 <title>NOINLINE pragma</title>
4054 <indexterm><primary>NOINLINE</primary></indexterm>
4055 <indexterm><primary>NOTINLINE</primary></indexterm>
4057 <para>The <literal>NOINLINE</literal> pragma does exactly what
4058 you'd expect: it stops the named function from being inlined
4059 by the compiler. You shouldn't ever need to do this, unless
4060 you're very cautious about code size.</para>
4062 <para><literal>NOTINLINE</literal> is a synonym for
4063 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4064 specified by Haskell 98 as the standard way to disable
4065 inlining, so it should be used if you want your code to be
4069 <sect3 id="phase-control">
4070 <title>Phase control</title>
4072 <para> Sometimes you want to control exactly when in GHC's
4073 pipeline the INLINE pragma is switched on. Inlining happens
4074 only during runs of the <emphasis>simplifier</emphasis>. Each
4075 run of the simplifier has a different <emphasis>phase
4076 number</emphasis>; the phase number decreases towards zero.
4077 If you use <option>-dverbose-core2core</option> you'll see the
4078 sequence of phase numbers for successive runs of the
4079 simpifier. In an INLINE pragma you can optionally specify a
4080 phase number, thus:</para>
4084 <para>You can say "inline <literal>f</literal> in Phase 2
4085 and all subsequent phases":
4087 {-# INLINE [2] f #-}
4093 <para>You can say "inline <literal>g</literal> in all
4094 phases up to, but not including, Phase 3":
4096 {-# INLINE [~3] g #-}
4102 <para>If you omit the phase indicator, you mean "inline in
4107 <para>You can use a phase number on a NOINLINE pragma too:</para>
4111 <para>You can say "do not inline <literal>f</literal>
4112 until Phase 2; in Phase 2 and subsequently behave as if
4113 there was no pragma at all":
4115 {-# NOINLINE [2] f #-}
4121 <para>You can say "do not inline <literal>g</literal> in
4122 Phase 3 or any subsequent phase; before that, behave as if
4123 there was no pragma":
4125 {-# NOINLINE [~3] g #-}
4131 <para>If you omit the phase indicator, you mean "never
4132 inline this function".</para>
4136 <para>The same phase-numbering control is available for RULES
4137 (<xref LinkEnd="rewrite-rules">).</para>
4141 <sect2 id="line-pragma">
4142 <title>LINE pragma</title>
4144 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4145 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4146 <para>This pragma is similar to C's <literal>#line</literal>
4147 pragma, and is mainly for use in automatically generated Haskell
4148 code. It lets you specify the line number and filename of the
4149 original code; for example</para>
4152 {-# LINE 42 "Foo.vhs" #-}
4155 <para>if you'd generated the current file from something called
4156 <filename>Foo.vhs</filename> and this line corresponds to line
4157 42 in the original. GHC will adjust its error messages to refer
4158 to the line/file named in the <literal>LINE</literal>
4162 <sect2 id="options-pragma">
4163 <title>OPTIONS pragma</title>
4164 <indexterm><primary>OPTIONS</primary>
4166 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4169 <para>The <literal>OPTIONS</literal> pragma is used to specify
4170 additional options that are given to the compiler when compiling
4171 this source file. See <xref linkend="source-file-options"> for
4176 <title>RULES pragma</title>
4178 <para>The RULES pragma lets you specify rewrite rules. It is
4179 described in <xref LinkEnd="rewrite-rules">.</para>
4182 <sect2 id="specialize-pragma">
4183 <title>SPECIALIZE pragma</title>
4185 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4186 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4187 <indexterm><primary>overloading, death to</primary></indexterm>
4189 <para>(UK spelling also accepted.) For key overloaded
4190 functions, you can create extra versions (NB: more code space)
4191 specialised to particular types. Thus, if you have an
4192 overloaded function:</para>
4195 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4198 <para>If it is heavily used on lists with
4199 <literal>Widget</literal> keys, you could specialise it as
4203 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4206 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4207 be put anywhere its type signature could be put.</para>
4209 <para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
4210 version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
4211 rewrites a call to the un-specialised function into a call to the specialised
4212 one. You can, instead, provide your own specialised function and your own rewrite rule.
4213 For example, suppose that:
4215 genericLookup :: Ord a => Table a b -> a -> b
4216 intLookup :: Table Int b -> Int -> b
4218 where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
4219 that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
4221 {-# RULES "intLookup" genericLookup = intLookup #-}
4223 (see <xref linkend="rule-spec">). It is <emphasis>Your
4224 Responsibility</emphasis> to make sure that
4225 <function>intLookup</function> really behaves as a specialised
4226 version of <function>genericLookup</function>!!!</para>
4228 <para>An example in which using <literal>RULES</literal> for
4229 specialisation will Win Big:
4232 toDouble :: Real a => a -> Double
4233 toDouble = fromRational . toRational
4235 {-# RULES "toDouble/Int" toDouble = i2d #-}
4236 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4239 The <function>i2d</function> function is virtually one machine
4240 instruction; the default conversion—via an intermediate
4241 <literal>Rational</literal>—is obscenely expensive by
4246 <sect2 id="specialize-instance-pragma">
4247 <title>SPECIALIZE instance pragma
4251 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4252 <indexterm><primary>overloading, death to</primary></indexterm>
4253 Same idea, except for instance declarations. For example:
4256 instance (Eq a) => Eq (Foo a) where {
4257 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4261 The pragma must occur inside the <literal>where</literal> part
4262 of the instance declaration.
4265 Compatible with HBC, by the way, except perhaps in the placement
4271 <sect2 id="unpack-pragma">
4272 <title>UNPACK pragma</title>
4274 <indexterm><primary>UNPACK</primary></indexterm>
4276 <para>The <literal>UNPACK</literal> indicates to the compiler
4277 that it should unpack the contents of a constructor field into
4278 the constructor itself, removing a level of indirection. For
4282 data T = T {-# UNPACK #-} !Float
4283 {-# UNPACK #-} !Float
4286 <para>will create a constructor <literal>T</literal> containing
4287 two unboxed floats. This may not always be an optimisation: if
4288 the <Function>T</Function> constructor is scrutinised and the
4289 floats passed to a non-strict function for example, they will
4290 have to be reboxed (this is done automatically by the
4293 <para>Unpacking constructor fields should only be used in
4294 conjunction with <option>-O</option>, in order to expose
4295 unfoldings to the compiler so the reboxing can be removed as
4296 often as possible. For example:</para>
4300 f (T f1 f2) = f1 + f2
4303 <para>The compiler will avoid reboxing <Function>f1</Function>
4304 and <Function>f2</Function> by inlining <Function>+</Function>
4305 on floats, but only when <option>-O</option> is on.</para>
4307 <para>Any single-constructor data is eligible for unpacking; for
4311 data T = T {-# UNPACK #-} !(Int,Int)
4314 <para>will store the two <literal>Int</literal>s directly in the
4315 <Function>T</Function> constructor, by flattening the pair.
4316 Multi-level unpacking is also supported:</para>
4319 data T = T {-# UNPACK #-} !S
4320 data S = S {-# UNPACK #-} !Int {-# UNPACK #-} !Int
4323 <para>will store two unboxed <literal>Int#</literal>s
4324 directly in the <Function>T</Function> constructor. The
4325 unpacker can see through newtypes, too.</para>
4327 <para>If a field cannot be unpacked, you will not get a warning,
4328 so it might be an idea to check the generated code with
4329 <option>-ddump-simpl</option>.</para>
4331 <para>See also the <option>-funbox-strict-fields</option> flag,
4332 which essentially has the effect of adding
4333 <literal>{-# UNPACK #-}</literal> to every strict
4334 constructor field.</para>
4339 <!-- ======================= REWRITE RULES ======================== -->
4341 <sect1 id="rewrite-rules">
4342 <title>Rewrite rules
4344 <indexterm><primary>RULES pagma</primary></indexterm>
4345 <indexterm><primary>pragma, RULES</primary></indexterm>
4346 <indexterm><primary>rewrite rules</primary></indexterm></title>
4349 The programmer can specify rewrite rules as part of the source program
4350 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4351 the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
4352 and (b) the <option>-frules-off</option> flag
4353 (<xref LinkEnd="options-f">) is not specified.
4361 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4368 <title>Syntax</title>
4371 From a syntactic point of view:
4377 There may be zero or more rules in a <literal>RULES</literal> pragma.
4384 Each rule has a name, enclosed in double quotes. The name itself has
4385 no significance at all. It is only used when reporting how many times the rule fired.
4391 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
4392 immediately after the name of the rule. Thus:
4395 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4398 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4399 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4408 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4409 is set, so you must lay out your rules starting in the same column as the
4410 enclosing definitions.
4417 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4418 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4419 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4420 by spaces, just like in a type <literal>forall</literal>.
4426 A pattern variable may optionally have a type signature.
4427 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4428 For example, here is the <literal>foldr/build</literal> rule:
4431 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4432 foldr k z (build g) = g k z
4435 Since <function>g</function> has a polymorphic type, it must have a type signature.
4442 The left hand side of a rule must consist of a top-level variable applied
4443 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4446 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4447 "wrong2" forall f. f True = True
4450 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4457 A rule does not need to be in the same module as (any of) the
4458 variables it mentions, though of course they need to be in scope.
4464 Rules are automatically exported from a module, just as instance declarations are.
4475 <title>Semantics</title>
4478 From a semantic point of view:
4484 Rules are only applied if you use the <option>-O</option> flag.
4490 Rules are regarded as left-to-right rewrite rules.
4491 When GHC finds an expression that is a substitution instance of the LHS
4492 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4493 By "a substitution instance" we mean that the LHS can be made equal to the
4494 expression by substituting for the pattern variables.
4501 The LHS and RHS of a rule are typechecked, and must have the
4509 GHC makes absolutely no attempt to verify that the LHS and RHS
4510 of a rule have the same meaning. That is undecideable in general, and
4511 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4518 GHC makes no attempt to make sure that the rules are confluent or
4519 terminating. For example:
4522 "loop" forall x,y. f x y = f y x
4525 This rule will cause the compiler to go into an infinite loop.
4532 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4538 GHC currently uses a very simple, syntactic, matching algorithm
4539 for matching a rule LHS with an expression. It seeks a substitution
4540 which makes the LHS and expression syntactically equal modulo alpha
4541 conversion. The pattern (rule), but not the expression, is eta-expanded if
4542 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4543 But not beta conversion (that's called higher-order matching).
4547 Matching is carried out on GHC's intermediate language, which includes
4548 type abstractions and applications. So a rule only matches if the
4549 types match too. See <xref LinkEnd="rule-spec"> below.
4555 GHC keeps trying to apply the rules as it optimises the program.
4556 For example, consider:
4565 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4566 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4567 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4568 not be substituted, and the rule would not fire.
4575 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4576 that appears on the LHS of a rule</emphasis>, because once you have substituted
4577 for something you can't match against it (given the simple minded
4578 matching). So if you write the rule
4581 "map/map" forall f,g. map f . map g = map (f.g)
4584 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4585 It will only match something written with explicit use of ".".
4586 Well, not quite. It <emphasis>will</emphasis> match the expression
4592 where <function>wibble</function> is defined:
4595 wibble f g = map f . map g
4598 because <function>wibble</function> will be inlined (it's small).
4600 Later on in compilation, GHC starts inlining even things on the
4601 LHS of rules, but still leaves the rules enabled. This inlining
4602 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4609 All rules are implicitly exported from the module, and are therefore
4610 in force in any module that imports the module that defined the rule, directly
4611 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4612 in force when compiling A.) The situation is very similar to that for instance
4624 <title>List fusion</title>
4627 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4628 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4629 intermediate list should be eliminated entirely.
4633 The following are good producers:
4645 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4651 Explicit lists (e.g. <literal>[True, False]</literal>)
4657 The cons constructor (e.g <literal>3:4:[]</literal>)
4663 <function>++</function>
4669 <function>map</function>
4675 <function>filter</function>
4681 <function>iterate</function>, <function>repeat</function>
4687 <function>zip</function>, <function>zipWith</function>
4696 The following are good consumers:
4708 <function>array</function> (on its second argument)
4714 <function>length</function>
4720 <function>++</function> (on its first argument)
4726 <function>foldr</function>
4732 <function>map</function>
4738 <function>filter</function>
4744 <function>concat</function>
4750 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4756 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4757 will fuse with one but not the other)
4763 <function>partition</function>
4769 <function>head</function>
4775 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4781 <function>sequence_</function>
4787 <function>msum</function>
4793 <function>sortBy</function>
4802 So, for example, the following should generate no intermediate lists:
4805 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4811 This list could readily be extended; if there are Prelude functions that you use
4812 a lot which are not included, please tell us.
4816 If you want to write your own good consumers or producers, look at the
4817 Prelude definitions of the above functions to see how to do so.
4822 <sect2 id="rule-spec">
4823 <title>Specialisation
4827 Rewrite rules can be used to get the same effect as a feature
4828 present in earlier version of GHC:
4831 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4834 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4835 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4836 specialising the original definition of <function>fromIntegral</function> the programmer is
4837 promising that it is safe to use <function>int8ToInt16</function> instead.
4841 This feature is no longer in GHC. But rewrite rules let you do the
4846 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4850 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4851 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4852 GHC adds the type and dictionary applications to get the typed rule
4855 forall (d1::Integral Int8) (d2::Num Int16) .
4856 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4860 this rule does not need to be in the same file as fromIntegral,
4861 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4862 have an original definition available to specialise).
4868 <title>Controlling what's going on</title>
4876 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4882 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4883 If you add <option>-dppr-debug</option> you get a more detailed listing.
4889 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4892 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4893 {-# INLINE build #-}
4897 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4898 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4899 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4900 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4907 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4908 see how to write rules that will do fusion and yet give an efficient
4909 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4919 <sect2 id="core-pragma">
4920 <title>CORE pragma</title>
4922 <indexterm><primary>CORE pragma</primary></indexterm>
4923 <indexterm><primary>pragma, CORE</primary></indexterm>
4924 <indexterm><primary>core, annotation</primary></indexterm>
4927 The external core format supports <quote>Note</quote> annotations;
4928 the <literal>CORE</literal> pragma gives a way to specify what these
4929 should be in your Haskell source code. Syntactically, core
4930 annotations are attached to expressions and take a Haskell string
4931 literal as an argument. The following function definition shows an
4935 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4938 Sematically, this is equivalent to:
4946 However, when external for is generated (via
4947 <option>-fext-core</option>), there will be Notes attached to the
4948 expressions <function>show</function> and <VarName>x</VarName>.
4949 The core function declaration for <function>f</function> is:
4953 f :: %forall a . GHCziShow.ZCTShow a ->
4954 a -> GHCziBase.ZMZN GHCziBase.Char =
4955 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4957 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4959 (tpl1::GHCziBase.Int ->
4961 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4963 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4964 (tpl3::GHCziBase.ZMZN a ->
4965 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4973 Here, we can see that the function <function>show</function> (which
4974 has been expanded out to a case expression over the Show dictionary)
4975 has a <literal>%note</literal> attached to it, as does the
4976 expression <VarName>eta</VarName> (which used to be called
4977 <VarName>x</VarName>).
4984 <sect1 id="generic-classes">
4985 <title>Generic classes</title>
4987 <para>(Note: support for generic classes is currently broken in
4991 The ideas behind this extension are described in detail in "Derivable type classes",
4992 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4993 An example will give the idea:
5001 fromBin :: [Int] -> (a, [Int])
5003 toBin {| Unit |} Unit = []
5004 toBin {| a :+: b |} (Inl x) = 0 : toBin x
5005 toBin {| a :+: b |} (Inr y) = 1 : toBin y
5006 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
5008 fromBin {| Unit |} bs = (Unit, bs)
5009 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
5010 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
5011 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
5012 (y,bs'') = fromBin bs'
5015 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
5016 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
5017 which are defined thus in the library module <literal>Generics</literal>:
5021 data a :+: b = Inl a | Inr b
5022 data a :*: b = a :*: b
5025 Now you can make a data type into an instance of Bin like this:
5027 instance (Bin a, Bin b) => Bin (a,b)
5028 instance Bin a => Bin [a]
5030 That is, just leave off the "where" clause. Of course, you can put in the
5031 where clause and over-ride whichever methods you please.
5035 <title> Using generics </title>
5036 <para>To use generics you need to</para>
5039 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
5040 <option>-fgenerics</option> (to generate extra per-data-type code),
5041 and <option>-package lang</option> (to make the <literal>Generics</literal> library
5045 <para>Import the module <literal>Generics</literal> from the
5046 <literal>lang</literal> package. This import brings into
5047 scope the data types <literal>Unit</literal>,
5048 <literal>:*:</literal>, and <literal>:+:</literal>. (You
5049 don't need this import if you don't mention these types
5050 explicitly; for example, if you are simply giving instance
5051 declarations.)</para>
5056 <sect2> <title> Changes wrt the paper </title>
5058 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
5059 can be written infix (indeed, you can now use
5060 any operator starting in a colon as an infix type constructor). Also note that
5061 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
5062 Finally, note that the syntax of the type patterns in the class declaration
5063 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5064 alone would ambiguous when they appear on right hand sides (an extension we
5065 anticipate wanting).
5069 <sect2> <title>Terminology and restrictions</title>
5071 Terminology. A "generic default method" in a class declaration
5072 is one that is defined using type patterns as above.
5073 A "polymorphic default method" is a default method defined as in Haskell 98.
5074 A "generic class declaration" is a class declaration with at least one
5075 generic default method.
5083 Alas, we do not yet implement the stuff about constructor names and
5090 A generic class can have only one parameter; you can't have a generic
5091 multi-parameter class.
5097 A default method must be defined entirely using type patterns, or entirely
5098 without. So this is illegal:
5101 op :: a -> (a, Bool)
5102 op {| Unit |} Unit = (Unit, True)
5105 However it is perfectly OK for some methods of a generic class to have
5106 generic default methods and others to have polymorphic default methods.
5112 The type variable(s) in the type pattern for a generic method declaration
5113 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:
5117 op {| p :*: q |} (x :*: y) = op (x :: p)
5125 The type patterns in a generic default method must take one of the forms:
5131 where "a" and "b" are type variables. Furthermore, all the type patterns for
5132 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5133 must use the same type variables. So this is illegal:
5137 op {| a :+: b |} (Inl x) = True
5138 op {| p :+: q |} (Inr y) = False
5140 The type patterns must be identical, even in equations for different methods of the class.
5141 So this too is illegal:
5145 op1 {| a :*: b |} (x :*: y) = True
5148 op2 {| p :*: q |} (x :*: y) = False
5150 (The reason for this restriction is that we gather all the equations for a particular type consructor
5151 into a single generic instance declaration.)
5157 A generic method declaration must give a case for each of the three type constructors.
5163 The type for a generic method can be built only from:
5165 <listitem> <para> Function arrows </para> </listitem>
5166 <listitem> <para> Type variables </para> </listitem>
5167 <listitem> <para> Tuples </para> </listitem>
5168 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5170 Here are some example type signatures for generic methods:
5173 op2 :: Bool -> (a,Bool)
5174 op3 :: [Int] -> a -> a
5177 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5181 This restriction is an implementation restriction: we just havn't got around to
5182 implementing the necessary bidirectional maps over arbitrary type constructors.
5183 It would be relatively easy to add specific type constructors, such as Maybe and list,
5184 to the ones that are allowed.</para>
5189 In an instance declaration for a generic class, the idea is that the compiler
5190 will fill in the methods for you, based on the generic templates. However it can only
5195 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5200 No constructor of the instance type has unboxed fields.
5204 (Of course, these things can only arise if you are already using GHC extensions.)
5205 However, you can still give an instance declarations for types which break these rules,
5206 provided you give explicit code to override any generic default methods.
5214 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5215 what the compiler does with generic declarations.
5220 <sect2> <title> Another example </title>
5222 Just to finish with, here's another example I rather like:
5226 nCons {| Unit |} _ = 1
5227 nCons {| a :*: b |} _ = 1
5228 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5231 tag {| Unit |} _ = 1
5232 tag {| a :*: b |} _ = 1
5233 tag {| a :+: b |} (Inl x) = tag x
5234 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5243 ;;; Local Variables: ***
5245 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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