2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
6 <indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-fgenerics</option></term>
114 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
116 <para>See <xref LinkEnd="generic-classes">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fno-implicit-prelude</option></term>
124 <para><indexterm><primary>-fno-implicit-prelude
125 option</primary></indexterm> GHC normally imports
126 <filename>Prelude.hi</filename> files for you. If you'd
127 rather it didn't, then give it a
128 <option>-fno-implicit-prelude</option> option. The idea
129 is that you can then import a Prelude of your own. (But
130 don't call it <literal>Prelude</literal>; the Haskell
131 module namespace is flat, and you must not conflict with
132 any Prelude module.)</para>
134 <para>Even though you have not imported the Prelude, most of
135 the built-in syntax still refers to the built-in Haskell
136 Prelude types and values, as specified by the Haskell
137 Report. For example, the type <literal>[Int]</literal>
138 still means <literal>Prelude.[] Int</literal>; tuples
139 continue to refer to the standard Prelude tuples; the
140 translation for list comprehensions continues to use
141 <literal>Prelude.map</literal> etc.</para>
143 <para>However, <option>-fno-implicit-prelude</option> does
144 change the handling of certain built-in syntax: see
145 <xref LinkEnd="rebindable-syntax">.</para>
153 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
154 <!-- included from primitives.sgml -->
155 <!-- &primitives; -->
156 <sect1 id="primitives">
157 <title>Unboxed types and primitive operations</title>
159 <para>GHC is built on a raft of primitive data types and operations.
160 While you really can use this stuff to write fast code,
161 we generally find it a lot less painful, and more satisfying in the
162 long run, to use higher-level language features and libraries. With
163 any luck, the code you write will be optimised to the efficient
164 unboxed version in any case. And if it isn't, we'd like to know
167 <para>We do not currently have good, up-to-date documentation about the
168 primitives, perhaps because they are mainly intended for internal use.
169 There used to be a long section about them here in the User Guide, but it
170 became out of date, and wrong information is worse than none.</para>
172 <para>The Real Truth about what primitive types there are, and what operations
173 work over those types, is held in the file
174 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
175 This file is used directly to generate GHC's primitive-operation definitions, so
176 it is always correct! It is also intended for processing into text.</para>
179 the result of such processing is part of the description of the
181 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
182 Core language</ulink>.
183 So that document is a good place to look for a type-set version.
184 We would be very happy if someone wanted to volunteer to produce an SGML
185 back end to the program that processes <filename>primops.txt</filename> so that
186 we could include the results here in the User Guide.</para>
188 <para>What follows here is a brief summary of some main points.</para>
190 <sect2 id="glasgow-unboxed">
195 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
198 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
199 that values of that type are represented by a pointer to a heap
200 object. The representation of a Haskell <literal>Int</literal>, for
201 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
202 type, however, is represented by the value itself, no pointers or heap
203 allocation are involved.
207 Unboxed types correspond to the “raw machine” types you
208 would use in C: <literal>Int#</literal> (long int),
209 <literal>Double#</literal> (double), <literal>Addr#</literal>
210 (void *), etc. The <emphasis>primitive operations</emphasis>
211 (PrimOps) on these types are what you might expect; e.g.,
212 <literal>(+#)</literal> is addition on
213 <literal>Int#</literal>s, and is the machine-addition that we all
214 know and love—usually one instruction.
218 Primitive (unboxed) types cannot be defined in Haskell, and are
219 therefore built into the language and compiler. Primitive types are
220 always unlifted; that is, a value of a primitive type cannot be
221 bottom. We use the convention that primitive types, values, and
222 operations have a <literal>#</literal> suffix.
226 Primitive values are often represented by a simple bit-pattern, such
227 as <literal>Int#</literal>, <literal>Float#</literal>,
228 <literal>Double#</literal>. But this is not necessarily the case:
229 a primitive value might be represented by a pointer to a
230 heap-allocated object. Examples include
231 <literal>Array#</literal>, the type of primitive arrays. A
232 primitive array is heap-allocated because it is too big a value to fit
233 in a register, and would be too expensive to copy around; in a sense,
234 it is accidental that it is represented by a pointer. If a pointer
235 represents a primitive value, then it really does point to that value:
236 no unevaluated thunks, no indirections…nothing can be at the
237 other end of the pointer than the primitive value.
241 There are some restrictions on the use of primitive types, the main
242 one being that you can't pass a primitive value to a polymorphic
243 function or store one in a polymorphic data type. This rules out
244 things like <literal>[Int#]</literal> (i.e. lists of primitive
245 integers). The reason for this restriction is that polymorphic
246 arguments and constructor fields are assumed to be pointers: if an
247 unboxed integer is stored in one of these, the garbage collector would
248 attempt to follow it, leading to unpredictable space leaks. Or a
249 <function>seq</function> operation on the polymorphic component may
250 attempt to dereference the pointer, with disastrous results. Even
251 worse, the unboxed value might be larger than a pointer
252 (<literal>Double#</literal> for instance).
256 Nevertheless, A numerically-intensive program using unboxed types can
257 go a <emphasis>lot</emphasis> faster than its “standard”
258 counterpart—we saw a threefold speedup on one example.
263 <sect2 id="unboxed-tuples">
264 <title>Unboxed Tuples
268 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
269 they're available by default with <option>-fglasgow-exts</option>. An
270 unboxed tuple looks like this:
282 where <literal>e_1..e_n</literal> are expressions of any
283 type (primitive or non-primitive). The type of an unboxed tuple looks
288 Unboxed tuples are used for functions that need to return multiple
289 values, but they avoid the heap allocation normally associated with
290 using fully-fledged tuples. When an unboxed tuple is returned, the
291 components are put directly into registers or on the stack; the
292 unboxed tuple itself does not have a composite representation. Many
293 of the primitive operations listed in this section return unboxed
298 There are some pretty stringent restrictions on the use of unboxed tuples:
307 Unboxed tuple types are subject to the same restrictions as
308 other unboxed types; i.e. they may not be stored in polymorphic data
309 structures or passed to polymorphic functions.
316 Unboxed tuples may only be constructed as the direct result of
317 a function, and may only be deconstructed with a <literal>case</literal> expression.
318 eg. the following are valid:
322 f x y = (# x+1, y-1 #)
323 g x = case f x x of { (# a, b #) -> a + b }
327 but the following are invalid:
341 No variable can have an unboxed tuple type. This is illegal:
345 f :: (# Int, Int #) -> (# Int, Int #)
350 because <literal>x</literal> has an unboxed tuple type.
360 Note: we may relax some of these restrictions in the future.
364 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
365 tuples to avoid unnecessary allocation during sequences of operations.
372 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
374 <sect1 id="syntax-extns">
375 <title>Syntactic extensions</title>
377 <!-- ====================== HIERARCHICAL MODULES ======================= -->
379 <sect2 id="hierarchical-modules">
380 <title>Hierarchical Modules</title>
382 <para>GHC supports a small extension to the syntax of module
383 names: a module name is allowed to contain a dot
384 <literal>‘.’</literal>. This is also known as the
385 “hierarchical module namespace” extension, because
386 it extends the normally flat Haskell module namespace into a
387 more flexible hierarchy of modules.</para>
389 <para>This extension has very little impact on the language
390 itself; modules names are <emphasis>always</emphasis> fully
391 qualified, so you can just think of the fully qualified module
392 name as <quote>the module name</quote>. In particular, this
393 means that the full module name must be given after the
394 <literal>module</literal> keyword at the beginning of the
395 module; for example, the module <literal>A.B.C</literal> must
398 <programlisting>module A.B.C</programlisting>
401 <para>It is a common strategy to use the <literal>as</literal>
402 keyword to save some typing when using qualified names with
403 hierarchical modules. For example:</para>
406 import qualified Control.Monad.ST.Strict as ST
409 <para>Hierarchical modules have an impact on the way that GHC
410 searches for files. For a description, see <xref
411 linkend="finding-hierarchical-modules">.</para>
413 <para>GHC comes with a large collection of libraries arranged
414 hierarchically; see the accompanying library documentation.
415 There is an ongoing project to create and maintain a stable set
416 of <quote>core</quote> libraries used by several Haskell
417 compilers, and the libraries that GHC comes with represent the
418 current status of that project. For more details, see <ulink
419 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
420 Libraries</ulink>.</para>
424 <!-- ====================== PATTERN GUARDS ======================= -->
426 <sect2 id="pattern-guards">
427 <title>Pattern guards</title>
430 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
431 The discussion that follows is an abbreviated version of Simon Peyton Jones's original <ULink URL="http://research.microsoft.com/~simonpj/Haskell/guards.html">proposal</ULink>. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
435 Suppose we have an abstract data type of finite maps, with a
439 lookup :: FiniteMap -> Int -> Maybe Int
442 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
443 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
447 clunky env var1 var2 | ok1 && ok2 = val1 + val2
448 | otherwise = var1 + var2
459 The auxiliary functions are
463 maybeToBool :: Maybe a -> Bool
464 maybeToBool (Just x) = True
465 maybeToBool Nothing = False
467 expectJust :: Maybe a -> a
468 expectJust (Just x) = x
469 expectJust Nothing = error "Unexpected Nothing"
473 What is <function>clunky</function> doing? The guard <literal>ok1 &&
474 ok2</literal> checks that both lookups succeed, using
475 <function>maybeToBool</function> to convert the <function>Maybe</function>
476 types to booleans. The (lazily evaluated) <function>expectJust</function>
477 calls extract the values from the results of the lookups, and binds the
478 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
479 respectively. If either lookup fails, then clunky takes the
480 <literal>otherwise</literal> case and returns the sum of its arguments.
484 This is certainly legal Haskell, but it is a tremendously verbose and
485 un-obvious way to achieve the desired effect. Arguably, a more direct way
486 to write clunky would be to use case expressions:
490 clunky env var1 var1 = case lookup env var1 of
492 Just val1 -> case lookup env var2 of
494 Just val2 -> val1 + val2
500 This is a bit shorter, but hardly better. Of course, we can rewrite any set
501 of pattern-matching, guarded equations as case expressions; that is
502 precisely what the compiler does when compiling equations! The reason that
503 Haskell provides guarded equations is because they allow us to write down
504 the cases we want to consider, one at a time, independently of each other.
505 This structure is hidden in the case version. Two of the right-hand sides
506 are really the same (<function>fail</function>), and the whole expression
507 tends to become more and more indented.
511 Here is how I would write clunky:
516 | Just val1 <- lookup env var1
517 , Just val2 <- lookup env var2
519 ...other equations for clunky...
523 The semantics should be clear enough. The qualifers are matched in order.
524 For a <literal><-</literal> qualifier, which I call a pattern guard, the
525 right hand side is evaluated and matched against the pattern on the left.
526 If the match fails then the whole guard fails and the next equation is
527 tried. If it succeeds, then the appropriate binding takes place, and the
528 next qualifier is matched, in the augmented environment. Unlike list
529 comprehensions, however, the type of the expression to the right of the
530 <literal><-</literal> is the same as the type of the pattern to its
531 left. The bindings introduced by pattern guards scope over all the
532 remaining guard qualifiers, and over the right hand side of the equation.
536 Just as with list comprehensions, boolean expressions can be freely mixed
537 with among the pattern guards. For example:
548 Haskell's current guards therefore emerge as a special case, in which the
549 qualifier list has just one element, a boolean expression.
553 <!-- ===================== Recursive do-notation =================== -->
555 <sect2 id="mdo-notation">
556 <title>The recursive do-notation
559 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
560 "A recursive do for Haskell",
561 Levent Erkok, John Launchbury",
562 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
565 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
566 that is, the variables bound in a do-expression are visible only in the textually following
567 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
568 group. It turns out that several applications can benefit from recursive bindings in
569 the do-notation, and this extension provides the necessary syntactic support.
572 Here is a simple (yet contrived) example:
575 import Control.Monad.Fix
577 justOnes = mdo xs <- Just (1:xs)
581 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
585 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
588 class Monad m => MonadFix m where
589 mfix :: (a -> m a) -> m a
592 The function <literal>mfix</literal>
593 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
594 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
595 For details, see the above mentioned reference.
598 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
599 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
600 for Haskell's internal state monad (strict and lazy, respectively).
603 There are three important points in using the recursive-do notation:
606 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
607 than <literal>do</literal>).
611 You should <literal>import Control.Monad.Fix</literal>.
612 (Note: Strictly speaking, this import is required only when you need to refer to the name
613 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
614 are encouraged to always import this module when using the mdo-notation.)
618 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
624 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
625 contains up to date information on recursive monadic bindings.
629 Historical note: The old implementation of the mdo-notation (and most
630 of the existing documents) used the name
631 <literal>MonadRec</literal> for the class and the corresponding library.
632 This name is not supported by GHC.
638 <sect2> <title> Infix type constructors </title>
640 <para>GHC supports infix type constructors, much as it supports infix data constructors. For example:
644 data a :+: b = Inl a | Inr b
646 f :: a `Either` b -> a :+: b
651 syntax of an infix type constructor is just like that of an infix data constructor: either
652 it's an operator beginning with ":", or it is an ordinary (alphabetic) type constructor enclosed in
656 When you give a fixity declaration, the fixity applies to both the data constructor and the
657 type constructor with the specified name. You cannot give different fixities to the type constructor T
658 and the data constructor T.
664 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
666 <sect2 id="parallel-list-comprehensions">
667 <title>Parallel List Comprehensions</title>
668 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
670 <indexterm><primary>parallel list comprehensions</primary>
673 <para>Parallel list comprehensions are a natural extension to list
674 comprehensions. List comprehensions can be thought of as a nice
675 syntax for writing maps and filters. Parallel comprehensions
676 extend this to include the zipWith family.</para>
678 <para>A parallel list comprehension has multiple independent
679 branches of qualifier lists, each separated by a `|' symbol. For
680 example, the following zips together two lists:</para>
683 [ (x, y) | x <- xs | y <- ys ]
686 <para>The behavior of parallel list comprehensions follows that of
687 zip, in that the resulting list will have the same length as the
688 shortest branch.</para>
690 <para>We can define parallel list comprehensions by translation to
691 regular comprehensions. Here's the basic idea:</para>
693 <para>Given a parallel comprehension of the form: </para>
696 [ e | p1 <- e11, p2 <- e12, ...
697 | q1 <- e21, q2 <- e22, ...
702 <para>This will be translated to: </para>
705 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
706 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
711 <para>where `zipN' is the appropriate zip for the given number of
716 <sect2 id="rebindable-syntax">
717 <title>Rebindable syntax</title>
720 <para>GHC allows most kinds of built-in syntax to be rebound by
721 the user, to facilitate replacing the <literal>Prelude</literal>
722 with a home-grown version, for example.</para>
724 <para>You may want to define your own numeric class
725 hierarchy. It completely defeats that purpose if the
726 literal "1" means "<literal>Prelude.fromInteger
727 1</literal>", which is what the Haskell Report specifies.
728 So the <option>-fno-implicit-prelude</option> flag causes
729 the following pieces of built-in syntax to refer to
730 <emphasis>whatever is in scope</emphasis>, not the Prelude
735 <para>Integer and fractional literals mean
736 "<literal>fromInteger 1</literal>" and
737 "<literal>fromRational 3.2</literal>", not the
738 Prelude-qualified versions; both in expressions and in
740 <para>However, the standard Prelude <literal>Eq</literal> class
741 is still used for the equality test necessary for literal patterns.</para>
745 <para>Negation (e.g. "<literal>- (f x)</literal>")
746 means "<literal>negate (f x)</literal>" (not
747 <literal>Prelude.negate</literal>).</para>
751 <para>In an n+k pattern, the standard Prelude
752 <literal>Ord</literal> class is still used for comparison,
753 but the necessary subtraction uses whatever
754 "<literal>(-)</literal>" is in scope (not
755 "<literal>Prelude.(-)</literal>").</para>
759 <para>"Do" notation is translated using whatever
760 functions <literal>(>>=)</literal>,
761 <literal>(>>)</literal>, <literal>fail</literal>, and
762 <literal>return</literal>, are in scope (not the Prelude
763 versions). List comprehensions, and parallel array
764 comprehensions, are unaffected. </para></listitem>
767 <para>Be warned: this is an experimental facility, with fewer checks than
768 usual. In particular, it is essential that the functions GHC finds in scope
769 must have the appropriate types, namely:
771 fromInteger :: forall a. (...) => Integer -> a
772 fromRational :: forall a. (...) => Rational -> a
773 negate :: forall a. (...) => a -> a
774 (-) :: forall a. (...) => a -> a -> a
775 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
776 (>>) :: forall m a. (...) => m a -> m b -> m b
777 return :: forall m a. (...) => a -> m a
778 fail :: forall m a. (...) => String -> m a
780 (The (...) part can be any context including the empty context; that part
782 If the functions don't have the right type, very peculiar things may
783 happen. Use <literal>-dcore-lint</literal> to
784 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
790 <!-- TYPE SYSTEM EXTENSIONS -->
791 <sect1 id="type-extensions">
792 <title>Type system extensions</title>
794 <sect2 id="nullary-types">
795 <title>Data types with no constructors</title>
797 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
798 a data type with no constructors. For example:</para>
802 data T a -- T :: * -> *
805 <para>Syntactically, the declaration lacks the "= constrs" part. The
806 type can be parameterised over types of any kind, but if the kind is
807 not <literal>*</literal> then an explicit kind annotation must be used
808 (see <xref linkend="sec-kinding">).</para>
810 <para>Such data types have only one value, namely bottom.
811 Nevertheless, they can be useful when defining "phantom types".</para>
814 <sect2 id="infix-tycons">
815 <title>Infix type constructors</title>
818 GHC allows type constructors to be operators, and to be written infix, very much
819 like expressions. More specifically:
822 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
823 The lexical syntax is the same as that for data constructors.
826 Types can be written infix. For example <literal>Int :*: Bool</literal>.
830 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
831 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
834 Fixities may be declared for type constructors just as for data constructors. However,
835 one cannot distinguish between the two in a fixity declaration; a fixity declaration
836 sets the fixity for a data constructor and the corresponding type constructor. For example:
840 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
841 and similarly for <literal>:*:</literal>.
842 <literal>Int `a` Bool</literal>.
845 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
848 Data type and type-synonym declarations can be written infix. E.g.
850 data a :*: b = Foo a b
851 type a :+: b = Either a b
855 The only thing that differs between operators in types and operators in expressions is that
856 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
857 are not allowed in types. Reason: the uniform thing to do would be to make them type
858 variables, but that's not very useful. A less uniform but more useful thing would be to
859 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
860 lists. So for now we just exclude them.
867 <sect2 id="sec-kinding">
868 <title>Explicitly-kinded quantification</title>
871 Haskell infers the kind of each type variable. Sometimes it is nice to be able
872 to give the kind explicitly as (machine-checked) documentation,
873 just as it is nice to give a type signature for a function. On some occasions,
874 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
875 John Hughes had to define the data type:
877 data Set cxt a = Set [a]
878 | Unused (cxt a -> ())
880 The only use for the <literal>Unused</literal> constructor was to force the correct
881 kind for the type variable <literal>cxt</literal>.
884 GHC now instead allows you to specify the kind of a type variable directly, wherever
885 a type variable is explicitly bound. Namely:
887 <listitem><para><literal>data</literal> declarations:
889 data Set (cxt :: * -> *) a = Set [a]
890 </Screen></para></listitem>
891 <listitem><para><literal>type</literal> declarations:
893 type T (f :: * -> *) = f Int
894 </Screen></para></listitem>
895 <listitem><para><literal>class</literal> declarations:
897 class (Eq a) => C (f :: * -> *) a where ...
898 </Screen></para></listitem>
899 <listitem><para><literal>forall</literal>'s in type signatures:
901 f :: forall (cxt :: * -> *). Set cxt Int
902 </Screen></para></listitem>
907 The parentheses are required. Some of the spaces are required too, to
908 separate the lexemes. If you write <literal>(f::*->*)</literal> you
909 will get a parse error, because "<literal>::*->*</literal>" is a
910 single lexeme in Haskell.
914 As part of the same extension, you can put kind annotations in types
917 f :: (Int :: *) -> Int
918 g :: forall a. a -> (a :: *)
922 atype ::= '(' ctype '::' kind ')
924 The parentheses are required.
929 <sect2 id="class-method-types">
930 <title>Class method types
933 Haskell 98 prohibits class method types to mention constraints on the
934 class type variable, thus:
937 fromList :: [a] -> s a
938 elem :: Eq a => a -> s a -> Bool
940 The type of <literal>elem</literal> is illegal in Haskell 98, because it
941 contains the constraint <literal>Eq a</literal>, constrains only the
942 class type variable (in this case <literal>a</literal>).
945 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
950 <sect2 id="multi-param-type-classes">
951 <title>Multi-parameter type classes
955 This section documents GHC's implementation of multi-parameter type
956 classes. There's lots of background in the paper <ULink
957 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
958 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
963 <sect3 id="type-restrictions">
967 GHC imposes the following restrictions on the form of a qualified
968 type, whether declared in a type signature
969 or inferred. Consider the type:
972 forall tv1..tvn (c1, ...,cn) => type
975 (Here, I write the "foralls" explicitly, although the Haskell source
976 language omits them; in Haskell 1.4, all the free type variables of an
977 explicit source-language type signature are universally quantified,
978 except for the class type variables in a class declaration. However,
979 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
988 <emphasis>Each universally quantified type variable
989 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
991 A type variable is "reachable" if it it is functionally dependent
992 (see <xref linkend="functional-dependencies">)
993 on the type variables free in <literal>type</literal>.
994 The reason for this is that a value with a type that does not obey
995 this restriction could not be used without introducing
997 Here, for example, is an illegal type:
1001 forall a. Eq a => Int
1005 When a value with this type was used, the constraint <literal>Eq tv</literal>
1006 would be introduced where <literal>tv</literal> is a fresh type variable, and
1007 (in the dictionary-translation implementation) the value would be
1008 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
1009 can never know which instance of <literal>Eq</literal> to use because we never
1010 get any more information about <literal>tv</literal>.
1017 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1018 universally quantified type variables <literal>tvi</literal></emphasis>.
1020 For example, this type is OK because <literal>C a b</literal> mentions the
1021 universally quantified type variable <literal>b</literal>:
1025 forall a. C a b => burble
1029 The next type is illegal because the constraint <literal>Eq b</literal> does not
1030 mention <literal>a</literal>:
1034 forall a. Eq b => burble
1038 The reason for this restriction is milder than the other one. The
1039 excluded types are never useful or necessary (because the offending
1040 context doesn't need to be witnessed at this point; it can be floated
1041 out). Furthermore, floating them out increases sharing. Lastly,
1042 excluding them is a conservative choice; it leaves a patch of
1043 territory free in case we need it later.
1054 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1055 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1062 f :: Eq (m a) => [m a] -> [m a]
1069 This choice recovers principal types, a property that Haskell 1.4 does not have.
1075 <title>Class declarations</title>
1083 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1087 class Collection c a where
1088 union :: c a -> c a -> c a
1099 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1100 of "acyclic" involves only the superclass relationships. For example,
1106 op :: D b => a -> b -> b
1109 class C a => D a where { ... }
1113 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1114 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1115 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1122 <emphasis>There are no restrictions on the context in a class declaration
1123 (which introduces superclasses), except that the class hierarchy must
1124 be acyclic</emphasis>. So these class declarations are OK:
1128 class Functor (m k) => FiniteMap m k where
1131 class (Monad m, Monad (t m)) => Transform t m where
1132 lift :: m a -> (t m) a
1142 <emphasis>All of the class type variables must be reachable (in the sense
1143 mentioned in <xref linkend="type-restrictions">)
1144 from the free varibles of each method type
1145 </emphasis>. For example:
1149 class Coll s a where
1151 insert :: s -> a -> s
1155 is not OK, because the type of <literal>empty</literal> doesn't mention
1156 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1157 types, and has the same motivation.
1159 Sometimes, offending class declarations exhibit misunderstandings. For
1160 example, <literal>Coll</literal> might be rewritten
1164 class Coll s a where
1166 insert :: s a -> a -> s a
1170 which makes the connection between the type of a collection of
1171 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1172 Occasionally this really doesn't work, in which case you can split the
1180 class CollE s => Coll s a where
1181 insert :: s -> a -> s
1194 <sect3 id="instance-decls">
1195 <title>Instance declarations</title>
1203 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1208 instance context1 => C type1 where ...
1209 instance context2 => C type2 where ...
1213 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1215 However, if you give the command line option
1216 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1217 option</primary></indexterm> then overlapping instance declarations are permitted.
1218 However, GHC arranges never to commit to using an instance declaration
1219 if another instance declaration also applies, either now or later.
1225 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1231 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1232 (but not identical to <literal>type1</literal>), or vice versa.
1236 Notice that these rules
1241 make it clear which instance decl to use
1242 (pick the most specific one that matches)
1249 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1250 Reason: you can pick which instance decl
1251 "matches" based on the type.
1256 However the rules are over-conservative. Two instance declarations can overlap,
1257 but it can still be clear in particular situations which to use. For example:
1259 instance C (Int,a) where ...
1260 instance C (a,Bool) where ...
1262 These are rejected by GHC's rules, but it is clear what to do when trying
1263 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1264 cannot apply. Yell if this restriction bites you.
1267 GHC is also conservative about committing to an overlapping instance. For example:
1269 class C a where { op :: a -> a }
1270 instance C [Int] where ...
1271 instance C a => C [a] where ...
1273 f :: C b => [b] -> [b]
1276 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1277 GHC does not commit to the second instance declaration, because in a paricular
1278 call of f, b might be instantiate to Int, so the first instance declaration
1279 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1280 GHC will instead silently pick the second instance, without complaining about
1281 the problem of subsequent instantiations.
1284 Regrettably, GHC doesn't guarantee to detect overlapping instance
1285 declarations if they appear in different modules. GHC can "see" the
1286 instance declarations in the transitive closure of all the modules
1287 imported by the one being compiled, so it can "see" all instance decls
1288 when it is compiling <literal>Main</literal>. However, it currently chooses not
1289 to look at ones that can't possibly be of use in the module currently
1290 being compiled, in the interests of efficiency. (Perhaps we should
1291 change that decision, at least for <literal>Main</literal>.)
1298 <emphasis>There are no restrictions on the type in an instance
1299 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1300 The instance "head" is the bit after the "=>" in an instance decl. For
1301 example, these are OK:
1305 instance C Int a where ...
1307 instance D (Int, Int) where ...
1309 instance E [[a]] where ...
1313 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1314 For example, this is OK:
1318 instance Stateful (ST s) (MutVar s) where ...
1321 See <xref linkend="undecidable-instances"> for an experimental
1322 extension to lift this restriction.
1328 <emphasis>Unlike Haskell 1.4, instance heads may use type
1329 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1330 writing the RHS of the type synonym definition. For example:
1334 type Point = (Int,Int)
1335 instance C Point where ...
1336 instance C [Point] where ...
1340 is legal. However, if you added
1344 instance C (Int,Int) where ...
1348 as well, then the compiler will complain about the overlapping
1349 (actually, identical) instance declarations. As always, type synonyms
1350 must be fully applied. You cannot, for example, write:
1355 instance Monad P where ...
1359 This design decision is independent of all the others, and easily
1360 reversed, but it makes sense to me.
1367 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1368 be type variables</emphasis>. Thus
1372 instance C a b => Eq (a,b) where ...
1380 instance C Int b => Foo b where ...
1384 is not OK. See <xref linkend="undecidable-instances"> for an experimental
1385 extension to lift this restriction.
1400 <sect2 id="undecidable-instances">
1401 <title>Undecidable instances</title>
1403 <para>The rules for instance declarations state that:
1405 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1406 an instance declaration <emphasis>must not</emphasis> be a type variable.
1408 <listitem><para>All of the types in the <emphasis>context</emphasis> of
1409 an instance declaration <emphasis>must</emphasis> be type variables.
1412 These restrictions ensure that
1413 context reduction terminates: each reduction step removes one type
1414 constructor. For example, the following would make the type checker
1415 loop if it wasn't excluded:
1417 instance C a => C a where ...
1419 There are two situations in which the rule is a bit of a pain. First,
1420 if one allows overlapping instance declarations then it's quite
1421 convenient to have a "default instance" declaration that applies if
1422 something more specific does not:
1431 Second, sometimes you might want to use the following to get the
1432 effect of a "class synonym":
1436 class (C1 a, C2 a, C3 a) => C a where { }
1438 instance (C1 a, C2 a, C3 a) => C a where { }
1442 This allows you to write shorter signatures:
1454 f :: (C1 a, C2 a, C3 a) => ...
1458 Voluminous correspondence on the Haskell mailing list has convinced me
1459 that it's worth experimenting with more liberal rules. If you use
1460 the experimental flag <option>-fallow-undecidable-instances</option>
1461 <indexterm><primary>-fallow-undecidable-instances
1462 option</primary></indexterm>, you can use arbitrary
1463 types in both an instance context and instance head. Termination is ensured by having a
1464 fixed-depth recursion stack. If you exceed the stack depth you get a
1465 sort of backtrace, and the opportunity to increase the stack depth
1466 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1469 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1470 allowing these idioms interesting idioms.
1474 <sect2 id="implicit-parameters">
1475 <title>Implicit parameters
1478 <para> Implicit paramters are implemented as described in
1479 "Implicit parameters: dynamic scoping with static types",
1480 J Lewis, MB Shields, E Meijer, J Launchbury,
1481 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1484 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1486 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1487 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1488 context. In Haskell, all variables are statically bound. Dynamic
1489 binding of variables is a notion that goes back to Lisp, but was later
1490 discarded in more modern incarnations, such as Scheme. Dynamic binding
1491 can be very confusing in an untyped language, and unfortunately, typed
1492 languages, in particular Hindley-Milner typed languages like Haskell,
1493 only support static scoping of variables.
1496 However, by a simple extension to the type class system of Haskell, we
1497 can support dynamic binding. Basically, we express the use of a
1498 dynamically bound variable as a constraint on the type. These
1499 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1500 function uses a dynamically-bound variable <literal>?x</literal>
1501 of type <literal>t'</literal>". For
1502 example, the following expresses the type of a sort function,
1503 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1505 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1507 The dynamic binding constraints are just a new form of predicate in the type class system.
1510 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1511 where <literal>x</literal> is
1512 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1513 Use of this construct also introduces a new
1514 dynamic-binding constraint in the type of the expression.
1515 For example, the following definition
1516 shows how we can define an implicitly parameterized sort function in
1517 terms of an explicitly parameterized <literal>sortBy</literal> function:
1519 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1521 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1527 <title>Implicit-parameter type constraints</title>
1529 Dynamic binding constraints behave just like other type class
1530 constraints in that they are automatically propagated. Thus, when a
1531 function is used, its implicit parameters are inherited by the
1532 function that called it. For example, our <literal>sort</literal> function might be used
1533 to pick out the least value in a list:
1535 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1536 least xs = fst (sort xs)
1538 Without lifting a finger, the <literal>?cmp</literal> parameter is
1539 propagated to become a parameter of <literal>least</literal> as well. With explicit
1540 parameters, the default is that parameters must always be explicit
1541 propagated. With implicit parameters, the default is to always
1545 An implicit-parameter type constraint differs from other type class constraints in the
1546 following way: All uses of a particular implicit parameter must have
1547 the same type. This means that the type of <literal>(?x, ?x)</literal>
1548 is <literal>(?x::a) => (a,a)</literal>, and not
1549 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1553 <para> You can't have an implicit parameter in the context of a class or instance
1554 declaration. For example, both these declarations are illegal:
1556 class (?x::Int) => C a where ...
1557 instance (?x::a) => Foo [a] where ...
1559 Reason: exactly which implicit parameter you pick up depends on exactly where
1560 you invoke a function. But the ``invocation'' of instance declarations is done
1561 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1562 Easiest thing is to outlaw the offending types.</para>
1564 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1566 f :: (?x :: [a]) => Int -> Int
1569 g :: (Read a, Show a) => String -> String
1572 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1573 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1574 quite unambiguous, and fixes the type <literal>a</literal>.
1579 <title>Implicit-parameter bindings</title>
1582 An implicit parameter is <emphasis>bound</emphasis> using the standard
1583 <literal>let</literal> or <literal>where</literal> binding forms.
1584 For example, we define the <literal>min</literal> function by binding
1585 <literal>cmp</literal>.
1588 min = let ?cmp = (<=) in least
1592 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1593 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1594 (including in a list comprehension, or do-notation, or pattern guards),
1595 or a <literal>where</literal> clause.
1596 Note the following points:
1599 An implicit-parameter binding group must be a
1600 collection of simple bindings to implicit-style variables (no
1601 function-style bindings, and no type signatures); these bindings are
1602 neither polymorphic or recursive.
1605 You may not mix implicit-parameter bindings with ordinary bindings in a
1606 single <literal>let</literal>
1607 expression; use two nested <literal>let</literal>s instead.
1608 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1612 You may put multiple implicit-parameter bindings in a
1613 single binding group; but they are <emphasis>not</emphasis> treated
1614 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1615 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1616 parameter. The bindings are not nested, and may be re-ordered without changing
1617 the meaning of the program.
1618 For example, consider:
1620 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1622 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1623 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1625 f :: (?x::Int) => Int -> Int
1634 <sect2 id="linear-implicit-parameters">
1635 <title>Linear implicit parameters
1638 Linear implicit parameters are an idea developed by Koen Claessen,
1639 Mark Shields, and Simon PJ. They address the long-standing
1640 problem that monads seem over-kill for certain sorts of problem, notably:
1643 <listitem> <para> distributing a supply of unique names </para> </listitem>
1644 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1645 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1649 Linear implicit parameters are just like ordinary implicit parameters,
1650 except that they are "linear" -- that is, they cannot be copied, and
1651 must be explicitly "split" instead. Linear implicit parameters are
1652 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1653 (The '/' in the '%' suggests the split!)
1658 import GHC.Exts( Splittable )
1660 data NameSupply = ...
1662 splitNS :: NameSupply -> (NameSupply, NameSupply)
1663 newName :: NameSupply -> Name
1665 instance Splittable NameSupply where
1669 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1670 f env (Lam x e) = Lam x' (f env e)
1673 env' = extend env x x'
1674 ...more equations for f...
1676 Notice that the implicit parameter %ns is consumed
1678 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1679 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1683 So the translation done by the type checker makes
1684 the parameter explicit:
1686 f :: NameSupply -> Env -> Expr -> Expr
1687 f ns env (Lam x e) = Lam x' (f ns1 env e)
1689 (ns1,ns2) = splitNS ns
1691 env = extend env x x'
1693 Notice the call to 'split' introduced by the type checker.
1694 How did it know to use 'splitNS'? Because what it really did
1695 was to introduce a call to the overloaded function 'split',
1696 defined by the class <literal>Splittable</literal>:
1698 class Splittable a where
1701 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1702 split for name supplies. But we can simply write
1708 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1710 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1711 <literal>GHC.Exts</literal>.
1716 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1717 are entirely distinct implicit parameters: you
1718 can use them together and they won't intefere with each other. </para>
1721 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1723 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1724 in the context of a class or instance declaration. </para></listitem>
1728 <sect3><title>Warnings</title>
1731 The monomorphism restriction is even more important than usual.
1732 Consider the example above:
1734 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1735 f env (Lam x e) = Lam x' (f env e)
1738 env' = extend env x x'
1740 If we replaced the two occurrences of x' by (newName %ns), which is
1741 usually a harmless thing to do, we get:
1743 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1744 f env (Lam x e) = Lam (newName %ns) (f env e)
1746 env' = extend env x (newName %ns)
1748 But now the name supply is consumed in <emphasis>three</emphasis> places
1749 (the two calls to newName,and the recursive call to f), so
1750 the result is utterly different. Urk! We don't even have
1754 Well, this is an experimental change. With implicit
1755 parameters we have already lost beta reduction anyway, and
1756 (as John Launchbury puts it) we can't sensibly reason about
1757 Haskell programs without knowing their typing.
1762 <sect3><title>Recursive functions</title>
1763 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1766 foo :: %x::T => Int -> [Int]
1768 foo n = %x : foo (n-1)
1770 where T is some type in class Splittable.</para>
1772 Do you get a list of all the same T's or all different T's
1773 (assuming that split gives two distinct T's back)?
1775 If you supply the type signature, taking advantage of polymorphic
1776 recursion, you get what you'd probably expect. Here's the
1777 translated term, where the implicit param is made explicit:
1780 foo x n = let (x1,x2) = split x
1781 in x1 : foo x2 (n-1)
1783 But if you don't supply a type signature, GHC uses the Hindley
1784 Milner trick of using a single monomorphic instance of the function
1785 for the recursive calls. That is what makes Hindley Milner type inference
1786 work. So the translation becomes
1790 foom n = x : foom (n-1)
1794 Result: 'x' is not split, and you get a list of identical T's. So the
1795 semantics of the program depends on whether or not foo has a type signature.
1798 You may say that this is a good reason to dislike linear implicit parameters
1799 and you'd be right. That is why they are an experimental feature.
1805 <sect2 id="functional-dependencies">
1806 <title>Functional dependencies
1809 <para> Functional dependencies are implemented as described by Mark Jones
1810 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1811 In Proceedings of the 9th European Symposium on Programming,
1812 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1816 Functional dependencies are introduced by a vertical bar in the syntax of a
1817 class declaration; e.g.
1819 class (Monad m) => MonadState s m | m -> s where ...
1821 class Foo a b c | a b -> c where ...
1823 There should be more documentation, but there isn't (yet). Yell if you need it.
1828 <sect2 id="universal-quantification">
1829 <title>Arbitrary-rank polymorphism
1833 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1834 allows us to say exactly what this means. For example:
1842 g :: forall b. (b -> b)
1844 The two are treated identically.
1848 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1849 explicit universal quantification in
1851 For example, all the following types are legal:
1853 f1 :: forall a b. a -> b -> a
1854 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1856 f2 :: (forall a. a->a) -> Int -> Int
1857 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1859 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1861 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1862 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1863 The <literal>forall</literal> makes explicit the universal quantification that
1864 is implicitly added by Haskell.
1867 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1868 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1869 shows, the polymorphic type on the left of the function arrow can be overloaded.
1872 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1873 they have rank-2 types on the left of a function arrow.
1876 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1877 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1878 that restriction has now been lifted.)
1879 In particular, a forall-type (also called a "type scheme"),
1880 including an operational type class context, is legal:
1882 <listitem> <para> On the left of a function arrow </para> </listitem>
1883 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1884 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1885 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1886 field type signatures.</para> </listitem>
1887 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1888 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1890 There is one place you cannot put a <literal>forall</literal>:
1891 you cannot instantiate a type variable with a forall-type. So you cannot
1892 make a forall-type the argument of a type constructor. So these types are illegal:
1894 x1 :: [forall a. a->a]
1895 x2 :: (forall a. a->a, Int)
1896 x3 :: Maybe (forall a. a->a)
1898 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1899 a type variable any more!
1908 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1909 the types of the constructor arguments. Here are several examples:
1915 data T a = T1 (forall b. b -> b -> b) a
1917 data MonadT m = MkMonad { return :: forall a. a -> m a,
1918 bind :: forall a b. m a -> (a -> m b) -> m b
1921 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1927 The constructors have rank-2 types:
1933 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1934 MkMonad :: forall m. (forall a. a -> m a)
1935 -> (forall a b. m a -> (a -> m b) -> m b)
1937 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1943 Notice that you don't need to use a <literal>forall</literal> if there's an
1944 explicit context. For example in the first argument of the
1945 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1946 prefixed to the argument type. The implicit <literal>forall</literal>
1947 quantifies all type variables that are not already in scope, and are
1948 mentioned in the type quantified over.
1952 As for type signatures, implicit quantification happens for non-overloaded
1953 types too. So if you write this:
1956 data T a = MkT (Either a b) (b -> b)
1959 it's just as if you had written this:
1962 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1965 That is, since the type variable <literal>b</literal> isn't in scope, it's
1966 implicitly universally quantified. (Arguably, it would be better
1967 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1968 where that is what is wanted. Feedback welcomed.)
1972 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1973 the constructor to suitable values, just as usual. For example,
1984 a3 = MkSwizzle reverse
1987 a4 = let r x = Just x
1994 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1995 mkTs f x y = [T1 f x, T1 f y]
2001 The type of the argument can, as usual, be more general than the type
2002 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
2003 does not need the <literal>Ord</literal> constraint.)
2007 When you use pattern matching, the bound variables may now have
2008 polymorphic types. For example:
2014 f :: T a -> a -> (a, Char)
2015 f (T1 w k) x = (w k x, w 'c' 'd')
2017 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2018 g (MkSwizzle s) xs f = s (map f (s xs))
2020 h :: MonadT m -> [m a] -> m [a]
2021 h m [] = return m []
2022 h m (x:xs) = bind m x $ \y ->
2023 bind m (h m xs) $ \ys ->
2030 In the function <function>h</function> we use the record selectors <literal>return</literal>
2031 and <literal>bind</literal> to extract the polymorphic bind and return functions
2032 from the <literal>MonadT</literal> data structure, rather than using pattern
2038 <title>Type inference</title>
2041 In general, type inference for arbitrary-rank types is undecideable.
2042 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2043 to get a decidable algorithm by requiring some help from the programmer.
2044 We do not yet have a formal specification of "some help" but the rule is this:
2047 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2048 provides an explicit polymorphic type for x, or GHC's type inference will assume
2049 that x's type has no foralls in it</emphasis>.
2052 What does it mean to "provide" an explicit type for x? You can do that by
2053 giving a type signature for x directly, using a pattern type signature
2054 (<xref linkend="scoped-type-variables">), thus:
2056 \ f :: (forall a. a->a) -> (f True, f 'c')
2058 Alternatively, you can give a type signature to the enclosing
2059 context, which GHC can "push down" to find the type for the variable:
2061 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2063 Here the type signature on the expression can be pushed inwards
2064 to give a type signature for f. Similarly, and more commonly,
2065 one can give a type signature for the function itself:
2067 h :: (forall a. a->a) -> (Bool,Char)
2068 h f = (f True, f 'c')
2070 You don't need to give a type signature if the lambda bound variable
2071 is a constructor argument. Here is an example we saw earlier:
2073 f :: T a -> a -> (a, Char)
2074 f (T1 w k) x = (w k x, w 'c' 'd')
2076 Here we do not need to give a type signature to <literal>w</literal>, because
2077 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2084 <sect3 id="implicit-quant">
2085 <title>Implicit quantification</title>
2088 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2089 user-written types, if and only if there is no explicit <literal>forall</literal>,
2090 GHC finds all the type variables mentioned in the type that are not already
2091 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2095 f :: forall a. a -> a
2102 h :: forall b. a -> b -> b
2108 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2111 f :: (a -> a) -> Int
2113 f :: forall a. (a -> a) -> Int
2115 f :: (forall a. a -> a) -> Int
2118 g :: (Ord a => a -> a) -> Int
2119 -- MEANS the illegal type
2120 g :: forall a. (Ord a => a -> a) -> Int
2122 g :: (forall a. Ord a => a -> a) -> Int
2124 The latter produces an illegal type, which you might think is silly,
2125 but at least the rule is simple. If you want the latter type, you
2126 can write your for-alls explicitly. Indeed, doing so is strongly advised
2132 <sect2 id="type-synonyms">
2133 <title>Liberalised type synonyms
2137 Type synonmys are like macros at the type level, and
2138 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2139 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
2141 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2142 in a type synonym, thus:
2144 type Discard a = forall b. Show b => a -> b -> (a, String)
2149 g :: Discard Int -> (Int,Bool) -- A rank-2 type
2156 You can write an unboxed tuple in a type synonym:
2158 type Pr = (# Int, Int #)
2166 You can apply a type synonym to a forall type:
2168 type Foo a = a -> a -> Bool
2170 f :: Foo (forall b. b->b)
2172 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2174 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2179 You can apply a type synonym to a partially applied type synonym:
2181 type Generic i o = forall x. i x -> o x
2184 foo :: Generic Id []
2186 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2188 foo :: forall x. x -> [x]
2196 GHC currently does kind checking before expanding synonyms (though even that
2200 After expanding type synonyms, GHC does validity checking on types, looking for
2201 the following mal-formedness which isn't detected simply by kind checking:
2204 Type constructor applied to a type involving for-alls.
2207 Unboxed tuple on left of an arrow.
2210 Partially-applied type synonym.
2214 this will be rejected:
2216 type Pr = (# Int, Int #)
2221 because GHC does not allow unboxed tuples on the left of a function arrow.
2226 <title>For-all hoisting</title>
2228 It is often convenient to use generalised type synonyms at the right hand
2229 end of an arrow, thus:
2231 type Discard a = forall b. a -> b -> a
2233 g :: Int -> Discard Int
2236 Simply expanding the type synonym would give
2238 g :: Int -> (forall b. Int -> b -> Int)
2240 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2242 g :: forall b. Int -> Int -> b -> Int
2244 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2245 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2246 performs the transformation:</emphasis>
2248 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2250 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2252 (In fact, GHC tries to retain as much synonym information as possible for use in
2253 error messages, but that is a usability issue.) This rule applies, of course, whether
2254 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2255 valid way to write <literal>g</literal>'s type signature:
2257 g :: Int -> Int -> forall b. b -> Int
2261 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2264 type Foo a = (?x::Int) => Bool -> a
2269 g :: (?x::Int) => Bool -> Bool -> Int
2275 <sect2 id="existential-quantification">
2276 <title>Existentially quantified data constructors
2280 The idea of using existential quantification in data type declarations
2281 was suggested by Laufer (I believe, thought doubtless someone will
2282 correct me), and implemented in Hope+. It's been in Lennart
2283 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2284 proved very useful. Here's the idea. Consider the declaration:
2290 data Foo = forall a. MkFoo a (a -> Bool)
2297 The data type <literal>Foo</literal> has two constructors with types:
2303 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2310 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2311 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2312 For example, the following expression is fine:
2318 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2324 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2325 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2326 isUpper</function> packages a character with a compatible function. These
2327 two things are each of type <literal>Foo</literal> and can be put in a list.
2331 What can we do with a value of type <literal>Foo</literal>?. In particular,
2332 what happens when we pattern-match on <function>MkFoo</function>?
2338 f (MkFoo val fn) = ???
2344 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2345 are compatible, the only (useful) thing we can do with them is to
2346 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2353 f (MkFoo val fn) = fn val
2359 What this allows us to do is to package heterogenous values
2360 together with a bunch of functions that manipulate them, and then treat
2361 that collection of packages in a uniform manner. You can express
2362 quite a bit of object-oriented-like programming this way.
2365 <sect3 id="existential">
2366 <title>Why existential?
2370 What has this to do with <emphasis>existential</emphasis> quantification?
2371 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2377 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2383 But Haskell programmers can safely think of the ordinary
2384 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2385 adding a new existential quantification construct.
2391 <title>Type classes</title>
2394 An easy extension (implemented in <Command>hbc</Command>) is to allow
2395 arbitrary contexts before the constructor. For example:
2401 data Baz = forall a. Eq a => Baz1 a a
2402 | forall b. Show b => Baz2 b (b -> b)
2408 The two constructors have the types you'd expect:
2414 Baz1 :: forall a. Eq a => a -> a -> Baz
2415 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2421 But when pattern matching on <function>Baz1</function> the matched values can be compared
2422 for equality, and when pattern matching on <function>Baz2</function> the first matched
2423 value can be converted to a string (as well as applying the function to it).
2424 So this program is legal:
2431 f (Baz1 p q) | p == q = "Yes"
2433 f (Baz2 v fn) = show (fn v)
2439 Operationally, in a dictionary-passing implementation, the
2440 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2441 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2442 extract it on pattern matching.
2446 Notice the way that the syntax fits smoothly with that used for
2447 universal quantification earlier.
2453 <title>Restrictions</title>
2456 There are several restrictions on the ways in which existentially-quantified
2457 constructors can be use.
2466 When pattern matching, each pattern match introduces a new,
2467 distinct, type for each existential type variable. These types cannot
2468 be unified with any other type, nor can they escape from the scope of
2469 the pattern match. For example, these fragments are incorrect:
2477 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2478 is the result of <function>f1</function>. One way to see why this is wrong is to
2479 ask what type <function>f1</function> has:
2483 f1 :: Foo -> a -- Weird!
2487 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2492 f1 :: forall a. Foo -> a -- Wrong!
2496 The original program is just plain wrong. Here's another sort of error
2500 f2 (Baz1 a b) (Baz1 p q) = a==q
2504 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2505 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2506 from the two <function>Baz1</function> constructors.
2514 You can't pattern-match on an existentially quantified
2515 constructor in a <literal>let</literal> or <literal>where</literal> group of
2516 bindings. So this is illegal:
2520 f3 x = a==b where { Baz1 a b = x }
2523 Instead, use a <literal>case</literal> expression:
2526 f3 x = case x of Baz1 a b -> a==b
2529 In general, you can only pattern-match
2530 on an existentially-quantified constructor in a <literal>case</literal> expression or
2531 in the patterns of a function definition.
2533 The reason for this restriction is really an implementation one.
2534 Type-checking binding groups is already a nightmare without
2535 existentials complicating the picture. Also an existential pattern
2536 binding at the top level of a module doesn't make sense, because it's
2537 not clear how to prevent the existentially-quantified type "escaping".
2538 So for now, there's a simple-to-state restriction. We'll see how
2546 You can't use existential quantification for <literal>newtype</literal>
2547 declarations. So this is illegal:
2551 newtype T = forall a. Ord a => MkT a
2555 Reason: a value of type <literal>T</literal> must be represented as a pair
2556 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2557 That contradicts the idea that <literal>newtype</literal> should have no
2558 concrete representation. You can get just the same efficiency and effect
2559 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2560 overloading involved, then there is more of a case for allowing
2561 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2562 because the <literal>data</literal> version does carry an implementation cost,
2563 but single-field existentially quantified constructors aren't much
2564 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2565 stands, unless there are convincing reasons to change it.
2573 You can't use <literal>deriving</literal> to define instances of a
2574 data type with existentially quantified data constructors.
2576 Reason: in most cases it would not make sense. For example:#
2579 data T = forall a. MkT [a] deriving( Eq )
2582 To derive <literal>Eq</literal> in the standard way we would need to have equality
2583 between the single component of two <function>MkT</function> constructors:
2587 (MkT a) == (MkT b) = ???
2590 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2591 It's just about possible to imagine examples in which the derived instance
2592 would make sense, but it seems altogether simpler simply to prohibit such
2593 declarations. Define your own instances!
2605 <sect2 id="scoped-type-variables">
2606 <title>Scoped type variables
2610 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2611 variable</emphasis>. For example
2617 f (xs::[a]) = ys ++ ys
2626 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2627 This brings the type variable <literal>a</literal> into scope; it scopes over
2628 all the patterns and right hand sides for this equation for <function>f</function>.
2629 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2633 Pattern type signatures are completely orthogonal to ordinary, separate
2634 type signatures. The two can be used independently or together.
2635 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2636 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2637 implicitly universally quantified. (If there are no type variables in
2638 scope, all type variables mentioned in the signature are universally
2639 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2640 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2641 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2642 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2643 it becomes possible to do so.
2647 Scoped type variables are implemented in both GHC and Hugs. Where the
2648 implementations differ from the specification below, those differences
2653 So much for the basic idea. Here are the details.
2657 <title>What a pattern type signature means</title>
2659 A type variable brought into scope by a pattern type signature is simply
2660 the name for a type. The restriction they express is that all occurrences
2661 of the same name mean the same type. For example:
2663 f :: [Int] -> Int -> Int
2664 f (xs::[a]) (y::a) = (head xs + y) :: a
2666 The pattern type signatures on the left hand side of
2667 <literal>f</literal> express the fact that <literal>xs</literal>
2668 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2669 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2670 specifies that this expression must have the same type <literal>a</literal>.
2671 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2672 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2673 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2674 rules, which specified that a pattern-bound type variable should be universally quantified.)
2675 For example, all of these are legal:</para>
2678 t (x::a) (y::a) = x+y*2
2680 f (x::a) (y::b) = [x,y] -- a unifies with b
2682 g (x::a) = x + 1::Int -- a unifies with Int
2684 h x = let k (y::a) = [x,y] -- a is free in the
2685 in k x -- environment
2687 k (x::a) True = ... -- a unifies with Int
2688 k (x::Int) False = ...
2691 w (x::a) = x -- a unifies with [b]
2697 <title>Scope and implicit quantification</title>
2705 All the type variables mentioned in a pattern,
2706 that are not already in scope,
2707 are brought into scope by the pattern. We describe this set as
2708 the <emphasis>type variables bound by the pattern</emphasis>.
2711 f (x::a) = let g (y::(a,b)) = fst y
2715 The pattern <literal>(x::a)</literal> brings the type variable
2716 <literal>a</literal> into scope, as well as the term
2717 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2718 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2719 and brings into scope the type variable <literal>b</literal>.
2725 The type variable(s) bound by the pattern have the same scope
2726 as the term variable(s) bound by the pattern. For example:
2729 f (x::a) = <...rhs of f...>
2730 (p::b, q::b) = (1,2)
2731 in <...body of let...>
2733 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2734 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2735 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2736 just like <literal>p</literal> and <literal>q</literal> do.
2737 Indeed, the newly bound type variables also scope over any ordinary, separate
2738 type signatures in the <literal>let</literal> group.
2745 The type variables bound by the pattern may be
2746 mentioned in ordinary type signatures or pattern
2747 type signatures anywhere within their scope.
2754 In ordinary type signatures, any type variable mentioned in the
2755 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2763 Ordinary type signatures do not bring any new type variables
2764 into scope (except in the type signature itself!). So this is illegal:
2771 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2772 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2773 and that is an incorrect typing.
2780 The pattern type signature is a monotype:
2785 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2789 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2790 not to type schemes.
2794 There is no implicit universal quantification on pattern type signatures (in contrast to
2795 ordinary type signatures).
2805 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2806 scope over the methods defined in the <literal>where</literal> part. For example:
2820 (Not implemented in Hugs yet, Dec 98).
2831 <title>Where a pattern type signature can occur</title>
2834 A pattern type signature can occur in any pattern. For example:
2839 A pattern type signature can be on an arbitrary sub-pattern, not
2844 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2853 Pattern type signatures, including the result part, can be used
2854 in lambda abstractions:
2857 (\ (x::a, y) :: a -> x)
2864 Pattern type signatures, including the result part, can be used
2865 in <literal>case</literal> expressions:
2869 case e of { (x::a, y) :: a -> x }
2877 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2878 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2879 token or a parenthesised type of some sort). To see why,
2880 consider how one would parse this:
2894 Pattern type signatures can bind existential type variables.
2899 data T = forall a. MkT [a]
2902 f (MkT [t::a]) = MkT t3
2915 Pattern type signatures
2916 can be used in pattern bindings:
2919 f x = let (y, z::a) = x in ...
2920 f1 x = let (y, z::Int) = x in ...
2921 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2922 f3 :: (b->b) = \x -> x
2925 In all such cases, the binding is not generalised over the pattern-bound
2926 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2927 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2928 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2929 In contrast, the binding
2934 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2935 in <literal>f4</literal>'s scope.
2945 <title>Result type signatures</title>
2948 The result type of a function can be given a signature, thus:
2952 f (x::a) :: [a] = [x,x,x]
2956 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2957 result type. Sometimes this is the only way of naming the type variable
2962 f :: Int -> [a] -> [a]
2963 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2964 in \xs -> map g (reverse xs `zip` xs)
2969 The type variables bound in a result type signature scope over the right hand side
2970 of the definition. However, consider this corner-case:
2972 rev1 :: [a] -> [a] = \xs -> reverse xs
2974 foo ys = rev (ys::[a])
2976 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2977 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2978 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2979 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2980 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2983 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2984 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2988 rev1 :: [a] -> [a] = \xs -> reverse xs
2993 Result type signatures are not yet implemented in Hugs.
3000 <sect2 id="newtype-deriving">
3001 <title>Generalised derived instances for newtypes</title>
3004 When you define an abstract type using <literal>newtype</literal>, you may want
3005 the new type to inherit some instances from its representation. In
3006 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3007 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3008 other classes you have to write an explicit instance declaration. For
3009 example, if you define
3012 newtype Dollars = Dollars Int
3015 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3016 explicitly define an instance of <literal>Num</literal>:
3019 instance Num Dollars where
3020 Dollars a + Dollars b = Dollars (a+b)
3023 All the instance does is apply and remove the <literal>newtype</literal>
3024 constructor. It is particularly galling that, since the constructor
3025 doesn't appear at run-time, this instance declaration defines a
3026 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3027 dictionary, only slower!
3031 <sect3> <title> Generalising the deriving clause </title>
3033 GHC now permits such instances to be derived instead, so one can write
3035 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3038 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3039 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3040 derives an instance declaration of the form
3043 instance Num Int => Num Dollars
3046 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3050 We can also derive instances of constructor classes in a similar
3051 way. For example, suppose we have implemented state and failure monad
3052 transformers, such that
3055 instance Monad m => Monad (State s m)
3056 instance Monad m => Monad (Failure m)
3058 In Haskell 98, we can define a parsing monad by
3060 type Parser tok m a = State [tok] (Failure m) a
3063 which is automatically a monad thanks to the instance declarations
3064 above. With the extension, we can make the parser type abstract,
3065 without needing to write an instance of class <literal>Monad</literal>, via
3068 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3071 In this case the derived instance declaration is of the form
3073 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3076 Notice that, since <literal>Monad</literal> is a constructor class, the
3077 instance is a <emphasis>partial application</emphasis> of the new type, not the
3078 entire left hand side. We can imagine that the type declaration is
3079 ``eta-converted'' to generate the context of the instance
3084 We can even derive instances of multi-parameter classes, provided the
3085 newtype is the last class parameter. In this case, a ``partial
3086 application'' of the class appears in the <literal>deriving</literal>
3087 clause. For example, given the class
3090 class StateMonad s m | m -> s where ...
3091 instance Monad m => StateMonad s (State s m) where ...
3093 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3095 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3096 deriving (Monad, StateMonad [tok])
3099 The derived instance is obtained by completing the application of the
3100 class to the new type:
3103 instance StateMonad [tok] (State [tok] (Failure m)) =>
3104 StateMonad [tok] (Parser tok m)
3109 As a result of this extension, all derived instances in newtype
3110 declarations are treated uniformly (and implemented just by reusing
3111 the dictionary for the representation type), <emphasis>except</emphasis>
3112 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3113 the newtype and its representation.
3117 <sect3> <title> A more precise specification </title>
3119 Derived instance declarations are constructed as follows. Consider the
3120 declaration (after expansion of any type synonyms)
3123 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3129 <literal>S</literal> is a type constructor,
3132 <literal>t1...tk</literal> are types,
3135 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3136 the <literal>ti</literal>, and
3139 the <literal>ci</literal> are partial applications of
3140 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3141 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3144 Then, for each <literal>ci</literal>, the derived instance
3147 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3149 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3150 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3154 As an example which does <emphasis>not</emphasis> work, consider
3156 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3158 Here we cannot derive the instance
3160 instance Monad (State s m) => Monad (NonMonad m)
3163 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3164 and so cannot be "eta-converted" away. It is a good thing that this
3165 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3166 not, in fact, a monad --- for the same reason. Try defining
3167 <literal>>>=</literal> with the correct type: you won't be able to.
3171 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3172 important, since we can only derive instances for the last one. If the
3173 <literal>StateMonad</literal> class above were instead defined as
3176 class StateMonad m s | m -> s where ...
3179 then we would not have been able to derive an instance for the
3180 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3181 classes usually have one "main" parameter for which deriving new
3182 instances is most interesting.
3190 <!-- ==================== End of type system extensions ================= -->
3192 <!-- ====================== TEMPLATE HASKELL ======================= -->
3194 <sect1 id="template-haskell">
3195 <title>Template Haskell</title>
3197 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. The background
3198 the main technical innovations are discussed in "<ulink
3199 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3200 Template Meta-programming for Haskell</ulink>", in
3201 Proc Haskell Workshop 2002.
3204 <para> The first example from that paper is set out below as a worked example to help get you started.
3208 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3209 Tim Sheard is going to expand it.)
3212 <sect2> <title> Syntax </title>
3214 Template Haskell has the following new syntactic constructions. You need to use the flag
3215 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
3219 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3220 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3221 There must be no space between the "$" and the identifier or parenthesis. This use
3222 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3223 of "." as an infix operator. If you want the infix operator, put spaces around it.
3225 <para> A splice can occur in place of
3227 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3228 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3229 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3231 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3232 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3238 A expression quotation is written in Oxford brackets, thus:
3240 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3241 the quotation has type <literal>Expr</literal>.</para></listitem>
3242 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3243 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3244 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3245 the quotation has type <literal>Type</literal>.</para></listitem>
3246 </itemizedlist></para></listitem>
3249 Reification is written thus:
3251 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3252 has type <literal>Dec</literal>. </para></listitem>
3253 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3254 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3255 <listitem><para> Still to come: fixities </para></listitem>
3257 </itemizedlist></para>
3265 <sect2> <title> Using Template Haskell </title>
3269 The data types and monadic constructor functions for Template Haskell are in the library
3270 <literal>Language.Haskell.THSyntax</literal>.
3274 You can only run a function at compile time if it is imported from another module. That is,
3275 you can't define a function in a module, and call it from within a splice in the same module.
3276 (It would make sense to do so, but it's hard to implement.)
3280 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3283 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3284 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3285 compiles and runs a program, and then looks at the result. So it's important that
3286 the program it compiles produces results whose representations are identical to
3287 those of the compiler itself.
3291 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3292 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3297 <sect2> <title> A Template Haskell Worked Example </title>
3298 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3299 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3305 -- Import our template "pr"
3306 import Printf ( pr )
3308 -- The splice operator $ takes the Haskell source code
3309 -- generated at compile time by "pr" and splices it into
3310 -- the argument of "putStrLn".
3311 main = putStrLn ( $(pr "Hello") )
3318 -- Skeletal printf from the paper.
3319 -- It needs to be in a separate module to the one where
3320 -- you intend to use it.
3322 -- Import some Template Haskell syntax
3323 import Language.Haskell.THSyntax
3325 -- Describe a format string
3326 data Format = D | S | L String
3328 -- Parse a format string. This is left largely to you
3329 -- as we are here interested in building our first ever
3330 -- Template Haskell program and not in building printf.
3331 parse :: String -> [Format]
3334 -- Generate Haskell source code from a parsed representation
3335 -- of the format string. This code will be spliced into
3336 -- the module which calls "pr", at compile time.
3337 gen :: [Format] -> Expr
3338 gen [D] = [| \n -> show n |]
3339 gen [S] = [| \s -> s |]
3340 gen [L s] = string s
3342 -- Here we generate the Haskell code for the splice
3343 -- from an input format string.
3344 pr :: String -> Expr
3345 pr s = gen (parse s)
3348 <para>Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows):
3351 ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe
3354 <para>Run "main.exe" and here is your output:
3366 <!-- ==================== ASSERTIONS ================= -->
3368 <sect1 id="sec-assertions">
3370 <indexterm><primary>Assertions</primary></indexterm>
3374 If you want to make use of assertions in your standard Haskell code, you
3375 could define a function like the following:
3381 assert :: Bool -> a -> a
3382 assert False x = error "assertion failed!"
3389 which works, but gives you back a less than useful error message --
3390 an assertion failed, but which and where?
3394 One way out is to define an extended <function>assert</function> function which also
3395 takes a descriptive string to include in the error message and
3396 perhaps combine this with the use of a pre-processor which inserts
3397 the source location where <function>assert</function> was used.
3401 Ghc offers a helping hand here, doing all of this for you. For every
3402 use of <function>assert</function> in the user's source:
3408 kelvinToC :: Double -> Double
3409 kelvinToC k = assert (k >= 0.0) (k+273.15)
3415 Ghc will rewrite this to also include the source location where the
3422 assert pred val ==> assertError "Main.hs|15" pred val
3428 The rewrite is only performed by the compiler when it spots
3429 applications of <function>Control.Exception.assert</function>, so you
3430 can still define and use your own versions of
3431 <function>assert</function>, should you so wish. If not, import
3432 <literal>Control.Exception</literal> to make use
3433 <function>assert</function> in your code.
3437 To have the compiler ignore uses of assert, use the compiler option
3438 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3439 option</primary></indexterm> That is, expressions of the form
3440 <literal>assert pred e</literal> will be rewritten to
3441 <literal>e</literal>.
3445 Assertion failures can be caught, see the documentation for the
3446 <literal>Control.Exception</literal> library for the details.
3452 <!-- =============================== PRAGMAS =========================== -->
3454 <sect1 id="pragmas">
3455 <title>Pragmas</title>
3457 <indexterm><primary>pragma</primary></indexterm>
3459 <para>GHC supports several pragmas, or instructions to the
3460 compiler placed in the source code. Pragmas don't normally affect
3461 the meaning of the program, but they might affect the efficiency
3462 of the generated code.</para>
3464 <para>Pragmas all take the form
3466 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3468 where <replaceable>word</replaceable> indicates the type of
3469 pragma, and is followed optionally by information specific to that
3470 type of pragma. Case is ignored in
3471 <replaceable>word</replaceable>. The various values for
3472 <replaceable>word</replaceable> that GHC understands are described
3473 in the following sections; any pragma encountered with an
3474 unrecognised <replaceable>word</replaceable> is (silently)
3477 <sect2 id="inline-pragma">
3478 <title>INLINE pragma
3480 <indexterm><primary>INLINE and NOINLINE pragmas</primary></indexterm>
3481 <indexterm><primary>pragma, INLINE</primary></indexterm></title>
3484 GHC (with <option>-O</option>, as always) tries to inline (or “unfold”)
3485 functions/values that are “small enough,” thus avoiding the call
3486 overhead and possibly exposing other more-wonderful optimisations.
3487 Normally, if GHC decides a function is “too expensive” to inline, it
3488 will not do so, nor will it export that unfolding for other modules to
3493 The sledgehammer you can bring to bear is the
3494 <literal>INLINE</literal><indexterm><primary>INLINE pragma</primary></indexterm> pragma, used thusly:
3497 key_function :: Int -> String -> (Bool, Double)
3499 #ifdef __GLASGOW_HASKELL__
3500 {-# INLINE key_function #-}
3503 (You don't need to do the C pre-processor carry-on unless you're going
3504 to stick the code through HBC—it doesn't like <literal>INLINE</literal> pragmas.)
3508 The major effect of an <literal>INLINE</literal> pragma is to declare a function's
3509 “cost” to be very low. The normal unfolding machinery will then be
3510 very keen to inline it.
3514 Syntactially, an <literal>INLINE</literal> pragma for a function can be put anywhere its type
3515 signature could be put.
3519 <literal>INLINE</literal> pragmas are a particularly good idea for the
3520 <literal>then</literal>/<literal>return</literal> (or <literal>bind</literal>/<literal>unit</literal>) functions in a monad.
3521 For example, in GHC's own <literal>UniqueSupply</literal> monad code, we have:
3524 #ifdef __GLASGOW_HASKELL__
3525 {-# INLINE thenUs #-}
3526 {-# INLINE returnUs #-}
3532 <sect3 id="noinline-pragma">
3533 <title>The NOINLINE pragma </title>
3535 <indexterm><primary>NOINLINE pragma</primary></indexterm>
3536 <indexterm><primary>pragma</primary><secondary>NOINLINE</secondary></indexterm>
3537 <indexterm><primary>NOTINLINE pragma</primary></indexterm>
3538 <indexterm><primary>pragma</primary><secondary>NOTINLINE</secondary></indexterm>
3541 The <literal>NOINLINE</literal> pragma does exactly what you'd expect:
3542 it stops the named function from being inlined by the compiler. You
3543 shouldn't ever need to do this, unless you're very cautious about code
3547 <para><literal>NOTINLINE</literal> is a synonym for
3548 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is specified
3549 by Haskell 98 as the standard way to disable inlining, so it should be
3550 used if you want your code to be portable).</para>
3554 <sect3 id="phase-control">
3555 <title>Phase control</title>
3557 <para> Sometimes you want to control exactly when in GHC's pipeline
3558 the INLINE pragma is switched on. Inlining happens only during runs of
3559 the <emphasis>simplifier</emphasis>. Each run of the simplifier has a different
3560 <emphasis>phase number</emphasis>; the phase number decreases towards zero.
3561 If you use <option>-dverbose-core2core</option>
3562 you'll see the sequence of phase numbers for successive runs of the simpifier.
3563 In an INLINE pragma you can optionally specify a phase number, thus:
3565 <listitem> <para>You can say "inline <literal>f</literal> in Phase 2 and all subsequent
3568 {-# INLINE [2] f #-}
3572 <listitem> <para>You can say "inline <literal>g</literal> in all phases up to, but
3573 not including, Phase 3":
3575 {-# INLINE [~3] g #-}
3579 <listitem> <para>If you omit the phase indicator, you mean "inline in all phases".
3582 You can use a phase number on a NOINLINE pragma too:
3584 <listitem> <para>You can say "do not inline <literal>f</literal> until Phase 2; in
3585 Phase 2 and subsequently behave as if there was no pragma at all":
3587 {-# NOINLINE [2] f #-}
3591 <listitem> <para>You can say "do not inline <literal>g</literal> in Phase 3 or any subsequent phase;
3592 before that, behave as if there was no pragma":
3594 {-# NOINLINE [~3] g #-}
3598 <listitem> <para>If you omit the phase indicator, you mean "never inline this function".
3602 <para>The same phase-numbering control is available for RULES (<xref LinkEnd="rewrite-rules">).</para>
3610 <title>RULES pragma</title>
3613 The RULES pragma lets you specify rewrite rules. It is described in
3614 <xref LinkEnd="rewrite-rules">.
3620 <sect2 id="specialize-pragma">
3621 <title>SPECIALIZE pragma</title>
3623 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3624 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
3625 <indexterm><primary>overloading, death to</primary></indexterm>
3627 <para>(UK spelling also accepted.) For key overloaded
3628 functions, you can create extra versions (NB: more code space)
3629 specialised to particular types. Thus, if you have an
3630 overloaded function:</para>
3633 hammeredLookup :: Ord key => [(key, value)] -> key -> value
3636 <para>If it is heavily used on lists with
3637 <literal>Widget</literal> keys, you could specialise it as
3641 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
3644 <para>A <literal>SPECIALIZE</literal> pragma for a function can
3645 be put anywhere its type signature could be put.</para>
3647 <para>To get very fancy, you can also specify a named function
3648 to use for the specialised value, as in:</para>
3651 {-# RULES "hammeredLookup" hammeredLookup = blah #-}
3654 <para>where <literal>blah</literal> is an implementation of
3655 <literal>hammerdLookup</literal> written specialy for
3656 <literal>Widget</literal> lookups. It's <emphasis>Your
3657 Responsibility</emphasis> to make sure that
3658 <function>blah</function> really behaves as a specialised
3659 version of <function>hammeredLookup</function>!!!</para>
3661 <para>Note we use the <literal>RULE</literal> pragma here to
3662 indicate that <literal>hammeredLookup</literal> applied at a
3663 certain type should be replaced by <literal>blah</literal>. See
3664 <xref linkend="rules"> for more information on
3665 <literal>RULES</literal>.</para>
3667 <para>An example in which using <literal>RULES</literal> for
3668 specialisation will Win Big:
3671 toDouble :: Real a => a -> Double
3672 toDouble = fromRational . toRational
3674 {-# RULES "toDouble/Int" toDouble = i2d #-}
3675 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
3678 The <function>i2d</function> function is virtually one machine
3679 instruction; the default conversion—via an intermediate
3680 <literal>Rational</literal>—is obscenely expensive by
3685 <sect2 id="specialize-instance-pragma">
3686 <title>SPECIALIZE instance pragma
3690 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
3691 <indexterm><primary>overloading, death to</primary></indexterm>
3692 Same idea, except for instance declarations. For example:
3695 instance (Eq a) => Eq (Foo a) where {
3696 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
3700 The pragma must occur inside the <literal>where</literal> part
3701 of the instance declaration.
3704 Compatible with HBC, by the way, except perhaps in the placement
3710 <sect2 id="line-pragma">
3715 <indexterm><primary>LINE pragma</primary></indexterm>
3716 <indexterm><primary>pragma, LINE</primary></indexterm>
3720 This pragma is similar to C's <literal>#line</literal> pragma, and is mainly for use in
3721 automatically generated Haskell code. It lets you specify the line
3722 number and filename of the original code; for example
3728 {-# LINE 42 "Foo.vhs" #-}
3734 if you'd generated the current file from something called <filename>Foo.vhs</filename>
3735 and this line corresponds to line 42 in the original. GHC will adjust
3736 its error messages to refer to the line/file named in the <literal>LINE</literal>
3742 <sect2 id="deprecated-pragma">
3743 <title>DEPRECATED pragma</title>
3746 The DEPRECATED pragma lets you specify that a particular function, class, or type, is deprecated.
3747 There are two forms.
3751 You can deprecate an entire module thus:</para>
3753 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3757 When you compile any module that import <literal>Wibble</literal>, GHC will print
3758 the specified message.</para>
3763 You can deprecate a function, class, or type, with the following top-level declaration:
3766 {-# DEPRECATED f, C, T "Don't use these" #-}
3769 When you compile any module that imports and uses any of the specifed entities,
3770 GHC will print the specified message.
3774 <para>You can suppress the warnings with the flag <option>-fno-warn-deprecations</option>.</para>
3780 <!-- ======================= REWRITE RULES ======================== -->
3782 <sect1 id="rewrite-rules">
3783 <title>Rewrite rules
3785 <indexterm><primary>RULES pagma</primary></indexterm>
3786 <indexterm><primary>pragma, RULES</primary></indexterm>
3787 <indexterm><primary>rewrite rules</primary></indexterm></title>
3790 The programmer can specify rewrite rules as part of the source program
3791 (in a pragma). GHC applies these rewrite rules wherever it can.
3799 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
3806 <title>Syntax</title>
3809 From a syntactic point of view:
3815 There may be zero or more rules in a <literal>RULES</literal> pragma.
3822 Each rule has a name, enclosed in double quotes. The name itself has
3823 no significance at all. It is only used when reporting how many times the rule fired.
3829 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
3830 immediately after the name of the rule. Thus:
3833 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
3836 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
3837 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
3846 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
3847 is set, so you must lay out your rules starting in the same column as the
3848 enclosing definitions.
3855 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
3856 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
3857 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
3858 by spaces, just like in a type <literal>forall</literal>.
3864 A pattern variable may optionally have a type signature.
3865 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
3866 For example, here is the <literal>foldr/build</literal> rule:
3869 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
3870 foldr k z (build g) = g k z
3873 Since <function>g</function> has a polymorphic type, it must have a type signature.
3880 The left hand side of a rule must consist of a top-level variable applied
3881 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
3884 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
3885 "wrong2" forall f. f True = True
3888 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
3895 A rule does not need to be in the same module as (any of) the
3896 variables it mentions, though of course they need to be in scope.
3902 Rules are automatically exported from a module, just as instance declarations are.
3913 <title>Semantics</title>
3916 From a semantic point of view:
3922 Rules are only applied if you use the <option>-O</option> flag.
3928 Rules are regarded as left-to-right rewrite rules.
3929 When GHC finds an expression that is a substitution instance of the LHS
3930 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
3931 By "a substitution instance" we mean that the LHS can be made equal to the
3932 expression by substituting for the pattern variables.
3939 The LHS and RHS of a rule are typechecked, and must have the
3947 GHC makes absolutely no attempt to verify that the LHS and RHS
3948 of a rule have the same meaning. That is undecideable in general, and
3949 infeasible in most interesting cases. The responsibility is entirely the programmer's!
3956 GHC makes no attempt to make sure that the rules are confluent or
3957 terminating. For example:
3960 "loop" forall x,y. f x y = f y x
3963 This rule will cause the compiler to go into an infinite loop.
3970 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
3976 GHC currently uses a very simple, syntactic, matching algorithm
3977 for matching a rule LHS with an expression. It seeks a substitution
3978 which makes the LHS and expression syntactically equal modulo alpha
3979 conversion. The pattern (rule), but not the expression, is eta-expanded if
3980 necessary. (Eta-expanding the epression can lead to laziness bugs.)
3981 But not beta conversion (that's called higher-order matching).
3985 Matching is carried out on GHC's intermediate language, which includes
3986 type abstractions and applications. So a rule only matches if the
3987 types match too. See <xref LinkEnd="rule-spec"> below.
3993 GHC keeps trying to apply the rules as it optimises the program.
3994 For example, consider:
4003 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4004 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4005 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4006 not be substituted, and the rule would not fire.
4013 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4014 that appears on the LHS of a rule</emphasis>, because once you have substituted
4015 for something you can't match against it (given the simple minded
4016 matching). So if you write the rule
4019 "map/map" forall f,g. map f . map g = map (f.g)
4022 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4023 It will only match something written with explicit use of ".".
4024 Well, not quite. It <emphasis>will</emphasis> match the expression
4030 where <function>wibble</function> is defined:
4033 wibble f g = map f . map g
4036 because <function>wibble</function> will be inlined (it's small).
4038 Later on in compilation, GHC starts inlining even things on the
4039 LHS of rules, but still leaves the rules enabled. This inlining
4040 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4047 All rules are implicitly exported from the module, and are therefore
4048 in force in any module that imports the module that defined the rule, directly
4049 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4050 in force when compiling A.) The situation is very similar to that for instance
4062 <title>List fusion</title>
4065 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4066 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4067 intermediate list should be eliminated entirely.
4071 The following are good producers:
4083 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4089 Explicit lists (e.g. <literal>[True, False]</literal>)
4095 The cons constructor (e.g <literal>3:4:[]</literal>)
4101 <function>++</function>
4107 <function>map</function>
4113 <function>filter</function>
4119 <function>iterate</function>, <function>repeat</function>
4125 <function>zip</function>, <function>zipWith</function>
4134 The following are good consumers:
4146 <function>array</function> (on its second argument)
4152 <function>length</function>
4158 <function>++</function> (on its first argument)
4164 <function>foldr</function>
4170 <function>map</function>
4176 <function>filter</function>
4182 <function>concat</function>
4188 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4194 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4195 will fuse with one but not the other)
4201 <function>partition</function>
4207 <function>head</function>
4213 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4219 <function>sequence_</function>
4225 <function>msum</function>
4231 <function>sortBy</function>
4240 So, for example, the following should generate no intermediate lists:
4243 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4249 This list could readily be extended; if there are Prelude functions that you use
4250 a lot which are not included, please tell us.
4254 If you want to write your own good consumers or producers, look at the
4255 Prelude definitions of the above functions to see how to do so.
4260 <sect2 id="rule-spec">
4261 <title>Specialisation
4265 Rewrite rules can be used to get the same effect as a feature
4266 present in earlier version of GHC:
4269 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4272 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4273 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4274 specialising the original definition of <function>fromIntegral</function> the programmer is
4275 promising that it is safe to use <function>int8ToInt16</function> instead.
4279 This feature is no longer in GHC. But rewrite rules let you do the
4284 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4288 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4289 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4290 GHC adds the type and dictionary applications to get the typed rule
4293 forall (d1::Integral Int8) (d2::Num Int16) .
4294 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4298 this rule does not need to be in the same file as fromIntegral,
4299 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4300 have an original definition available to specialise).
4306 <title>Controlling what's going on</title>
4314 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4320 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4321 If you add <option>-dppr-debug</option> you get a more detailed listing.
4327 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4330 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4331 {-# INLINE build #-}
4335 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4336 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4337 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4338 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4345 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4346 see how to write rules that will do fusion and yet give an efficient
4347 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4357 <sect2 id="core-pragma">
4358 <title>CORE pragma</title>
4360 <indexterm><primary>CORE pragma</primary></indexterm>
4361 <indexterm><primary>pragma, CORE</primary></indexterm>
4362 <indexterm><primary>core, annotation</primary></indexterm>
4365 The external core format supports <quote>Note</quote> annotations;
4366 the <literal>CORE</literal> pragma gives a way to specify what these
4367 should be in your Haskell source code. Syntactically, core
4368 annotations are attached to expressions and take a Haskell string
4369 literal as an argument. The following function definition shows an
4373 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4376 Sematically, this is equivalent to:
4384 However, when external for is generated (via
4385 <option>-fext-core</option>), there will be Notes attached to the
4386 expressions <function>show</function> and <VarName>x</VarName>.
4387 The core function declaration for <function>f</function> is:
4391 f :: %forall a . GHCziShow.ZCTShow a ->
4392 a -> GHCziBase.ZMZN GHCziBase.Char =
4393 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4395 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4397 (tpl1::GHCziBase.Int ->
4399 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4401 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4402 (tpl3::GHCziBase.ZMZN a ->
4403 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4411 Here, we can see that the function <function>show</function> (which
4412 has been expanded out to a case expression over the Show dictionary)
4413 has a <literal>%note</literal> attached to it, as does the
4414 expression <VarName>eta</VarName> (which used to be called
4415 <VarName>x</VarName>).
4422 <sect1 id="generic-classes">
4423 <title>Generic classes</title>
4425 <para>(Note: support for generic classes is currently broken in
4429 The ideas behind this extension are described in detail in "Derivable type classes",
4430 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4431 An example will give the idea:
4439 fromBin :: [Int] -> (a, [Int])
4441 toBin {| Unit |} Unit = []
4442 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4443 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4444 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4446 fromBin {| Unit |} bs = (Unit, bs)
4447 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4448 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4449 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4450 (y,bs'') = fromBin bs'
4453 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4454 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4455 which are defined thus in the library module <literal>Generics</literal>:
4459 data a :+: b = Inl a | Inr b
4460 data a :*: b = a :*: b
4463 Now you can make a data type into an instance of Bin like this:
4465 instance (Bin a, Bin b) => Bin (a,b)
4466 instance Bin a => Bin [a]
4468 That is, just leave off the "where" clause. Of course, you can put in the
4469 where clause and over-ride whichever methods you please.
4473 <title> Using generics </title>
4474 <para>To use generics you need to</para>
4477 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4478 <option>-fgenerics</option> (to generate extra per-data-type code),
4479 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4483 <para>Import the module <literal>Generics</literal> from the
4484 <literal>lang</literal> package. This import brings into
4485 scope the data types <literal>Unit</literal>,
4486 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4487 don't need this import if you don't mention these types
4488 explicitly; for example, if you are simply giving instance
4489 declarations.)</para>
4494 <sect2> <title> Changes wrt the paper </title>
4496 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4497 can be written infix (indeed, you can now use
4498 any operator starting in a colon as an infix type constructor). Also note that
4499 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4500 Finally, note that the syntax of the type patterns in the class declaration
4501 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
4502 alone would ambiguous when they appear on right hand sides (an extension we
4503 anticipate wanting).
4507 <sect2> <title>Terminology and restrictions</title>
4509 Terminology. A "generic default method" in a class declaration
4510 is one that is defined using type patterns as above.
4511 A "polymorphic default method" is a default method defined as in Haskell 98.
4512 A "generic class declaration" is a class declaration with at least one
4513 generic default method.
4521 Alas, we do not yet implement the stuff about constructor names and
4528 A generic class can have only one parameter; you can't have a generic
4529 multi-parameter class.
4535 A default method must be defined entirely using type patterns, or entirely
4536 without. So this is illegal:
4539 op :: a -> (a, Bool)
4540 op {| Unit |} Unit = (Unit, True)
4543 However it is perfectly OK for some methods of a generic class to have
4544 generic default methods and others to have polymorphic default methods.
4550 The type variable(s) in the type pattern for a generic method declaration
4551 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:
4555 op {| p :*: q |} (x :*: y) = op (x :: p)
4563 The type patterns in a generic default method must take one of the forms:
4569 where "a" and "b" are type variables. Furthermore, all the type patterns for
4570 a single type constructor (<literal>:*:</literal>, say) must be identical; they
4571 must use the same type variables. So this is illegal:
4575 op {| a :+: b |} (Inl x) = True
4576 op {| p :+: q |} (Inr y) = False
4578 The type patterns must be identical, even in equations for different methods of the class.
4579 So this too is illegal:
4583 op1 {| a :*: b |} (x :*: y) = True
4586 op2 {| p :*: q |} (x :*: y) = False
4588 (The reason for this restriction is that we gather all the equations for a particular type consructor
4589 into a single generic instance declaration.)
4595 A generic method declaration must give a case for each of the three type constructors.
4601 The type for a generic method can be built only from:
4603 <listitem> <para> Function arrows </para> </listitem>
4604 <listitem> <para> Type variables </para> </listitem>
4605 <listitem> <para> Tuples </para> </listitem>
4606 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
4608 Here are some example type signatures for generic methods:
4611 op2 :: Bool -> (a,Bool)
4612 op3 :: [Int] -> a -> a
4615 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
4619 This restriction is an implementation restriction: we just havn't got around to
4620 implementing the necessary bidirectional maps over arbitrary type constructors.
4621 It would be relatively easy to add specific type constructors, such as Maybe and list,
4622 to the ones that are allowed.</para>
4627 In an instance declaration for a generic class, the idea is that the compiler
4628 will fill in the methods for you, based on the generic templates. However it can only
4633 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
4638 No constructor of the instance type has unboxed fields.
4642 (Of course, these things can only arise if you are already using GHC extensions.)
4643 However, you can still give an instance declarations for types which break these rules,
4644 provided you give explicit code to override any generic default methods.
4652 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
4653 what the compiler does with generic declarations.
4658 <sect2> <title> Another example </title>
4660 Just to finish with, here's another example I rather like:
4664 nCons {| Unit |} _ = 1
4665 nCons {| a :*: b |} _ = 1
4666 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
4669 tag {| Unit |} _ = 1
4670 tag {| a :*: b |} _ = 1
4671 tag {| a :+: b |} (Inl x) = tag x
4672 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
4681 ;;; Local Variables: ***
4683 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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