2 <indexterm><primary>language, GHC</primary></indexterm>
3 <indexterm><primary>extensions, GHC</primary></indexterm>
4 As with all known Haskell systems, GHC implements some extensions to
5 the language. To use them, you'll need to give a <option>-fglasgow-exts</option>
6 <indexterm><primary>-fglasgow-exts option</primary></indexterm> option.
10 Virtually all of the Glasgow extensions serve to give you access to
11 the underlying facilities with which we implement Haskell. Thus, you
12 can get at the Raw Iron, if you are willing to write some non-standard
13 code at a more primitive level. You need not be “stuck” on
14 performance because of the implementation costs of Haskell's
15 “high-level” features—you can always code “under” them. In an extreme case, you can write all your time-critical code in C, and then just glue it together with Haskell!
19 Before you get too carried away working at the lowest level (e.g.,
20 sloshing <literal>MutableByteArray#</literal>s around your
21 program), you may wish to check if there are libraries that provide a
22 “Haskellised veneer” over the features you want. The
23 separate libraries documentation describes all the libraries that come
27 <!-- LANGUAGE OPTIONS -->
28 <sect1 id="options-language">
29 <title>Language options</title>
31 <indexterm><primary>language</primary><secondary>option</secondary>
33 <indexterm><primary>options</primary><secondary>language</secondary>
35 <indexterm><primary>extensions</primary><secondary>options controlling</secondary>
38 <para> These flags control what variation of the language are
39 permitted. Leaving out all of them gives you standard Haskell
45 <term><option>-fglasgow-exts</option>:</term>
46 <indexterm><primary><option>-fglasgow-exts</option></primary></indexterm>
48 <para>This simultaneously enables all of the extensions to
49 Haskell 98 described in <xref
50 linkend="ghc-language-features">, except where otherwise
56 <term><option>-ffi</option> and <option>-fffi</option>:</term>
57 <indexterm><primary><option>-ffi</option></primary></indexterm>
58 <indexterm><primary><option>-fffi</option></primary></indexterm>
60 <para>This option enables the language extension defined in the
61 Haskell 98 Foreign Function Interface Addendum plus deprecated
62 syntax of previous versions of the FFI for backwards
68 <term><option>-fwith</option>:</term>
69 <indexterm><primary><option>-fwith</option></primary></indexterm>
71 <para>This option enables the deprecated <literal>with</literal>
72 keyword for implicit parameters; it is merely provided for backwards
74 It is independent of the <option>-fglasgow-exts</option>
80 <term><option>-fno-monomorphism-restriction</option>:</term>
81 <indexterm><primary><option>-fno-monomorphism-restriction</option></primary></indexterm>
83 <para> Switch off the Haskell 98 monomorphism restriction.
84 Independent of the <option>-fglasgow-exts</option>
90 <term><option>-fallow-overlapping-instances</option></term>
91 <term><option>-fallow-undecidable-instances</option></term>
92 <term><option>-fallow-incoherent-instances</option></term>
93 <term><option>-fcontext-stack</option></term>
94 <indexterm><primary><option>-fallow-overlapping-instances</option></primary></indexterm>
95 <indexterm><primary><option>-fallow-undecidable-instances</option></primary></indexterm>
96 <indexterm><primary><option>-fcontext-stack</option></primary></indexterm>
98 <para> See <xref LinkEnd="instance-decls">. Only relevant
99 if you also use <option>-fglasgow-exts</option>.</para>
104 <term><option>-finline-phase</option></term>
105 <indexterm><primary><option>-finline-phase</option></primary></indexterm>
107 <para>See <xref LinkEnd="rewrite-rules">. Only relevant if
108 you also use <option>-fglasgow-exts</option>.</para>
113 <term><option>-farrows</option></term>
114 <indexterm><primary><option>-farrows</option></primary></indexterm>
116 <para>See <xref LinkEnd="arrow-notation">. Independent of
117 <option>-fglasgow-exts</option>.</para>
122 <term><option>-fgenerics</option></term>
123 <indexterm><primary><option>-fgenerics</option></primary></indexterm>
125 <para>See <xref LinkEnd="generic-classes">. Independent of
126 <option>-fglasgow-exts</option>.</para>
131 <term><option>-fno-implicit-prelude</option></term>
133 <para><indexterm><primary>-fno-implicit-prelude
134 option</primary></indexterm> GHC normally imports
135 <filename>Prelude.hi</filename> files for you. If you'd
136 rather it didn't, then give it a
137 <option>-fno-implicit-prelude</option> option. The idea
138 is that you can then import a Prelude of your own. (But
139 don't call it <literal>Prelude</literal>; the Haskell
140 module namespace is flat, and you must not conflict with
141 any Prelude module.)</para>
143 <para>Even though you have not imported the Prelude, most of
144 the built-in syntax still refers to the built-in Haskell
145 Prelude types and values, as specified by the Haskell
146 Report. For example, the type <literal>[Int]</literal>
147 still means <literal>Prelude.[] Int</literal>; tuples
148 continue to refer to the standard Prelude tuples; the
149 translation for list comprehensions continues to use
150 <literal>Prelude.map</literal> etc.</para>
152 <para>However, <option>-fno-implicit-prelude</option> does
153 change the handling of certain built-in syntax: see
154 <xref LinkEnd="rebindable-syntax">.</para>
162 <!-- UNBOXED TYPES AND PRIMITIVE OPERATIONS -->
163 <!-- included from primitives.sgml -->
164 <!-- &primitives; -->
165 <sect1 id="primitives">
166 <title>Unboxed types and primitive operations</title>
168 <para>GHC is built on a raft of primitive data types and operations.
169 While you really can use this stuff to write fast code,
170 we generally find it a lot less painful, and more satisfying in the
171 long run, to use higher-level language features and libraries. With
172 any luck, the code you write will be optimised to the efficient
173 unboxed version in any case. And if it isn't, we'd like to know
176 <para>We do not currently have good, up-to-date documentation about the
177 primitives, perhaps because they are mainly intended for internal use.
178 There used to be a long section about them here in the User Guide, but it
179 became out of date, and wrong information is worse than none.</para>
181 <para>The Real Truth about what primitive types there are, and what operations
182 work over those types, is held in the file
183 <filename>fptools/ghc/compiler/prelude/primops.txt</filename>.
184 This file is used directly to generate GHC's primitive-operation definitions, so
185 it is always correct! It is also intended for processing into text.</para>
188 the result of such processing is part of the description of the
190 url="http://haskell.cs.yale.edu/ghc/docs/papers/core.ps.gz">External
191 Core language</ulink>.
192 So that document is a good place to look for a type-set version.
193 We would be very happy if someone wanted to volunteer to produce an SGML
194 back end to the program that processes <filename>primops.txt</filename> so that
195 we could include the results here in the User Guide.</para>
197 <para>What follows here is a brief summary of some main points.</para>
199 <sect2 id="glasgow-unboxed">
204 <indexterm><primary>Unboxed types (Glasgow extension)</primary></indexterm>
207 <para>Most types in GHC are <firstterm>boxed</firstterm>, which means
208 that values of that type are represented by a pointer to a heap
209 object. The representation of a Haskell <literal>Int</literal>, for
210 example, is a two-word heap object. An <firstterm>unboxed</firstterm>
211 type, however, is represented by the value itself, no pointers or heap
212 allocation are involved.
216 Unboxed types correspond to the “raw machine” types you
217 would use in C: <literal>Int#</literal> (long int),
218 <literal>Double#</literal> (double), <literal>Addr#</literal>
219 (void *), etc. The <emphasis>primitive operations</emphasis>
220 (PrimOps) on these types are what you might expect; e.g.,
221 <literal>(+#)</literal> is addition on
222 <literal>Int#</literal>s, and is the machine-addition that we all
223 know and love—usually one instruction.
227 Primitive (unboxed) types cannot be defined in Haskell, and are
228 therefore built into the language and compiler. Primitive types are
229 always unlifted; that is, a value of a primitive type cannot be
230 bottom. We use the convention that primitive types, values, and
231 operations have a <literal>#</literal> suffix.
235 Primitive values are often represented by a simple bit-pattern, such
236 as <literal>Int#</literal>, <literal>Float#</literal>,
237 <literal>Double#</literal>. But this is not necessarily the case:
238 a primitive value might be represented by a pointer to a
239 heap-allocated object. Examples include
240 <literal>Array#</literal>, the type of primitive arrays. A
241 primitive array is heap-allocated because it is too big a value to fit
242 in a register, and would be too expensive to copy around; in a sense,
243 it is accidental that it is represented by a pointer. If a pointer
244 represents a primitive value, then it really does point to that value:
245 no unevaluated thunks, no indirections…nothing can be at the
246 other end of the pointer than the primitive value.
250 There are some restrictions on the use of primitive types, the main
251 one being that you can't pass a primitive value to a polymorphic
252 function or store one in a polymorphic data type. This rules out
253 things like <literal>[Int#]</literal> (i.e. lists of primitive
254 integers). The reason for this restriction is that polymorphic
255 arguments and constructor fields are assumed to be pointers: if an
256 unboxed integer is stored in one of these, the garbage collector would
257 attempt to follow it, leading to unpredictable space leaks. Or a
258 <function>seq</function> operation on the polymorphic component may
259 attempt to dereference the pointer, with disastrous results. Even
260 worse, the unboxed value might be larger than a pointer
261 (<literal>Double#</literal> for instance).
265 Nevertheless, A numerically-intensive program using unboxed types can
266 go a <emphasis>lot</emphasis> faster than its “standard”
267 counterpart—we saw a threefold speedup on one example.
272 <sect2 id="unboxed-tuples">
273 <title>Unboxed Tuples
277 Unboxed tuples aren't really exported by <literal>GHC.Exts</literal>,
278 they're available by default with <option>-fglasgow-exts</option>. An
279 unboxed tuple looks like this:
291 where <literal>e_1..e_n</literal> are expressions of any
292 type (primitive or non-primitive). The type of an unboxed tuple looks
297 Unboxed tuples are used for functions that need to return multiple
298 values, but they avoid the heap allocation normally associated with
299 using fully-fledged tuples. When an unboxed tuple is returned, the
300 components are put directly into registers or on the stack; the
301 unboxed tuple itself does not have a composite representation. Many
302 of the primitive operations listed in this section return unboxed
307 There are some pretty stringent restrictions on the use of unboxed tuples:
316 Unboxed tuple types are subject to the same restrictions as
317 other unboxed types; i.e. they may not be stored in polymorphic data
318 structures or passed to polymorphic functions.
325 Unboxed tuples may only be constructed as the direct result of
326 a function, and may only be deconstructed with a <literal>case</literal> expression.
327 eg. the following are valid:
331 f x y = (# x+1, y-1 #)
332 g x = case f x x of { (# a, b #) -> a + b }
336 but the following are invalid:
350 No variable can have an unboxed tuple type. This is illegal:
354 f :: (# Int, Int #) -> (# Int, Int #)
359 because <literal>x</literal> has an unboxed tuple type.
369 Note: we may relax some of these restrictions in the future.
373 The <literal>IO</literal> and <literal>ST</literal> monads use unboxed
374 tuples to avoid unnecessary allocation during sequences of operations.
381 <!-- ====================== SYNTACTIC EXTENSIONS ======================= -->
383 <sect1 id="syntax-extns">
384 <title>Syntactic extensions</title>
386 <!-- ====================== HIERARCHICAL MODULES ======================= -->
388 <sect2 id="hierarchical-modules">
389 <title>Hierarchical Modules</title>
391 <para>GHC supports a small extension to the syntax of module
392 names: a module name is allowed to contain a dot
393 <literal>‘.’</literal>. This is also known as the
394 “hierarchical module namespace” extension, because
395 it extends the normally flat Haskell module namespace into a
396 more flexible hierarchy of modules.</para>
398 <para>This extension has very little impact on the language
399 itself; modules names are <emphasis>always</emphasis> fully
400 qualified, so you can just think of the fully qualified module
401 name as <quote>the module name</quote>. In particular, this
402 means that the full module name must be given after the
403 <literal>module</literal> keyword at the beginning of the
404 module; for example, the module <literal>A.B.C</literal> must
407 <programlisting>module A.B.C</programlisting>
410 <para>It is a common strategy to use the <literal>as</literal>
411 keyword to save some typing when using qualified names with
412 hierarchical modules. For example:</para>
415 import qualified Control.Monad.ST.Strict as ST
418 <para>For details on how GHC searches for source and interface
419 files in the presence of hierarchical modules, see <xref
420 linkend="search-path">.</para>
422 <para>GHC comes with a large collection of libraries arranged
423 hierarchically; see the accompanying library documentation.
424 There is an ongoing project to create and maintain a stable set
425 of <quote>core</quote> libraries used by several Haskell
426 compilers, and the libraries that GHC comes with represent the
427 current status of that project. For more details, see <ulink
428 url="http://www.haskell.org/~simonmar/libraries/libraries.html">Haskell
429 Libraries</ulink>.</para>
433 <!-- ====================== PATTERN GUARDS ======================= -->
435 <sect2 id="pattern-guards">
436 <title>Pattern guards</title>
439 <indexterm><primary>Pattern guards (Glasgow extension)</primary></indexterm>
440 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.)
444 Suppose we have an abstract data type of finite maps, with a
448 lookup :: FiniteMap -> Int -> Maybe Int
451 The lookup returns <function>Nothing</function> if the supplied key is not in the domain of the mapping, and <function>(Just v)</function> otherwise,
452 where <VarName>v</VarName> is the value that the key maps to. Now consider the following definition:
456 clunky env var1 var2 | ok1 && ok2 = val1 + val2
457 | otherwise = var1 + var2
468 The auxiliary functions are
472 maybeToBool :: Maybe a -> Bool
473 maybeToBool (Just x) = True
474 maybeToBool Nothing = False
476 expectJust :: Maybe a -> a
477 expectJust (Just x) = x
478 expectJust Nothing = error "Unexpected Nothing"
482 What is <function>clunky</function> doing? The guard <literal>ok1 &&
483 ok2</literal> checks that both lookups succeed, using
484 <function>maybeToBool</function> to convert the <function>Maybe</function>
485 types to booleans. The (lazily evaluated) <function>expectJust</function>
486 calls extract the values from the results of the lookups, and binds the
487 returned values to <VarName>val1</VarName> and <VarName>val2</VarName>
488 respectively. If either lookup fails, then clunky takes the
489 <literal>otherwise</literal> case and returns the sum of its arguments.
493 This is certainly legal Haskell, but it is a tremendously verbose and
494 un-obvious way to achieve the desired effect. Arguably, a more direct way
495 to write clunky would be to use case expressions:
499 clunky env var1 var1 = case lookup env var1 of
501 Just val1 -> case lookup env var2 of
503 Just val2 -> val1 + val2
509 This is a bit shorter, but hardly better. Of course, we can rewrite any set
510 of pattern-matching, guarded equations as case expressions; that is
511 precisely what the compiler does when compiling equations! The reason that
512 Haskell provides guarded equations is because they allow us to write down
513 the cases we want to consider, one at a time, independently of each other.
514 This structure is hidden in the case version. Two of the right-hand sides
515 are really the same (<function>fail</function>), and the whole expression
516 tends to become more and more indented.
520 Here is how I would write clunky:
525 | Just val1 <- lookup env var1
526 , Just val2 <- lookup env var2
528 ...other equations for clunky...
532 The semantics should be clear enough. The qualifers are matched in order.
533 For a <literal><-</literal> qualifier, which I call a pattern guard, the
534 right hand side is evaluated and matched against the pattern on the left.
535 If the match fails then the whole guard fails and the next equation is
536 tried. If it succeeds, then the appropriate binding takes place, and the
537 next qualifier is matched, in the augmented environment. Unlike list
538 comprehensions, however, the type of the expression to the right of the
539 <literal><-</literal> is the same as the type of the pattern to its
540 left. The bindings introduced by pattern guards scope over all the
541 remaining guard qualifiers, and over the right hand side of the equation.
545 Just as with list comprehensions, boolean expressions can be freely mixed
546 with among the pattern guards. For example:
557 Haskell's current guards therefore emerge as a special case, in which the
558 qualifier list has just one element, a boolean expression.
562 <!-- ===================== Recursive do-notation =================== -->
564 <sect2 id="mdo-notation">
565 <title>The recursive do-notation
568 <para> The recursive do-notation (also known as mdo-notation) is implemented as described in
569 "A recursive do for Haskell",
570 Levent Erkok, John Launchbury",
571 Haskell Workshop 2002, pages: 29-37. Pittsburgh, Pennsylvania.
574 The do-notation of Haskell does not allow <emphasis>recursive bindings</emphasis>,
575 that is, the variables bound in a do-expression are visible only in the textually following
576 code block. Compare this to a let-expression, where bound variables are visible in the entire binding
577 group. It turns out that several applications can benefit from recursive bindings in
578 the do-notation, and this extension provides the necessary syntactic support.
581 Here is a simple (yet contrived) example:
584 import Control.Monad.Fix
586 justOnes = mdo xs <- Just (1:xs)
590 As you can guess <literal>justOnes</literal> will evaluate to <literal>Just [1,1,1,...</literal>.
594 The Control.Monad.Fix library introduces the <literal>MonadFix</literal> class. It's definition is:
597 class Monad m => MonadFix m where
598 mfix :: (a -> m a) -> m a
601 The function <literal>mfix</literal>
602 dictates how the required recursion operation should be performed. If recursive bindings are required for a monad,
603 then that monad must be declared an instance of the <literal>MonadFix</literal> class.
604 For details, see the above mentioned reference.
607 The following instances of <literal>MonadFix</literal> are automatically provided: List, Maybe, IO.
608 Furthermore, the Control.Monad.ST and Control.Monad.ST.Lazy modules provide the instances of the MonadFix class
609 for Haskell's internal state monad (strict and lazy, respectively).
612 There are three important points in using the recursive-do notation:
615 The recursive version of the do-notation uses the keyword <literal>mdo</literal> (rather
616 than <literal>do</literal>).
620 You should <literal>import Control.Monad.Fix</literal>.
621 (Note: Strictly speaking, this import is required only when you need to refer to the name
622 <literal>MonadFix</literal> in your program, but the import is always safe, and the programmers
623 are encouraged to always import this module when using the mdo-notation.)
627 As with other extensions, ghc should be given the flag <literal>-fglasgow-exts</literal>
633 The web page: <ulink url="http://www.cse.ogi.edu/PacSoft/projects/rmb">http://www.cse.ogi.edu/PacSoft/projects/rmb</ulink>
634 contains up to date information on recursive monadic bindings.
638 Historical note: The old implementation of the mdo-notation (and most
639 of the existing documents) used the name
640 <literal>MonadRec</literal> for the class and the corresponding library.
641 This name is not supported by GHC.
647 <!-- ===================== PARALLEL LIST COMPREHENSIONS =================== -->
649 <sect2 id="parallel-list-comprehensions">
650 <title>Parallel List Comprehensions</title>
651 <indexterm><primary>list comprehensions</primary><secondary>parallel</secondary>
653 <indexterm><primary>parallel list comprehensions</primary>
656 <para>Parallel list comprehensions are a natural extension to list
657 comprehensions. List comprehensions can be thought of as a nice
658 syntax for writing maps and filters. Parallel comprehensions
659 extend this to include the zipWith family.</para>
661 <para>A parallel list comprehension has multiple independent
662 branches of qualifier lists, each separated by a `|' symbol. For
663 example, the following zips together two lists:</para>
666 [ (x, y) | x <- xs | y <- ys ]
669 <para>The behavior of parallel list comprehensions follows that of
670 zip, in that the resulting list will have the same length as the
671 shortest branch.</para>
673 <para>We can define parallel list comprehensions by translation to
674 regular comprehensions. Here's the basic idea:</para>
676 <para>Given a parallel comprehension of the form: </para>
679 [ e | p1 <- e11, p2 <- e12, ...
680 | q1 <- e21, q2 <- e22, ...
685 <para>This will be translated to: </para>
688 [ e | ((p1,p2), (q1,q2), ...) <- zipN [(p1,p2) | p1 <- e11, p2 <- e12, ...]
689 [(q1,q2) | q1 <- e21, q2 <- e22, ...]
694 <para>where `zipN' is the appropriate zip for the given number of
699 <sect2 id="rebindable-syntax">
700 <title>Rebindable syntax</title>
703 <para>GHC allows most kinds of built-in syntax to be rebound by
704 the user, to facilitate replacing the <literal>Prelude</literal>
705 with a home-grown version, for example.</para>
707 <para>You may want to define your own numeric class
708 hierarchy. It completely defeats that purpose if the
709 literal "1" means "<literal>Prelude.fromInteger
710 1</literal>", which is what the Haskell Report specifies.
711 So the <option>-fno-implicit-prelude</option> flag causes
712 the following pieces of built-in syntax to refer to
713 <emphasis>whatever is in scope</emphasis>, not the Prelude
718 <para>Integer and fractional literals mean
719 "<literal>fromInteger 1</literal>" and
720 "<literal>fromRational 3.2</literal>", not the
721 Prelude-qualified versions; both in expressions and in
723 <para>However, the standard Prelude <literal>Eq</literal> class
724 is still used for the equality test necessary for literal patterns.</para>
728 <para>Negation (e.g. "<literal>- (f x)</literal>")
729 means "<literal>negate (f x)</literal>" (not
730 <literal>Prelude.negate</literal>).</para>
734 <para>In an n+k pattern, the standard Prelude
735 <literal>Ord</literal> class is still used for comparison,
736 but the necessary subtraction uses whatever
737 "<literal>(-)</literal>" is in scope (not
738 "<literal>Prelude.(-)</literal>").</para>
742 <para>"Do" notation is translated using whatever
743 functions <literal>(>>=)</literal>,
744 <literal>(>>)</literal>, <literal>fail</literal>, and
745 <literal>return</literal>, are in scope (not the Prelude
746 versions). List comprehensions, and parallel array
747 comprehensions, are unaffected. </para></listitem>
750 <para>Be warned: this is an experimental facility, with fewer checks than
751 usual. In particular, it is essential that the functions GHC finds in scope
752 must have the appropriate types, namely:
754 fromInteger :: forall a. (...) => Integer -> a
755 fromRational :: forall a. (...) => Rational -> a
756 negate :: forall a. (...) => a -> a
757 (-) :: forall a. (...) => a -> a -> a
758 (>>=) :: forall m a. (...) => m a -> (a -> m b) -> m b
759 (>>) :: forall m a. (...) => m a -> m b -> m b
760 return :: forall m a. (...) => a -> m a
761 fail :: forall m a. (...) => String -> m a
763 (The (...) part can be any context including the empty context; that part
765 If the functions don't have the right type, very peculiar things may
766 happen. Use <literal>-dcore-lint</literal> to
767 typecheck the desugared program. If Core Lint is happy you should be all right.</para>
773 <!-- TYPE SYSTEM EXTENSIONS -->
774 <sect1 id="type-extensions">
775 <title>Type system extensions</title>
777 <sect2 id="nullary-types">
778 <title>Data types with no constructors</title>
780 <para>With the <option>-fglasgow-exts</option> flag, GHC lets you declare
781 a data type with no constructors. For example:</para>
785 data T a -- T :: * -> *
788 <para>Syntactically, the declaration lacks the "= constrs" part. The
789 type can be parameterised over types of any kind, but if the kind is
790 not <literal>*</literal> then an explicit kind annotation must be used
791 (see <xref linkend="sec-kinding">).</para>
793 <para>Such data types have only one value, namely bottom.
794 Nevertheless, they can be useful when defining "phantom types".</para>
797 <sect2 id="infix-tycons">
798 <title>Infix type constructors</title>
801 GHC allows type constructors to be operators, and to be written infix, very much
802 like expressions. More specifically:
805 A type constructor can be an operator, beginning with a colon; e.g. <literal>:*:</literal>.
806 The lexical syntax is the same as that for data constructors.
809 Types can be written infix. For example <literal>Int :*: Bool</literal>.
813 as for expressions, both for type constructors and type variables; e.g. <literal>Int `Either` Bool</literal>, or
814 <literal>Int `a` Bool</literal>. Similarly, parentheses work the same; e.g. <literal>(:*:) Int Bool</literal>.
817 Fixities may be declared for type constructors just as for data constructors. However,
818 one cannot distinguish between the two in a fixity declaration; a fixity declaration
819 sets the fixity for a data constructor and the corresponding type constructor. For example:
823 sets the fixity for both type constructor <literal>T</literal> and data constructor <literal>T</literal>,
824 and similarly for <literal>:*:</literal>.
825 <literal>Int `a` Bool</literal>.
828 Function arrow is <literal>infixr</literal> with fixity 0. (This might change; I'm not sure what it should be.)
831 Data type and type-synonym declarations can be written infix. E.g.
833 data a :*: b = Foo a b
834 type a :+: b = Either a b
838 The only thing that differs between operators in types and operators in expressions is that
839 ordinary non-constructor operators, such as <literal>+</literal> and <literal>*</literal>
840 are not allowed in types. Reason: the uniform thing to do would be to make them type
841 variables, but that's not very useful. A less uniform but more useful thing would be to
842 allow them to be type <emphasis>constructors</emphasis>. But that gives trouble in export
843 lists. So for now we just exclude them.
850 <sect2 id="sec-kinding">
851 <title>Explicitly-kinded quantification</title>
854 Haskell infers the kind of each type variable. Sometimes it is nice to be able
855 to give the kind explicitly as (machine-checked) documentation,
856 just as it is nice to give a type signature for a function. On some occasions,
857 it is essential to do so. For example, in his paper "Restricted Data Types in Haskell" (Haskell Workshop 1999)
858 John Hughes had to define the data type:
860 data Set cxt a = Set [a]
861 | Unused (cxt a -> ())
863 The only use for the <literal>Unused</literal> constructor was to force the correct
864 kind for the type variable <literal>cxt</literal>.
867 GHC now instead allows you to specify the kind of a type variable directly, wherever
868 a type variable is explicitly bound. Namely:
870 <listitem><para><literal>data</literal> declarations:
872 data Set (cxt :: * -> *) a = Set [a]
873 </Screen></para></listitem>
874 <listitem><para><literal>type</literal> declarations:
876 type T (f :: * -> *) = f Int
877 </Screen></para></listitem>
878 <listitem><para><literal>class</literal> declarations:
880 class (Eq a) => C (f :: * -> *) a where ...
881 </Screen></para></listitem>
882 <listitem><para><literal>forall</literal>'s in type signatures:
884 f :: forall (cxt :: * -> *). Set cxt Int
885 </Screen></para></listitem>
890 The parentheses are required. Some of the spaces are required too, to
891 separate the lexemes. If you write <literal>(f::*->*)</literal> you
892 will get a parse error, because "<literal>::*->*</literal>" is a
893 single lexeme in Haskell.
897 As part of the same extension, you can put kind annotations in types
900 f :: (Int :: *) -> Int
901 g :: forall a. a -> (a :: *)
905 atype ::= '(' ctype '::' kind ')
907 The parentheses are required.
912 <sect2 id="class-method-types">
913 <title>Class method types
916 Haskell 98 prohibits class method types to mention constraints on the
917 class type variable, thus:
920 fromList :: [a] -> s a
921 elem :: Eq a => a -> s a -> Bool
923 The type of <literal>elem</literal> is illegal in Haskell 98, because it
924 contains the constraint <literal>Eq a</literal>, constrains only the
925 class type variable (in this case <literal>a</literal>).
928 With the <option>-fglasgow-exts</option> GHC lifts this restriction.
933 <sect2 id="multi-param-type-classes">
934 <title>Multi-parameter type classes
938 This section documents GHC's implementation of multi-parameter type
939 classes. There's lots of background in the paper <ULink
940 URL="http://research.microsoft.com/~simonpj/multi.ps.gz" >Type
941 classes: exploring the design space</ULink > (Simon Peyton Jones, Mark
946 <sect3 id="type-restrictions">
950 GHC imposes the following restrictions on the form of a qualified
951 type, whether declared in a type signature
952 or inferred. Consider the type:
955 forall tv1..tvn (c1, ...,cn) => type
958 (Here, I write the "foralls" explicitly, although the Haskell source
959 language omits them; in Haskell 1.4, all the free type variables of an
960 explicit source-language type signature are universally quantified,
961 except for the class type variables in a class declaration. However,
962 in GHC, you can give the foralls if you want. See <xref LinkEnd="universal-quantification">).
971 <emphasis>Each universally quantified type variable
972 <literal>tvi</literal> must be reachable from <literal>type</literal></emphasis>.
974 A type variable is "reachable" if it it is functionally dependent
975 (see <xref linkend="functional-dependencies">)
976 on the type variables free in <literal>type</literal>.
977 The reason for this is that a value with a type that does not obey
978 this restriction could not be used without introducing
980 Here, for example, is an illegal type:
984 forall a. Eq a => Int
988 When a value with this type was used, the constraint <literal>Eq tv</literal>
989 would be introduced where <literal>tv</literal> is a fresh type variable, and
990 (in the dictionary-translation implementation) the value would be
991 applied to a dictionary for <literal>Eq tv</literal>. The difficulty is that we
992 can never know which instance of <literal>Eq</literal> to use because we never
993 get any more information about <literal>tv</literal>.
1000 <emphasis>Every constraint <literal>ci</literal> must mention at least one of the
1001 universally quantified type variables <literal>tvi</literal></emphasis>.
1003 For example, this type is OK because <literal>C a b</literal> mentions the
1004 universally quantified type variable <literal>b</literal>:
1008 forall a. C a b => burble
1012 The next type is illegal because the constraint <literal>Eq b</literal> does not
1013 mention <literal>a</literal>:
1017 forall a. Eq b => burble
1021 The reason for this restriction is milder than the other one. The
1022 excluded types are never useful or necessary (because the offending
1023 context doesn't need to be witnessed at this point; it can be floated
1024 out). Furthermore, floating them out increases sharing. Lastly,
1025 excluding them is a conservative choice; it leaves a patch of
1026 territory free in case we need it later.
1037 Unlike Haskell 1.4, constraints in types do <emphasis>not</emphasis> have to be of
1038 the form <emphasis>(class type-variables)</emphasis>. Thus, these type signatures
1045 f :: Eq (m a) => [m a] -> [m a]
1052 This choice recovers principal types, a property that Haskell 1.4 does not have.
1058 <title>Class declarations</title>
1066 <emphasis>Multi-parameter type classes are permitted</emphasis>. For example:
1070 class Collection c a where
1071 union :: c a -> c a -> c a
1082 <emphasis>The class hierarchy must be acyclic</emphasis>. However, the definition
1083 of "acyclic" involves only the superclass relationships. For example,
1089 op :: D b => a -> b -> b
1092 class C a => D a where { ... }
1096 Here, <literal>C</literal> is a superclass of <literal>D</literal>, but it's OK for a
1097 class operation <literal>op</literal> of <literal>C</literal> to mention <literal>D</literal>. (It
1098 would not be OK for <literal>D</literal> to be a superclass of <literal>C</literal>.)
1105 <emphasis>There are no restrictions on the context in a class declaration
1106 (which introduces superclasses), except that the class hierarchy must
1107 be acyclic</emphasis>. So these class declarations are OK:
1111 class Functor (m k) => FiniteMap m k where
1114 class (Monad m, Monad (t m)) => Transform t m where
1115 lift :: m a -> (t m) a
1125 <emphasis>All of the class type variables must be reachable (in the sense
1126 mentioned in <xref linkend="type-restrictions">)
1127 from the free varibles of each method type
1128 </emphasis>. For example:
1132 class Coll s a where
1134 insert :: s -> a -> s
1138 is not OK, because the type of <literal>empty</literal> doesn't mention
1139 <literal>a</literal>. This rule is a consequence of Rule 1(a), above, for
1140 types, and has the same motivation.
1142 Sometimes, offending class declarations exhibit misunderstandings. For
1143 example, <literal>Coll</literal> might be rewritten
1147 class Coll s a where
1149 insert :: s a -> a -> s a
1153 which makes the connection between the type of a collection of
1154 <literal>a</literal>'s (namely <literal>(s a)</literal>) and the element type <literal>a</literal>.
1155 Occasionally this really doesn't work, in which case you can split the
1163 class CollE s => Coll s a where
1164 insert :: s -> a -> s
1177 <sect3 id="instance-decls">
1178 <title>Instance declarations</title>
1186 <emphasis>Instance declarations may not overlap</emphasis>. The two instance
1191 instance context1 => C type1 where ...
1192 instance context2 => C type2 where ...
1196 "overlap" if <literal>type1</literal> and <literal>type2</literal> unify
1198 However, if you give the command line option
1199 <option>-fallow-overlapping-instances</option><indexterm><primary>-fallow-overlapping-instances
1200 option</primary></indexterm> then overlapping instance declarations are permitted.
1201 However, GHC arranges never to commit to using an instance declaration
1202 if another instance declaration also applies, either now or later.
1208 EITHER <literal>type1</literal> and <literal>type2</literal> do not unify
1214 OR <literal>type2</literal> is a substitution instance of <literal>type1</literal>
1215 (but not identical to <literal>type1</literal>), or vice versa.
1219 Notice that these rules
1224 make it clear which instance decl to use
1225 (pick the most specific one that matches)
1232 do not mention the contexts <literal>context1</literal>, <literal>context2</literal>
1233 Reason: you can pick which instance decl
1234 "matches" based on the type.
1239 However the rules are over-conservative. Two instance declarations can overlap,
1240 but it can still be clear in particular situations which to use. For example:
1242 instance C (Int,a) where ...
1243 instance C (a,Bool) where ...
1245 These are rejected by GHC's rules, but it is clear what to do when trying
1246 to solve the constraint <literal>C (Int,Int)</literal> because the second instance
1247 cannot apply. Yell if this restriction bites you.
1250 GHC is also conservative about committing to an overlapping instance. For example:
1252 class C a where { op :: a -> a }
1253 instance C [Int] where ...
1254 instance C a => C [a] where ...
1256 f :: C b => [b] -> [b]
1259 From the RHS of f we get the constraint <literal>C [b]</literal>. But
1260 GHC does not commit to the second instance declaration, because in a paricular
1261 call of f, b might be instantiate to Int, so the first instance declaration
1262 would be appropriate. So GHC rejects the program. If you add <option>-fallow-incoherent-instances</option>
1263 GHC will instead silently pick the second instance, without complaining about
1264 the problem of subsequent instantiations.
1267 Regrettably, GHC doesn't guarantee to detect overlapping instance
1268 declarations if they appear in different modules. GHC can "see" the
1269 instance declarations in the transitive closure of all the modules
1270 imported by the one being compiled, so it can "see" all instance decls
1271 when it is compiling <literal>Main</literal>. However, it currently chooses not
1272 to look at ones that can't possibly be of use in the module currently
1273 being compiled, in the interests of efficiency. (Perhaps we should
1274 change that decision, at least for <literal>Main</literal>.)
1281 <emphasis>There are no restrictions on the type in an instance
1282 <emphasis>head</emphasis>, except that at least one must not be a type variable</emphasis>.
1283 The instance "head" is the bit after the "=>" in an instance decl. For
1284 example, these are OK:
1288 instance C Int a where ...
1290 instance D (Int, Int) where ...
1292 instance E [[a]] where ...
1296 Note that instance heads <emphasis>may</emphasis> contain repeated type variables.
1297 For example, this is OK:
1301 instance Stateful (ST s) (MutVar s) where ...
1304 See <xref linkend="undecidable-instances"> for an experimental
1305 extension to lift this restriction.
1311 <emphasis>Unlike Haskell 1.4, instance heads may use type
1312 synonyms</emphasis>. As always, using a type synonym is just shorthand for
1313 writing the RHS of the type synonym definition. For example:
1317 type Point = (Int,Int)
1318 instance C Point where ...
1319 instance C [Point] where ...
1323 is legal. However, if you added
1327 instance C (Int,Int) where ...
1331 as well, then the compiler will complain about the overlapping
1332 (actually, identical) instance declarations. As always, type synonyms
1333 must be fully applied. You cannot, for example, write:
1338 instance Monad P where ...
1342 This design decision is independent of all the others, and easily
1343 reversed, but it makes sense to me.
1350 <emphasis>The types in an instance-declaration <emphasis>context</emphasis> must all
1351 be type variables</emphasis>. Thus
1355 instance C a b => Eq (a,b) where ...
1363 instance C Int b => Foo b where ...
1367 is not OK. See <xref linkend="undecidable-instances"> for an experimental
1368 extension to lift this restriction.
1383 <sect2 id="undecidable-instances">
1384 <title>Undecidable instances</title>
1386 <para>The rules for instance declarations state that:
1388 <listitem><para>At least one of the types in the <emphasis>head</emphasis> of
1389 an instance declaration <emphasis>must not</emphasis> be a type variable.
1391 <listitem><para>All of the types in the <emphasis>context</emphasis> of
1392 an instance declaration <emphasis>must</emphasis> be type variables.
1395 These restrictions ensure that
1396 context reduction terminates: each reduction step removes one type
1397 constructor. For example, the following would make the type checker
1398 loop if it wasn't excluded:
1400 instance C a => C a where ...
1402 There are two situations in which the rule is a bit of a pain. First,
1403 if one allows overlapping instance declarations then it's quite
1404 convenient to have a "default instance" declaration that applies if
1405 something more specific does not:
1414 Second, sometimes you might want to use the following to get the
1415 effect of a "class synonym":
1419 class (C1 a, C2 a, C3 a) => C a where { }
1421 instance (C1 a, C2 a, C3 a) => C a where { }
1425 This allows you to write shorter signatures:
1437 f :: (C1 a, C2 a, C3 a) => ...
1441 Voluminous correspondence on the Haskell mailing list has convinced me
1442 that it's worth experimenting with more liberal rules. If you use
1443 the experimental flag <option>-fallow-undecidable-instances</option>
1444 <indexterm><primary>-fallow-undecidable-instances
1445 option</primary></indexterm>, you can use arbitrary
1446 types in both an instance context and instance head. Termination is ensured by having a
1447 fixed-depth recursion stack. If you exceed the stack depth you get a
1448 sort of backtrace, and the opportunity to increase the stack depth
1449 with <option>-fcontext-stack</option><emphasis>N</emphasis>.
1452 I'm on the lookout for a less brutal solution: a simple rule that preserves decidability while
1453 allowing these idioms interesting idioms.
1457 <sect2 id="implicit-parameters">
1458 <title>Implicit parameters
1461 <para> Implicit paramters are implemented as described in
1462 "Implicit parameters: dynamic scoping with static types",
1463 J Lewis, MB Shields, E Meijer, J Launchbury,
1464 27th ACM Symposium on Principles of Programming Languages (POPL'00),
1467 <para>(Most of the following, stil rather incomplete, documentation is due to Jeff Lewis.)</para>
1469 A variable is called <emphasis>dynamically bound</emphasis> when it is bound by the calling
1470 context of a function and <emphasis>statically bound</emphasis> when bound by the callee's
1471 context. In Haskell, all variables are statically bound. Dynamic
1472 binding of variables is a notion that goes back to Lisp, but was later
1473 discarded in more modern incarnations, such as Scheme. Dynamic binding
1474 can be very confusing in an untyped language, and unfortunately, typed
1475 languages, in particular Hindley-Milner typed languages like Haskell,
1476 only support static scoping of variables.
1479 However, by a simple extension to the type class system of Haskell, we
1480 can support dynamic binding. Basically, we express the use of a
1481 dynamically bound variable as a constraint on the type. These
1482 constraints lead to types of the form <literal>(?x::t') => t</literal>, which says "this
1483 function uses a dynamically-bound variable <literal>?x</literal>
1484 of type <literal>t'</literal>". For
1485 example, the following expresses the type of a sort function,
1486 implicitly parameterized by a comparison function named <literal>cmp</literal>.
1488 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1490 The dynamic binding constraints are just a new form of predicate in the type class system.
1493 An implicit parameter occurs in an expression using the special form <literal>?x</literal>,
1494 where <literal>x</literal> is
1495 any valid identifier (e.g. <literal>ord ?x</literal> is a valid expression).
1496 Use of this construct also introduces a new
1497 dynamic-binding constraint in the type of the expression.
1498 For example, the following definition
1499 shows how we can define an implicitly parameterized sort function in
1500 terms of an explicitly parameterized <literal>sortBy</literal> function:
1502 sortBy :: (a -> a -> Bool) -> [a] -> [a]
1504 sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]
1510 <title>Implicit-parameter type constraints</title>
1512 Dynamic binding constraints behave just like other type class
1513 constraints in that they are automatically propagated. Thus, when a
1514 function is used, its implicit parameters are inherited by the
1515 function that called it. For example, our <literal>sort</literal> function might be used
1516 to pick out the least value in a list:
1518 least :: (?cmp :: a -> a -> Bool) => [a] -> a
1519 least xs = fst (sort xs)
1521 Without lifting a finger, the <literal>?cmp</literal> parameter is
1522 propagated to become a parameter of <literal>least</literal> as well. With explicit
1523 parameters, the default is that parameters must always be explicit
1524 propagated. With implicit parameters, the default is to always
1528 An implicit-parameter type constraint differs from other type class constraints in the
1529 following way: All uses of a particular implicit parameter must have
1530 the same type. This means that the type of <literal>(?x, ?x)</literal>
1531 is <literal>(?x::a) => (a,a)</literal>, and not
1532 <literal>(?x::a, ?x::b) => (a, b)</literal>, as would be the case for type
1536 <para> You can't have an implicit parameter in the context of a class or instance
1537 declaration. For example, both these declarations are illegal:
1539 class (?x::Int) => C a where ...
1540 instance (?x::a) => Foo [a] where ...
1542 Reason: exactly which implicit parameter you pick up depends on exactly where
1543 you invoke a function. But the ``invocation'' of instance declarations is done
1544 behind the scenes by the compiler, so it's hard to figure out exactly where it is done.
1545 Easiest thing is to outlaw the offending types.</para>
1547 Implicit-parameter constraints do not cause ambiguity. For example, consider:
1549 f :: (?x :: [a]) => Int -> Int
1552 g :: (Read a, Show a) => String -> String
1555 Here, <literal>g</literal> has an ambiguous type, and is rejected, but <literal>f</literal>
1556 is fine. The binding for <literal>?x</literal> at <literal>f</literal>'s call site is
1557 quite unambiguous, and fixes the type <literal>a</literal>.
1562 <title>Implicit-parameter bindings</title>
1565 An implicit parameter is <emphasis>bound</emphasis> using the standard
1566 <literal>let</literal> or <literal>where</literal> binding forms.
1567 For example, we define the <literal>min</literal> function by binding
1568 <literal>cmp</literal>.
1571 min = let ?cmp = (<=) in least
1575 A group of implicit-parameter bindings may occur anywhere a normal group of Haskell
1576 bindings can occur, except at top level. That is, they can occur in a <literal>let</literal>
1577 (including in a list comprehension, or do-notation, or pattern guards),
1578 or a <literal>where</literal> clause.
1579 Note the following points:
1582 An implicit-parameter binding group must be a
1583 collection of simple bindings to implicit-style variables (no
1584 function-style bindings, and no type signatures); these bindings are
1585 neither polymorphic or recursive.
1588 You may not mix implicit-parameter bindings with ordinary bindings in a
1589 single <literal>let</literal>
1590 expression; use two nested <literal>let</literal>s instead.
1591 (In the case of <literal>where</literal> you are stuck, since you can't nest <literal>where</literal> clauses.)
1595 You may put multiple implicit-parameter bindings in a
1596 single binding group; but they are <emphasis>not</emphasis> treated
1597 as a mutually recursive group (as ordinary <literal>let</literal> bindings are).
1598 Instead they are treated as a non-recursive group, simultaneously binding all the implicit
1599 parameter. The bindings are not nested, and may be re-ordered without changing
1600 the meaning of the program.
1601 For example, consider:
1603 f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
1605 The use of <literal>?x</literal> in the binding for <literal>?y</literal> does not "see"
1606 the binding for <literal>?x</literal>, so the type of <literal>f</literal> is
1608 f :: (?x::Int) => Int -> Int
1617 <sect2 id="linear-implicit-parameters">
1618 <title>Linear implicit parameters
1621 Linear implicit parameters are an idea developed by Koen Claessen,
1622 Mark Shields, and Simon PJ. They address the long-standing
1623 problem that monads seem over-kill for certain sorts of problem, notably:
1626 <listitem> <para> distributing a supply of unique names </para> </listitem>
1627 <listitem> <para> distributing a suppply of random numbers </para> </listitem>
1628 <listitem> <para> distributing an oracle (as in QuickCheck) </para> </listitem>
1632 Linear implicit parameters are just like ordinary implicit parameters,
1633 except that they are "linear" -- that is, they cannot be copied, and
1634 must be explicitly "split" instead. Linear implicit parameters are
1635 written '<literal>%x</literal>' instead of '<literal>?x</literal>'.
1636 (The '/' in the '%' suggests the split!)
1641 import GHC.Exts( Splittable )
1643 data NameSupply = ...
1645 splitNS :: NameSupply -> (NameSupply, NameSupply)
1646 newName :: NameSupply -> Name
1648 instance Splittable NameSupply where
1652 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1653 f env (Lam x e) = Lam x' (f env e)
1656 env' = extend env x x'
1657 ...more equations for f...
1659 Notice that the implicit parameter %ns is consumed
1661 <listitem> <para> once by the call to <literal>newName</literal> </para> </listitem>
1662 <listitem> <para> once by the recursive call to <literal>f</literal> </para></listitem>
1666 So the translation done by the type checker makes
1667 the parameter explicit:
1669 f :: NameSupply -> Env -> Expr -> Expr
1670 f ns env (Lam x e) = Lam x' (f ns1 env e)
1672 (ns1,ns2) = splitNS ns
1674 env = extend env x x'
1676 Notice the call to 'split' introduced by the type checker.
1677 How did it know to use 'splitNS'? Because what it really did
1678 was to introduce a call to the overloaded function 'split',
1679 defined by the class <literal>Splittable</literal>:
1681 class Splittable a where
1684 The instance for <literal>Splittable NameSupply</literal> tells GHC how to implement
1685 split for name supplies. But we can simply write
1691 g :: (Splittable a, %ns :: a) => b -> (b,a,a)
1693 The <literal>Splittable</literal> class is built into GHC. It's exported by module
1694 <literal>GHC.Exts</literal>.
1699 <listitem> <para> '<literal>?x</literal>' and '<literal>%x</literal>'
1700 are entirely distinct implicit parameters: you
1701 can use them together and they won't intefere with each other. </para>
1704 <listitem> <para> You can bind linear implicit parameters in 'with' clauses. </para> </listitem>
1706 <listitem> <para>You cannot have implicit parameters (whether linear or not)
1707 in the context of a class or instance declaration. </para></listitem>
1711 <sect3><title>Warnings</title>
1714 The monomorphism restriction is even more important than usual.
1715 Consider the example above:
1717 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1718 f env (Lam x e) = Lam x' (f env e)
1721 env' = extend env x x'
1723 If we replaced the two occurrences of x' by (newName %ns), which is
1724 usually a harmless thing to do, we get:
1726 f :: (%ns :: NameSupply) => Env -> Expr -> Expr
1727 f env (Lam x e) = Lam (newName %ns) (f env e)
1729 env' = extend env x (newName %ns)
1731 But now the name supply is consumed in <emphasis>three</emphasis> places
1732 (the two calls to newName,and the recursive call to f), so
1733 the result is utterly different. Urk! We don't even have
1737 Well, this is an experimental change. With implicit
1738 parameters we have already lost beta reduction anyway, and
1739 (as John Launchbury puts it) we can't sensibly reason about
1740 Haskell programs without knowing their typing.
1745 <sect3><title>Recursive functions</title>
1746 <para>Linear implicit parameters can be particularly tricky when you have a recursive function
1749 foo :: %x::T => Int -> [Int]
1751 foo n = %x : foo (n-1)
1753 where T is some type in class Splittable.</para>
1755 Do you get a list of all the same T's or all different T's
1756 (assuming that split gives two distinct T's back)?
1758 If you supply the type signature, taking advantage of polymorphic
1759 recursion, you get what you'd probably expect. Here's the
1760 translated term, where the implicit param is made explicit:
1763 foo x n = let (x1,x2) = split x
1764 in x1 : foo x2 (n-1)
1766 But if you don't supply a type signature, GHC uses the Hindley
1767 Milner trick of using a single monomorphic instance of the function
1768 for the recursive calls. That is what makes Hindley Milner type inference
1769 work. So the translation becomes
1773 foom n = x : foom (n-1)
1777 Result: 'x' is not split, and you get a list of identical T's. So the
1778 semantics of the program depends on whether or not foo has a type signature.
1781 You may say that this is a good reason to dislike linear implicit parameters
1782 and you'd be right. That is why they are an experimental feature.
1788 <sect2 id="functional-dependencies">
1789 <title>Functional dependencies
1792 <para> Functional dependencies are implemented as described by Mark Jones
1793 in “<ulink url="http://www.cse.ogi.edu/~mpj/pubs/fundeps.html">Type Classes with Functional Dependencies</ulink>”, Mark P. Jones,
1794 In Proceedings of the 9th European Symposium on Programming,
1795 ESOP 2000, Berlin, Germany, March 2000, Springer-Verlag LNCS 1782,
1799 Functional dependencies are introduced by a vertical bar in the syntax of a
1800 class declaration; e.g.
1802 class (Monad m) => MonadState s m | m -> s where ...
1804 class Foo a b c | a b -> c where ...
1806 There should be more documentation, but there isn't (yet). Yell if you need it.
1811 <sect2 id="universal-quantification">
1812 <title>Arbitrary-rank polymorphism
1816 Haskell type signatures are implicitly quantified. The new keyword <literal>forall</literal>
1817 allows us to say exactly what this means. For example:
1825 g :: forall b. (b -> b)
1827 The two are treated identically.
1831 However, GHC's type system supports <emphasis>arbitrary-rank</emphasis>
1832 explicit universal quantification in
1834 For example, all the following types are legal:
1836 f1 :: forall a b. a -> b -> a
1837 g1 :: forall a b. (Ord a, Eq b) => a -> b -> a
1839 f2 :: (forall a. a->a) -> Int -> Int
1840 g2 :: (forall a. Eq a => [a] -> a -> Bool) -> Int -> Int
1842 f3 :: ((forall a. a->a) -> Int) -> Bool -> Bool
1844 Here, <literal>f1</literal> and <literal>g1</literal> are rank-1 types, and
1845 can be written in standard Haskell (e.g. <literal>f1 :: a->b->a</literal>).
1846 The <literal>forall</literal> makes explicit the universal quantification that
1847 is implicitly added by Haskell.
1850 The functions <literal>f2</literal> and <literal>g2</literal> have rank-2 types;
1851 the <literal>forall</literal> is on the left of a function arrrow. As <literal>g2</literal>
1852 shows, the polymorphic type on the left of the function arrow can be overloaded.
1855 The functions <literal>f3</literal> and <literal>g3</literal> have rank-3 types;
1856 they have rank-2 types on the left of a function arrow.
1859 GHC allows types of arbitrary rank; you can nest <literal>forall</literal>s
1860 arbitrarily deep in function arrows. (GHC used to be restricted to rank 2, but
1861 that restriction has now been lifted.)
1862 In particular, a forall-type (also called a "type scheme"),
1863 including an operational type class context, is legal:
1865 <listitem> <para> On the left of a function arrow </para> </listitem>
1866 <listitem> <para> On the right of a function arrow (see <xref linkend="hoist">) </para> </listitem>
1867 <listitem> <para> As the argument of a constructor, or type of a field, in a data type declaration. For
1868 example, any of the <literal>f1,f2,f3,g1,g2,g3</literal> above would be valid
1869 field type signatures.</para> </listitem>
1870 <listitem> <para> As the type of an implicit parameter </para> </listitem>
1871 <listitem> <para> In a pattern type signature (see <xref linkend="scoped-type-variables">) </para> </listitem>
1873 There is one place you cannot put a <literal>forall</literal>:
1874 you cannot instantiate a type variable with a forall-type. So you cannot
1875 make a forall-type the argument of a type constructor. So these types are illegal:
1877 x1 :: [forall a. a->a]
1878 x2 :: (forall a. a->a, Int)
1879 x3 :: Maybe (forall a. a->a)
1881 Of course <literal>forall</literal> becomes a keyword; you can't use <literal>forall</literal> as
1882 a type variable any more!
1891 In a <literal>data</literal> or <literal>newtype</literal> declaration one can quantify
1892 the types of the constructor arguments. Here are several examples:
1898 data T a = T1 (forall b. b -> b -> b) a
1900 data MonadT m = MkMonad { return :: forall a. a -> m a,
1901 bind :: forall a b. m a -> (a -> m b) -> m b
1904 newtype Swizzle = MkSwizzle (Ord a => [a] -> [a])
1910 The constructors have rank-2 types:
1916 T1 :: forall a. (forall b. b -> b -> b) -> a -> T a
1917 MkMonad :: forall m. (forall a. a -> m a)
1918 -> (forall a b. m a -> (a -> m b) -> m b)
1920 MkSwizzle :: (Ord a => [a] -> [a]) -> Swizzle
1926 Notice that you don't need to use a <literal>forall</literal> if there's an
1927 explicit context. For example in the first argument of the
1928 constructor <function>MkSwizzle</function>, an implicit "<literal>forall a.</literal>" is
1929 prefixed to the argument type. The implicit <literal>forall</literal>
1930 quantifies all type variables that are not already in scope, and are
1931 mentioned in the type quantified over.
1935 As for type signatures, implicit quantification happens for non-overloaded
1936 types too. So if you write this:
1939 data T a = MkT (Either a b) (b -> b)
1942 it's just as if you had written this:
1945 data T a = MkT (forall b. Either a b) (forall b. b -> b)
1948 That is, since the type variable <literal>b</literal> isn't in scope, it's
1949 implicitly universally quantified. (Arguably, it would be better
1950 to <emphasis>require</emphasis> explicit quantification on constructor arguments
1951 where that is what is wanted. Feedback welcomed.)
1955 You construct values of types <literal>T1, MonadT, Swizzle</literal> by applying
1956 the constructor to suitable values, just as usual. For example,
1967 a3 = MkSwizzle reverse
1970 a4 = let r x = Just x
1977 mkTs :: (forall b. b -> b -> b) -> a -> [T a]
1978 mkTs f x y = [T1 f x, T1 f y]
1984 The type of the argument can, as usual, be more general than the type
1985 required, as <literal>(MkSwizzle reverse)</literal> shows. (<function>reverse</function>
1986 does not need the <literal>Ord</literal> constraint.)
1990 When you use pattern matching, the bound variables may now have
1991 polymorphic types. For example:
1997 f :: T a -> a -> (a, Char)
1998 f (T1 w k) x = (w k x, w 'c' 'd')
2000 g :: (Ord a, Ord b) => Swizzle -> [a] -> (a -> b) -> [b]
2001 g (MkSwizzle s) xs f = s (map f (s xs))
2003 h :: MonadT m -> [m a] -> m [a]
2004 h m [] = return m []
2005 h m (x:xs) = bind m x $ \y ->
2006 bind m (h m xs) $ \ys ->
2013 In the function <function>h</function> we use the record selectors <literal>return</literal>
2014 and <literal>bind</literal> to extract the polymorphic bind and return functions
2015 from the <literal>MonadT</literal> data structure, rather than using pattern
2021 <title>Type inference</title>
2024 In general, type inference for arbitrary-rank types is undecideable.
2025 GHC uses an algorithm proposed by Odersky and Laufer ("Putting type annotations to work", POPL'96)
2026 to get a decidable algorithm by requiring some help from the programmer.
2027 We do not yet have a formal specification of "some help" but the rule is this:
2030 <emphasis>For a lambda-bound or case-bound variable, x, either the programmer
2031 provides an explicit polymorphic type for x, or GHC's type inference will assume
2032 that x's type has no foralls in it</emphasis>.
2035 What does it mean to "provide" an explicit type for x? You can do that by
2036 giving a type signature for x directly, using a pattern type signature
2037 (<xref linkend="scoped-type-variables">), thus:
2039 \ f :: (forall a. a->a) -> (f True, f 'c')
2041 Alternatively, you can give a type signature to the enclosing
2042 context, which GHC can "push down" to find the type for the variable:
2044 (\ f -> (f True, f 'c')) :: (forall a. a->a) -> (Bool,Char)
2046 Here the type signature on the expression can be pushed inwards
2047 to give a type signature for f. Similarly, and more commonly,
2048 one can give a type signature for the function itself:
2050 h :: (forall a. a->a) -> (Bool,Char)
2051 h f = (f True, f 'c')
2053 You don't need to give a type signature if the lambda bound variable
2054 is a constructor argument. Here is an example we saw earlier:
2056 f :: T a -> a -> (a, Char)
2057 f (T1 w k) x = (w k x, w 'c' 'd')
2059 Here we do not need to give a type signature to <literal>w</literal>, because
2060 it is an argument of constructor <literal>T1</literal> and that tells GHC all
2067 <sect3 id="implicit-quant">
2068 <title>Implicit quantification</title>
2071 GHC performs implicit quantification as follows. <emphasis>At the top level (only) of
2072 user-written types, if and only if there is no explicit <literal>forall</literal>,
2073 GHC finds all the type variables mentioned in the type that are not already
2074 in scope, and universally quantifies them.</emphasis> For example, the following pairs are
2078 f :: forall a. a -> a
2085 h :: forall b. a -> b -> b
2091 Notice that GHC does <emphasis>not</emphasis> find the innermost possible quantification
2094 f :: (a -> a) -> Int
2096 f :: forall a. (a -> a) -> Int
2098 f :: (forall a. a -> a) -> Int
2101 g :: (Ord a => a -> a) -> Int
2102 -- MEANS the illegal type
2103 g :: forall a. (Ord a => a -> a) -> Int
2105 g :: (forall a. Ord a => a -> a) -> Int
2107 The latter produces an illegal type, which you might think is silly,
2108 but at least the rule is simple. If you want the latter type, you
2109 can write your for-alls explicitly. Indeed, doing so is strongly advised
2115 <sect2 id="type-synonyms">
2116 <title>Liberalised type synonyms
2120 Type synonmys are like macros at the type level, and
2121 GHC does validity checking on types <emphasis>only after expanding type synonyms</emphasis>.
2122 That means that GHC can be very much more liberal about type synonyms than Haskell 98:
2124 <listitem> <para>You can write a <literal>forall</literal> (including overloading)
2125 in a type synonym, thus:
2127 type Discard a = forall b. Show b => a -> b -> (a, String)
2132 g :: Discard Int -> (Int,Bool) -- A rank-2 type
2139 You can write an unboxed tuple in a type synonym:
2141 type Pr = (# Int, Int #)
2149 You can apply a type synonym to a forall type:
2151 type Foo a = a -> a -> Bool
2153 f :: Foo (forall b. b->b)
2155 After expanding the synonym, <literal>f</literal> has the legal (in GHC) type:
2157 f :: (forall b. b->b) -> (forall b. b->b) -> Bool
2162 You can apply a type synonym to a partially applied type synonym:
2164 type Generic i o = forall x. i x -> o x
2167 foo :: Generic Id []
2169 After epxanding the synonym, <literal>foo</literal> has the legal (in GHC) type:
2171 foo :: forall x. x -> [x]
2179 GHC currently does kind checking before expanding synonyms (though even that
2183 After expanding type synonyms, GHC does validity checking on types, looking for
2184 the following mal-formedness which isn't detected simply by kind checking:
2187 Type constructor applied to a type involving for-alls.
2190 Unboxed tuple on left of an arrow.
2193 Partially-applied type synonym.
2197 this will be rejected:
2199 type Pr = (# Int, Int #)
2204 because GHC does not allow unboxed tuples on the left of a function arrow.
2209 <title>For-all hoisting</title>
2211 It is often convenient to use generalised type synonyms at the right hand
2212 end of an arrow, thus:
2214 type Discard a = forall b. a -> b -> a
2216 g :: Int -> Discard Int
2219 Simply expanding the type synonym would give
2221 g :: Int -> (forall b. Int -> b -> Int)
2223 but GHC "hoists" the <literal>forall</literal> to give the isomorphic type
2225 g :: forall b. Int -> Int -> b -> Int
2227 In general, the rule is this: <emphasis>to determine the type specified by any explicit
2228 user-written type (e.g. in a type signature), GHC expands type synonyms and then repeatedly
2229 performs the transformation:</emphasis>
2231 <emphasis>type1</emphasis> -> forall a1..an. <emphasis>context2</emphasis> => <emphasis>type2</emphasis>
2233 forall a1..an. <emphasis>context2</emphasis> => <emphasis>type1</emphasis> -> <emphasis>type2</emphasis>
2235 (In fact, GHC tries to retain as much synonym information as possible for use in
2236 error messages, but that is a usability issue.) This rule applies, of course, whether
2237 or not the <literal>forall</literal> comes from a synonym. For example, here is another
2238 valid way to write <literal>g</literal>'s type signature:
2240 g :: Int -> Int -> forall b. b -> Int
2244 When doing this hoisting operation, GHC eliminates duplicate constraints. For
2247 type Foo a = (?x::Int) => Bool -> a
2252 g :: (?x::Int) => Bool -> Bool -> Int
2258 <sect2 id="existential-quantification">
2259 <title>Existentially quantified data constructors
2263 The idea of using existential quantification in data type declarations
2264 was suggested by Laufer (I believe, thought doubtless someone will
2265 correct me), and implemented in Hope+. It's been in Lennart
2266 Augustsson's <Command>hbc</Command> Haskell compiler for several years, and
2267 proved very useful. Here's the idea. Consider the declaration:
2273 data Foo = forall a. MkFoo a (a -> Bool)
2280 The data type <literal>Foo</literal> has two constructors with types:
2286 MkFoo :: forall a. a -> (a -> Bool) -> Foo
2293 Notice that the type variable <literal>a</literal> in the type of <function>MkFoo</function>
2294 does not appear in the data type itself, which is plain <literal>Foo</literal>.
2295 For example, the following expression is fine:
2301 [MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
2307 Here, <literal>(MkFoo 3 even)</literal> packages an integer with a function
2308 <function>even</function> that maps an integer to <literal>Bool</literal>; and <function>MkFoo 'c'
2309 isUpper</function> packages a character with a compatible function. These
2310 two things are each of type <literal>Foo</literal> and can be put in a list.
2314 What can we do with a value of type <literal>Foo</literal>?. In particular,
2315 what happens when we pattern-match on <function>MkFoo</function>?
2321 f (MkFoo val fn) = ???
2327 Since all we know about <literal>val</literal> and <function>fn</function> is that they
2328 are compatible, the only (useful) thing we can do with them is to
2329 apply <function>fn</function> to <literal>val</literal> to get a boolean. For example:
2336 f (MkFoo val fn) = fn val
2342 What this allows us to do is to package heterogenous values
2343 together with a bunch of functions that manipulate them, and then treat
2344 that collection of packages in a uniform manner. You can express
2345 quite a bit of object-oriented-like programming this way.
2348 <sect3 id="existential">
2349 <title>Why existential?
2353 What has this to do with <emphasis>existential</emphasis> quantification?
2354 Simply that <function>MkFoo</function> has the (nearly) isomorphic type
2360 MkFoo :: (exists a . (a, a -> Bool)) -> Foo
2366 But Haskell programmers can safely think of the ordinary
2367 <emphasis>universally</emphasis> quantified type given above, thereby avoiding
2368 adding a new existential quantification construct.
2374 <title>Type classes</title>
2377 An easy extension (implemented in <Command>hbc</Command>) is to allow
2378 arbitrary contexts before the constructor. For example:
2384 data Baz = forall a. Eq a => Baz1 a a
2385 | forall b. Show b => Baz2 b (b -> b)
2391 The two constructors have the types you'd expect:
2397 Baz1 :: forall a. Eq a => a -> a -> Baz
2398 Baz2 :: forall b. Show b => b -> (b -> b) -> Baz
2404 But when pattern matching on <function>Baz1</function> the matched values can be compared
2405 for equality, and when pattern matching on <function>Baz2</function> the first matched
2406 value can be converted to a string (as well as applying the function to it).
2407 So this program is legal:
2414 f (Baz1 p q) | p == q = "Yes"
2416 f (Baz2 v fn) = show (fn v)
2422 Operationally, in a dictionary-passing implementation, the
2423 constructors <function>Baz1</function> and <function>Baz2</function> must store the
2424 dictionaries for <literal>Eq</literal> and <literal>Show</literal> respectively, and
2425 extract it on pattern matching.
2429 Notice the way that the syntax fits smoothly with that used for
2430 universal quantification earlier.
2436 <title>Restrictions</title>
2439 There are several restrictions on the ways in which existentially-quantified
2440 constructors can be use.
2449 When pattern matching, each pattern match introduces a new,
2450 distinct, type for each existential type variable. These types cannot
2451 be unified with any other type, nor can they escape from the scope of
2452 the pattern match. For example, these fragments are incorrect:
2460 Here, the type bound by <function>MkFoo</function> "escapes", because <literal>a</literal>
2461 is the result of <function>f1</function>. One way to see why this is wrong is to
2462 ask what type <function>f1</function> has:
2466 f1 :: Foo -> a -- Weird!
2470 What is this "<literal>a</literal>" in the result type? Clearly we don't mean
2475 f1 :: forall a. Foo -> a -- Wrong!
2479 The original program is just plain wrong. Here's another sort of error
2483 f2 (Baz1 a b) (Baz1 p q) = a==q
2487 It's ok to say <literal>a==b</literal> or <literal>p==q</literal>, but
2488 <literal>a==q</literal> is wrong because it equates the two distinct types arising
2489 from the two <function>Baz1</function> constructors.
2497 You can't pattern-match on an existentially quantified
2498 constructor in a <literal>let</literal> or <literal>where</literal> group of
2499 bindings. So this is illegal:
2503 f3 x = a==b where { Baz1 a b = x }
2506 Instead, use a <literal>case</literal> expression:
2509 f3 x = case x of Baz1 a b -> a==b
2512 In general, you can only pattern-match
2513 on an existentially-quantified constructor in a <literal>case</literal> expression or
2514 in the patterns of a function definition.
2516 The reason for this restriction is really an implementation one.
2517 Type-checking binding groups is already a nightmare without
2518 existentials complicating the picture. Also an existential pattern
2519 binding at the top level of a module doesn't make sense, because it's
2520 not clear how to prevent the existentially-quantified type "escaping".
2521 So for now, there's a simple-to-state restriction. We'll see how
2529 You can't use existential quantification for <literal>newtype</literal>
2530 declarations. So this is illegal:
2534 newtype T = forall a. Ord a => MkT a
2538 Reason: a value of type <literal>T</literal> must be represented as a pair
2539 of a dictionary for <literal>Ord t</literal> and a value of type <literal>t</literal>.
2540 That contradicts the idea that <literal>newtype</literal> should have no
2541 concrete representation. You can get just the same efficiency and effect
2542 by using <literal>data</literal> instead of <literal>newtype</literal>. If there is no
2543 overloading involved, then there is more of a case for allowing
2544 an existentially-quantified <literal>newtype</literal>, because the <literal>data</literal>
2545 because the <literal>data</literal> version does carry an implementation cost,
2546 but single-field existentially quantified constructors aren't much
2547 use. So the simple restriction (no existential stuff on <literal>newtype</literal>)
2548 stands, unless there are convincing reasons to change it.
2556 You can't use <literal>deriving</literal> to define instances of a
2557 data type with existentially quantified data constructors.
2559 Reason: in most cases it would not make sense. For example:#
2562 data T = forall a. MkT [a] deriving( Eq )
2565 To derive <literal>Eq</literal> in the standard way we would need to have equality
2566 between the single component of two <function>MkT</function> constructors:
2570 (MkT a) == (MkT b) = ???
2573 But <VarName>a</VarName> and <VarName>b</VarName> have distinct types, and so can't be compared.
2574 It's just about possible to imagine examples in which the derived instance
2575 would make sense, but it seems altogether simpler simply to prohibit such
2576 declarations. Define your own instances!
2588 <sect2 id="scoped-type-variables">
2589 <title>Scoped type variables
2593 A <emphasis>pattern type signature</emphasis> can introduce a <emphasis>scoped type
2594 variable</emphasis>. For example
2600 f (xs::[a]) = ys ++ ys
2609 The pattern <literal>(xs::[a])</literal> includes a type signature for <VarName>xs</VarName>.
2610 This brings the type variable <literal>a</literal> into scope; it scopes over
2611 all the patterns and right hand sides for this equation for <function>f</function>.
2612 In particular, it is in scope at the type signature for <VarName>y</VarName>.
2616 Pattern type signatures are completely orthogonal to ordinary, separate
2617 type signatures. The two can be used independently or together.
2618 At ordinary type signatures, such as that for <VarName>ys</VarName>, any type variables
2619 mentioned in the type signature <emphasis>that are not in scope</emphasis> are
2620 implicitly universally quantified. (If there are no type variables in
2621 scope, all type variables mentioned in the signature are universally
2622 quantified, which is just as in Haskell 98.) In this case, since <VarName>a</VarName>
2623 is in scope, it is not universally quantified, so the type of <VarName>ys</VarName> is
2624 the same as that of <VarName>xs</VarName>. In Haskell 98 it is not possible to declare
2625 a type for <VarName>ys</VarName>; a major benefit of scoped type variables is that
2626 it becomes possible to do so.
2630 Scoped type variables are implemented in both GHC and Hugs. Where the
2631 implementations differ from the specification below, those differences
2636 So much for the basic idea. Here are the details.
2640 <title>What a pattern type signature means</title>
2642 A type variable brought into scope by a pattern type signature is simply
2643 the name for a type. The restriction they express is that all occurrences
2644 of the same name mean the same type. For example:
2646 f :: [Int] -> Int -> Int
2647 f (xs::[a]) (y::a) = (head xs + y) :: a
2649 The pattern type signatures on the left hand side of
2650 <literal>f</literal> express the fact that <literal>xs</literal>
2651 must be a list of things of some type <literal>a</literal>; and that <literal>y</literal>
2652 must have this same type. The type signature on the expression <literal>(head xs)</literal>
2653 specifies that this expression must have the same type <literal>a</literal>.
2654 <emphasis>There is no requirement that the type named by "<literal>a</literal>" is
2655 in fact a type variable</emphasis>. Indeed, in this case, the type named by "<literal>a</literal>" is
2656 <literal>Int</literal>. (This is a slight liberalisation from the original rather complex
2657 rules, which specified that a pattern-bound type variable should be universally quantified.)
2658 For example, all of these are legal:</para>
2661 t (x::a) (y::a) = x+y*2
2663 f (x::a) (y::b) = [x,y] -- a unifies with b
2665 g (x::a) = x + 1::Int -- a unifies with Int
2667 h x = let k (y::a) = [x,y] -- a is free in the
2668 in k x -- environment
2670 k (x::a) True = ... -- a unifies with Int
2671 k (x::Int) False = ...
2674 w (x::a) = x -- a unifies with [b]
2680 <title>Scope and implicit quantification</title>
2688 All the type variables mentioned in a pattern,
2689 that are not already in scope,
2690 are brought into scope by the pattern. We describe this set as
2691 the <emphasis>type variables bound by the pattern</emphasis>.
2694 f (x::a) = let g (y::(a,b)) = fst y
2698 The pattern <literal>(x::a)</literal> brings the type variable
2699 <literal>a</literal> into scope, as well as the term
2700 variable <literal>x</literal>. The pattern <literal>(y::(a,b))</literal>
2701 contains an occurrence of the already-in-scope type variable <literal>a</literal>,
2702 and brings into scope the type variable <literal>b</literal>.
2708 The type variable(s) bound by the pattern have the same scope
2709 as the term variable(s) bound by the pattern. For example:
2712 f (x::a) = <...rhs of f...>
2713 (p::b, q::b) = (1,2)
2714 in <...body of let...>
2716 Here, the type variable <literal>a</literal> scopes over the right hand side of <literal>f</literal>,
2717 just like <literal>x</literal> does; while the type variable <literal>b</literal> scopes over the
2718 body of the <literal>let</literal>, and all the other definitions in the <literal>let</literal>,
2719 just like <literal>p</literal> and <literal>q</literal> do.
2720 Indeed, the newly bound type variables also scope over any ordinary, separate
2721 type signatures in the <literal>let</literal> group.
2728 The type variables bound by the pattern may be
2729 mentioned in ordinary type signatures or pattern
2730 type signatures anywhere within their scope.
2737 In ordinary type signatures, any type variable mentioned in the
2738 signature that is in scope is <emphasis>not</emphasis> universally quantified.
2746 Ordinary type signatures do not bring any new type variables
2747 into scope (except in the type signature itself!). So this is illegal:
2754 It's illegal because <VarName>a</VarName> is not in scope in the body of <function>f</function>,
2755 so the ordinary signature <literal>x::a</literal> is equivalent to <literal>x::forall a.a</literal>;
2756 and that is an incorrect typing.
2763 The pattern type signature is a monotype:
2768 A pattern type signature cannot contain any explicit <literal>forall</literal> quantification.
2772 The type variables bound by a pattern type signature can only be instantiated to monotypes,
2773 not to type schemes.
2777 There is no implicit universal quantification on pattern type signatures (in contrast to
2778 ordinary type signatures).
2788 The type variables in the head of a <literal>class</literal> or <literal>instance</literal> declaration
2789 scope over the methods defined in the <literal>where</literal> part. For example:
2803 (Not implemented in Hugs yet, Dec 98).
2814 <title>Where a pattern type signature can occur</title>
2817 A pattern type signature can occur in any pattern. For example:
2822 A pattern type signature can be on an arbitrary sub-pattern, not
2827 f ((x,y)::(a,b)) = (y,x) :: (b,a)
2836 Pattern type signatures, including the result part, can be used
2837 in lambda abstractions:
2840 (\ (x::a, y) :: a -> x)
2847 Pattern type signatures, including the result part, can be used
2848 in <literal>case</literal> expressions:
2852 case e of { (x::a, y) :: a -> x }
2860 To avoid ambiguity, the type after the “<literal>::</literal>” in a result
2861 pattern signature on a lambda or <literal>case</literal> must be atomic (i.e. a single
2862 token or a parenthesised type of some sort). To see why,
2863 consider how one would parse this:
2877 Pattern type signatures can bind existential type variables.
2882 data T = forall a. MkT [a]
2885 f (MkT [t::a]) = MkT t3
2898 Pattern type signatures
2899 can be used in pattern bindings:
2902 f x = let (y, z::a) = x in ...
2903 f1 x = let (y, z::Int) = x in ...
2904 f2 (x::(Int,a)) = let (y, z::a) = x in ...
2905 f3 :: (b->b) = \x -> x
2908 In all such cases, the binding is not generalised over the pattern-bound
2909 type variables. Thus <literal>f3</literal> is monomorphic; <literal>f3</literal>
2910 has type <literal>b -> b</literal> for some type <literal>b</literal>,
2911 and <emphasis>not</emphasis> <literal>forall b. b -> b</literal>.
2912 In contrast, the binding
2917 makes a polymorphic function, but <literal>b</literal> is not in scope anywhere
2918 in <literal>f4</literal>'s scope.
2928 <title>Result type signatures</title>
2931 The result type of a function can be given a signature, thus:
2935 f (x::a) :: [a] = [x,x,x]
2939 The final <literal>:: [a]</literal> after all the patterns gives a signature to the
2940 result type. Sometimes this is the only way of naming the type variable
2945 f :: Int -> [a] -> [a]
2946 f n :: ([a] -> [a]) = let g (x::a, y::a) = (y,x)
2947 in \xs -> map g (reverse xs `zip` xs)
2952 The type variables bound in a result type signature scope over the right hand side
2953 of the definition. However, consider this corner-case:
2955 rev1 :: [a] -> [a] = \xs -> reverse xs
2957 foo ys = rev (ys::[a])
2959 The signature on <literal>rev1</literal> is considered a pattern type signature, not a result
2960 type signature, and the type variables it binds have the same scope as <literal>rev1</literal>
2961 itself (i.e. the right-hand side of <literal>rev1</literal> and the rest of the module too).
2962 In particular, the expression <literal>(ys::[a])</literal> is OK, because the type variable <literal>a</literal>
2963 is in scope (otherwise it would mean <literal>(ys::forall a.[a])</literal>, which would be rejected).
2966 As mentioned above, <literal>rev1</literal> is made monomorphic by this scoping rule.
2967 For example, the following program would be rejected, because it claims that <literal>rev1</literal>
2971 rev1 :: [a] -> [a] = \xs -> reverse xs
2976 Result type signatures are not yet implemented in Hugs.
2983 <sect2 id="deriving-typeable">
2984 <title>Deriving clause for classes <literal>Typeable</literal> and <literal>Data</literal></title>
2987 Haskell 98 allows the programmer to add "<literal>deriving( Eq, Ord )</literal>" to a data type
2988 declaration, to generate a standard instance declaration for classes specified in the <literal>deriving</literal> clause.
2989 In Haskell 98, the only classes that may appear in the <literal>deriving</literal> clause are the standard
2990 classes <literal>Eq</literal>, <literal>Ord</literal>,
2991 <literal>Enum</literal>, <literal>Ix</literal>, <literal>Bounded</literal>, <literal>Read</literal>, and <literal>Show</literal>.
2994 GHC extends this list with two more classes that may be automatically derived
2995 (provided the <option>-fglasgow-exts</option> flag is specified):
2996 <literal>Typeable</literal>, and <literal>Data</literal>. These classes are defined in the library
2997 modules <literal>Data.Dynamic</literal> and <literal>Data.Generics</literal> respectively, and the
2998 appropriate class must be in scope before it can be mentioned in the <literal>deriving</literal> clause.
3002 <sect2 id="newtype-deriving">
3003 <title>Generalised derived instances for newtypes</title>
3006 When you define an abstract type using <literal>newtype</literal>, you may want
3007 the new type to inherit some instances from its representation. In
3008 Haskell 98, you can inherit instances of <literal>Eq</literal>, <literal>Ord</literal>,
3009 <literal>Enum</literal> and <literal>Bounded</literal> by deriving them, but for any
3010 other classes you have to write an explicit instance declaration. For
3011 example, if you define
3014 newtype Dollars = Dollars Int
3017 and you want to use arithmetic on <literal>Dollars</literal>, you have to
3018 explicitly define an instance of <literal>Num</literal>:
3021 instance Num Dollars where
3022 Dollars a + Dollars b = Dollars (a+b)
3025 All the instance does is apply and remove the <literal>newtype</literal>
3026 constructor. It is particularly galling that, since the constructor
3027 doesn't appear at run-time, this instance declaration defines a
3028 dictionary which is <emphasis>wholly equivalent</emphasis> to the <literal>Int</literal>
3029 dictionary, only slower!
3033 <sect3> <title> Generalising the deriving clause </title>
3035 GHC now permits such instances to be derived instead, so one can write
3037 newtype Dollars = Dollars Int deriving (Eq,Show,Num)
3040 and the implementation uses the <emphasis>same</emphasis> <literal>Num</literal> dictionary
3041 for <literal>Dollars</literal> as for <literal>Int</literal>. Notionally, the compiler
3042 derives an instance declaration of the form
3045 instance Num Int => Num Dollars
3048 which just adds or removes the <literal>newtype</literal> constructor according to the type.
3052 We can also derive instances of constructor classes in a similar
3053 way. For example, suppose we have implemented state and failure monad
3054 transformers, such that
3057 instance Monad m => Monad (State s m)
3058 instance Monad m => Monad (Failure m)
3060 In Haskell 98, we can define a parsing monad by
3062 type Parser tok m a = State [tok] (Failure m) a
3065 which is automatically a monad thanks to the instance declarations
3066 above. With the extension, we can make the parser type abstract,
3067 without needing to write an instance of class <literal>Monad</literal>, via
3070 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3073 In this case the derived instance declaration is of the form
3075 instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
3078 Notice that, since <literal>Monad</literal> is a constructor class, the
3079 instance is a <emphasis>partial application</emphasis> of the new type, not the
3080 entire left hand side. We can imagine that the type declaration is
3081 ``eta-converted'' to generate the context of the instance
3086 We can even derive instances of multi-parameter classes, provided the
3087 newtype is the last class parameter. In this case, a ``partial
3088 application'' of the class appears in the <literal>deriving</literal>
3089 clause. For example, given the class
3092 class StateMonad s m | m -> s where ...
3093 instance Monad m => StateMonad s (State s m) where ...
3095 then we can derive an instance of <literal>StateMonad</literal> for <literal>Parser</literal>s by
3097 newtype Parser tok m a = Parser (State [tok] (Failure m) a)
3098 deriving (Monad, StateMonad [tok])
3101 The derived instance is obtained by completing the application of the
3102 class to the new type:
3105 instance StateMonad [tok] (State [tok] (Failure m)) =>
3106 StateMonad [tok] (Parser tok m)
3111 As a result of this extension, all derived instances in newtype
3112 declarations are treated uniformly (and implemented just by reusing
3113 the dictionary for the representation type), <emphasis>except</emphasis>
3114 <literal>Show</literal> and <literal>Read</literal>, which really behave differently for
3115 the newtype and its representation.
3119 <sect3> <title> A more precise specification </title>
3121 Derived instance declarations are constructed as follows. Consider the
3122 declaration (after expansion of any type synonyms)
3125 newtype T v1...vn = T' (S t1...tk vk+1...vn) deriving (c1...cm)
3131 <literal>S</literal> is a type constructor,
3134 <literal>t1...tk</literal> are types,
3137 <literal>vk+1...vn</literal> are type variables which do not occur in any of
3138 the <literal>ti</literal>, and
3141 the <literal>ci</literal> are partial applications of
3142 classes of the form <literal>C t1'...tj'</literal>, where the arity of <literal>C</literal>
3143 is exactly <literal>j+1</literal>. That is, <literal>C</literal> lacks exactly one type argument.
3146 Then, for each <literal>ci</literal>, the derived instance
3149 instance ci (S t1...tk vk+1...v) => ci (T v1...vp)
3151 where <literal>p</literal> is chosen so that <literal>T v1...vp</literal> is of the
3152 right <emphasis>kind</emphasis> for the last parameter of class <literal>Ci</literal>.
3156 As an example which does <emphasis>not</emphasis> work, consider
3158 newtype NonMonad m s = NonMonad (State s m s) deriving Monad
3160 Here we cannot derive the instance
3162 instance Monad (State s m) => Monad (NonMonad m)
3165 because the type variable <literal>s</literal> occurs in <literal>State s m</literal>,
3166 and so cannot be "eta-converted" away. It is a good thing that this
3167 <literal>deriving</literal> clause is rejected, because <literal>NonMonad m</literal> is
3168 not, in fact, a monad --- for the same reason. Try defining
3169 <literal>>>=</literal> with the correct type: you won't be able to.
3173 Notice also that the <emphasis>order</emphasis> of class parameters becomes
3174 important, since we can only derive instances for the last one. If the
3175 <literal>StateMonad</literal> class above were instead defined as
3178 class StateMonad m s | m -> s where ...
3181 then we would not have been able to derive an instance for the
3182 <literal>Parser</literal> type above. We hypothesise that multi-parameter
3183 classes usually have one "main" parameter for which deriving new
3184 instances is most interesting.
3192 <!-- ==================== End of type system extensions ================= -->
3194 <!-- ====================== TEMPLATE HASKELL ======================= -->
3196 <sect1 id="template-haskell">
3197 <title>Template Haskell</title>
3199 <para>Template Haskell allows you to do compile-time meta-programming in Haskell. There is a "home page" for
3200 Template Haskell at <ulink url="http://www.haskell.org/th/">
3201 http://www.haskell.org/th/</ulink>, while
3203 the main technical innovations is discussed in "<ulink
3204 url="http://research.microsoft.com/~simonpj/papers/meta-haskell">
3205 Template Meta-programming for Haskell</ulink>" (Proc Haskell Workshop 2002).
3208 <para> The first example from that paper is set out below as a worked example to help get you started.
3212 The documentation here describes the realisation in GHC. (It's rather sketchy just now;
3213 Tim Sheard is going to expand it.)
3216 <sect2> <title> Syntax </title>
3218 Template Haskell has the following new syntactic constructions. You need to use the flag
3219 <literal>-fglasgow-exts</literal> to switch these syntactic extensions on.
3223 A splice is written <literal>$x</literal>, where <literal>x</literal> is an
3224 identifier, or <literal>$(...)</literal>, where the "..." is an arbitrary expression.
3225 There must be no space between the "$" and the identifier or parenthesis. This use
3226 of "$" overrides its meaning as an infix operator, just as "M.x" overrides the meaning
3227 of "." as an infix operator. If you want the infix operator, put spaces around it.
3229 <para> A splice can occur in place of
3231 <listitem><para> an expression; the spliced expression must have type <literal>Expr</literal></para></listitem>
3232 <listitem><para> a list of top-level declarations; ; the spliced expression must have type <literal>Q [Dec]</literal></para></listitem>
3233 <listitem><para> a type; the spliced expression must have type <literal>Type</literal>.</para></listitem>
3235 (Note that the syntax for a declaration splice uses "<literal>$</literal>" not "<literal>splice</literal>" as in
3236 the paper. Also the type of the enclosed expression must be <literal>Q [Dec]</literal>, not <literal>[Q Dec]</literal>
3242 A expression quotation is written in Oxford brackets, thus:
3244 <listitem><para> <literal>[| ... |]</literal>, where the "..." is an expression;
3245 the quotation has type <literal>Expr</literal>.</para></listitem>
3246 <listitem><para> <literal>[d| ... |]</literal>, where the "..." is a list of top-level declarations;
3247 the quotation has type <literal>Q [Dec]</literal>.</para></listitem>
3248 <listitem><para> <literal>[t| ... |]</literal>, where the "..." is a type;
3249 the quotation has type <literal>Type</literal>.</para></listitem>
3250 </itemizedlist></para></listitem>
3253 Reification is written thus:
3255 <listitem><para> <literal>reifyDecl T</literal>, where <literal>T</literal> is a type constructor; this expression
3256 has type <literal>Dec</literal>. </para></listitem>
3257 <listitem><para> <literal>reifyDecl C</literal>, where <literal>C</literal> is a class; has type <literal>Dec</literal>.</para></listitem>
3258 <listitem><para> <literal>reifyType f</literal>, where <literal>f</literal> is an identifier; has type <literal>Typ</literal>.</para></listitem>
3259 <listitem><para> Still to come: fixities </para></listitem>
3261 </itemizedlist></para>
3269 <sect2> <title> Using Template Haskell </title>
3273 The data types and monadic constructor functions for Template Haskell are in the library
3274 <literal>Language.Haskell.THSyntax</literal>.
3278 You can only run a function at compile time if it is imported from another module. That is,
3279 you can't define a function in a module, and call it from within a splice in the same module.
3280 (It would make sense to do so, but it's hard to implement.)
3284 The flag <literal>-ddump-splices</literal> shows the expansion of all top-level splices as they happen.
3287 If you are building GHC from source, you need at least a stage-2 bootstrap compiler to
3288 run Template Haskell. A stage-1 compiler will reject the TH constructs. Reason: TH
3289 compiles and runs a program, and then looks at the result. So it's important that
3290 the program it compiles produces results whose representations are identical to
3291 those of the compiler itself.
3295 <para> Template Haskell works in any mode (<literal>--make</literal>, <literal>--interactive</literal>,
3296 or file-at-a-time). There used to be a restriction to the former two, but that restriction
3301 <sect2> <title> A Template Haskell Worked Example </title>
3302 <para>To help you get over the confidence barrier, try out this skeletal worked example.
3303 First cut and paste the two modules below into "Main.hs" and "Printf.hs":</para>
3309 -- Import our template "pr"
3310 import Printf ( pr )
3312 -- The splice operator $ takes the Haskell source code
3313 -- generated at compile time by "pr" and splices it into
3314 -- the argument of "putStrLn".
3315 main = putStrLn ( $(pr "Hello") )
3322 -- Skeletal printf from the paper.
3323 -- It needs to be in a separate module to the one where
3324 -- you intend to use it.
3326 -- Import some Template Haskell syntax
3327 import Language.Haskell.THSyntax
3329 -- Describe a format string
3330 data Format = D | S | L String
3332 -- Parse a format string. This is left largely to you
3333 -- as we are here interested in building our first ever
3334 -- Template Haskell program and not in building printf.
3335 parse :: String -> [Format]
3338 -- Generate Haskell source code from a parsed representation
3339 -- of the format string. This code will be spliced into
3340 -- the module which calls "pr", at compile time.
3341 gen :: [Format] -> Expr
3342 gen [D] = [| \n -> show n |]
3343 gen [S] = [| \s -> s |]
3344 gen [L s] = string s
3346 -- Here we generate the Haskell code for the splice
3347 -- from an input format string.
3348 pr :: String -> Expr
3349 pr s = gen (parse s)
3352 <para>Now run the compiler (here we are using a "stage three" build of GHC, at a Cygwin prompt on Windows):
3355 ghc/compiler/stage3/ghc-inplace --make -fglasgow-exts -package haskell-src main.hs -o main.exe
3358 <para>Run "main.exe" and here is your output:
3370 <!-- ===================== Arrow notation =================== -->
3372 <sect1 id="arrow-notation">
3373 <title>Arrow notation
3376 <para>Arrows are a generalization of monads introduced by John Hughes.
3377 For more details, see
3382 “Generalising Monads to Arrows”,
3383 John Hughes, in <citetitle>Science of Computer Programming</citetitle> 37,
3384 pp67–111, May 2000.
3390 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/notation.html">A New Notation for Arrows</ulink>”,
3391 Ross Paterson, in <citetitle>ICFP</citetitle>, Sep 2001.
3397 “<ulink url="http://www.soi.city.ac.uk/~ross/papers/fop.html">Arrows and Computation</ulink>”,
3398 Ross Paterson, in <citetitle>The Fun of Programming</citetitle>,
3404 and the arrows web page at
3405 <ulink url="http://www.haskell.org/arrows/"><literal>http://www.haskell.org/arrows/</literal></ulink>.
3406 With the <option>-farrows</option> flag, GHC supports the arrow
3407 notation described in the second of these papers.
3408 What follows is a brief introduction to the notation;
3409 it won't make much sense unless you've read Hughes's paper.
3410 This notation is translated to ordinary Haskell,
3411 using combinators from the
3412 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3416 <para>The extension adds a new kind of expression for defining arrows,
3417 of the form <literal>proc pat -> cmd</literal>,
3418 where <literal>proc</literal> is a new keyword.
3419 The variables of the pattern are bound in the body of the
3420 <literal>proc</literal>-expression,
3421 which is a new sort of thing called a <firstterm>command</firstterm>.
3422 The syntax of commands is as follows:
3424 cmd ::= exp1 -< exp2
3425 | exp1 -<< exp2
3426 | do { cstmt1 .. cstmtn ; cmd }
3428 | if exp then cmd1 else cmd2
3429 | case exp of { calts }
3431 | (| aexp cmd1 .. cmdn |)
3432 | \ pat1 .. patn -> cmd
3438 | rec { cstmt1 .. cstmtn }
3441 Commands produce values, but (like monadic computations)
3442 may yield more than one value,
3443 or none, and may do other things as well.
3444 For the most part, familiarity with monadic notation is a good guide to
3446 However the values of expressions, even monadic ones,
3447 are determined by the values of the variables they contain;
3448 this is not necessarily the case for commands.
3452 A simple example of the new notation is the expression
3454 proc x -> f -< x+1
3456 We call this a <firstterm>procedure</firstterm> or
3457 <firstterm>arrow abstraction</firstterm>.
3458 As with a lambda expression, the variable <literal>x</literal>
3459 is a new variable bound within the <literal>proc</literal>-expression.
3460 It refers to the input to the arrow.
3461 In the above example, <literal>-<</literal> is not an identifier but an
3462 new reserved symbol used for building commands from an expression of arrow
3463 type and an expression to be fed as input to that arrow.
3464 (The weird look will make more sense later.)
3465 It may be read as analogue of application for arrows.
3466 The above example is equivalent to the Haskell expression
3468 arr (\ x -> x+1) >>> f
3470 That would make no sense if the expression to the left of
3471 <literal>-<</literal> involves the bound variable <literal>x</literal>.
3472 More generally, the expression to the left of <literal>-<</literal>
3473 may not involve any <firstterm>local variable</firstterm>,
3474 i.e. a variable bound in the current arrow abstraction.
3475 For such a situation there is a variant <literal>-<<</literal>, as in
3477 proc x -> f x -<< x+1
3479 which is equivalent to
3481 arr (\ x -> (f, x+1)) >>> app
3483 so in this case the arrow must belong to the <literal>ArrowApply</literal>
3485 Such an arrow is equivalent to a monad, so if you're using this form
3486 you may find a monadic formulation more convenient.
3490 <title>do-notation for commands</title>
3493 Another form of command is a form of <literal>do</literal>-notation.
3494 For example, you can write
3503 You can read this much like ordinary <literal>do</literal>-notation,
3504 but with commands in place of monadic expressions.
3505 The first line sends the value of <literal>x+1</literal> as an input to
3506 the arrow <literal>f</literal>, and matches its output against
3507 <literal>y</literal>.
3508 In the next line, the output is discarded.
3509 The arrow <literal>returnA</literal> is defined in the
3510 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3511 module as <literal>arr id</literal>.
3512 The above example is treated as an abbreviation for
3514 arr (\ x -> (x, x)) >>>
3515 first (arr (\ x -> x+1) >>> f) >>>
3516 arr (\ (y, x) -> (y, (x, y))) >>>
3517 first (arr (\ y -> 2*y) >>> g) >>>
3519 arr (\ (x, y) -> let z = x+y in ((x, z), z)) >>>
3520 first (arr (\ (x, z) -> x*z) >>> h) >>>
3521 arr (\ (t, z) -> t+z) >>>
3524 Note that variables not used later in the composition are projected out.
3525 After simplification using rewrite rules (see <xref linkEnd="rewrite-rules">)
3527 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>
3528 module, this reduces to
3530 arr (\ x -> (x+1, x)) >>>
3532 arr (\ (y, x) -> (2*y, (x, y))) >>>
3534 arr (\ (_, (x, y)) -> let z = x+y in (x*z, z)) >>>
3536 arr (\ (t, z) -> t+z)
3538 which is what you might have written by hand.
3539 With arrow notation, GHC keeps track of all those tuples of variables for you.
3543 Note that although the above translation suggests that
3544 <literal>let</literal>-bound variables like <literal>z</literal> must be
3545 monomorphic, the actual translation produces Core,
3546 so polymorphic variables are allowed.
3550 It's also possible to have mutually recursive bindings,
3551 using the new <literal>rec</literal> keyword, as in the following example:
3553 counter :: ArrowCircuit a => a Bool Int
3554 counter = proc reset -> do
3555 rec output <- returnA -< if reset then 0 else next
3556 next <- delay 0 -< output+1
3557 returnA -< output
3559 The translation of such forms uses the <literal>loop</literal> combinator,
3560 so the arrow concerned must belong to the <literal>ArrowLoop</literal> class.
3566 <title>Conditional commands</title>
3569 In the previous example, we used a conditional expression to construct the
3571 Sometimes we want to conditionally execute different commands, as in
3578 which is translated to
3580 arr (\ (x,y) -> if f x y then Left x else Right y) >>>
3581 (arr (\x -> x+1) >>> f) ||| (arr (\y -> y+2) >>> g)
3583 Since the translation uses <literal>|||</literal>,
3584 the arrow concerned must belong to the <literal>ArrowChoice</literal> class.
3588 There are also <literal>case</literal> commands, like
3594 y <- h -< (x1, x2)
3598 The syntax is the same as for <literal>case</literal> expressions,
3599 except that the bodies of the alternatives are commands rather than expressions.
3600 The translation is similar to that of <literal>if</literal> commands.
3606 <title>Defining your own control structures</title>
3609 As we're seen, arrow notation provides constructs,
3610 modelled on those for expressions,
3611 for sequencing, value recursion and conditionals.
3612 But suitable combinators,
3613 which you can define in ordinary Haskell,
3614 may also be used to build new commands out of existing ones.
3615 The basic idea is that a command defines an arrow from environments to values.
3616 These environments assign values to the free local variables of the command.
3617 Thus combinators that produce arrows from arrows
3618 may also be used to build commands from commands.
3619 For example, the <literal>ArrowChoice</literal> class includes a combinator
3621 ArrowChoice a => (<+>) :: a e c -> a e c -> a e c
3623 so we can use it to build commands:
3628 symbol Plus -< ()
3629 y <- term -< ()
3632 symbol Minus -< ()
3633 y <- term -< ()
3636 This is equivalent to
3638 expr' = (proc x -> returnA -< x)
3639 <+> (proc x -> do
3640 symbol Plus -< ()
3641 y <- term -< ()
3643 <+> (proc x -> do
3644 symbol Minus -< ()
3645 y <- term -< ()
3648 It is essential that this operator be polymorphic in <literal>e</literal>
3649 (representing the environment input to the command
3650 and thence to its subcommands)
3651 and satisfy the corresponding naturality property
3653 arr k >>> (f <+> g) = (arr k >>> f) <+> (arr k >>> g)
3655 at least for strict <literal>k</literal>.
3656 (This should be automatic if you're not using <literal>seq</literal>.)
3657 This ensures that environments seen by the subcommands are environments
3658 of the whole command,
3659 and also allows the translation to safely trim these environments.
3660 The operator must also not use any variable defined within the current
3665 We could define our own operator
3667 untilA :: ArrowChoice a => a e () -> a e Bool -> a e ()
3668 untilA body cond = proc x ->
3669 if cond x then returnA -< ()
3672 untilA body cond -< x
3674 and use it in the same way.
3675 Of course this infix syntax only makes sense for binary operators;
3676 there is also a more general syntax involving special brackets:
3680 (|untilA (increment -< x+y) (within 0.5 -< x)|)
3687 <title>Primitive constructs</title>
3690 Some operators will need to pass additional inputs to their subcommands.
3691 For example, in an arrow type supporting exceptions,
3692 the operator that attaches an exception handler will wish to pass the
3693 exception that occurred to the handler.
3694 Such an operator might have a type
3696 handleA :: ... => a e c -> a (e,Ex) c -> a e c
3698 where <literal>Ex</literal> is the type of exceptions handled.
3699 You could then use this with arrow notation by writing a command
3701 body `handleA` \ ex -> handler
3703 so that if an exception is raised in the command <literal>body</literal>,
3704 the variable <literal>ex</literal> is bound to the value of the exception
3705 and the command <literal>handler</literal>,
3706 which typically refers to <literal>ex</literal>, is entered.
3707 Though the syntax here looks like a functional lambda,
3708 we are talking about commands, and something different is going on.
3709 The input to the arrow represented by a command consists of values for
3710 the free local variables in the command, plus a stack of anonymous values.
3711 In all the prior examples, this stack was empty.
3712 In the second argument to <literal>handleA</literal>,
3713 this stack consists of one value, the value of the exception.
3714 The command form of lambda merely gives this value a name.
3719 the values on the stack are paired to the right of the environment.
3720 So when designing operators like <literal>handleA</literal> that pass
3721 extra inputs to their subcommands,
3722 More precisely, the type of each argument of the operator (and its result)
3723 should have the form
3725 a (...(e,t1), ... tn) t
3727 where <replaceable>e</replaceable> is a polymorphic variable
3728 (representing the environment)
3729 and <replaceable>ti</replaceable> are the types of the values on the stack,
3730 with <replaceable>t1</replaceable> being the <quote>top</quote>.
3731 The polymorphic variable <replaceable>e</replaceable> must not occur in
3732 <replaceable>a</replaceable>, <replaceable>ti</replaceable> or
3733 <replaceable>t</replaceable>.
3734 However the arrows involved need not be the same.
3735 Here are some more examples of suitable operators:
3737 bracketA :: ... => a e b -> a (e,b) c -> a (e,c) d -> a e d
3738 runReader :: ... => a e c -> a' (e,State) c
3739 runState :: ... => a e c -> a' (e,State) (c,State)
3741 We can supply the extra input required by commands built with the last two
3742 by applying them to ordinary expressions, as in
3746 (|runReader (do { ... })|) s
3748 which adds <literal>s</literal> to the stack of inputs to the command
3749 built using <literal>runReader</literal>.
3753 The command versions of lambda abstraction and application are analogous to
3754 the expression versions.
3755 In particular, the beta and eta rules describe equivalences of commands.
3756 These three features (operators, lambda abstraction and application)
3757 are the core of the notation; everything else can be built using them,
3758 though the results would be somewhat clumsy.
3759 For example, we could simulate <literal>do</literal>-notation by defining
3761 bind :: Arrow a => a e b -> a (e,b) c -> a e c
3762 u `bind` f = returnA &&& u >>> f
3764 bind_ :: Arrow a => a e b -> a e c -> a e c
3765 u `bind_` f = u `bind` (arr fst >>> f)
3767 We could simulate <literal>do</literal> by defining
3769 cond :: ArrowChoice a => a e b -> a e b -> a (e,Bool) b
3770 cond f g = arr (\ (e,b) -> if b then Left e else Right e) >>> f ||| g
3777 <title>Differences with the paper</title>
3782 <para>Instead of a single form of arrow application (arrow tail) with two
3783 translations, the implementation provides two forms
3784 <quote><literal>-<</literal></quote> (first-order)
3785 and <quote><literal>-<<</literal></quote> (higher-order).
3790 <para>User-defined operators are flagged with banana brackets instead of
3791 a new <literal>form</literal> keyword.
3800 <title>Portability</title>
3803 Although only GHC implements arrow notation directly,
3804 there is also a preprocessor
3806 <ulink url="http://www.haskell.org/arrows/">arrows web page></ulink>)
3807 that translates arrow notation into Haskell 98
3808 for use with other Haskell systems.
3809 You would still want to check arrow programs with GHC;
3810 tracing type errors in the preprocessor output is not easy.
3811 Modules intended for both GHC and the preprocessor must observe some
3812 additional restrictions:
3817 The module must import
3818 <ulink url="../base/Control.Arrow.html"><literal>Control.Arrow</literal></ulink>.
3824 The preprocessor cannot cope with other Haskell extensions.
3825 These would have to go in separate modules.
3831 Because the preprocessor targets Haskell (rather than Core),
3832 <literal>let</literal>-bound variables are monomorphic.
3843 <!-- ==================== ASSERTIONS ================= -->
3845 <sect1 id="sec-assertions">
3847 <indexterm><primary>Assertions</primary></indexterm>
3851 If you want to make use of assertions in your standard Haskell code, you
3852 could define a function like the following:
3858 assert :: Bool -> a -> a
3859 assert False x = error "assertion failed!"
3866 which works, but gives you back a less than useful error message --
3867 an assertion failed, but which and where?
3871 One way out is to define an extended <function>assert</function> function which also
3872 takes a descriptive string to include in the error message and
3873 perhaps combine this with the use of a pre-processor which inserts
3874 the source location where <function>assert</function> was used.
3878 Ghc offers a helping hand here, doing all of this for you. For every
3879 use of <function>assert</function> in the user's source:
3885 kelvinToC :: Double -> Double
3886 kelvinToC k = assert (k >= 0.0) (k+273.15)
3892 Ghc will rewrite this to also include the source location where the
3899 assert pred val ==> assertError "Main.hs|15" pred val
3905 The rewrite is only performed by the compiler when it spots
3906 applications of <function>Control.Exception.assert</function>, so you
3907 can still define and use your own versions of
3908 <function>assert</function>, should you so wish. If not, import
3909 <literal>Control.Exception</literal> to make use
3910 <function>assert</function> in your code.
3914 To have the compiler ignore uses of assert, use the compiler option
3915 <option>-fignore-asserts</option>. <indexterm><primary>-fignore-asserts
3916 option</primary></indexterm> That is, expressions of the form
3917 <literal>assert pred e</literal> will be rewritten to
3918 <literal>e</literal>.
3922 Assertion failures can be caught, see the documentation for the
3923 <literal>Control.Exception</literal> library for the details.
3929 <!-- =============================== PRAGMAS =========================== -->
3931 <sect1 id="pragmas">
3932 <title>Pragmas</title>
3934 <indexterm><primary>pragma</primary></indexterm>
3936 <para>GHC supports several pragmas, or instructions to the
3937 compiler placed in the source code. Pragmas don't normally affect
3938 the meaning of the program, but they might affect the efficiency
3939 of the generated code.</para>
3941 <para>Pragmas all take the form
3943 <literal>{-# <replaceable>word</replaceable> ... #-}</literal>
3945 where <replaceable>word</replaceable> indicates the type of
3946 pragma, and is followed optionally by information specific to that
3947 type of pragma. Case is ignored in
3948 <replaceable>word</replaceable>. The various values for
3949 <replaceable>word</replaceable> that GHC understands are described
3950 in the following sections; any pragma encountered with an
3951 unrecognised <replaceable>word</replaceable> is (silently)
3954 <sect2 id="deprecated-pragma">
3955 <title>DEPRECATED pragma</title>
3956 <indexterm><primary>DEPRECATED</primary>
3959 <para>The DEPRECATED pragma lets you specify that a particular
3960 function, class, or type, is deprecated. There are two
3965 <para>You can deprecate an entire module thus:</para>
3967 module Wibble {-# DEPRECATED "Use Wobble instead" #-} where
3970 <para>When you compile any module that import
3971 <literal>Wibble</literal>, GHC will print the specified
3976 <para>You can deprecate a function, class, or type, with the
3977 following top-level declaration:</para>
3979 {-# DEPRECATED f, C, T "Don't use these" #-}
3981 <para>When you compile any module that imports and uses any
3982 of the specifed entities, GHC will print the specified
3987 <para>You can suppress the warnings with the flag
3988 <option>-fno-warn-deprecations</option>.</para>
3991 <sect2 id="inline-noinline-pragma">
3992 <title>INLINE and NOINLINE pragmas</title>
3994 <para>These pragmas control the inlining of function
3997 <sect3 id="inline-pragma">
3998 <title>INLINE pragma</title>
3999 <indexterm><primary>INLINE</primary></indexterm>
4001 <para>GHC (with <option>-O</option>, as always) tries to
4002 inline (or “unfold”) functions/values that are
4003 “small enough,” thus avoiding the call overhead
4004 and possibly exposing other more-wonderful optimisations.
4005 Normally, if GHC decides a function is “too
4006 expensive” to inline, it will not do so, nor will it
4007 export that unfolding for other modules to use.</para>
4009 <para>The sledgehammer you can bring to bear is the
4010 <literal>INLINE</literal><indexterm><primary>INLINE
4011 pragma</primary></indexterm> pragma, used thusly:</para>
4014 key_function :: Int -> String -> (Bool, Double)
4016 #ifdef __GLASGOW_HASKELL__
4017 {-# INLINE key_function #-}
4021 <para>(You don't need to do the C pre-processor carry-on
4022 unless you're going to stick the code through HBC—it
4023 doesn't like <literal>INLINE</literal> pragmas.)</para>
4025 <para>The major effect of an <literal>INLINE</literal> pragma
4026 is to declare a function's “cost” to be very low.
4027 The normal unfolding machinery will then be very keen to
4030 <para>Syntactially, an <literal>INLINE</literal> pragma for a
4031 function can be put anywhere its type signature could be
4034 <para><literal>INLINE</literal> pragmas are a particularly
4036 <literal>then</literal>/<literal>return</literal> (or
4037 <literal>bind</literal>/<literal>unit</literal>) functions in
4038 a monad. For example, in GHC's own
4039 <literal>UniqueSupply</literal> monad code, we have:</para>
4042 #ifdef __GLASGOW_HASKELL__
4043 {-# INLINE thenUs #-}
4044 {-# INLINE returnUs #-}
4048 <para>See also the <literal>NOINLINE</literal> pragma (<xref
4049 linkend="noinline-pragma">).</para>
4052 <sect3 id="noinline-pragma">
4053 <title>NOINLINE pragma</title>
4055 <indexterm><primary>NOINLINE</primary></indexterm>
4056 <indexterm><primary>NOTINLINE</primary></indexterm>
4058 <para>The <literal>NOINLINE</literal> pragma does exactly what
4059 you'd expect: it stops the named function from being inlined
4060 by the compiler. You shouldn't ever need to do this, unless
4061 you're very cautious about code size.</para>
4063 <para><literal>NOTINLINE</literal> is a synonym for
4064 <literal>NOINLINE</literal> (<literal>NOTINLINE</literal> is
4065 specified by Haskell 98 as the standard way to disable
4066 inlining, so it should be used if you want your code to be
4070 <sect3 id="phase-control">
4071 <title>Phase control</title>
4073 <para> Sometimes you want to control exactly when in GHC's
4074 pipeline the INLINE pragma is switched on. Inlining happens
4075 only during runs of the <emphasis>simplifier</emphasis>. Each
4076 run of the simplifier has a different <emphasis>phase
4077 number</emphasis>; the phase number decreases towards zero.
4078 If you use <option>-dverbose-core2core</option> you'll see the
4079 sequence of phase numbers for successive runs of the
4080 simpifier. In an INLINE pragma you can optionally specify a
4081 phase number, thus:</para>
4085 <para>You can say "inline <literal>f</literal> in Phase 2
4086 and all subsequent phases":
4088 {-# INLINE [2] f #-}
4094 <para>You can say "inline <literal>g</literal> in all
4095 phases up to, but not including, Phase 3":
4097 {-# INLINE [~3] g #-}
4103 <para>If you omit the phase indicator, you mean "inline in
4108 <para>You can use a phase number on a NOINLINE pragma too:</para>
4112 <para>You can say "do not inline <literal>f</literal>
4113 until Phase 2; in Phase 2 and subsequently behave as if
4114 there was no pragma at all":
4116 {-# NOINLINE [2] f #-}
4122 <para>You can say "do not inline <literal>g</literal> in
4123 Phase 3 or any subsequent phase; before that, behave as if
4124 there was no pragma":
4126 {-# NOINLINE [~3] g #-}
4132 <para>If you omit the phase indicator, you mean "never
4133 inline this function".</para>
4137 <para>The same phase-numbering control is available for RULES
4138 (<xref LinkEnd="rewrite-rules">).</para>
4142 <sect2 id="line-pragma">
4143 <title>LINE pragma</title>
4145 <indexterm><primary>LINE</primary><secondary>pragma</secondary></indexterm>
4146 <indexterm><primary>pragma</primary><secondary>LINE</secondary></indexterm>
4147 <para>This pragma is similar to C's <literal>#line</literal>
4148 pragma, and is mainly for use in automatically generated Haskell
4149 code. It lets you specify the line number and filename of the
4150 original code; for example</para>
4153 {-# LINE 42 "Foo.vhs" #-}
4156 <para>if you'd generated the current file from something called
4157 <filename>Foo.vhs</filename> and this line corresponds to line
4158 42 in the original. GHC will adjust its error messages to refer
4159 to the line/file named in the <literal>LINE</literal>
4163 <sect2 id="options-pragma">
4164 <title>OPTIONS pragma</title>
4165 <indexterm><primary>OPTIONS</primary>
4167 <indexterm><primary>pragma</primary><secondary>OPTIONS</secondary>
4170 <para>The <literal>OPTIONS</literal> pragma is used to specify
4171 additional options that are given to the compiler when compiling
4172 this source file. See <xref linkend="source-file-options"> for
4177 <title>RULES pragma</title>
4179 <para>The RULES pragma lets you specify rewrite rules. It is
4180 described in <xref LinkEnd="rewrite-rules">.</para>
4183 <sect2 id="specialize-pragma">
4184 <title>SPECIALIZE pragma</title>
4186 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4187 <indexterm><primary>pragma, SPECIALIZE</primary></indexterm>
4188 <indexterm><primary>overloading, death to</primary></indexterm>
4190 <para>(UK spelling also accepted.) For key overloaded
4191 functions, you can create extra versions (NB: more code space)
4192 specialised to particular types. Thus, if you have an
4193 overloaded function:</para>
4196 hammeredLookup :: Ord key => [(key, value)] -> key -> value
4199 <para>If it is heavily used on lists with
4200 <literal>Widget</literal> keys, you could specialise it as
4204 {-# SPECIALIZE hammeredLookup :: [(Widget, value)] -> Widget -> value #-}
4207 <para>A <literal>SPECIALIZE</literal> pragma for a function can
4208 be put anywhere its type signature could be put.</para>
4210 <para>A <literal>SPECIALIZE</literal> has the effect of generating (a) a specialised
4211 version of the function and (b) a rewrite rule (see <xref linkend="rules">) that
4212 rewrites a call to the un-specialised function into a call to the specialised
4213 one. You can, instead, provide your own specialised function and your own rewrite rule.
4214 For example, suppose that:
4216 genericLookup :: Ord a => Table a b -> a -> b
4217 intLookup :: Table Int b -> Int -> b
4219 where <literal>intLookup</literal> is an implementation of <literal>genericLookup</literal>
4220 that works very fast for keys of type <literal>Int</literal>. Then you can write the rule
4222 {-# RULES "intLookup" genericLookup = intLookup #-}
4224 (see <xref linkend="rule-spec">). It is <emphasis>Your
4225 Responsibility</emphasis> to make sure that
4226 <function>intLookup</function> really behaves as a specialised
4227 version of <function>genericLookup</function>!!!</para>
4229 <para>An example in which using <literal>RULES</literal> for
4230 specialisation will Win Big:
4233 toDouble :: Real a => a -> Double
4234 toDouble = fromRational . toRational
4236 {-# RULES "toDouble/Int" toDouble = i2d #-}
4237 i2d (I# i) = D# (int2Double# i) -- uses Glasgow prim-op directly
4240 The <function>i2d</function> function is virtually one machine
4241 instruction; the default conversion—via an intermediate
4242 <literal>Rational</literal>—is obscenely expensive by
4247 <sect2 id="specialize-instance-pragma">
4248 <title>SPECIALIZE instance pragma
4252 <indexterm><primary>SPECIALIZE pragma</primary></indexterm>
4253 <indexterm><primary>overloading, death to</primary></indexterm>
4254 Same idea, except for instance declarations. For example:
4257 instance (Eq a) => Eq (Foo a) where {
4258 {-# SPECIALIZE instance Eq (Foo [(Int, Bar)]) #-}
4262 The pragma must occur inside the <literal>where</literal> part
4263 of the instance declaration.
4266 Compatible with HBC, by the way, except perhaps in the placement
4276 <!-- ======================= REWRITE RULES ======================== -->
4278 <sect1 id="rewrite-rules">
4279 <title>Rewrite rules
4281 <indexterm><primary>RULES pagma</primary></indexterm>
4282 <indexterm><primary>pragma, RULES</primary></indexterm>
4283 <indexterm><primary>rewrite rules</primary></indexterm></title>
4286 The programmer can specify rewrite rules as part of the source program
4287 (in a pragma). GHC applies these rewrite rules wherever it can, provided (a)
4288 the <option>-O</option> flag (<xref LinkEnd="options-optimise">) is on,
4289 and (b) the <option>-frules-off</option> flag
4290 (<xref LinkEnd="options-f">) is not specified.
4298 "map/map" forall f g xs. map f (map g xs) = map (f.g) xs
4305 <title>Syntax</title>
4308 From a syntactic point of view:
4314 There may be zero or more rules in a <literal>RULES</literal> pragma.
4321 Each rule has a name, enclosed in double quotes. The name itself has
4322 no significance at all. It is only used when reporting how many times the rule fired.
4328 A rule may optionally have a phase-control number (see <xref LinkEnd="phase-control">),
4329 immediately after the name of the rule. Thus:
4332 "map/map" [2] forall f g xs. map f (map g xs) = map (f.g) xs
4335 The "[2]" means that the rule is active in Phase 2 and subsequent phases. The inverse
4336 notation "[~2]" is also accepted, meaning that the rule is active up to, but not including,
4345 Layout applies in a <literal>RULES</literal> pragma. Currently no new indentation level
4346 is set, so you must lay out your rules starting in the same column as the
4347 enclosing definitions.
4354 Each variable mentioned in a rule must either be in scope (e.g. <function>map</function>),
4355 or bound by the <literal>forall</literal> (e.g. <function>f</function>, <function>g</function>, <function>xs</function>). The variables bound by
4356 the <literal>forall</literal> are called the <emphasis>pattern</emphasis> variables. They are separated
4357 by spaces, just like in a type <literal>forall</literal>.
4363 A pattern variable may optionally have a type signature.
4364 If the type of the pattern variable is polymorphic, it <emphasis>must</emphasis> have a type signature.
4365 For example, here is the <literal>foldr/build</literal> rule:
4368 "fold/build" forall k z (g::forall b. (a->b->b) -> b -> b) .
4369 foldr k z (build g) = g k z
4372 Since <function>g</function> has a polymorphic type, it must have a type signature.
4379 The left hand side of a rule must consist of a top-level variable applied
4380 to arbitrary expressions. For example, this is <emphasis>not</emphasis> OK:
4383 "wrong1" forall e1 e2. case True of { True -> e1; False -> e2 } = e1
4384 "wrong2" forall f. f True = True
4387 In <literal>"wrong1"</literal>, the LHS is not an application; in <literal>"wrong2"</literal>, the LHS has a pattern variable
4394 A rule does not need to be in the same module as (any of) the
4395 variables it mentions, though of course they need to be in scope.
4401 Rules are automatically exported from a module, just as instance declarations are.
4412 <title>Semantics</title>
4415 From a semantic point of view:
4421 Rules are only applied if you use the <option>-O</option> flag.
4427 Rules are regarded as left-to-right rewrite rules.
4428 When GHC finds an expression that is a substitution instance of the LHS
4429 of a rule, it replaces the expression by the (appropriately-substituted) RHS.
4430 By "a substitution instance" we mean that the LHS can be made equal to the
4431 expression by substituting for the pattern variables.
4438 The LHS and RHS of a rule are typechecked, and must have the
4446 GHC makes absolutely no attempt to verify that the LHS and RHS
4447 of a rule have the same meaning. That is undecideable in general, and
4448 infeasible in most interesting cases. The responsibility is entirely the programmer's!
4455 GHC makes no attempt to make sure that the rules are confluent or
4456 terminating. For example:
4459 "loop" forall x,y. f x y = f y x
4462 This rule will cause the compiler to go into an infinite loop.
4469 If more than one rule matches a call, GHC will choose one arbitrarily to apply.
4475 GHC currently uses a very simple, syntactic, matching algorithm
4476 for matching a rule LHS with an expression. It seeks a substitution
4477 which makes the LHS and expression syntactically equal modulo alpha
4478 conversion. The pattern (rule), but not the expression, is eta-expanded if
4479 necessary. (Eta-expanding the epression can lead to laziness bugs.)
4480 But not beta conversion (that's called higher-order matching).
4484 Matching is carried out on GHC's intermediate language, which includes
4485 type abstractions and applications. So a rule only matches if the
4486 types match too. See <xref LinkEnd="rule-spec"> below.
4492 GHC keeps trying to apply the rules as it optimises the program.
4493 For example, consider:
4502 The expression <literal>s (t xs)</literal> does not match the rule <literal>"map/map"</literal>, but GHC
4503 will substitute for <VarName>s</VarName> and <VarName>t</VarName>, giving an expression which does match.
4504 If <VarName>s</VarName> or <VarName>t</VarName> was (a) used more than once, and (b) large or a redex, then it would
4505 not be substituted, and the rule would not fire.
4512 In the earlier phases of compilation, GHC inlines <emphasis>nothing
4513 that appears on the LHS of a rule</emphasis>, because once you have substituted
4514 for something you can't match against it (given the simple minded
4515 matching). So if you write the rule
4518 "map/map" forall f,g. map f . map g = map (f.g)
4521 this <emphasis>won't</emphasis> match the expression <literal>map f (map g xs)</literal>.
4522 It will only match something written with explicit use of ".".
4523 Well, not quite. It <emphasis>will</emphasis> match the expression
4529 where <function>wibble</function> is defined:
4532 wibble f g = map f . map g
4535 because <function>wibble</function> will be inlined (it's small).
4537 Later on in compilation, GHC starts inlining even things on the
4538 LHS of rules, but still leaves the rules enabled. This inlining
4539 policy is controlled by the per-simplification-pass flag <option>-finline-phase</option><emphasis>n</emphasis>.
4546 All rules are implicitly exported from the module, and are therefore
4547 in force in any module that imports the module that defined the rule, directly
4548 or indirectly. (That is, if A imports B, which imports C, then C's rules are
4549 in force when compiling A.) The situation is very similar to that for instance
4561 <title>List fusion</title>
4564 The RULES mechanism is used to implement fusion (deforestation) of common list functions.
4565 If a "good consumer" consumes an intermediate list constructed by a "good producer", the
4566 intermediate list should be eliminated entirely.
4570 The following are good producers:
4582 Enumerations of <literal>Int</literal> and <literal>Char</literal> (e.g. <literal>['a'..'z']</literal>).
4588 Explicit lists (e.g. <literal>[True, False]</literal>)
4594 The cons constructor (e.g <literal>3:4:[]</literal>)
4600 <function>++</function>
4606 <function>map</function>
4612 <function>filter</function>
4618 <function>iterate</function>, <function>repeat</function>
4624 <function>zip</function>, <function>zipWith</function>
4633 The following are good consumers:
4645 <function>array</function> (on its second argument)
4651 <function>length</function>
4657 <function>++</function> (on its first argument)
4663 <function>foldr</function>
4669 <function>map</function>
4675 <function>filter</function>
4681 <function>concat</function>
4687 <function>unzip</function>, <function>unzip2</function>, <function>unzip3</function>, <function>unzip4</function>
4693 <function>zip</function>, <function>zipWith</function> (but on one argument only; if both are good producers, <function>zip</function>
4694 will fuse with one but not the other)
4700 <function>partition</function>
4706 <function>head</function>
4712 <function>and</function>, <function>or</function>, <function>any</function>, <function>all</function>
4718 <function>sequence_</function>
4724 <function>msum</function>
4730 <function>sortBy</function>
4739 So, for example, the following should generate no intermediate lists:
4742 array (1,10) [(i,i*i) | i <- map (+ 1) [0..9]]
4748 This list could readily be extended; if there are Prelude functions that you use
4749 a lot which are not included, please tell us.
4753 If you want to write your own good consumers or producers, look at the
4754 Prelude definitions of the above functions to see how to do so.
4759 <sect2 id="rule-spec">
4760 <title>Specialisation
4764 Rewrite rules can be used to get the same effect as a feature
4765 present in earlier version of GHC:
4768 {-# SPECIALIZE fromIntegral :: Int8 -> Int16 = int8ToInt16 #-}
4771 This told GHC to use <function>int8ToInt16</function> instead of <function>fromIntegral</function> whenever
4772 the latter was called with type <literal>Int8 -> Int16</literal>. That is, rather than
4773 specialising the original definition of <function>fromIntegral</function> the programmer is
4774 promising that it is safe to use <function>int8ToInt16</function> instead.
4778 This feature is no longer in GHC. But rewrite rules let you do the
4783 "fromIntegral/Int8/Int16" fromIntegral = int8ToInt16
4787 This slightly odd-looking rule instructs GHC to replace <function>fromIntegral</function>
4788 by <function>int8ToInt16</function> <emphasis>whenever the types match</emphasis>. Speaking more operationally,
4789 GHC adds the type and dictionary applications to get the typed rule
4792 forall (d1::Integral Int8) (d2::Num Int16) .
4793 fromIntegral Int8 Int16 d1 d2 = int8ToInt16
4797 this rule does not need to be in the same file as fromIntegral,
4798 unlike the <literal>SPECIALISE</literal> pragmas which currently do (so that they
4799 have an original definition available to specialise).
4805 <title>Controlling what's going on</title>
4813 Use <option>-ddump-rules</option> to see what transformation rules GHC is using.
4819 Use <option>-ddump-simpl-stats</option> to see what rules are being fired.
4820 If you add <option>-dppr-debug</option> you get a more detailed listing.
4826 The defintion of (say) <function>build</function> in <FileName>GHC/Base.lhs</FileName> looks llike this:
4829 build :: forall a. (forall b. (a -> b -> b) -> b -> b) -> [a]
4830 {-# INLINE build #-}
4834 Notice the <literal>INLINE</literal>! That prevents <literal>(:)</literal> from being inlined when compiling
4835 <literal>PrelBase</literal>, so that an importing module will “see” the <literal>(:)</literal>, and can
4836 match it on the LHS of a rule. <literal>INLINE</literal> prevents any inlining happening
4837 in the RHS of the <literal>INLINE</literal> thing. I regret the delicacy of this.
4844 In <filename>libraries/base/GHC/Base.lhs</filename> look at the rules for <function>map</function> to
4845 see how to write rules that will do fusion and yet give an efficient
4846 program even if fusion doesn't happen. More rules in <filename>GHC/List.lhs</filename>.
4856 <sect2 id="core-pragma">
4857 <title>CORE pragma</title>
4859 <indexterm><primary>CORE pragma</primary></indexterm>
4860 <indexterm><primary>pragma, CORE</primary></indexterm>
4861 <indexterm><primary>core, annotation</primary></indexterm>
4864 The external core format supports <quote>Note</quote> annotations;
4865 the <literal>CORE</literal> pragma gives a way to specify what these
4866 should be in your Haskell source code. Syntactically, core
4867 annotations are attached to expressions and take a Haskell string
4868 literal as an argument. The following function definition shows an
4872 f x = ({-# CORE "foo" #-} show) ({-# CORE "bar" #-} x)
4875 Sematically, this is equivalent to:
4883 However, when external for is generated (via
4884 <option>-fext-core</option>), there will be Notes attached to the
4885 expressions <function>show</function> and <VarName>x</VarName>.
4886 The core function declaration for <function>f</function> is:
4890 f :: %forall a . GHCziShow.ZCTShow a ->
4891 a -> GHCziBase.ZMZN GHCziBase.Char =
4892 \ @ a (zddShow::GHCziShow.ZCTShow a) (eta::a) ->
4894 %case zddShow %of (tpl::GHCziShow.ZCTShow a)
4896 (tpl1::GHCziBase.Int ->
4898 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4900 (tpl2::a -> GHCziBase.ZMZN GHCziBase.Char)
4901 (tpl3::GHCziBase.ZMZN a ->
4902 GHCziBase.ZMZN GHCziBase.Char -> GHCziBase.ZMZN GHCziBase.Cha
4910 Here, we can see that the function <function>show</function> (which
4911 has been expanded out to a case expression over the Show dictionary)
4912 has a <literal>%note</literal> attached to it, as does the
4913 expression <VarName>eta</VarName> (which used to be called
4914 <VarName>x</VarName>).
4921 <sect1 id="generic-classes">
4922 <title>Generic classes</title>
4924 <para>(Note: support for generic classes is currently broken in
4928 The ideas behind this extension are described in detail in "Derivable type classes",
4929 Ralf Hinze and Simon Peyton Jones, Haskell Workshop, Montreal Sept 2000, pp94-105.
4930 An example will give the idea:
4938 fromBin :: [Int] -> (a, [Int])
4940 toBin {| Unit |} Unit = []
4941 toBin {| a :+: b |} (Inl x) = 0 : toBin x
4942 toBin {| a :+: b |} (Inr y) = 1 : toBin y
4943 toBin {| a :*: b |} (x :*: y) = toBin x ++ toBin y
4945 fromBin {| Unit |} bs = (Unit, bs)
4946 fromBin {| a :+: b |} (0:bs) = (Inl x, bs') where (x,bs') = fromBin bs
4947 fromBin {| a :+: b |} (1:bs) = (Inr y, bs') where (y,bs') = fromBin bs
4948 fromBin {| a :*: b |} bs = (x :*: y, bs'') where (x,bs' ) = fromBin bs
4949 (y,bs'') = fromBin bs'
4952 This class declaration explains how <literal>toBin</literal> and <literal>fromBin</literal>
4953 work for arbitrary data types. They do so by giving cases for unit, product, and sum,
4954 which are defined thus in the library module <literal>Generics</literal>:
4958 data a :+: b = Inl a | Inr b
4959 data a :*: b = a :*: b
4962 Now you can make a data type into an instance of Bin like this:
4964 instance (Bin a, Bin b) => Bin (a,b)
4965 instance Bin a => Bin [a]
4967 That is, just leave off the "where" clause. Of course, you can put in the
4968 where clause and over-ride whichever methods you please.
4972 <title> Using generics </title>
4973 <para>To use generics you need to</para>
4976 <para>Use the flags <option>-fglasgow-exts</option> (to enable the extra syntax),
4977 <option>-fgenerics</option> (to generate extra per-data-type code),
4978 and <option>-package lang</option> (to make the <literal>Generics</literal> library
4982 <para>Import the module <literal>Generics</literal> from the
4983 <literal>lang</literal> package. This import brings into
4984 scope the data types <literal>Unit</literal>,
4985 <literal>:*:</literal>, and <literal>:+:</literal>. (You
4986 don't need this import if you don't mention these types
4987 explicitly; for example, if you are simply giving instance
4988 declarations.)</para>
4993 <sect2> <title> Changes wrt the paper </title>
4995 Note that the type constructors <literal>:+:</literal> and <literal>:*:</literal>
4996 can be written infix (indeed, you can now use
4997 any operator starting in a colon as an infix type constructor). Also note that
4998 the type constructors are not exactly as in the paper (Unit instead of 1, etc).
4999 Finally, note that the syntax of the type patterns in the class declaration
5000 uses "<literal>{|</literal>" and "<literal>|}</literal>" brackets; curly braces
5001 alone would ambiguous when they appear on right hand sides (an extension we
5002 anticipate wanting).
5006 <sect2> <title>Terminology and restrictions</title>
5008 Terminology. A "generic default method" in a class declaration
5009 is one that is defined using type patterns as above.
5010 A "polymorphic default method" is a default method defined as in Haskell 98.
5011 A "generic class declaration" is a class declaration with at least one
5012 generic default method.
5020 Alas, we do not yet implement the stuff about constructor names and
5027 A generic class can have only one parameter; you can't have a generic
5028 multi-parameter class.
5034 A default method must be defined entirely using type patterns, or entirely
5035 without. So this is illegal:
5038 op :: a -> (a, Bool)
5039 op {| Unit |} Unit = (Unit, True)
5042 However it is perfectly OK for some methods of a generic class to have
5043 generic default methods and others to have polymorphic default methods.
5049 The type variable(s) in the type pattern for a generic method declaration
5050 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:
5054 op {| p :*: q |} (x :*: y) = op (x :: p)
5062 The type patterns in a generic default method must take one of the forms:
5068 where "a" and "b" are type variables. Furthermore, all the type patterns for
5069 a single type constructor (<literal>:*:</literal>, say) must be identical; they
5070 must use the same type variables. So this is illegal:
5074 op {| a :+: b |} (Inl x) = True
5075 op {| p :+: q |} (Inr y) = False
5077 The type patterns must be identical, even in equations for different methods of the class.
5078 So this too is illegal:
5082 op1 {| a :*: b |} (x :*: y) = True
5085 op2 {| p :*: q |} (x :*: y) = False
5087 (The reason for this restriction is that we gather all the equations for a particular type consructor
5088 into a single generic instance declaration.)
5094 A generic method declaration must give a case for each of the three type constructors.
5100 The type for a generic method can be built only from:
5102 <listitem> <para> Function arrows </para> </listitem>
5103 <listitem> <para> Type variables </para> </listitem>
5104 <listitem> <para> Tuples </para> </listitem>
5105 <listitem> <para> Arbitrary types not involving type variables </para> </listitem>
5107 Here are some example type signatures for generic methods:
5110 op2 :: Bool -> (a,Bool)
5111 op3 :: [Int] -> a -> a
5114 Here, op1, op2, op3 are OK, but op4 is rejected, because it has a type variable
5118 This restriction is an implementation restriction: we just havn't got around to
5119 implementing the necessary bidirectional maps over arbitrary type constructors.
5120 It would be relatively easy to add specific type constructors, such as Maybe and list,
5121 to the ones that are allowed.</para>
5126 In an instance declaration for a generic class, the idea is that the compiler
5127 will fill in the methods for you, based on the generic templates. However it can only
5132 The instance type is simple (a type constructor applied to type variables, as in Haskell 98).
5137 No constructor of the instance type has unboxed fields.
5141 (Of course, these things can only arise if you are already using GHC extensions.)
5142 However, you can still give an instance declarations for types which break these rules,
5143 provided you give explicit code to override any generic default methods.
5151 The option <option>-ddump-deriv</option> dumps incomprehensible stuff giving details of
5152 what the compiler does with generic declarations.
5157 <sect2> <title> Another example </title>
5159 Just to finish with, here's another example I rather like:
5163 nCons {| Unit |} _ = 1
5164 nCons {| a :*: b |} _ = 1
5165 nCons {| a :+: b |} _ = nCons (bot::a) + nCons (bot::b)
5168 tag {| Unit |} _ = 1
5169 tag {| a :*: b |} _ = 1
5170 tag {| a :+: b |} (Inl x) = tag x
5171 tag {| a :+: b |} (Inr y) = nCons (bot::a) + tag y
5180 ;;; Local Variables: ***
5182 ;;; sgml-parent-document: ("users_guide.sgml" "book" "chapter" "sect1") ***
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